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DOCUMENT RESUME ED 330 572 SE 052 082 TITLE The State of Mathematics Achievement in New York: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment! Family Environment; *Grade 8; Homework; Junior kig Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS National Assessment of Educational Progress; *New York; *Numeracy; State Mathematics Assessments; Trial State Assesnient (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In New York, 2,302 students in 91 public schools were assessed. This report describes the mathematics proficiency of New York eighth-graders, compares their overall performance to students in the Northeast region of the United States and the nation (using data from the UAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, P arents' educational level, and gender). To provide a context for the assessment data, participating students, their mathematics teachers, and principals completed questionnaires which focused on: instructional conten', (curriculum coverage, amount of homework); delivery of math instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, New York students had an average proficiency of 261 compared to 261 nationwide. Many fewer students (New York-13%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of its. in NEW YORK The Trial State Assessment at Grade Right 'T "F 'PVPIAB'E t U II DEPARTMENT Of EDUCATION Cr MK'0 Of Eduodonat Reibeared WW1 0.1P,OvVrelf E. IDLIC TIONAL RESOURCES INFORMATION CENTER rERIO tie ,ts document miss peen reproduced es receved t,om tne persOn or orgamistson wttatnet,no .1 r M.nor Chling3 na.r peen mede to "prove reproduchon gustily Pomt 01 v Ktv. o optmons Itraltyf rnrsdoeu ment dp cult neceSSatoy reeresent OE RI' Posri.on o, policy Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD, the National Assessment of Educational Progress (NAEP), is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Sincc 1969, assessmems have been conducted periodically in reading. mathematics, science, writing, history/geography. and other fields. By making objective information on student performance available to policymakers at the national, state, and local levels, NAEP is an integral part of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAFP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics, the U.S. Department of Education. The Commissioner of Education Statistics is responsible. by law, for carrying out the NAEP project through competitive awards to qualified organizations. NAEP reports directly to tbe Commissioner, who is also responsible for providing continuing reviews, including validation studies and solicitation of public comment, on NAEP's conduct and usefulness. In 1988, Congress created the National Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The board is responsible for selecting the subject areas to be assessed, which may incluur adding to those specified by Congress; identifying appropriate achievement goals for ereh age and grade; developing assessment objectives; developing test specifications', desigaing the assessment methodology: developing guidelines and standards for data analysis and cor reporting and disseminating results: developing standards and procedures for interstate, regional. and national comparisons: improving the form and use of the National Assessment: and ensuring that all items selmted for use in the National Assessment arc free from racial, cultural, gender, or regional bias. The National Assessment Governing Board Richard A. Boyd, Chairman Executive Director Martha Holden Jennings Foundation Cleveland. Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.O.C.LS. Saratoga Springs, New York Franck Alexander Associate Superintendent California Department of Hucat on Sacramento, California David P. Battini High School History Teacher Cairo-Durham High School Cairo. New York Parris C. Battle Teacher Horace Mann Elementary School Miami. Florida Mary R. Blanton Attorney Cromwell. Porter, Blanton & Blanton Salisbury. North Carolina Boyd W. Boehije Attorney Gaass, Klyn. & Boehlje Pella, Iowa Linda R. Bryant Teacher Oreenway Middle School Teacher Center Pittsburgh, Pennsylvania Honorabk Michael N. Castle Governor of Delaware Carve! State Office Building Wilmington, Delaware Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hartford, Connecticut Chester E. Finn, Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.C. Michael S. Glode Wyoming St .te Board of Education Saratoga. Wyoming Christine Johnson Principal Abraham Lincoln High School Denver. Colorado John Lindley Principal South Colby Elementary School Port Orchard. Washington Carl J. Moser Director of Schools The Lutheran Church Missouri Synod International Center St. Louis. Missouri Mark D. Musick Presideat Southern Regional Education Board Atlanta, Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith. Arkansas 3 Matthew W. Prophet, Jr. Superintendent Portland Oregon School District Portland. Oregon Honorable William T. Randall Commissioner of Llucation State Department of Education Denver, Colorado Dorothy K. Rkh President Home and School Institute Special Projects Office Washington. D.C. Honorable Richard W. Riley Attorney Nelson, Mullins. Riley and scarborough Columbia, South Carolina Thomas Topuzcs Attorney Law Offices of Frank Rogozienski Coronado. California Herbert J. Walberg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Researth and Improvement (Ex-Officio) U.S. Department of Education Washington. Roy Truby Executive Director. NAGB Washington. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement in NEW YORK The Trial State Assessment at Grade Eight Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education U.S. Department of Education Lamar Alexander Secretary Office or Educati Alai Research and Improvement Bmno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Congress, Catalog Card Number: 91-61478 I3BN: 0-88685-14-9 The wort upon which this publication is based was performed for the National Centerfor Education Statistics. Office of Educational Research and Improvement. by Educational Testing Service. Educational Testing Savice is an equal upponunity/affinnative action employer. Educational Testing Service, ETS, and am registered trademarks of EducationalTesting Service. Table of Contents EXECUTIVE SUMMARY INTRODUCTION 7 Overview O.' the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of New York 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in New York Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 Levels of Mathematics Proficiency 19 Content Area Perfoimance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race/Ethnicity 24 Type of Community /7 Parents' Education Level 29 Gender Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT In PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics" 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Delivered' 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calcubtors Used" 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics? 67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching . ...... 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism 7t Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 iv THE 1990 NAEP TRIAL STATE ASSESSMENT New York THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congyess passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessmet4i'; on a trial basis, in addition to continuing its primary mission, the national assessment . ihat NAEP has conducted since its inception. As a result of the legislation, the 1990 NAFP progam included a Trial State Assessment Program in cighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefull designed to represent the eighth-grade public-school population in a state or territory. Withiri each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degee of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT New Y ork 11 In New York, 91 public schools participated in the assessment. The weighted school participation rate was 86 percent, which means that all of the eighth-grade students in this sample of schools were representative of 86 percent of the eighth-grade public-school students in New York. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 4 percent of the eighth-grade public-school population wa3 classified as Limited English Proficient (LEP), while 9 percent had an individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualind Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 2 percent and 5 percent of the population, respectively. In total, 2,.?02 eighth-grade New York public-school students were assessed. The weighted student participation rate was 93 percent. This means that the sample of students who took part in the assessment was representative of 93 percent of the eligible tighth-grade public-school student population in New York. Students' Mathematics Performance The average proficiency of eighth-gade public-school students from New York on the NAEP mathematics scale is 261. This proficiency is no different from that of students actoss the nation (261). Average proficiency on the NAFP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAFP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 on the NAEP scale. 9 2 THE 1990 NAEP TRIAL STATE ASSESSMENT New York In New York, 96 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in New York (13 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in New York performed comparably to students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the New York eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In New York: White students had higher average mathematics proficiency than did Black or Hispanic students and about the same mathematics proficiency as did Asian students. Further, a greater percentage of White students than Black or Ilispanic students but a smaller percentage of White than Asian students attained level 300. The results by type of community indicate that the average mathematics performance of the New York students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas or areas classified as "other" and about the same as that of students attending schools in extreme rural areas. In New York, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 32 points higher than that of students whose parents did not graduate from high :;chool. The results by gender show that there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in New York. In addition, there was no difference between the percentles of males and females in New York who attained level 300. Compared to the national results, females in New York performed no differently from females across the country; males in New York performed no differently from males across the country. THE 1990 NAEP TRIAL STATE ASSESSMENT 3 New York A Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplanented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information about student achievement. Some of the salient results for the public-school students in New York are as follows: About three-quarters of the students in New York (74 percent) were in schools where mathematics was identified as a special priority. This is about the same percentage as that for the nation (63 percent). In New York, 86 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in New York were taking eighth-grade mathematics (73 percent) than were taking a course in pre-algebra or algebra (20 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. According to their teachers, the greatest percentage of eighth, grade students in public schools in New York spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. Students whose teachers placed heavy instructional emphasis on Geometry, Data Analysis, Statistics, and Probability, and Algebra and Functions had higher proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. Students whose teachers placed heavy instructional emphasis on Numbers and Operations had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT New York In New York, 20 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 35 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In New York, 38 percent of the students never used a calculator to work problems in class, while 40 percent almost always did. In New York, 69 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. Many of the students (84 percent) had teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in New York who had four types cf reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of these materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. Some of the eighth-grade public-school students in New York (12 percent) watched one hour or less of television each day; 17 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. THE 1990 NAEP TRIAL STATE ASSESSMENT 5 New York THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-wade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Oelaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands THE 1990 NAEP TRIAL STATE ASSESSMENT 7 New York This report describes the performance of the eighth-grade public-school students in New York and consists of three sections: This Introduction provides backgound information about the Trial State Assessment and this report. It also provides a profile of the eighth-grade public-school students in New York. Part One describes the mathematics performance of the eighth-grade public-school students in New York, the Northeast region, and the nation. Part Two relatcs students' mathematics peifonnance to contextual information about the mathematics policies and instruction in schools in New York, the Northeast region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survey instrwnent for the eighth grade and shall conduct a demonstration of the instrument in 1990 in States which wish to participate, with the purpose of determining whether such an assessment yields valid, reliable State representative data. (Section 406 (1)(2)(C)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(i))) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoringindicated a high degree of quality' and uniformity across sessions. 8 TUE 1990 NAEP TRIAL STATE ASSESSMENT New York The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patter d after the consensus process described in Public I..aw 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council of Chief State School Officers in mid-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,' the fonnal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the fmal objeeives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-gade public-school students in New York, in the Northeast region, and for the nation. Results also are provided for groups of students defined by shared characteristics -- race/ethnicity, type of community, parents' education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for New York are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nationally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAEP program was necessary because the voluntary nature of the Trial State Assessment Program did not guarantee representative national or regional results, since not every state participated in the program. National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematks (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 9 New York RACE/ETHNICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispaiiic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Procedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for New York. TYPE OF COMMUNITY Results are provided for four mutually exclusive community types -- advantaged urban, disadvantaged urban, extreme rural, and other -- as defined below: Advantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are in professional or managerial positions. Disadvantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are on welfare or are not regularly employed. Extreme Rural: Students in this goup live outside metropolh.....n statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. 10 THE 1990 NAEP TRIAL STATE ASSESSMENT New York GENDER Results are reported separately for males and females. REGION The United States has been divided into four regions: Northeast, Southeast, Central, and West. States included in each reg;on are shown in Figure 1. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. HGURE 1 I Regions of the Country THE NATION'S REPORT CARO NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Alabzma Illinois Alaska Delaware Arkansas Indiana Arizona District of Columbia Florida Iowa California Maine Georgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana New Jersey North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohio Oklahoma Rhode island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT 11 New York Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulgions and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error bc taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistically significant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) -- regardless of whether the sample means or sample proportions appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the difference is not statistically significant), the means or proportions are described as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the apparent magnitude of the difference between sample means or proportions to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular got p had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two poups, the confidence interval included zero,and thus no difference could be assumed between the groups. When three or more groups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed en greater detail in the Procedural Appendix. 12 THE 1990 NAEP TRIAL STATE ASSESSMENT New York It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). k THE 1990 NAEP TRIAL STATE ASSESSMENT 13 New York Profile of New York EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table I provides a profile of the demographic characteristics of the eighth-grade public-school students in New York, the Northeast region, and the nation. This profile is based on data collected from the students and schools participating in the Trial State Assessment. TABLE I I Profile of New York Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS 19SO NAEP TRIAL STATE ASSESSMENT New York Northeast Nation DEMOGRAPHIC SUBGROUPS Percentage Percentage Percentage Race/Ethnicity White 60 ( 1.9) 80 ( 4.2) 70 ( 0.5) Black 17 ( 1.6) 12 ( 4.2) 16 ( 0.3) Hispanic 17 ( 1.7) 6 ( 1.2) 10 ( 0.4) Asian 4 ( 0.6) ( 1.1) 2 ( 0.5) American Indian 1 ( 0.3) 1 ( 0.3) 2 ( 0.7) Type of Community Advantaged urban 16 ( 3.6) 23 ( 7.3; 10 ( 3.3) Disadvantaged urban 29 ( 4.6) 8 ( 5.7) 10 ( 2.8) Extreme rural 3 ( 1.2) 14 (10.3) 10 ( 3.0) Other 53 ( 5.4) 55 (11.2) 70 ( 4.4) Parents' Education Did not finish high school 8 ( 0.7) 7 ( 2.2) 10 ( 0.8) Graduated high school 22 ( 0.9) 23 ( 3.3) 25 ( 1.2) Some education after high school 17 ( 0.9) 15 ( 3.0) 17 ( 0.6) Graduated college 40 ( 1.2) 49 ( 5.8) 39 ( 1.9) Gender Male 49 ( 1.3) SO ( 21) 51 ( 1.1) Female 51 ( 13) 50 ( 2.1) 49 ( 1.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages for Race Ethnicity may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 THE 1990 NAEP TRIAL STATE ASSESSMEN1 New York SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for New York schools and students sampled for the 1990 Trial State Assessment. In New York, 91 public schools participated in the assessment. The weighted school participation rate was 86 percent, which means that all of the eighth-grade students in this sample of schools were representative of 86 percent of the eighth-grade public-school students in New York. TABLE 2 I Profile of the Population Assessed in New York EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution Weighted school participation rate after substituton Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating schools ae% 86% 105 91 0 91 EIGHTH-GRADE PUBUC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students seleCted to participate in the assessment Number of students withdrawn from the assessment Percentage of students who ware of Limited English Proficiency Percentage of students excluded from the assessment due to Limited English Proficiency Percentage of students who had an Individualized Education Plan Percentage of students excluded from the assessment due to Individualized Education Plan status Number of students to be assessed Number of students assessed 2% 9% 5% 2,491 2,302 For one school in New York, an assessment was conducted, but the matenals were destroyed in shipping via the t; S. Postal Service. The school was included in the counts of participating schools, both before and after sut Jtion. However, in the weighted results, the school was treated in the same manner as a nonparticipating school because no student responses were available for analysis and reporting. THE 1990 NAEP TRIAL STATE ASSESSMENT 15 New York In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 4 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 9 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 2 percent and 5 percent of the population, respectively. I a total, 2,302 eighth-grade New York public-school students were assessed. The weighted student participation rate was 93 percent. This means that the sample of students who took part in the assessment was representative of 93 percent of the eligible eighth-gade public-school student population in New ork. .c 16 THE 1990 NAEP TRIAL STATE ASSESSMENT New York THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in New York Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAFP mathematics scale, which ranges from 0 to 500. This part of the report containF two chapters that describe the mathematics proficiency of eighth-grade public-school students in New York. Chapter 1 compares the overall mathematics performance of the students in New York to students in the Northeast region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 summarizes the students' overall mathematics performance for subpopulations defmed by race!ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. OTh THE 1990 NAEP TRIAL STATE ASSESSMENT 17 New York CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from New York on the NAEP mathematics scale is 261. This proficiency is no different from that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School Mathematics Proficiency NAEP Mathematics Scale 200 225 250 275 300 500 Average Proliciency 044 New York 261 ( 1.3) Northeast 269 ( 3.4) Pro Nation 261 ( 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-4). If the confidence intervals for the populations do not overlap, there is a staUstically significant difference between the populations. 2 Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 18 THE 1990 NAEP TRIAL STATE ASSESSMENT New York LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are given in Figure 3. It is important to note that the defmitions of these levels are based solely on stWent performance on the 1990 mathematics assessment. The levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In New York, 96 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in New York (13 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). CONTENT AREA PERFORMANCE As previously indicated, the questions comprising the Trial State Assessment covered five content areas Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Figure 5 provides the New York, Northeast region, and national results for each content area. Students in New York performed comparably to students in the nation in all of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 New York FIGURE 3 J Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have Some degree of understanding of simple quantitative relationships Involving whole numbers. They can solve Simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-step word problems and Select the greatest four-digit number In a list. In measurement, these students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numerical sentences and extend simple pattern sequences. LEVEL 250 I Simple Multiplicative Reasoning and Two-Stop Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-step addition and subtraction problems Involving money. Using a calculator, they can identify solutions to other elementary two-Step word problems. In these basic problem-solving situations, they can identify Missing or extraneous information and have some knowledge of when to use computational estimation. They have a rudimentary understanding ot such concepts as whole number place value, "even," "factor," and "Multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, aria recognize a numerical expression Solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysts, they can complete 3 bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and probability. In algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions. 06 20 THE 1990 NAEP TRIAL STATE ASSESSMENT New York FIGURE 3 I Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasoning and Problem Solving involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations Students at this level are able to represent, interpret, and perform simple operations with fractions and decimal numbers. They are Able to lOcate fractions and decimals on number lines, Simplify fractions, and recogniZe the equivalence between common fractions and decimals, Including pictorial representations. They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate Some evidence of using mathematical notation to interpret expressions, Including those with exponents and negative integers. in measurement, these students Can find the perimeters and areas ot rectangles, recognize relationships among cOmmon units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open linear sentencfss and inequalities by substitution, and checking and graphing an interval representing a compound inequality when it is described In words. They can determine and apply a rule for simple functional relations and extend a num :al pattern. LEVEL 350 Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to include some properties of exponents. They can recognize scientific nptation on a calculator and make the transition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and Mang to solve problems. They can find the circumferences of circles and the surface areas of solid . es. In geometry, they can apply tne Pythagorean theorem to solve problems involving indirect measurement. Thesb students also can apply their knowledge of the properties of geometric figures to solve problems, such as determining the slope of a line. In data analysis, these students can compute means from frequency tables and determine the probability of a Simple event. In algebra, they can identify an equation describing a linear relation provided in a table and solve literal equations and a system of two linear equations. They are developing an understanding of linear functions and their graphs, as well as functional notation, including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. 04 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 New York FIGURE 4 I Levels of Eighth-Grade Public-School I Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation 141 1.4,4 0 20 40 SO 80 Percentage at or Above Proficiency Levels The stanuard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 100 22 THE 1990 NAEP TRIAL STATE ASSESSMENT Percentage ( 0.1) ( 0.5) ( 0.2) 13 ( 1.0) 16 ( 2.7) 12 ( 1.2) 62 ( 1.9) 72 ( 4.8) 64 ( 1.6) 96 ( 0.6) 99 ( 0.6) 97 ( 0.7) New York FIGURE 5 I Eighth-Grade Public-School Mathematics i content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation 0 200 225 250 275 300 Average Proficiency 283 ( 1.3) 271 ( 3.1) 266 ( 1.4) 255 ( 1.6) 286 ( 4.7) 258 ( 1.7) 259 ( 1.4) 268 ( 3.6) 259 ( 1.4) 263 ( 1.7) 273 ( 3.6) 262 ( 1.8) 260 ( 1.2) 267 ( 3.4) 29) ( 1.3) SOO Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by P-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT 23 New York CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY The Trial State Assessment results can be compared according to the different racial/ethnic goups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Black, Hispanic, and Asian students from New York are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black or Hispanic students and about the same mathematics proficiency as did Asian students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Black or Hispanic students but a smaller percentage of White than Asian students attained level 300. 24 THE 1990 NAEP TRIAL STATE ASSESSMENT New York FIGURE 6 I Average Eighth-Grade Public-School Mathematics Proficiency by Race/Ethnicity NAEP islatheinelics Scale sow Average 200 22$ 250 275 300 500 Proficiency tsw.4 1-404 $4 11NOWNr. IIMIINIMIIMINIMINNIIm...M. New York White 1.1) Black *Si ( 2,1) Hispanic 237 Asian v ( SOP Northeast White Black Hispanic 274 C 3.0) 1 ( 7.6$ Iwo Asian C ***) Natter, White 1111. ( 1.5) Black 231 ( 2.1) Hispanic 243 ( 2.6) Asian 260 ( 5.6)1 The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within + 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations, ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is Msufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 25 New York flt RAIMN1 REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARD Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian LEVEL 250 State White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian LEVEL 200 State White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 110 3 2, 26 THE 1990 NAEP TRIAL STATE ASSESSMENT II ( 1.5) 2 ( 0.4) 3 ( 1.1) 32 ( 5.3)1 ( 2.5) 3 ( 4.1)1) I. ) 16 ( 1.5) 2 ( 1.3) 3 ( 1.1) 31 ( 6.2)1 NO ( 1.3) 29 ( 5.0) 32 ( 3.9) 78 ( 6.5)1 7$ ( 4.8) 39 (10.9)1 pt. ( e 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) 80 ( 5.6)1 ( 0.3) 90 ( 1,9) 89 ( 1.8) OS ( 2.8)1 100 ( 0.0) 93 ( 3,0); ) mis* ) 00 ( 0,4) 99 ( 3.1) 93 ( 1.6) ( 2.5)1 New York TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, disadvantaged urban areas, extreme rural areas, and areas classified as "other". (These are the "type of community" groups in New York with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the New York students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas or areas classified as "other" and about the same as that of students attending schools in extreme rural areas. FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community NAEP Mathematics Scale 200 225 250 275 300 500 Average 1tsif Now York Advantaged urban Disadvantaged urban Extreme rural Other Northoast Advantaged urban 279 ( 11140$ Disadvantaged urban (10.9$ Extreme rural Other 212 I 3.0) Nation Advantaged urban 511 ( sityi Disadvantaged urban 11412 ( tap 1-11 h--41 Extreme rural 2119 ( 4.1$ HI Other 1141 ( 12) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-0. If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 27 New York FIGURE 9 LEVEL 300 Stat. Adv. urban DIsildv. urban Ext. rural Other Region Adv. urban Olsadv. urban Ext. rural Other Nation Adv. urban Olsadv. urban Ext. rural Other LEVEL 250 Stat Adv. urban Oisadv. urban Ext. rural Other Region Adv. urban Disaclv. urban Ext. rural Other Nation Mv. urban Dtsadv. urban Ext. rural Other LEVEL 200 State Adv. urban Dtsadv. urban Ext. ru-al Other Region Aciv. urban Disadv. urban Ext. rural Other Nation Adv. urban Dtsadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathemecs Proficiency by Type of Community THE WOWS REPORT CARD 14141 1.1.01 liwt01114 Ifr1111NIEMPM114 lipm 1-100-1 11101111111111.14 20 40 60 60 Percentage at or Above Proficiency Levels The standard errors are presented in paientheses. With about 95 percent certainty, the value for each populaJon of interest is within 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by I-4-4). if the confidence mtervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a rehable estimate (fewer than 62 students). 3 4 100 28 TIM 1990 NAEP TRIAL STATE ASSESSMENT 25 ( 3.1)! 6 ( 2.3) V ( 4.0)? 14 ( 1.4) 22 ( 8.7)1 11 ( 4,9)1 ( 10 ( 2.6) 26 ( 4.8)1 7 ( 2.1)1 0 ( 2.3)1 12 ( 1.2) BS ( 2.7)1 31 ( 3.6) 110 ( 6.1)i TS ( 2.1) ( 0.5)1 39 ( 11 .9)/ 0/01 ( e 77 ( 4,4) 83 ( 4.6)' 4$ ( 5.0)1 58 ( 6.2)i 64 ( 2.3) 100 1 0.0) 90 ( 2.0) 100 ( 0.0) 99 ( 0.5) 100 ( 0.0) 03 ( 2.7)1 ging ( 99 ( 0.8) 100 ( 0.0) 96 ( 1.5)1 97 ( 2.8)t 97 ( 1.0) New York PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In New York, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 32 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, about the same percentage of students in New York (40 percent) and in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 8 percent for New York and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School I Mathematics Proficiency by Parents' Education NAEP Mathematics Scale 200 225 250 275 300 SOO Average Proficiency New York 1.1".11 HS non-graduate 242 ( 2.6) 0+4 HS graduate 2113 ( 1.7) P+4 Some college 204 ( 2.0) 1+9 College graduate 03( 11.4) Northeast HS non-graduate H."4 HS graduate ( 23) 4+4 Some college 2111( 2,4) College graduate 2112 ( 3.4) Nation 141 HS non-graduate 243 ( 2.0) HS graduate 224 ( 1,S) Some college 2411( 11) Pee College graduate 274( 1.6) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within :t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by F+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations, *** Sample size is msufficient to permit a reliable estimate (fewer than 62 students). TIIE 1990 NAEP TRIAL STATE ASSESSMENT 29 New York lit tier 41 REfORT FIGURE 1 1 I Levels of Eighth-Grade Public-School CARD Mathematics Proficiency by Parents' Education LEVEL 300 State HS non-gr3d. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 State HS non-grad. NS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation NS non-grad. NS graduate Some college College grad. o 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within .t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-0-1), If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 30 THE 1990 NAEP TRIAL STATE ASSESSMENT 1 ( 1.0) 5 ( 0.9) 13 ( 2.1) 22 ( 2.1) ( ".) 6 ( 2.8) 13 ( 2.7) 26 ( 4.3) I ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.9) 30 ( 4.4) 56 ( 2.9) 00 ( 2.9) 76 ( 1.7) ( 82 ( 5.9) 71 ( 4.5) ( 4.6) 37 ( 4.6) 86 ( 2.7) 71 ( 2.6) 70 ( 2.0) 93 ( 2.6) 96 ( 1.3) 97 ( 1.2) 90 ( 0.8) futs ( ...) 90 ( 0.9) ( 1,4) 90 ( 0.4) OS ( 1.9) 97 ( 0.8) Oa ( 0.7) 99 ( 0.7) New York GENDER As shown in Figure 12, there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in New York. Compared to the national results, females in New York performed no differently from females across the country; males in New York performed no differently from males across the country. FIGURE 12 1 Average Eighth-Grade Public-School I Mathematics Proficiency by Gender NAEP Mathematics Scale 200 225 250 275 300 500 1NE IMPORT = A Average Proficiency POI PM f-t1 10-0,^4 P41 PM ONP.P.11.1011PIMM. New York Male 1112 ( 14) Female 210 ( Le) Northaast Male 270 ( 4.1) Female MO 3.2) Nation Male 212 ( 1.8) Female SSO ( 1.3) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in New York who attained level 200. The percentage of females in New York who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in New York who attained level 200 was similar to the percentage of males in the nation who attained level 200. 3 ""Pi THE 1990 NAEP TRIAL STATE ASSESSMENT 31 New York FIGURE 13 I Levels of Eighth-Grade Public-School i Mathematics Proficiency by Gender LEVEL 300 State Male Female Region Male Female Nation Male Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female THE NATION'S cARD Am" Nti Ilmeampree INwww4111ftmearsoMb4 14 pa=411.N.4 104"of Percentage ( 1A) 12 ( 1.1) 19 ( 3.3) 13 ( 3.8) 14 ( 1.7) 10 ( 1.3) ( 2.2) 61 ( 2.3) 72 ( 5.8) 72 ( 4.5) ( 2.0) 64 ( 1.8) m4 97 0.8) 96 0.9) 90 0.7) 99 (0.7) #4.1 97 0.9) 44 97 0.8) 0 20 40 60 80 mt, 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is withili i 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 3 c' 32 THE 1990 NAEP TRIAL STATE ASSESSMENT New York In addition, there was no difference between the percentages of males and females in New York who attained level 300. The percentage of females in New York who attained level 300 was similar to the percentage of females in the nation who attained level 300. Also, the percentage of males in New York who attained level 300 was similar to the percentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. THE 1990 NAEP TRIAL STATE ASSESSMENT 33 New York TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopuiations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS IWO NAEP TRIAL STATE ASSESSMENT Numbers and Operations Musurement Geometry Data Analysis' Statittina, and Probability Algebra and Rincuons TOTAL Proficiency Proficiency Proficiency Profidency Preliciettcy State 283 ( 1.3) 255 ( 1.1) 259 ( 1.4) 263 ( 1.7) 260 ( 1.2) Region 271 1 3.1) 2$6 ( 4.,) 26$ ( 3.6) 273 ( 3.6) 267 ( 3.4) Nation 266 ( 1.4) 258 ( 1.7) 259 ( 1.4) 262 ( 1.8) 200 ( 1.3) RACE/ETHNICITY White State 275 ( 1.2) 270 ( 1.4) 272 ( 1.3) 279 ( 1.4) 2/1 ( 1.2) Region 275 ( 3.1) 272 ( 4.6) 272 ( 3.1) 279 ( 3.1) 271 ( 3.0) Nation 273 ( 1.6) 267 ( 2.0) 267 ( 1$) 272 ( 1.8) 268 ( 1A) Black State 243 ( 2.7) 222 ( 3.5) 233 ( 3.0) 3.7) 242 ( 2.3) Region 250 ( 5.4)1 233 ( 9.4)1 243 ( 9.9)1 24 ( 8.2)1 242 ( 92)1 Nation 244 ( 3.1) 227 ( 3.8) 234 ( 22) 231 ( 3.6) 237 ( 2.7) Hispanic State Region 241 ( 4.4. 2.6) 231 ( ( 3.7) tin 239 ( 114 ( 2.3) Milt) 232 ( Irk* 4.0) 238 ( 2.8 Nation 248 ( 2.7) 238 ( 3,4) 243 ( 32) 239 ( 3.4) 243 ( 3.1) Aslan State Region 281 ( 4.6)1 0,4) 274 ( ( 7.1)1 278 ( **is 6.8)1 285 ( 73)1 278 ( ( 4.1)1 Nation 265 ( 5,9)1 276 ( 8.3)i 275 ( 5.9)1 282 ( 6.9)1 278 ( 6.7)1 TYPE OF COMMUNITY Advantaged urban State 281 ( 2.2)1 283 ( 3.2)1 27$ ( 2.8)1 287 ( 2.9)1 277 ( 2.5)1 Region 282 ( 6.5)1 279 ( 8.8)1 275 ( 9.6)1 282 ( 8.5)1 273 (10.1)1 Nation 283 ( 3.2)1 281 ( 3.2)1 277 ( 5.2)1 285 ( 4.8)1 277 ( 4.8)1 Disadvantaged urban State 243 ( 2.4) 229 ( 33) 237 ( 2.6) 235 ( 3.1) 241 ( 2.1) Region 251 ( 7.2)1 238 (13.6)1 242 (13.5)1 245 (11.8)1 243 (12.6)1 Nation 255 ( 11)1 242 ( 4.9)1 248 ( 3.7)1 247 ( 4.8)1 247 ( 3.2)1 Extreme rural State 275 ( 4.0)1 209 ( 3.0)1 278 ( 4.3)1 279 ( 3.2)1 270 ( 3.8)1 Region VP, 4-11.0 ( ( Nation 258 ( 4.3)I 254 ( 42)1 253 ( 44)1 257 ( 5.0)1 258 ( 4.8)1 Other State 272 ( 1.6) 264 ( 1.9) 268 ( 1.6) 274 ( 2.1) 268 ( 1.6) Region 274 ( 3.7) 266 ( 6.5) 272 ( 3.3) 277 ( 3.9) 271 ( 3.4) Nation 206 ( 1.9) 257 ( 2.4) 259 ( 1-7) 261 ( 2.2) 261 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 34 THE 1990 NAEP TRIAL STATE ASSESSMENT York TABLE 3 I Eighth-Grade Public-School Mathematics (continued) I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measuramert Geometry Data Analysis' Statistics, and Probability Algebra and Functions TOTAL Proficiency Proficiency Proficiency Proficiem Proficiency State 263 ( 1.3) 255 ( 1.6) 259 ( 1.4) 261 7) 2130 ( 1.2) Region 271 ( 3.1) 206 ( 4.7) 266 ( 3.6) 2'2 I s 'I) 267 ( 3.4) Nation 206 ( 1.4) 258 ( 1.7) 250 ( 1.4) a , -3) 260 ( 1.3) PARENTS EDUCATION NS non-graduate State Region 245 ( 2.7) .44) 242 ( *114 ( 2.8) Mel 239 ( 4.3) 244 ( 2.6) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 22) 240 ( 3.1) 242 ( 3.0) NS graduate State 255 ( 1.6) 245 ( 2.4) 252 ( 2.0) 255 ( 2.3) 253 ( 1.8) Region 280 ( 2.7) 255 ( 5.1) 258 ( 3.2) 264 ( 4.6) 254 ( 2.9) Nation 259 ( 1.8) 243 ( 2.1) 252 ( 1.6) 253 ( 22) 253 ( 2.0) Sm.! college State 267 ( 2.1) 259 ( 2.9) 262 ( 2.3) 269 ( 2.1) 264 ( 22) Region 267 ( 2.3) 201 ( 5.7) 267 ( 3.4) 273 ( 3.4) 262 ( 2.9) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 263 ( 2.2) College graduate State 276 ( 1.5) 269 ( 2.0) 271 ( 1.8) 278 ( 1.8) 272 ( 1.3) Region 285 ( 3.8) 279 ( 5.5) 277 ( 3.8) 287 ( 3.5) 280 ( 3.6) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 276 ( 2.2) 273 ( 1.7) GENDER Male State 265 ( 1.8) 259 ( 1.6) 261 ( 1.6) 265 ( 2,1) 261 ( 1.5) Region 272 ( 3.9) 271 ( 5.9) 269 ( 4.0) 274 ( 4.1) 266 ( 4.1) Nation 266 ( 2.0) 262 ( 2.3) 260 ( 1.7) 262 ( 2.1) 260 V 3) Foliate State 262 ( 1.7) 251 ( 2,0) 258 ( 1.7) 262 ( 2.3) 260 ( 1.5) Region 270 ( 3.1) 261 ( 4.3) 266 ( 4.1) 273 ( 3.6) 268 ( 3.7) Nation 266 ( 1.4) 253 ( 1.6) 258 ( 1,5) 261 ( 1.9) 260 ( 1.4) a The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each popvlation of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4i THE 1990 NAEP TRIAL. STATE ASSESSMENT 35 New York ME NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valt. Ne in and of itself, but it becomes more useful for improving instruction and set when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the. 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information on student achievement. It is important to note that the NAEP data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qmlifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational.process in the country. THE 1990 NAEP TRIAL S'i ATE ASSESSMEN1 37 New York Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by tr,00ks or worksheets. Also, it is widely recognized that home environment has an ei:ot .nous impact on future academic achievement. Yet, as shown in Chapters 3 and 7, large proportions of students report having spent much more time each day watching television than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 3$ THE 1990 NAEP TRIAL STATE ASSESSMENT New York CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.' This chapter focuses on curricular and instructional content issues in New York public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: About three-quarters of the eighth-grade students in New York (74 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curtis McKnight, et al., The Underach;c.dtg Currkulum. Assessing U.S. School Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign, IL: Stipes Publishing Company, 1987). Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 39 New York ln New York, 86 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Almost all of the students in New York (97 percent) were taught mathematics by teachers who teach only one subject. About three-quarters (73 percent) of the students in New York were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was less prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in I New York Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 19011 NAEP TRIAL STATE ASSESSMENT New York Northeast Nation Percentage of eighth-grade students in public schools that identified mathematics as receiving special emphasis in school-wide goals and objectives, instruction, 1n-service training, etc. Percentage of eighth-grade public-school students who are offered a course in algebra for high School course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who teach only mathematics Percentage of eighth-grade students in public schools who are assigned to a mathematics class by their ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics instruction per week Percentage Percentage Percentage 74 ( 4.9) 45 f18.5) 63 ( 5.9) 86 ( 3.6) 90 ', 7.3) 7$ ( 4.6) 97 ( 2.0) 100 ( 0.0) 91 ( 3.3) 73 ( 3.6) 71 (101) 63 ( 4.0) 10 ( 2.0) 14 ( 55) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 40 THE 1990 NAEP TRIAL STATE ASSESSMENT New York CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in New York are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in New York were taking eighth-grade mathematics (73 percent) than were taking a course in pre-algebra or algebra (20 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in New York who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT New York Northeast Nation Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency What kind of mathematics class are you taking this year7 Eighth-grade mathematics 73 ( 1.8) 63 ( 5.8) 62 ( 2.1) 252 ( 1.4) 259 ( 2.9) 251 ( 1.4) Pre-algebra ( 1-2) 16 ( 3.9) 19 ( 1.9) 273 ( 2.7) 278 ( 6.7)1 272 ( 2.4) Algebra 13 ( 1.1) 18 ( 3.3) 15 ( 1.2) 291 ( 2.7) 297 ( 3.6) 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 700 percent because a small number of students reported taking other mathematics courses. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. e 4± THE 1990 NAEP TRIAL STATE ASSESSMENT 41 New York Further, from Table A5 in the Data Appendix:* About the same percentage of females (21 percent) and males (20 percent) in New York were enrolled in pre-algebra or algebra courses. In New York, 21 percent of White students, 19 percent of Black students, 16 percent of Hispanic students, and 38 percent of Asian students were enrolled in pre-algebra or algebra courses. Similarly, 23 percent of students attending schools in advantaged urban areas, 17 percent in schools in disadvantaged urban areas, 18 percent in schools in extreme rural areas, and 20 percent in schools in areas classified as "other" were enrolled in pre-algebra or algebra courses. MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to their teachers, the greatest percentage ofeighth-grade students in public schools in New York spent either 15 or 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes daily. Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix): In New York, 2 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 1 percent of the students in New York and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. 4 For every table in the body of the report thct includes esumates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations -- race ethnicity, type of community, parents' education level, and gender. 42 THE 1990 NAEP TRIAL STATE ASSESSMENT New York The results by race/ethnicity show that 1 percent of White students, 2 percent of Black students, 2 percent of Hispanic students, and 4 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 1 percent of White students, 4 percent of Black students, 2 percent of Hispanic students, and 0 percent of Asian students spent no time doing mathematics homework. In addition, 3 percent of students attending schooh in advantaged urban areas, 3 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 0 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 0 percent of students attending schools in advantaged urban areas, 2 percent in schools in disadvantaged urban areas, 0 percent in bc.hools in extreme rural areas, and 1 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT New York Northeast Nation 1 I About flow much time do students spend on mathematics homework each dap _ None 16 minutes 30 minutes 45 minutes An hour or more Percentage Peruentage Percentage and and and Proficiency Proficiency Proficiency 38 ( 3.0) 255 ( 2.5) 49 ( 3.0) 264 ( 2.4) 10 ( 1.8) 270 ( 5.3) 1 ( 0.7) *It* ( *1111 54 (132) 264 ( 4.7)' 35 (12.5) 270 ( 4.1)1 9 ( 2.7) es) 43 ( 4.2) 256 ( 2.3) 43 ( 4.3) 266 ( 2.6) 10 ( 1.9) 272 ( 5.7)1 4 ( 0.9) 278 ( 5.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 7: 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 43 New York TABLE 7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 19110 NAEP TRIAL. STATE ASSESSMENT New York Northeast Nation _ About how much time do you usually spend each day on mathematics homework? 1 Percentage end Proficiency Remota,* and Proficiency Percentage end Prondency None 4 ( 0.5) ( 1.2) 9 ( 0.8) 255 ( 3.2) ( 251 ( 2.8) 15 minutes 40 ( 1.6) 37 ( 3.3) 31 ( 2.0) 282 ( 1.7) 269 ( 2.4) 264 ( 1.9) 30 minutes 36 ( 1.3) 34 ( 2.6) 32 ( 12) 265 ( 1.8) 271 ( 8.0) 263 ( 1.9) 4$ miwAes 12 ( 0.8) 15 ( 2.3) 16 ( 1.0) 259 ( 2,6) 272 ( 6.5) 266 ( 1.0) An hour or more 8 ( 246 ( 0.6) 3.0) 8 ( 1.7) .41 12 ( 258 ( 1.1) '3.1) 4. The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within :1- 2 standard errors of the estimate for the sample. ". Sample size is insufficient to permit a rehable estimate (fewer than 62 students). And, according to the students (Table 7 and Table A7 in the Data Appendix): In New York, relatively few of the students (4 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 8 percent of the students in New York and 12 percent of students in the nation spent an hour or more each day on mathematics homework. The results by race/ethnicity show that 6 percent of White students, 12 percent of Black students, 13 percent of Hispanic students, and 8 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 4 percent of White students, 5 percent of Black students, 5 percent of Hispanic students, and 0 percent of Asian students spent no time doing mathematics homework. 44 THE 1990 NAEP TRIAL STATE ASSESSMENT New York In addition, 5 percent of students attending schools in advantaged urban areas, 11 percent in schools in disadvantaged urban areas, 11 percent in schools in extreme rural areas, and 6 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 3 percent of students attending schools in advantaged urban areas, 5 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 4 percent in schools in areas classified as "other" spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computasion, estimation, functions, algebra, statistics, probability, geometry, and measurements Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. 5 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 5 ) THE 1990 NAEP TRIAL STATE ASSESSMENT 45 New York The responses of the assessed students' teachers to the topic emphasis questions for each content area were combined to create a new variable. For each question in a particular content area, a value of 3 was given to "heavy emphasis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Geometry, Data Analysis, Statistics, and Probability, and Algebra and Functions had higher proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. Students whose teachers placed heavy instructional emphasis on Numbers and Operations had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. 5 I. THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE 8 I Teachers' Reports on the Emphasis Given to Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT New York Northeast Nation Penterittoe and Pm Agency Pereentage and Proacioncy Partenen. and lindkdaney teacher 'emphasis categories by content areas Numbers end Operations Heavy emphaSis 44 ( 3.7) 41 ( 8.9) 49 ( 3.8) 255 ( 2.2) 2643 ( 2.9) 260(1.5) Little or IV emphasis 13 ( 1.8) 15 ( 2.1) 290 ( 4.0) I** ( *el 287 ( 3.4) Illeastrement Heavy emphasis 13 ( 2.3) 32 (11.5) 17 ( 3.0) 258 ( 4.0) 257 (11.7)1 250 ( 5.6) Little or no emphasis 40 ( 3.5) 34 ( 8.3) 33 ( 4.0) 255 ( 3.0) 282 ( 4.8)I 272 ( 4.0) Geometry Heavy emphasis 40 ( 3.0) 48 (11.9) 28 ( 3.8) 265 ( 2.7) 264 ( 8.1)1 260 ( 3.2) Little or no emphasis 9 ( 1.3) ( 1.0) 21 ( 3.3) 248 ( 4.9) ( 264 ( 5.4) Data Analysts, Statistics, and Probability Heavy emphasis 24 ( 272 ( 2.8) 3.9) 12 *.. ( 6.1)) 14 ( 269 ( 2.2) 4.3) Little or no emphasis 43 ( 2.8) 48 (10.1) 53 ( 4.4) 254 ( 3.0) 279 ( 54)1 261 ( 2.9) Algebra and Functions Heavy emphasis 49 ( 3.0) 52 (11.5) 46 ( 3.6) 274 ( 2.0) 273 ( 8.6)1 275 ( 2$) Little or no emphasis 14 ( 1.7) 14 ( OS) 20 ( 3.0) 231 ( 3.3) 243 ( 3.0) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ' Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 47 New York SUMMARY Although many types of mathematics learning can take place outside of the school environment, thare are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: About three-quarters of the eighth-grade students in New York (74 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In New York, 86 percent of the students could take an algebra course in eighth grade for hish-school course placement or credit. A greater percentage of students in New York were taking eighth-grade mathematics (73 pcscent) than were taking a course in pre-algebra or algebra (20 percent). Across the nation, 62 percent were taking eighth-gyade mathematics and 34 percent were taking a course in pre -algebra or algebra. According to their teachers, the greatest percentage of eighth-grade students in public schools in New York spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Aernss the nation, teachers reportgi that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. In New York, relatively few of the students (4 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 8 percent of the students in New York and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instructional emphasis on Geometry. Data Analysis, Statistics, and Probability, and Algebra and Functions had higher proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. Students whose teachers placed heavy instructional emphasis on Numbers and Operations had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. 45 THE 1990 NAEP TP1AL STATE ASSESSMENT New York CHAPTER 4 lezza-Ax-.9 SUM IMMO 1 1111riM111111111111 11111111-111-111111111 MO 11111111111111-111MIlle 1111111Viamsifigg VMS. Mall. Vona. ,Olov.alli 411101. iii IMAM 1811111111 1111',11111 BOOM Wauaauuuuuui How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning or for those who come from different cultural backgrounds is an important aspect of teaching.' An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. 6 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 49 New York From Table 9 and Table A9 in the Data Appendix: In New York, 20 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 35 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In New York, 43 percent of students attending schools in advantaged urban areas, 11 percent in schools in disadvantaged urban areas, 14 percent in schools in extreme rural areas, and 21 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. O By comparison, in New York, 16 percent of students attending schools in advantaged urban areas, 49 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 29 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had higher mathematics achievement levels than those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of i Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 MEP TRIAL STATE ASSESSMENT Wm York Northeast Nation Which of the following statements is true about how well supplied you are by your Percentage Percentage Percentage school system with the instructional and and and materials and other resources you reed to teach your class? Profidency 20 ( 2.7) Proficiency 26 ( 8.6) Proficiency 13 ( 2.4) get all the resources I need. 287 ( 3.1) 271 ( 72)1 265 ( 42) I get most of the resoircu I need. 45 ( 3.5) 38 (11.7) 58 ( 4.0) 265 ( 1.9) 272 ( 2.9)1 285 ( 2.0) I get some or none of the resources I need. 35 ( 3.9) 38 (11.8) 31 ( 4.2) 248 ( 3.0) 274 ( 9.8)1 281 ( 2,9) The standard errors of the estimated statistics appear in parentheses. ft can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT New York PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: Less than half of the students in New York (31 percent) worked mathematics problems in small groups at least once a week; about one-quarter never worked mathematics problems in sniall groups (30 percent). The larpst percentage of the students (73 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, some never used such objects (14 percent). In New York, 60 percent of the students were assigned problems from a mathematics textbook almost every day; 9 percent worked textbook problems about once a week or less. Less than half of the students (43 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weeldy (27 percent). Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Curriculum Eighty-second Yearbook of the National Society for the Study of Education (Chicago, IL: University of Chicago Press, 1983). f; THE 1990 NAEP TRIAL STATE ASSESSMENT 51 New York TABLE 10 I Teachers' Reports on Patterns of Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAV TRIAL STATE ASSESSMENT New York Northeast Nation , Pasco Nage and Pertardago and Parcae lap and About how often do students work problems in small groups? Profkiency Proficiency Pnifidency At least *ma a wow( 31 ( 3.2) 44 ( 6.4) 50 ( 4.4) 259 ( 2.8) 264 ( 6.0)1 280 ( 2.2) Less than once a week 40 ( 3.4) 39 ( 8.8) 43 ( 4.1) 263 ( 2.3) 267 ( 5.0)/ 264 ( 2.3) Never 30 ( 3.0) 17 ( eh) 0 ( 2.0) 260 ( 2.7) 44 4 ) 277 ( 5.4)1 _ About how often do students use objects Percentage Pertentwge Percentage like rulers, counting blocks, or goometnc end and and solids? Proficiency Proficiency Proficiency At least once a week 13 ( 2.3) 257 ( 4.3) 14 ( 5.5) 4.44 ( in 22 ( 3.7) 254 ( 3.2) Less than once a week 73 ( 2.8) 78 ( 6.8) 69 ( 3.9) 282 ( 1,5) 269 ( 1.8) 283 ( 1.9) 14 ( 2.1) 9 ( 3,5) 9 ( 2.6) 254 ( 5.6) ( *) 282 ( 5.9)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent rtainty that, for each population of interest, the value for the entire population is within I 2 standard errors of the estimate for the sample ! Interpret with caution the nature of the sample does not allow accurate determination of the .iartabihty of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 52 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE 11 I Teachers' Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MAEP TRIAL STATE ASSESSMENT New York Northeast Nation Percents.* and PM Money Percentage and Proficiency Percentage end Pnalldenty About how often do students do problems from textbooks? Almost evwy day 60 ( 3.5) ST C 9.3) 62 ( 3.4) 267 ( 1.9) 278 ( 4.4) 267 ( 1.6) Several times a week 31 ( 2.9) 31 ( 8.3) 31 ( 3.1) 254 ( 3.6) 261 ( 8.2)I ( 2.9) About once a wook or Ins 9 ( 1.7) 13 ( 2.8) 7 ( 1.8) 242 ( 4.7) ( ***) 2150 ( 5.1)i About how often do students do problems Percentage Percentage Npraintage on worksheets? and and and Proficiency ProNciency Proficianey At least several times a week 43 ( 3.9) 53 (11.3) 34 ( 3.8) 260 ( 2.4) 262 ( 4.5)1 256 ( 2.3) About once a week 31 ( 2.9) 32 ( 8.2) 33 ( 3.4) 258 ( 2.9) 270 ( 3.4)1 260 ( 2.3) Less than weeldy 27 ( 3,4) 15 ( 4.6) 32 ( 3.6) 263 ( 3.1) 274 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of intevest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). The next section presents the students' responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. r. cz.) THE 1990 NAF.P TRIAL STATE ASSESSMENT 53 New York COLLABORATING IN SMALL GROUPS In New York, 58 percent of the students reported never working mathematics problems in small groups (see Table 12); 21 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1900 NAEP TRIAL STATE ASSESSMENT New York Northeast Nation Percentage and Proficiency Percentap and Proficiency Percentage and Proficiency r How often do you work in small groups in your mathematics class? J At least once a week 21 ( 1.5) 27 ( 6.7) 28 ( 2.5) 254 ( 2.6) 260 ( 4.8)1 258 ( 2.7) Less than once a week 20 1.4) 22 ( 2.8) 28 ( 1.4) 271 ( 2.1) 271 ( 5.0) 267 ( 2.0) Never 58 ( 2.1) 51 ( 7.9) 44 ( 2.9) 261 ( 1.5) 273 ( 4.6) 261 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. Examining the subpopulations (Table Al2 in the Data Appendix): In New York, 20 percent of students attending schools in advantaged urban areas, 24 percent in schools in disadvantaged urban areas, 22 percent in schools in extreme rural areas, and 20 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 20 percent of White students, 22 percent of Black students, 27 percent of Hispanic students, and 18 percent of Asian students worked mathematics problems in small groups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (21 percent and 21 percent, respectively). r tN W.; 54 THE 1990 NAEP TRIAL STATE ASSESSMENT New York USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A13 in the Data Appendix summarize these data: Uss than half of the students in New York (41 percent) never used mathematical objects; 27 percent used these objects at least once a week. Mathematical objects were used at least once a week by 27 percent of students attending schools in advantaged urban areas, 32 percent in schools in disadvantaged urban areas, 29 percent in schools in extreme rural areas, and 24 percent in schools in areas classified as "other". Males were more likely than females to use mathematical objects in their mathematics classes at least once a week (29 percent and 24 percent, respectively). In addition, 23 percent of White students, 32 percent of Black students, 34 percent of Hispanic students, and 24 percent of Asian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 19110 NAEP TRIAL STATE ASSESSMENT New York Northeast Nation How often do you work with objects like rulers, counting blocks, or geometnc solids in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Prolidency Al least once a week 27 ( 1.3) 30 ( 4.3) 28 ( 1.8) 254 ( 1.8) 265 ( 8.9) 258 ( 2.8) Less than once a week 32 ( 1.2) 30 ( 3.2) 31 ( 1,2) 271 ( 1.5) 277 ( 3.9) 269 ( 1.5) New 41 ( 2.0) 40 ( 4.8) 41 ( 2.2) 258 ( 1.8) 206 ( 3.91 259 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -t- 2 standard errors of the estimate for the sample. G THE 1990 NAEP TRIAL STATE ASSESSMENT 55 New York MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in New York who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table Al4 in the Data Appendix): More than half of the students in New York (63 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of the students in the nation. Textbooks were used almost every day by 63 percent of students attending schools in advantaged urban areas, 54 percent in schools in disadvantaged urban areas, 89 percent in schools in extreme rural areas, and 66 percent in schools in areas classified as "other". TABLE 14 I Students' Reports on the Frequency of i Mathematics Text Wok Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT New Yoe* Northeast Nation 1 I How often do you do mathematics problems from textbooks in your mathematics class? Percen(age and Proficiency Percentage and Proficiency Percentege and Proficiency Almost every day 63 ( 2.4) 72 ( 5.3) 74 ( 1.9) 266 ( 1.8) 275 ( 3.7) 267 ( 12) Several times a week 21 ( 1.2) 14 ( 1.6) 14 ( 0.8) 255 ( 1.9) 261 ( 4$) 252 ( 1.7) About once a week or less 17 ( 1.7) 14 ( 4.3) 12 ( 1.8) 248 ( 2.6) 249 ( 7.4)1 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 6 i 56 THE 1990 NAEP TP.1AL STI.TE ASSESSMENT New York And, for the frequency of worksheet usage (Table I S and Table A I S in the Data Appendix): Less than half of the students in New York (41 percent) used worksheets at least several times a week, compared to 38 percent in the nation. Worksheets were used at least several times a week by 48 percent of students attending schools in advantaged urban areas, 44 percent in schools in disadvantaged urban areas, 24 percent in schools in extreme rural areas, and 40 percent in schools in areas classified as "other". TABLE 15 Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMEN f New York Northeast Nation How often do you do mathematics problems on worksheets in your mathematics class? Percentage and Proticiency Percentage and Proficiency Parmintage and Proidency At least several times a week 41 ( 2.4) 44 ( 5.9) 38 ( 2.4) 258 ( 2.0) 261 ( 3.8) 253 ( 2.2) About once a week 22 ( 1.4) 22 ( 1.6) 25 ( 1.2) 263 ( 1.9) 268 ( 3.6) 281 ( 1.4) Less than wieldy 36 ( 2.3) 34 ( 8.5) 37 ( 2.5) 265 ( 2.2) 282 ( 4.3)1 272 ( 1.9) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard err of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. 4.; THE 1990 NAEP TRIAL STATE ASSESSMENT 57 New York TABLE 16 I Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics nstruction PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT 1 New York Northeast Nation _ Patterns of olaSsroom instruction Percentage of students who work mathematics problems in smat groups At least once a week Less than once a week Never Percentage of students who use obOots like rulers, counting blocks, or geometric solids At least once a week Less than once a week Never r Materials for mathematics instruction Percentage of students wno use a mathematics textbook Almost every day Several times a week About once a week or less Percentage of students wto use a mathematics worksheet At least several times a Week About once a week Less than weekly Percentage Percentage Penxintage Students Teachers Students Teachers Students Teachem 21 ( 1.5) 31 ( 3.2) 27 ( 8.7) 44 ( 6.4) 28 ( 2.5) 50 ( 4.4) 20 ( 1.4) 40 ( 3.4) 22 ( 2.8) 39 ( 8.6) 23 ( 1.4) 43 ( 4.1) 58 ( 2.1) 30 ( 3.0) 51 ( 7.9) 17 ( OS) 44 ( 2.9) 8 ( 2.0) 27 ( 1.3) 13 ( 2.3) 30 ( 4.3) 14 ( 53) 28 ( 1.8) 22 ( 3.7) 32 ( 1.2) 73 ( 2.8) 30 ( 3.2) 78 ( 8.8) 31 ( 1.2) 69 ( 3.9) 41 ( 2.0) 14 ( 2.1) 40 ( 4.8) 9 ( 3.5) 41 ( 22) 9 ( 2.6) Percentage Percentage Percentage Students Teachers Students Teachers Students Teachers 63 ( 2.4) 60 ( 3.5) 72 ( 5.3) 57 ( 9.3) 74 ( 1.9) 62 ( 3.4) 21 ( 1.2) 31 ( 2.9) 14 ( 1.6) 31 ( 8.3) 14 ( 0.8) 31 ( 3.1) 17 ( 1.7) 9 ( 1.7) 14 ( 4.3) 13 ( 2.8) 12 ( 1.8) 7 ( 1.8) 41 ( 2.4) 43 ( 3.9) 44 ( 5.9) 53 (11.3) 38 ( 2.4) 34 ( 3.8) 22 ( 1.4) 31 ( 2.9) 22 ( 1.8) 32 ( 8,2) 25 ( 1.2) 33 ( 3.4) 36 ( 2.3) 27 ( 3.4) 34 ( 6.5) 15 ( 4.6) 37 ( 2.5) 32 ( 3.6) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each populauon of interest, the value for the enure population is within 2 standard errors of the estimate for the sample. 6 58 THE 1990 NAEP TRIAL STATE ASSESSMENT New York SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery practices and resources. It appears that mathematics textbooks and worksheets continue to play a major role in mathern, tics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachers: Less than half of the students in New York (31 percent) worked mathematics problems in small groups at least once a week; about one-quarter never worked in small groups (30 percent). The largest percentage of the students (73 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and some never used such objects (14 percent). In New York, 60 percent of the students were assigned problems from a mathematics textbook almost every day; 9 percent worked textbook problems about once a week or less. Less than half of the students (43 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (27 percent). And, according to the students: In New York, 58 percent of the students never worked mathematics problems in small groups; 21 percent of the students worked mathematics problems in small groups at least once a week. I .ess than half of the students in New York (41 percent) never used mathematical objects; 27 percent used these objects at least once a week. More than half of the students in New York (63 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. Less than half of the students in New York (41 percent) used worksheets at least several times a week, compared to 38 percent in the nation. THE 1990 NAEP TRIAL STATE ASSESSMENT 59 New York CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks.' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. 6 National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Pnntxton. NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 6 r 60 THE 2990 NAEP TRIAL STATE ASSESSMENT New York Table 17 provides a profile of New York eighth-grade public schools' policies with mgard to calculator use: In comparison to 33 percent across the nation, 12 percent of the students in New York had teachers who allowed calculators to be used for tests. A smaller percentage of students in New York than in the nation had teachers who permitted unrestricted we of calculators (5 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of New York Policies on 1 Calculator Use PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT [ New York Northeast Nation Percentage of eighth-grade students in public schools whose teachers permit the unrestricted use of calculators Percentage of eighth-grade students in public schools whose teachers permit the use of calculators tor tests Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned by the school Percentage Percentep Percentage ( 1.2) 20 (11.8) 18 ( 3.4) 12 ( 2,5) 14 ( 9.2) 33 ( 4.5) 37 ( 4.3) 28 ( 8.2) 56 ( 4.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -i- 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 61 New York THE AVAILABILITY OF CALCULATORS In New York, most students or their families (96 percent) owned calculators (Table 18); however, fewer students (36 percent) had teachers who explained the use of calculators to them. From Table A 18 in the Data Appendix: In New York, 36 percent of White students, 35 percent of Black students, 37 percent of Hispanic students, and 32 percent of Asian students had teachers who explained how to use them. Females were as likely as males to have the use ofcalculators explained to them (36 percent and 36 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL. STATE ASSESSMENT Now York Northeast Nation p. Do you or your family own a Calculator? Percentage and ProNciency 96 ( 0.6) 262 ( 1.3) 4 ( 0.5) 236 ( 4.8) Percentage and Proliciency Peventage and Profidency ( 0.7) 269 ( 3.3) 2 ( 0.7) Percentage and ProNciency Percentage and Profidency 97 ( 0.4) 2e4 ( 1.3) 3 ( 0.4) 234 ( 3.8) Percentage and Proficiency Vet No Does your mathematics teacher explain how to use a Calculator for mathematics problems? _ this 36 ( 2.2) 30 ( 4.0) 49 ( 2.3) 257 ( 1.7) 258 ( 4.3) 258 ( 1.7) No 64 ( 2.2) 70 ( 4.0) 51 ( 2.3) 263 ( 1.4) 274 ( 3.8) 266 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 THE 1990 NAEP TRIAL STATE ASSESSMENT New York THE USE OF CALCULATORS As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment, students were asked how frequently (never, sometimes, almost always) they used calculatoi working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In New York, 38 percent of the students never used a calculator to work problems in class, while 40 percent almost always did. About one-quarter of the students (24 percent) never used a calculator to work problems at home, compared to 29 percent who almost always used one. Less than half of the students (44 percent) never used a calculator to take quizzes or tests, while 21 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19SO NAEP TRIAL STATE ASSESSMENT I New York Northeast Nation _ How often do you use a calculator for the following tasks? Percentage and Proficiency Percentage and Proeciency Percentage and Prod/slimy Working probJems in class Almost always 40 ( 1.2) 40 ( 4.0) 48 ( 1.5) 247 ( 1.6) 255 ( 3.9) 254 ( 1.5) Never 38 ( 1.8) 39 ( $.0) 23 ( 1.9) 277 ( 1.6) 282 ( 2.2) 272 ( 1.4) Doing problems at home Almost always 29 ( 1.3) 30 ( 3.3) 30 1.3) 251 ( 1.8) 264 ( 5.8) 261 ( 1.8) Never 24 ( 1.1) 22 ( 2.5) 19 ( 0.9) 273 ( 2.2) 275 ( 2.3) 263 ( 1.8) Taking quizzes or tests Almost always 21 ( 1.3) 23 ( 3.3) 27 ( 1.4) 242 ( 2.0) 256 ( 5.6) 253 ( 2.4) Never 44 ( 1.4) 45 ( 5.1) 30 ( 2.0) 279 ( 1.3) 284 ( 2.1) 274 ( 1.3) he standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within T 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 63 New York WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the questien did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 64 THE )990 NAEP TRIAL STATE ASSESSMENT New York The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in New York were in the High group than were in the Other group. About the same percentage of males and females were in the High group. In addition, 51 percent of White students, 37 percent of Black students, 37 percent of Hispanic students, and 50 percent of Asian students were in the High group. TABLE 20 J Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 NAEP TRIAL STATE ASSESSMENT Nur York Northust Nation -Catcutator-use" group Percentage and Madsen Percentage and Proldency Percentage and Proficiency High 46 ( 1.1) 44 ( 24) 42 ( 1.3) 269 ( 1A) 279 ( 3.8) 272 ( 1.6) Other 54 ( 1.1) 56 ( 2.5) 55 ( 1.3) 252 ( 1.8) 263 ( 2.9) 255 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within I 2 standard errors of the estimate for the sample. THE 1990 N AEP TRIAL STATE ASSESSMENT 65 New York SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instructional time to teaching students how to perform routine calculations by hand. Using calculators to replace this time-consuming process would create more instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 12 percent of the students in New York had teachers who allowed calculators to be used for tests. A smaller percentage of students in New York than in the nation had teachers who permitted unrestricted use of calculators (5 percent and 18 percent, respectively). In New York, most students or their families (96 percent) owned calculators; however, fewer students (36 percent) had teachers who explained the use of calculators to them. In New York, 38 percent of the students never used a calculator to work problems in class, while 40 percent almost always did. About one-quarter of the students (24 percent) never used a calculator to work problems at home, compared to 29 percent who almost always used one. Less than half of the students (44 percent) never used a calculator to take quizzes or tests, while 21 percent almost always did. 66 THE 1990 NAEP TRIAL STATE ASSESSMENT New York CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has become an issue of increasing importance to federal, state, and local governments. As part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.' Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In New York, 69 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's &gee. This compares to 44 percent for students across the nation. Many of the students (84 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. Many of the students (85 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT be New York TABLE 21 Profile of Eighth-Grade Public-School I Mathematics Teachers PERCENTAGE OF STUDENTS 11060 NAEP TRIAL STATE ASSESSMENT New York Northeast Nation _ Percentage of students *lune mathematics teachers reported having the following degrees Pimentos* Percentage Pententage Bachelor's degree Master's or specialist's degree 31 ( 18( 3.3) 3.3) 48 54 (15.0) (15.0) 58 ( 42 ( 4.2) 42) Doctorate or professional degree 2 ( 0.8) ( 0.0) 2 ( 1.4) Percentage of students *twee mathematics teachers have the foaming types of teaching certificates that we recognized by New York No regular certification 13 ( 2.0) 0 ( 0.0) 4 ( 12) Regular certification but less than the highest available 3 ( 1.1) 19 (11.5) 29 ( 4.3) Highest certification available (permanent or long-term) 84 ( 2.3) 81 (11.5) 66 ( 4.3) Percentage of students whoa* mathematics teachers have the following types of teaching certificates that are recognized by New York Mathematics (middle school or secondary) 85 ( 2.3) 89 ( 31) 84 ( 2.2) Education (elementary or middle school) 10 ( 1.7) 8 ( 3.8) 12 ( 2.6) Other 5 ( 1.7) 4 ( 3.7) 4 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of mterest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. 68 THE 1990 NAEP TRIAL STATE ASSESSMENT New York Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In New York, 48 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. About one-quarter of the eightb-grade public-school students in New York (30 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and Graduate Fields of Study PERCENTAGE OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT Now York Northeast Nation What was your undergraduate major? Percentage Percentage Percentage Mathematics 48 ( 3.6) 44 ( 92) 43 ( 3.9) Education 24 ( 2.6) 34 ( 8.0) ( 3.8) Other 28 ( 3.1) ( 8.1) 22 ( 3.3) What was your grafivate major? Percentage Percentage Percentage Mathematics 30 ( 3.0) 22 ( 9.7) 22 ( 3.4) Education 51 ( 3.5) 42 ( 8.2) 38 ( 3.6) Other or no graduate level study 19 ( 24) 37 ( 44) ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 69 New York Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In New York, 23 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Some of the students in New York (18 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. TABLE 23 1 Teachers' Reports on Their in-Service Training PERCENTAGE OF STUDENTS MOO NAEP TRIAL STATE ASSESSMENT New York Northeut Nation During the last year, how much time in total have you spent on In-service education In mathematics or the teaching of mathematics? None One to 15 hours 15 hours or more Percentage Percentage Percentage 18 ( 2.8) 25 ( 7.0) 11 ( 2.1) 59 ( 3.4) 37 ( 4.1) ( 4.1) 23 ( 2.5) 3$ ( $.4) 39 ( 3.8) The standard errors of the estimated statisticS appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT New York SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement." Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be.'1 In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In New York, 69 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. Many of the students (84 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In New York, 48 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. About one-quarter of the eighth-grade public-school students in New York (30 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. 1° Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Differences An International Assessment of Mathematics .',nd Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). ll lna V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement ArAEP's 1990 Assessment of the Nation and the Thal Assessment of the Stares (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 71 New York In New York, 23 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Some of the students in New York (18 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. 72 THE 1990 NAEP TRIAL STATE ASSESSMENT New York CHAPTER 7 The Conditions Beyond School that Facilitate Mathematics Learning and Teaching Because students spend much more time out of school each day than they do in school, it is reasonable to expect that out-of-school factors greatly influence students' attitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, encouragement, and participation in student learning experiences are powerful influences. Together, teachers and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment and mathematics proficiency, students participating in the Trial State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education. THE 1990 NAEP TRIAL STATE ASSESSMENT 73 New York kMOUNT OF READING MATERIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students participating in the Trial State Assessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports on Types of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ . MO /MEP TRIAL. STATE ASSESSMENT New York Northeast Nation =11111MI11111MOMPIMM1.....11Mil11=.11MIMMINIMMIMOO11111, Does your family have, or receive on a I regular basis, arty of the following items: more than 25 books, an encyclopedia. newspapers, magazines? Zero to two types Three types Four fYPos Percerdage and Proficiency Percentage and Proficiency Percentage and Proficiency 21 ( 1.2) 13 ( 2.0) 21 ( 1.0) 243 ( 2.4) 252 ( 3.9) 244 ( 2.0) 29 ( 1.0) 31 ( 2,7) 30 ( 1.0) 256 ( 1.4) 264 ( 2.9) 253 ( 1.7) 50 ( 1.4) 56 ( 3.7) 46 ( 1.3) 271 ( 1.2) 276 ( 4.3) 272 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. The data for New York reveal that: Students in New York who had all four of these types of materials in the home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT New York A smaller percentage of Black, Hispanic, and Asian students had all four types of these reading materials in their homes than did White students. A greater percentage of students attending schools in advantaged urban areas than in disadvantaged urban areas and about the same percentage of students in schools in advantaged urban areas as in extreme rural areas and areas classified as "other" had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1E00 NAEP TRIAL STATE ASSESSMENT New York Northeast Nation - How much television do you watch each day? One hour or lass Two hours Three hours 1 Four to five hours Six hours or more Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency usually 12 ( 0.6) 12 ( 1.3) 12 ( 0.8) 271 ( 2.2) 277 ( 4.4) 269 ( 2.2) 20 ( 0.8) 21 ( 2.3) 21 ( 0.9) 273 ( 2.0) 278 ( 3.1) 268 ( 1.8) 22 ( 1.0) 23 ( 1.2) 22 ( 0.8) 265 ( 1.7) 271 ( 3.5) 265 ( 1.7) 29 ( 0.9) 28 ( 2.6) 28 ( 1.1) 257 ( 14) 266 ( 4.1) 260 ( 1.7) 17 ( 1.0) 15 ( 3.3) 16 ( 1.0) 242 ( 2.3) 254 ( 5.5)1 245 ( 1.7) The standard errors of the estimated statirtics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within :t 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 75 New York From Table 25 and Table A25 in the Data Appendix: In New York, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Some of the eighth-grade public-school students in New York (12 percent) watched one hour or less of television each day; 17 percent watched six hours or more. About the same percentage of males and females tended to watch six or more hours of television daily. However, a smaller percentage of males than females watched one hour or less per day. In addition, 10 percent of White students, 37 percent of Black students, 26 percent of Hispanic students, and 7 percent of Asian students watched six hours or more of television each day. In comparison, 13 percent of White students, 6 percent of Black students, 10 percent of Hispanic students, and 22 percent of Asian stud:tits tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix: In New York, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in New York (41 percent) did not miss any school days in the month prior to the assessment, while 29 percent missed three days or more. In addition, 26 percent of White students, 35 percent of Black students, 36 percent of Hispanic students, ard IS percent of Asian students missed three or more days of school. S 76 THE 1990 NAEP TRIAL STATE ASSESSMENT New York Similarly, 27 percent of students attending schools in advantaged urban areas, 35 percent in schools in disadvantaged urban areas, 19 percent in schools in extreme rural areas, and 25 percent in schools in areas classified as "other" missed three or mom days of school. ,T TABLE 26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STM il V: .7"..S5MENT New Yonc Northeast Nation Percentage and Pnaidency Pacentaes and Proadoncy Porowdass and Proldency How many days of school did you miss last month? None 41 ( 1.1) 43 ( 22) 45( 1.1) 267 ( 1.4) 276 ( SA) 205 ( 1.6) One or two days 30 ( 1.0) 37 ( 3.1) 32 ( OA) 263 ( 1.8) 271 ( 2.5) ( 1.6) Three days or more 29 ( 1.3) 21 ( 3.0) 23 ( 1.1) 252 ( 2.0) 255 ( 55) 250 ( 1.a) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 77 New York STUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not onl-, to master essential skills and concepts but also to develop confidence in their mathematical abilities and to value mathematics as a discipline.' 2 Students were asked if they agreed or disagreed with five statements designed to elicit their perceptions of mathematics. These included statements about: Personal experience with mathematics, including students' enjoyment of mathematics and level of confidence in their mathematics abilities: I like mathematics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for solving everyday prothems. A student "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly agree" were given a value of 1 (indicating very positive _Attitudes about the sebject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception index according to whethei they tended to strongly agree wiih the Itatements (an index of tended to agree with the statements (an index of 2), oi tended to be undecided, to disagree, or to strongly disagree with the statements (an index of 3). Table 27 provides the data for the students' attitudes toward mathematics as defmed by their perception index. The following results were observed for New York: Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree'. category. About one-quarter of the students (27 percent) were in the "strongly awee" category (perception index of I). This compares to 27 percent across the nation. About one-quarter of the students in New York (22 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). " National Council of Teachers of Mathematics. and Evaluation Standards for School Mathematics (Reston. VA: National Council of Teachers of MathematIc, 1989). i) 78 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAV TRIAL STATE ASSESSMENT New York Northeast Nation Student 'perception ndex" groups Percentage and Proficiency Percentage and Pmeciency Percentage and Weeding, Strongly agree 27 ( 1.0) 26 ( 4.9) 27 ( 1.3) ("perception index" of 1) 269 ( 1.7) 276 ( 5.0)1 271 ( 1.9) A9ri 51 ( 1.1) 53 ( 3.0) 49 ( 1.0) ("perception index" of 2) 262 ( 1.5) 270 ( 4.5) 262 ( 1.7) Undecided, disagree, strongly disagree 22 ( 1.0) 21 ( 3.0) 24 ( 1.2) ("perception Index" of 3) 252 ( 1.7) 261 ( 5.8) 251 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. The data related to out-of-school factors show that: Students in New York who had four types ,Df reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar tc. the results for the nation, where students who had all four types of ma'erials showed higher mathematics proficiency than did students who had ATO to two types. THE 1990 NAEP TRIAL STATE ASSESSMENT 79 New York Some of the eighth-grade public-school students in New York (12 percent) watched one hour or less of television each day; 17 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Less than half of the students in New York (41 percent) did not miss any school days in the month prior to the assessment, while 29 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. About one-quarter of the students (27 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. r t-- .._ , .1 80 THE 1990 NAEP TRIAL STATE ASSESSMENT New York THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon which the assessment was based, and the procedures used to analyze the results. The objectives for the assessment .verr developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Educational Testing Service. The development of the Trial State Assessment Program benefited from the involvement of hundreds of representatives from State Education Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the prop-am. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The first step in implementing the 13113 design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. THE 1990 NAEP TRIAL STATE ASSESSMENT 81 New York The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general backgmund questions and the second consisting of mathematics backgroundquestions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required approximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every other block in one booklet Seven assessment booklets were used in the Trial State Assessment Program. The booklets were spiraled or interleaved in a systematic sequence so that each booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as described in the introduction to this report1 The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure A l). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales (Ince the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who ye various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on students' performance on the set of mathematics items they received. IRT provides a common bcale on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This common scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. National Assessment of Educational Progress, Mathematics Objeciives 1990 Assessment (PrInc.:Lon, NJ: Educational Testing Service, 1988). 82 THE 1990 NAEP TRIAL STATE ASSESSMENT New York FIGURE Al I Content Areas Assessed Numbers and Operations This content area focuseS On Students' understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-World situations, as well as computational and estimation Situations. Understanding numerical relationships as expressed in ratios, proportions, and percents is emphasized. Students' abilities in estimation, mental computation, use of calculators, generalization of numerical patterns, and verification of results are also included. IMeasurement This content area focuses on students' ability to describe real-world objects using numbers. Students are asked to identify attributes, select appropriate units, apply measurement concepts, end communicate measurement-related ideas to others. Questions are included that require an ability to read instruments using metric, customary, or nonstandard units, with emphasis on precision and accuracy. Questions requiring estimation, measurements, and applications of measurements of length, time, money, temperature, mass/weight, area, volume, capacity, and angles are also included in this content area. Geometry This content area focuses on students' knowledge of geometric figures and relationships and on their skills in working with this knowledge. These skills are important at all levels of schooling as well as in practical applications. Students need to be able to model and Visualize geometric figures in one, two, and three dimensions and to communicate geometric ideas. In addition, Students should be able to use informal reasoning to establish geometric relationships. Data Analysis, Statistics, and Probability 4 This content area focuses on data representation and analysis across ail disciplines and reflects the importance and prevalence of these activities in our society. Statistical knowledge and the ability to interpret data are necessary skills in the contemporary world. Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysis. IAlgebra and Functions ..1.111,1.1.11=11101.0010, This Content area is broad in scope, covering algebraic and functional concepts in more informal, exploratory ways for the eighth-grade Trial State Assessment. Proficiency in this concept area requires both manipulative facility and conceptual understanding: it involves the ability to use algebra as a means of representation and algebraic processing as a problem-Solving tool. Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. S THE 1999 NAEP TRIAL STATE ASSESSMENT 83 New York FIGURE A2 I Mathematical Abilities The following three categories of mathematical abilities are not to be construed 4.1., hierarchical. For example, problem solving Involves Interactions between conceptual knowledge and procedural skills, but what is considered complex problem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. Conceptual Understanding Students demonstrate conceptual understanding in mathematics when they provide evidence that the can recognize, label, and generate examples and counterexamples of concepts: can use and interrelate models, diagrams, and varied representations of concepts; can identify and apply principles; know and Can apply facts and dehnItions: can compare, contrast, and integrate related concepts and principles: can recognize, Interpret, and apply the signs, symbols, and terms used to represent concepts: and can interpret the assumptions and relations involving concepts in mathematical settings. Such understandings are essential to performing procedures in a meaningful way and applying them In problerm-solving situations. Procedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to select and apply appropriate procedures correctly, verify and justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors innerent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have been created as tools to meet specific needs in an efficient manner. it also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncomputational skills such as rounding and ordering. Problem Solving In problem solving, students are required to use their reasoning and anaiyi abilities when they encounter new situations. Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, data, models, and relevant mathematics: generate, extend, and modify procedures: use reasoning (i.e., spatial, inductive, deductive, statistical, and proportional): and judge the reasonableness arid correctness of solutions. S fl 84 THE 1990 NAEP TRIAL STATE ASSESSMENT New York A scale ranging from 0 to 500 was mated to report performance for each content area. Each content-area scale was based on the distribution of student petformance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In contrast, the NAEP scale anchoring is accomplished by describing what students at selected leveh know and can do. lie scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to defme levels at the extremes would therefore have been highly speculative. To define perfonnan c at each of the four levels on the scale, NAEP analyzed sets of mathematics items fro la the 1990 assessment that discriminated well between adjacent levels. The criteria for selecting these "benchmark" items were as follows: To define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To define performance at each of the higher levels on the scale, items were chosen that were: a) answered correctly by at least 65 percent of students whose proficiency was at or near that level; and b) answered incorrectly by a majority (at least 50 percent) of the students performing at or near the next lower level. The percentage of students at a level who answered the item correctly had to be at least 30 points higher than the percentage of students at the next lower level who answered it correctly. THE 1990 NAEP TRIAL STATE ASSESSMENT 85 New York Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students performing at each level. Eachof the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.2 Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and ie use of various instructional approaches. Because of the nature of the sampling fo the Trial State Assessment, the responses to the mathematics teacher questionnaLe do not necessarily represent all eighth-Evade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelrth-grade national assessment. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT New York FIGURE M f Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 (?) 0 rilia rib U. T. Lamas bid siess kw beim sa Ns are sift Nal doss Mom loads bah as Awn Arm she Nis ma las IA* she kiwi el kik shows. Isiielb Sas Ira Save is Soma Itslis Ise id 0 Tbe sib dis semis trib Tbe Sea 1011 et budis 0 no bse soldi Os 0,04r bob lbs saes EXAMPLE 2 DONN OF NUT MUD AT FARAWAY FANO Dals 0111.110sk 041010. Isom Ompikis V. tiro y howls al amps wow picked se Thussisyl CO SS 0 SO 0 TO SO OD 00 Mal issasf. THE 19 90 NAE? TRIAL STATE ASSESSMENT Grads 4 OraraN Pomertigs Percentage Minot 2211 2S1 63 91 Grads 4 antral Percentage Parcentav Correct ZS10 75 91 Grads Metall Percentage Parcontaaa Owed MI AR 76 67 Correct 73% for Anchor Levels: 212 2/2 100 COM& for Anchor Levels: 2/2 100 Correct 00% for Anchor Levels: SO MI 96 100 67 New York FIGURE A3 J Example Items for Mathematics Proficiency Levels (continued) ILevel 250: Sbnple Multiplicative Reasoning and Two-Step Problem Solving EXAMPLE 1 1.Wb&tistlievalucof a + when a I-, 3 Answer: EXAMPLE 2 NAM MGR IIURM USIL7S Wyss DIM II to Ild:=M1M11:1111 Me Ode Awe shows she Milo s aunty ft Mil Woo. On At ads Wow, asks s Oak rob so ithismo Amok dos Wk. Loki mat psis die auk $a . wish is mew IrkWar. Did yvia ass calculates so ads gultsdol0 0 Via 0 No EXAMPLE 3 6. Kathleen s pecknos beoebalk Imes !AA Myr hale 6 bosebaili She boa 24 bells. Which tomb, sentence will kip bee Mr, out how many bona she will Meg GI) 24 - 6 - CID 24 + 6 w 0 CI 24 + w eD 14 6 0 cD !don't know. Grade 8 Overall Petventese Correct 751 Percentage Cannot for Anchor longs: 224 2182 222 224 28 89 05 98 Grade °wall Percent's* Correct 73% Pen:0*9. Correct for Anchor Levels: 2411 222 IN 21 88 92 92 Grade 8 Overall Percentage Correct 77% Percentage Correct for Anchor Levels: 292 222 242 212 37 71 95 100 88 ThE 1990 NAM' TRIAL STATE ASSESSMENT New York FIGURE A3 J Example Items for Mathematics Proficiency Levels (continued) Level 300: Reasoning and Problem Solving Involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE I II. Which of the Mem* show the rods of fitpping the Aeon most, otree the lialt it EXAMPLE 2 ihe semial wee that e c3MIM Isildias. it ow 3, he b,u impossiusi by Bask model S iteih km& It eke sato soh te met se besot 35 bee WI whit be nelesemeeed by a se..6 maid haw awl bubo hIght n 0 3 s 7 eD DA realm the teshatilale so this email& os. 9 Grads 8 Overall Percentege Correct OM Percentage COMM! fa Anchor Lave's: 2Q11 2110 33 49 77 90 Grade 12 Overall Percentage correct 7514 Percentage Correct for Andlor Levels: iSX/ A2 48 79 93 Grade 8 Overall Percentage Correct: 5916 Percentage Correct for Mellor Lewis: MR UM 192 111/ 17 48 80 99 BEST COPY AVAILABLE THE 1990 KARP num. STATE ASSESSMENT 89 New York FIGURE A3 I Example Items for Mathematics Proficiency lievels (continued) Level 350: Rusvling and Problem SoNing involving Geometric Relationst4s, Algebraic Equations, end Beginning Statistics and Probability EXAMPLE 110 Clesedimes 11147 mkt w tha flaw* suer* .1 &Wow, 1 4 IL U ih al &Awn Is awtisvad. kow way aro wi k ii, Ow CD 100 EXAMPLE 2 IT. twolais how yew food yeer sewer to quiesita 16. Mawr Grade 8 Overall Percentage Correct: 34% Perventege Correct for Anchor Levels: 7/112 2110 13 19 53 88 Grade 12 Overall Penoentage Contot 49% Correct for Anchof Levels: aria Mg MI 22 48 90 Grade 8 Overall Percentage Corm!: 15% Percentage Correct for Anchor Levels: ISE IN SR 4 28 74 Grade 12 Overall Percentage Comm VS Percentage Correct for Mellor Levels: DM no SQ 3 22 74 90 'ME 1990 NAEP 'MAL sure ASSESSMENT New York SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEP's goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular wale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAFP) arc subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling en-or. Like almoat all estimates based on assessment measures, NAEP's total group and subgroup proficiency estimates are subject to a second source of uncertainty, in addition to sampling error. As previously noted, each student who participated in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropriate, (set of ^,he assessment questions -- or the entire set of questions -- somewhat ditLi-ent estimates of total group and subgroup proficiency might have been obtained. Thus, a second source of uncertainty arises because each student was administered a subset of the total pool of questions. G THE 1990 NAEP TRIAL STATE ASSESSMENT 91 New York In addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a backpound question in a certain way or the proportion of students in certain racial/ethnic groups) reflect only sampling error. NAEP uses a methodology called the jackknife procedure to estimate these standard errors. Drawing inferences from the Results One of the goals of the Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample ofstudents assessed. One uses the results from the sample -- taking into account the urwertainty associated with all sunples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population mums and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approAimately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. 92 TILE 1990 NAEP TRIAL. STATE ASSESSMENT New York Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defined by the responses of the assessed Kudents' mathematics teachers to questions in the mathematics teacher questionnaire. As an example, one might be interested in answering the question: Do students who reported spending 45 minutes or more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spend* 15 minutes or less? To answer the question posed above, one begins by compering the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is h:gher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in performance between the two groups in the population because of the uncertainty associated with the estimated ave-age proficiency of the groups in the sample. Remember that the intent is to make a statement about the entire population, not about the particular sample that was assessed. The data from the sample are used to make inferenccs about the population as a whole. As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the marmer in which the standard error for an individual group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups ± 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between groups in the population. If the interval does not contain zero, the difference between groups is statistically significant (different) at the .05 level. 9 C THE 1990 NAEP TRIAL STATE ASSESSMENT 93 New York As an example, suppose that one were interested in determining whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a paiticular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard errors for females and males were as follows: Group Average Proficiency Standard Error Female 259 1 2.0 Male 255 . 2.1 , The difference between the estimates of the mean proficiencies of females and males is four points (250 - 255). The standard error of this difference is Nr2.02 + 2.1 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to diaw the conclusions that are presented. If a statement appears in the report indicating that a particular group bad higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval includec: zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a statistically sigaificant difference in the population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. 3 The procedure described above (especially the estimation of the standard error of the difference) is, in a strict sense, only appropriate when the statistics being compared come from independent samples. For certain comparisons in the report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMENT New York The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significanre is being performed. However, in each chapter of this report, many differeat groups are being compared (i.e., multiple sets of confidence intervals are being analyzed). When one considers sets of confidence intervals, statistical theory indicates that the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. Ifone wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the mount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol "!". In such cases, the standard errors -- and any confidence intervals or significance tests involving these standard =ors -- should be interpreted cautiously. Further details concerning procedures for identifying such standard errors arc discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defmed by race/ethnicity and type of school community, as well as by gender and parents' education level. NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urtnn, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and/or backgtound variable results. As a result, data are not provided for the subgroups with very small sample Sins. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probability of .8 or greater. 1. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 New York The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school populatiot in the state or territory, divided by the standard deviation of the proficiency in the total population. If the true difference between subgroup and total goup mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical report. Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage Description of Text in Repott , p = 0 None 0 < p 5 10 Relatively few 10 < p 5 20 Some 20 < p 5 30 About one-quarter 30 < p 5 44 Less than half 44 < p 5 55 About half 55 < p 5 69 More than half 69 < p 5 79 About three-quarters 79 < p s 89 Many 89 < p < 100 Almost all p = 100 All 1C I 96 THE 1990 :AEP TRIAL STATE ASSESSMENT New York THE NATION'S REPORT CARO DATA APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains clrresponding data for each level of the four reporting subpopulations race/ethnicity, type of community, parents' education level, and gender. 10 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 97 New York TABLE A5 I Students' Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TR/AL Elidtb-grad STATE ASSESSMENT Matheina Iks Pre-aigebra Aliebra TOTAL Percentage Mact Preechincy Poventage and ProOdanew Perceltopt and Proficiency State 73 ( 1.6) ( 1.2) 13( 1.1) 252 ( 1.4) 273 ( 2.7) 291 ( 2.7) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 296 ( 2.4) RACE/ETHNICITY WWI* State 72 ( 2,3) 8 ( 1.5) 13 ( 1.5) 264 ( 1.1) 281 ( 32) 299 ( 3.5) Nation 59 ( 2.5) 21 ( 2.4) 17 ( 1.5) 259 ( 1.6) 277 ( 2.2) 300 ( 2.3) Black State 76 ( 3.4) 7 ( 1.8) 12 ( 2.1) 229 ( 22) .a. ( .....) .,-. ( ......) Nation 72 ( 4.7) 16 ( 3.0) 9 ( 2.2) 232 ( 3.4) 246 ( 6.4) ..... ( «fro) Hispanic State 77 ( 2.9) 7 ( 1.9) 10 ( 2.1) 231 ( 2.4) ...., ( .4.) .... ( ***) Nation 75 ( 4.4) 13 ( 3.9) 6 ( 1.5) 240 ( 2.4) il- ( +41 *4* ( *Mr ) Asian State 55 ( 8.3) 12 ( 3.8) 26 ( 6.4) Nation :2 ( 6.5) ..,,,,, ( ...) 21 ( 6.5) ... ( 4.) 41 ( 7.4) ..... ( .....) TYPE OF COMMUNITY Advantaged urban State 71 ( 3.9) 5 ( 1.3) 18 ( 3.6) 270 ( 2.0)I 311 ( 6.2)1 Nation 55 ( 9.4) 22 ( /.9) 21 ( 4.4) 269 ( 2.5)1 Disadvantaged urban State 77 ( 3.0) 5 ( 1.6) 12 ( 2.2) 229 ( 2.1) ( ft. Nation 65 ( 6.0) 16 ( 4.1) 14 ( 3.3) 240 ( 4.0)i 287 1 4.2)i Extreme rural State 75 ( 3.9) 3 ( 1.8) 15 ( 4.8) It*. ( 4.4* ) 0 ( Of ) Net ( 0 Mt Nation 74 ( 4,5) 14 ( 5.0) 7 ( 22) 249 ( 3.1)1 4,4. ( .....) ....p. ( .....) Other State /3 ( 2.9) 8 f 2.0) 11 ( 1$) 261 ( 1.8) 280 1 2.9)1 295 1 4.4) Nation 61 ( 2.2) 20 ( 2.1) 16 ( 14) 251 ( 2.0) 272 ( 2.8) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. ft can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 I 98 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A5 I Students' Reports on the Mathematics Class (ccintinued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pre-algebra Algebra TOTAL Percentage and ProNciency Percentage and Proaclency Pennontago and Pmliciancy State 73 ( 1.8) ( 1.2) 13 ( 1.1) 252 ( 1.4) 273 ( 2.7) 291 ( 2.7) Nation 82 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 296 ( 2.4) PARENTS' EDUCATION tiS non-graduate State 79 ( 3.7) ( 22) 10 ( 2.6) 239 ( 2.8) ( **Ilr Nation 77 ( 3.7) 3 ( 1.1) 241 ( 2.1) *41.1. 111 14$ graduate State 81 ( 2.2) 8 ( 1.6) 7 249 ( 1.9) Nation 70 ( 2.6) 1$ ( 2.4) 8 ( 1.1) 249 ( 1.9) 266 ( 3 5) 277 ( 52) Some college State 73 ( 2.9) 10 ( 2.0) 11 ( 1.9) 256 ( 2.3) 4,4r0 Nation 80 ( 3,1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 276 ( 2.8) 295 ( 3.2) College graduate State 65 ( 2.4) 8 ( 1.4) 19 ( 1.8) 281 ( 1.5) 277 ( 4.0) 300 ( 2.7) Nation 53 ( 2.7) 21 ( 2.3) 24 ( 1.7) 259 ( 1.5) 278 ( 2.8) 303 ( 2.3) GENDER Male State 73 ( 2.1) 7 ( 1.3) 13 ( 1.4) 254 ( 1.5) 278 ( 3.8) 291 ( 3.5) Nation 63 ( 2.1) 13 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 2.5) Resale State 73 ( 2.2) 8 ( 1.4) 13 ( 1.3) 250 ( 1.9) 270 ( 3.8) 291 ( 3.4) Nation 81 ( 2.8) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 289 ( 3.0) 223 ( 2.8) .11111. The standard errors of the estimated Statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value -or the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 99 New York TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT Nene 15 Minutes 30 Minutes - 46 Minutes An Hour or More TOTAL State Nation RACE/ETHNICITY Percentage ard Pralkdanay ( 0.6) 1 ( 0.3) 1 ( 0.7) 4114 041 I ( 0.3) 4 ( 2.3) *we ( eike) 1 ( 0.7) 2 ( 0.6) ( ***) 0 .8) 0 0.0) lk* W1P*) 0 1 0.0) ( 0 ( 0.0) I ( 0.9) n* ( 2 ( 1.5) ( .") ( 0.0) ( a") 0 ( 0.0) 0 ( 0.0) a") 1 ( 0.9) ( 0.4) ( ***) Parcentage and Prolidancy 36 ( 3.0) 255 ( 251 43 ( 4.2) 25e ( 2.3) 40 ( 3.7) 265 ( 2.1) 39 ( 4.5) 290 ( 2.2) 40 ( 4.5) 232 ( 3.6) 55 ( 72) 232 ( 3.1) 32 ( 4.2) 235 ( 4.9) 46 ( 7.6) 245 ( 3.0)1 23 ( 5.5) rwit ( 36 ( 8.3) 272 ( 4.0)1 61 (11.3) 273 ( 3.1)1 ( 6.9) 229 ( 3.2)1 41 (12.6) 236 ( 2.1)1 10 (13.7) 68 (14.9) 253 ( 5.4)1 43 ( 4.2) 263 ( 24) 37 ( 4.3) 256 ( 3.1) Percentage and Pralleknay 49 ( 3.0) 204 ( 2.4) 43 ( 4.3) 206 ( 2.6) 50 ( 3.9) 276 ( 2.2) 45 ( 5.1) 270 ( 2.7) 42 ( 5.4) 241 ( 4.3)1 40 ( 6.7) 248 ( 5.3) 49 ( 4.2) 237 ( 31) 34 ( 6.8) 251 ( 4.2)1 ( ( "41 49 ( 9.6) 283 ( 3.0)1 41 ( 5.3) 243 ( 5.0)1 36 ( 9.4) 253 ( 9.0)1 68 (19.5) 14 (10.9) ( 4,3) 270 ( 2.9) 49 ( 5.1) 265 ( 2.5) Percentage and Prandancy 10 ( 1.6) 270 ( 5.3) 10 ( 1.9) 272 ( 5.7)1 8 ( 2.0) 291 ( 8.5)1 11 ( 2.4) 277 ( 7.8)1 12 ( 2.7) 3 ( 1.2) 15 ( 4.5) 13 ( 2.9) .4* ( 20 ( 6.0) 4.44. 4-1.1 10 ( 5.4) ( 9 ( 5.8) 5 ( 3.4) 20 ( 4.4) 256 ( 9.1)1 12 ( 5.9) *MI ) 22 (33.1) ( 56) .441 6 ( 1.6) 10 ( 2.4) 276 ( 8.6)1 Paroantaga and ProOdancy ( 0.7) ( a") 4 ( 0.9) 275 ( 5.1)1 1 ( 0.8) 04.4, 4 ( 0.9) 279 ( 5.8)1 ( "*) ( 0.6) ( "") 2 ( 0.8) ( 7 ( 2.1) 4 ( 2.6) ( ***) 24 (102) ( 4,4,1 3 ( 3.4) 0 ( 0.0) 3 ( 1.6) 10 ( 6.2) *** ( ) 0 ( 0.0) 444 10 ( 7.3) 0 k 0.3) 4 ( 1.1) 282 (11,6)1 t. State Nation Slack State Nation Hispanic State Nation Asian State Nation 'UNITY Advantaged urban State Nation Disadvantaged State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "s Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 cs; 100 THE 1990 NAEP TRIAL17TATE ASSESSWINT New York TABLE A6 (continued) Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AM) AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes An Nour or More 1, Female State Nation TOTAL State Nation PARENTS' EDUCATION NS non-graduate State Nation KS graduate State Nation Soma college State Nation College graduate State Nation GENDER maw State Nation Percentage and Proficiency ( 0.3) *** ( 4.1 0 ( 0.0) .41 2 ( 1.1) 1 ( 0.5) **di 2 ( 1.1) *** (.") 1 ( 0.6) ** 444 2 1 ( 0.5) *4.) Percentage and Proficiency 38 ( 3.0) 255 ( 2.5) 43 ( 42) 256 ( 22) 41 ( .F.1) 238 ( 3.7) 49 ( $.3) 240 ( 2.8) 43 ( 3.8) 250 ( 3.2) 43 ( 52) 249 ( 3.1) 38 ( 3.8) 260 ( 3.5) 44 ( 5.4) 265 ( 2.6) 35 ( 3.7) 266 ( 2.6) 40 ( 4.7) 265 ( 2.5) 39 ( 3.1) 258 ( 2.8) 44 ( 4.4) 257 ( 2.9) 38 ( 3.4) 251 ( 2.71 41 ( 4./ 255 ( 2 Percentage and Pro &fancy 49 ( 3.0) 264 ( 2.4) 43 ( 4.3) 208 ( 2.6) 46 ( 5.3) 243 ( 48) 40 ( 8.1) 246 ( 3.7) 46 ( 4.1) 250 ( 2.6) 44 ( 5.8) 258 ( 2.7) 50 ( 4.6) 268 ( 22) 43 ( 5.8) 270 ( 3.6) 51 ( 3,5) 275 ( 2.9) 44 ( 4.1) 277 ( 3,0) sg ( 3.1) 264 ( 2.2) 43 ( 4.3) 268 ( 24) 49 ( 3.4) 264 ( 3.0) 43 ( 4.7) 264 ( 2.8) Percentage and Proficiency 10 ( 1.8) 270 ( 5,3) 10 ( 1.9) 272 ( 5.7)1 .44) ( 1.7) ( 8 ( 2.1) ( 3.1) ( *el 8 ( 2.4) ( 2.1) 441 11 ( 2.3) 283 ( 6.8)1 11 ( 2.3) 287 ( 6.1)1 9 ( 1.6) 274 ( 7.0) 9 ( 1.9) 273 ( 7.3)1 11 ( 2.2) 286 ( 4.9)1 11 ( 2.0) 272 ( 5.7)) Percentage and Profit:ism 1 ( 0.7) 4 ( 0.9) 278 ( 5.1)1 2 ( 2.0) 4*0(044) 4 ( 1,3) "4 ( 444) ( 0.4) arlrit 4,41) 3 ( 1.0) 1144 ( *44) 2 ( 1.0) 4 ( 1.0) " ( 4) 2 ( 1.1) "e) 5 ( 1.3) ( 1 ( 0.7) *44(4*4) 5 ( 1.3) 279 ( 7.7)1 2 ( 0.8) 4.4.4 4- 4 ( 0.9) Toe standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). loG THE Icio NAEP TRIAL STATE ASSESSMENT 303 New York TABLE A7 Students' Reports on the Amount of Time They 1 Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Mono 18 Wafts 30 Mkostoo 45 Minato, An Noir or Moro S. TOTAL State Nation Porton lago and *Ode Iley 4 ( 0.5) 255 ( 3.2) ( 02) 251 ( 2.6) 4 ( 0.6) .44 10 ( 1.0) 258 ( 3.4) 5 ( 1.3) ( ell 7 ( 1.5) .1,4) 5 ( 1.0) ( 12 ( 1.6) rfrk 14,1 ( 0.0) 444 ( 441 4 ( 2.0) ( 3 ( 1.1) ( *41 ( 25) *44 «rr) 12 ( 3.7) *** ) 8 ( 2.3) ( ***) 4 ( 0.6) *** ( ***) 9 ( 1.0) 250 ( 3.8) Pirosrdago Rercontago one And Proficiency Proficiency 40 ( 1.6) 36 ( 13) 262 ( 1.7) 265 ( 12) 31 ( 2.0) 32 ( 1.2) 264 ( 1.9) 263 ( 12) 43 ( 2.0 38 ( 1.8) 273 ( 1.4) 275 ( 12) 33 ( 2.4) 32 ( 1.3) 270 ( 1.9) 270 ( 2.1) 36 ( 3.0 33 ( 2.3) 236 ( 2.9) 237 ( 4.5) 26 ( 2.5) 33 ( 2.7) 241 32) 237 ( 3.5) 36 ( 3.9) 32 ( 3.6) 239 ( 4.5) 245 ( 4.5) 27 ( 3.0) 30 ( 2.8) 246 ( 3.6) 243 ( 3.4) 37 ( 4.5) 43 ( 4.7) ..**) ( 0+1 22 ( 4.8) 31 ( 5.6) .441 43 ( 3.7) 38 ( 3.5) 278 ( 2.3)1 284 ( 2.3)1 41 (12.5) 31 ( 6.6) 27$ ( 3.0)1 2$0 ( 4.6)1 36 ( 3.8) 35 ( 3.0) 238 ( 4.0)1 244 ( 3.1)1 24 ( 3.3) 31 ( 3.0) 253 ( 4.9)1 247 ( 4.7)! 25 ( 3.8) 50 ( 3.0) ( «oh) 1N4 49, ) 36 ( 4.6) 31 ( 2,9) 280 ( 3.5)! 255 ( 5.1)1 44 ( 2.4) 36 ( 2.0) 270 ( 12) 271 ( 2.1) 30 ( 1.8) 32 ( 13) 263 ( 2.3) 284 ( 2.3) White State Nation Black State Nation Hispattc State Nation Asian State Nation TYPE OF COMMUNITY A, *Waged urbasi State Nation Disadvantaged urban State Nation Extent* mai State Nation Other State Nation Portodogo Pero Wisp . 81108 Pro Odom Wel Mow 12 OS) 259 2.61 248 itel le 1.0 12 1.1 203 1.9) 25$ ( 5.1 10 ( 0.8) 275 ( 3.2) 15 ( 0.9) 277 ( 2.2) 14 ( 1,6) or, ( 00) 18 ( 2.3) 240 ( 3.6) 15 ( 22) 044 ( 4141 17 ( 2.1) 241 ( 4.3) 12 ( 4.9) ( .41 18 ( 3.9) .04) 12 ( 3.3) fn..) 13 ( 1.7) 20 ( 1.9) 250 ( 42)1 18 ( 3.8) 10 ( 1.1) 2ea ( 3.4) 15 ( 1.1) 267 ( 2.1) 8 ( 200 ( 4.1 11 ( 1.3 208 ( 33) 12 ( 12) ir,r) 18 ( 1.9) 232 ( 3.7) 13 ( 2.0) ( «in 14 ( 1.7) sod ( oval 8 ( 3.4) 25 ( 62) 5 ( 12) IhIM **1 7 ( 3.4) r.k.) 11 ( 22) ( 14 ( 22) 44.) 11 ( 8.6) 7 ( 2.7) ** ***) ( 0.5) 261 ( 5.2) 13 ( 1.1) 258 ( 3.8) AP The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is ,:isufficient to permit a reliable estimate (fewer than 62 students). 102 ' r THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A7 I Students' Reports on the Amount of Time They (continued) i Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minides An Noir or More TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage end Proficiency Pestentage Sid Proficiency State 4 ( 0.5) 40 ( 1.6) 36 ( 1.3) 12 ( 0.8) ( 0.6) 255 ( 3.2) 262 ( 1.7) 245 ( 1.8) 259 ( 2.6) 246 ( 3.0) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 18 ( 1.0) 12 ( 1.1) 251 ( 2.8) 264 ( 1.9) 263 ( 1.9) 266 ( 1.9) 258 ( 3.1) PARENTS EDUCATION NS nongraduate State 2 ( ( 1.1) 40 ( 238 ( 5.7) 4.3) 32 ( 4.3) 15 ( IP** 2.5) 1144,) 10 ( 2.9) 114r* ) Nation 17 ( 3.0) 26 ( 3.3) 34 ( 4.4) 12 ( 2.5) 10 ( 22) ( 248 ( 4.0) 246 ( 2.6) NS graduate State 4 ( VIM ( 0.8) 1.4111 45 ( 255 ( 3.0) 2.0) 34 ( 254 ( 2.9) 2.8) 10 ( *44 ( 1.5) MN) 7 ( 1.0) .44) Nation 10 ( 1.7) 33 ( 2.2) 31 ( 1.0) 16 ( 1.4) 11 ( 1.5) 246 ( 4.2) 259 ( 3.2) 254 ( 2.4) 256 ( 2.8) 244 ( 3.4) Some cofiege State ( 1.4) 41 ( 2.7) 36 ( 2.5) 9 ( 1.5) 8 ( 1.8) 287 ( 3.0) 271 ( 3.2) v.) Nation 9 ( *** 1.2) ***) 30 ( 266 ( 2.7) 3.0) 36 ( 266 ( 2.1) 2.6) 14 ( 274 ( 1.8) 3.5) 11 ( 1.5) College graduate State 2 ( 0.6) 39 ( 1.9) 39 ( 2.0) 12 ( 1.3) 7 ( 0.9) 275 ( 1.6) 276 ( 2.4) 272 ( 3.4) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Male State 43 ( 2.1) 35 ( 2.0) 10 ( 0.9) 7 ( 0.8) 267 ( 1.9) 265 ( 2.4) 263 ( 3.9) 239 ( 3.7) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 266 ( 2.4) 265 ( 3.0) 258 ( 4.1) Female State 3 ( 0.7) 38 ( 1.9) 37 ( 1.6) 13 ( 1.2) 9 ( 0.9) ( 257 ( 2.2) 265 ( 2.2) 258 ( 3.4) 251 ( 4.1) Nation ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 246 ( 4.1) 263 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent mrtainty that. for each population of intvest, the value for the entire population is within t 2 standard errors of the estimate for the sample. *** Sample size is insufncient to permit a reliable estimate (fewer than 62 st udents). THE 1990 NAEP TRIAL STATE ASSESSMENT 303 New York TABLE AS I Teachers' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY I 1990 MEP TRIAL STATE ASSESSMENT Rioters and Operations UmarmsM Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphat s Heavy Emphasis Little or No Emphasis TOTAL Percentage and Proficiency 44 ( 32) 255 ( 2.2) 49 ( 3.8) 200 ( 1.8) 41 ( 4.4) 286 ( 1.9) 48 ( 3.7) 267 ( 2.2) 48 ( 0.1) 239 ( 3.9) 54 ( 7.9) 243 ( 4.3) 56 ( 5.7) 236 ( 3.1) 47 ( 8.7) 24$ ( 4.8) 38 ( 9.1) 1") 32 ( 9.8) ..**) 49 ( 9.6) 270 ( 4.4)i 28 (13.0) tot 51 ( 5.4) 237 ( 2.6)1 48 (12.1) 255 ( 6.3)1 76 (32.8) 53 (12.4) 257 ( 7.1)1 39 ( 5.0) 263 ( 2.4) 52 ( 4.1) 200 ( 2.3) Pleventage and Proficiency 13 ( 1.8) 290 ( 4.0) 15 ( 2.1) 287 ( 3.4) 15 ( 2.1) 229 ( 3.0) 16 ( 2.4) 289 ( 3.5) 10 ( 2.8) we* ( 444 ) ( 3.3) ". ( ***) 8 ( 3.1) *** 8 ( 2.2) t ***) 24 ( 5.7) 4.4(4*4) 44. ) 12 trtt 16 ( 4.2) ttt) 9 ( 4.0) 4.4 0 ( 0.0) ( .41 ( «Hp) 14 ( 2.4) 297 ( 3.6)i 16 ( 2.7) 286 ( 3.6) Percentage Pommel!. and am= Proficiency Protickncy 13 ( 2.3) 40 ( 3.5) 258 ( 4.9) 255 ( 3.0) 17 ( 3.0 33 ( 4.0) 250 ( 5.8) 272 ( 4.4) 13 ( 3.1) 39 ( 4.3) 271 ( 5.1)1 271 ( 3.7) 14 ( 3.4) 36 ( 4.7) 259 ( 8.9)1 277 ( 4.3) 8 ( 1.8) 49 ( 6.1) * 221 ( 5.5) 25 ( 7.4) 23 ( 5.7) 228 ( 2.8)1 238 ( 8.1)1 17 ( 3.2) 35 ( 6.1) 229 ( 5.7) 23 ( 4.1) 34 ( 5.8) ( .44) 255 ( 4.4)1 17 ( 5.5) *** ( ***) 041P ( ) 23 ( 5.0) 44 ( 8.9) ( **) ***) 35 (10.2) 279 ( 5.7)i 9 ( 7.0) 40 ( 8.5) ( O* ) tikt .41 16 ( 3.6) 43 ( 8.3) 234 ( 9.4)1 231 ( 4.4)1 39 (10.3) 21 ( 6.5) 23$ ( 8.4)i ittt) 0 ( 0.0) 38 (51.7) «h. ( .44) 6 ( 4.9) 32 (11.7) ( .) 265 ( 9.1)1 12 ( 3.5) 39 ( 5.1) 208 ( 5.1)1 286 ( 4.2) 16 ( 3.9) 34 ( 5.3) 253 ( 7.1)1 270 ( 4.6) Percentage end Proficiency 40 ( 3.0) 285 ( 2.7) 28 ( 3.8) 200 ( 3.2) 40 ( 3.5) 274 ( 2.4) 27 ( 4.4) 265 ( 3.3) 41 ( 5.6) 239 ( 5.1) 33 ( 7.9) 242 ( 5.8)1 36 ( 4.5) 250 ( 4.3) 27 ( 6.8) t ) 47 ( 6.8) ttti tin ( 57 ( 9.3) 277 ( 5.4)! 3$ ( 9.4) 287 ( 4.9)1 41 ( 5.0) 245 ( 5 0)1 33 (11.8) 24$ ( 8.2)1 ( 0.0) ( *lit) 9 ( 6.1) IP* ( * ) 38 ( 4.2) 272 ( 2.7) 28 ( 4.6) 290 ( 3.9) Percentage and Proliciency 9( 1.3) 248 ( 4.9) 21 ( 3.3) 284 ( 5.4) 8 ( 1.7) 259 ( 3.5)1 22 ( 3.4) 273 ( 5.8) ( 2.0) 24 ( 7.3) 233 ( 4.7)1 10 ( 2.7) ttit ) 18 ( 5.5) tip* ( *el 11 ( 5.4) 14 ( 8.8) 10 ( 53) ( *) 13 ( 32) 9 ( 2.9) ( ***) 18 ( 7.6) ( 63 (14.0) ( ***) 16 ( 7.9) *** ( "") 24 ( 4.3) 265 ( 5.7) State Nation RACE/ETHNICITy White State Nation Slack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme nral State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is withir ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determinatiem of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A8 I Teachers' Reports on the Emphasis Given to (contin"ed) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1160 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measurement Geenteby Heavy Emphasis Littie or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAlt Percentage and Proficiency Perointige end Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Port *Map and Proficiency State 44 ( 3.7) 13 ( 1.8) 13 ( 2.3) 40 3.5) 40 ( 9 ( 1.3) 255 ( 290 ( 4.0) 258 ( 4 9) 255 3.0) 265 ( 2.7 246 ( 4.9) Nation 49 ( 3.8 15 ( 2.1) 17 ( 3.0) 33 ( 4.0) 28 ( 3.8 21 ( 3.3) 280 ( 14 237 ( 3.4) 250 ( 5.6) 272 ( 4.0) 2110 ( 3.2) 264 ( 5.4) EDUCAT!9 HS non-graduate State 58 ( 5.0) 7 ( 2.9) 15 ( 4.3) 33 ( 5.6) 37 ( 5.5) 10 ( 2.2) 241 ( 3.5) 4,44 ( 4.1 414 44*) 444 ( *** ( 444 ( **I Nation 60 6.9) 7 ( 2.3) 22 ( 5.3) 25 ( 5.3) 32 ( 0.3) 20 ( 6.1) 251 3.4) .44 ( 441 *44 ( 44) 4,44 ( 444) 444. ( 444) *44 444) MS gradual* State 48 ( 4.8, 7 ( 1.6) 11 ( 2.1) 41 ( 5.0) 32 ( 3.2) 12 ( 2.2) 250 ( 2.4) m ( ***) ( "4') 241 ( 4.8) 250 ( 4.2) ( *se) Nation 55 ( 4.8) 11 ( 2.8) 17 ( 3.9) 27 ( 5.0) 27 ( 44) 24 ( 5.1) 259 ( 2.9) *** ( "") 251 ( 6.1)1 253 ( 4.7)1 255 ( 4.2) 248 ( 4.8)1 Some Niblite State 43 ( 4.4) 10 ( 2.1) 14 ( 3.0) 31 ( 4.3) 41 ( 3.8) 8 ( 2.0) 257 ( 3.8) ( ***) *** ( ) 251 ( 4.9) 262 ( 4.0) *" ( ***) Nation 47 ( 4.4) 17 ( 3.3) 12 ( 2.7) 39 ( 5,5) 27 ( 5.0) 23 ( 4.1) 255 ( 2.6) 284 ( 4.1)1 *** ( ***) 279 ( 4.5) 262 ( 4.8)1 270 ( 4.7) CoNege graduate State 40 ( 4.0) 20 ( 2.5) 13 ( 3.0) 44 ( 3.7) 44 ( 3.7) 8 ( 1.8) 265 ( 3.2) 301 ( 3.8) 275 ( 6.8)1 289 ( 3.6) 278 ( 3.1) `" ( ***) Nation 44 ( 4.1) 19 ( 2.4) 18 ( 3.3) 37 ( 3.8) 28 ( 3.4) 21 ( 2.9) 2139 ( 2.6) 296 ( 3.4) 284 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 8.4) GENDER atele State 45 ( 4.3) 12 ( 1.8) 13 ( 2.4) 41 ( 4.2) 39 ( 3.2) 8 ( 1.8) 257 ( 2.13) 294 ( 5.8) 264 ( 6.3)1 2e0 C 3.4) 265 ( 3.8) 249 ( 8.2) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 281 ( 2.5) 287 ( 4.4) 258 ( 8.7) 275 ( 4.8) 283 ( 3.8) 208 ( 6.8) Female State 44 ( 3.6) 14 ( 1.8) 13 ( 2.8) 40 ( 3.2) 41 ( 3.3) 9 ( 1.4) . 253 ( 2.5) 287 ( 4.0) 252 ( 6.1) 249 ( 34) 254 ( 2.6) 244 ( 8.4) Nation 51 ( 3,0) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) ( 2.0) 266 ( 3.3) 241 ( 5.4) 268 ( 4.1) 258 1 3.3) 283 ( 5.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percelit because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 105 New York TABLE AS I Teachers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE LIATHEMATICS PROFICIENCY 118180 NAEP TRIAL STATE ASSESSMENT Data Analysts, Statistics, and Probability Algebra and Functions Heavy Emphasis il Ute or No Emphasis . Heavy Emphasis I Little or No Emphasis TOTAL Perciniatilt and Proficiency Percentage ano Pro Monty Percentage and Prolicieney Porcontage and Proficiency State 24 ( 2.8) 43 ( 2.8) 49 ( 3.0) 14 ( 1.7) 272 ( 3.9) 254 ( 3.0) 274 ( 2.0) 231 ( 3.3) Nation 14 ( 2.2) 53 ( 44) 46 ( 3.6) 20 ( 3.0) 26a ( 4.3) 261 ( 2.9) 275 ( 24) 243 3.0) II:ICE/ETHNICITY White State 21 ( 3.7) 43 ( 3.6) 54 ( 3.7) 10 ( 1.6) 288 ( 3.0) 270 ( 2.6) 281 ( 1.6) 242 ( 4.1) Nation 14 ( 2.4) 53 ( 5.0) 48 ( 42) 18 ( 2.8) 276 ( 4.1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) Slack State 26 ( 3.7) 245 (10.1) 48 ( S.6) 227 ( 5.0) 40 ( 52) 253 ( 5.4) 17 ( 3.6) *** ( 411 Nation 14 ( 3.4) .44 ( 53 ( 8.2) 225 ( 4.3) 39 ( 7.1) 253 ( 8.3) 27 ( 6.9) 226 ( 2.2)1 Hispanic State 28 ( 5.3) 40 ( 4.6) 36 ( 5.7) 28 ( 4.5) 246 ( 6.9)1 222 ( 5.4) 257 ( 5.9)1 219 ( 4.0)1 Nation 15 ( 4.1) ft* ( let ) se ( 6.3) 248 ( 4.4) 46 ( 5.9) 257 ( 4,0)1 18 ( 42) 4.4 ( Asian State 37 ( 8.7) 44. 32 ( 7.3) IHnt 82 ( 8.3) ( .41 15 ( 5.7) ( *I* ) Nation ( * 35 ( 7.1) 61 ( 8.1) .** 9 ( 4.9) ...) TYPE OF COMMUNITY Advantaged urban State 27 ( 9.4) 32 ( 8.1) 70 ( 6.3) 12 ( 3.9) 290 ( 6.2)? 272 ( 7.6)1 282 ( 2.9)1 Nation 11 ( 0.6) ....) 65 (19.4) 284 ( 7.4)4 41 ( 8.9) 296 ( 7.9)1 18 ( 5.3) ...) Disadvantaged urban State ( 5.4) 44 ( 5.4) 42 ( 6.6) 19 ( 4.2) 247 ( 7.6)1 227 ( 5.2)1 256 ( 5.1)1 220 ( 3.6)1 Nation 19 ( 9.4) 34 (11.4) 53 (41.8) 20 ( 9.4) 236 ( 82)t 254 ( 6.3)1 Extreme rural State ( 0.0) 86 (19.1) 14 (19.1) 22 (33.1) ( 4*. Nation ( 5.4) 65 (16.9) 33 ( 8.1) 42 (16.0) f-avh 254 ( 6.7)1 114-* ) 441 ( 5.9)1 Other State 19 ( 4.1) 44 ( 4.1) 49 ( 4.6) 10 ( 1.9) 285 ( 4.0)1 266 ( 3.7) 280 ( 1.8) 241 ( 5.0)1 Nation 15 ( 2.9) 53 ( 5.2) 47 ( 4,3) 17 ( 3.3) 267 ( 4.7) 260 ( 3.4) 276 ( 2.8) 245 ( 4.4)1 The standard errors of the estimated statistics appear tn parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" catzgory is not included. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). iLl 106 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE AS I Teachers' Reports on the Emphasis Given To (mtinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL, STATE ASSESSMENT . Data Analysis, Statistics, anti Probability . . Algebra and Functions , Heavy Emphasis Utt le or No Emphasis Heavy phasis Em _ - Little or No Emphasis TOTAL Percantap and Proackmay Ilicamitasa and Prolidency Pecontaga and Prolidancy Pastandags and Praidency State 24 ( 2.8) 43 ( 2.8) 49 ( 3.0) 14 ( 1.7) 272 3.9) 254 ( 3.0) 274 ( 2.0) 231 ( 3.3) Nation 14 ( 2.2) 53 ( 4.4) 46 (3.43) 20 ( 3.0) 269 ( 4.3) 261 ( 2.9) 27$ ( ZS) 243 ( 3.0) !ivENTS' EDUCA_M ItS non-graduats State 29 ( 5.5) foks. 37 ( 4.7) 311 ( 5.5) 17 ( 3.5) mg* Nation ( 3.0) ( 41 53 ( 7.7) 240 ( 6.2) 28 ( 42) 14* Min 29 (6.9) NS graduate State 18 ( 2.8) 49 ( 3.3; 99 ( 3A) 17 ( 2.7) 257 ( 7.1) 250 ( 4.1) 264 ( 32) 236 ( 3.7) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 201 ( 6.0)1 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Sohn coMpor State 25 ( 3.8) 277 ( 5.8) 43 ( 4.0) 42 ( 4.4) 275 ( 22) 12 ( 2.4) 1,9,1 Nation 13 ( 2.5) 57 ( 5.8) 270 ( 3.7) 4$ ( 4.8) 278 ( 3,0) 17 ( 3.1) *0* ( 04,1 Collage graduate State 26 ( 3.4) 40 ( 3.5) 58 t 32) 10 ( 1$) 287 ( 3.5) 284 ( 3.8) 285 ( 1.9) 230 ( 5.3) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 18 ( 2.4) 282 ( 4.5) 27$ ( 3.8) 288 ( 3.0) 249 ( 4.0) GENDER Male State 20 ( 2.7) 46 ( 3.1) 45 ( 3.4) 16 ( 2.0) 273 ( 5.3) 258 ( 3.7) 276 ( 2.9) 234 ( 4.1) Nation 13 ( 2.2) $4 ( 4.7) 44 ( 4.1) 22 ( 3.6) 275 ( 5.8) 280 ( 34) 276 ( 3.2) 243 ( 3.0) Fimal State 27 ( 3.1) 40 ( 3.0) 52 ( 3.2) 13 ( 2.0) 271 ( 4.1) 252 ( 3.5) 273 ( 1.9) 229 ( 3.9) Nation 16 ( 2.4) 53 ( 4.5) 48 ( 3.8) 18 ( 2.9) 263 ( 4.4) 282 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. 1 Interpret with caution - the nature of the sample does not allow accurate determination of the vat:ability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT 107 New York TABLE A9 I Teachers' Reports on the Availability of I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MG NAEP TRIAL 1 Get AP the Resources I 1 Get Most of the 1 Get Sone or None of STATE ASSESSMENT Need Resatirces I Need the Resoirces I Need TOTAlt and Proficiency Percentage and Prolidency Percentage aid Proadoncy State 20 ( 2.7) 45 ( 3.5) 35 ( SA) 267 ( 3.1) 265 ( 1.9) 248 ( 3.0) Nation 13 ( 2.4) 56 ( 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 261 ( 2.9) RACE/ETHNICITY White State 24 ( 3.5) 49 ( 4.2) 26 ( 42) 275 ( 2,5) 274 ( 1.5) 286 ( 2.9) Nation 11 ( 2.5) Se ( 4.6) 30 ( 4.8) 275 ( 3.5)1 270 1 2.3) 287 ( Slack State 12 ( 3.5) 33 ( 5.2) $5 ( 5.9) *IN) 244 ( 4.0) 230 ( 3.4) Nation ( 4.2) 52 ( 6.6) 33 ( 7.2) 241 ( 5.3)1 242 ( 2.4) 236 ( 4.9) Hispanic State 14 ( 3.1) 41 ( 7.0) 45 ( 7.4) 11,1-11 ( 242 ( 4.1) 232 ( 4.2)1 Nation 23 ( 7.6) 44 4.9) 34 ( 7.7) 246 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 Asian State r* * 46 ( 7.4) 4** ip-o*) 28 ( 7.4) Nation 19 ( 8.6) .**) 37 ( 7.7) 44 (12.7) felt TYPE OF COMMUNITY Advantaged urban State 43 ( 6.2) 280 ( 3.9)1 41 ( 7.5) 279 ( 5.8)1 16 ( 7.9) ( **-1 Nation 38 ( 9.2) 59 ( 8.9) 3 ( 3.1) 272 ( 8.5)1 286 ( 1.3)1 Disadvantaged urban State 11 ( 3.8) 40 6.2) 49 ( 6.8) *. 4-041) 248 ( 4.711 232 ( 2.6)1 Nation 10 ( 6.8) 40 (13.1) 50 (14.5) 251 ( 5.4)1 253 ( 5.5)1 Ex*reme rural State 14 (19.1) 86 (19.1) 0 ( 0.0) 4-.*) Nation 2 ( 2.6) 54 (10.4) 43 (10.3) 260 ( 8.8)1 257 ( 5.0)1 Other State 21 ( 4.1) 50 ( 5.9) 29 ( 5.2) 273 ( 3.0)1 270 ( 1,8) 260 ( Nation 11 ( 2.9) ( 5.4) 31 ( 5.6) 265 ( 3.9)1 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated stan, tics appear in parentheses. 11 can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A9 I Teachers' Reports on the Availability of (continued) I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL I Get AN the Resoirces I I Get Most of the I Get Some or None of STATE ASSESSMENT Need RiNetlreits I Need the Roseman I Need TOTAL Percentage mid Proficiency Percentaga and Prondency Parma... and Prefidency State 20 ( 2.7) 45 ( 3.5) 35 ( 3.9) 267 ( 3.1) 265 ( 1.9) 248 ( 3.0) Nation 13 ( 2.4) 56 ( 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 201 ( 2.9) PARENTS' EDUCATION HS noniraduate State 17 ( 3.6) 46 ( 5.8) 38 ( 8.4) 243 ( 4.1) *PR ( IMP1 Nation 8 ( 2.6)) 54 ( 244 ( 5.7) 2.7) 38 ( 243 ( 6.3) 3.5)1 $3 graduate State 17 ( 3.0) 40 ( 4.7) 35 ( 4.7) 256 ( 3.8) 258 ( 1.9) 244 ( 3.8) Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.9) 253 ( 44)1 258 ( 1.0) 256 ( 2.8) Some college State 23 ( 32) 42 ( 4.4) 35 ( 4.6) 269 ( 5.9) 271 ( 2.9) 250 ( 3.7) Nation 13 ( 3.3) 62 ( 4.3) 25 ( 4.1) 269 ( 2.5) 267 ( 3.8) College graduate State 23 ( 3.4) 45 ( 3.5) 31 ( 34) 277 ( 32) 277 ( 2.7) 260 ( 3.6) Nation 15 ( 2.9) 56 ( 4-3) 30 ( 5.1) 276 ( 5.4)1 270 ( 22) 273 ( 3.7) GENDER Male State 21 ( 3.1) 44 ( 3.5) 36 ( 4.0) 28$ ( 4.4) ( 2-3) 250 ( 3.4) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4.0) 264 ( 5.0)1 285 ( 2.6) 264 ( 3.3) Female State 20 ( 2.6) 46 ( 3.7) 33 ( 4.2) 268 ( 3.3) 201 ( 2.3) 247 ( 3.1) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 266 ( 3.9) 284 ( 2.0) 257 ( 3.0) AP The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 109 New York TABLE Atha I Teachers' Reports on the Frequency of Small 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1180 MEP TRIAL STATE ASSESSMENT At Lout Once a Ws* Less Than Coq a Weak Nowt' TOTAL Pardentage and Praia limy Pairoantage and PrafeklAdY Percents. and Proficiency State ( 32) 40 ( 3.4) 30 ( 3.0) 25a ( 2.8) 283 ( 2.3) 260 ( 2.7) Notion 50 ( 4.4) 43 ( 4.1) $ ( 2.0) 200 ( 22) 264 ( 2.3) 277 ( 54)1 RACE/ETHWITY White State 29 ( 3.8) 44 ( 4.1) 27 ( 3.7) 273 ( 2.5) 273 ( 2.4) 271 ( 2.2) Nation 49 ( 4.6) 43 ( 4.5) 8 ( 2.3) 265 ( 2.7) 271 ( 2.2) 285 ( 4.9)1 Black State 30 ( 5.1) 31 ( 4.9) 34 ( 4.1) 236 ( 42) 228 ( 32)1 245 ( 5.0) Nation 47 ( 8.1) 240 ( 3.4) 45 ( 7.0) 238 ( 4.0) 9 ( 4.1) ( &el Hispanic State 36 ( 5.9) 27 ( 5.7) 3$ ( 4.7) 237 ( 4.4)1 233 ( 3.3)1 241 ( 3.9) Nation 64 ( 7 2) 240 ( 2.5) 32 ( 6.9) 247 ( 6.3)1 4 ( 1.4) ***) Asian State 16 ( 6.0) «hi 61 ( 7.7) ( Mel 23 ( $2) rt.. Nation 80 ( 82) 4.11.* ( 37 ( 7.9) ( 44) 4 ( 2.7) TYPE OF COMMUNITY Advantaged urban State 17 ( 3.7) 63 ( 5.2) 20 ( 5.0) 281 ( 2.6)1 Nation 39 (224) 41 (17.9) 20 (12.2) 273 ( 6.0)t Disadvantaged urban State 33 ( 6.6) 34 ( 5.3) 33 ( 5.6) 241 ( 4.8)1 241 ( 4.8)1 238 ( 3.9), Nation 70 (111) 248 ( 4.8)1 21 ( 9.0) 249 ( 8.7)1 9 ( 8.5) ( ***) Extern* nral State 53 (70.8) 25 (37.7) *** 22 (33.1) 44 Nation 35 (14.6) 255 ( 5.5)1 56 (17.1) 258 ( 5.9)1 ( 9.6) 4+4,) Other State ( 4.8) 40 ( 5.2) 28 ( 5.0) 3.1) 269 ( 3.1) 268 ( 2.5)1 Nation 50 ( 4.4) 44 ( 4.5) 6 ( 1.8) 260 ( 2.4) 264 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. Sample size IS insufficient to permit a reliable estimate (fewer than 62 students). 110 liC THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE AlOa I Teachers' Reports on the Frequency of Small (cmtinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , UM NAEP TRIAL STATE ASSESSMENT - At Least Once a Wsek Less Than Once e Wet* I Never 1 TOTAL Pereentsge and Frolic:Way Penentele and Pralkieney Percentage end ProtIdeney State 31 ( 3.2) 40 ( 3e) 30( 3.0) 259 ( 2.8) 203 ( 2.3) 260 ( 2.7) Nation 50 ( 4.4) 43 ( 4.1) 6 ( 2.0) 260 ( 2.2) 264 ( 23) 277 ( 5.4)1 PARENTS' EDUCATION NS non-graduat State 39 ( 6.8) 31 ( 5.8) 30 ( 4.7) Nation 150 ( 64) 39 ( 64) ( 1.4) 244 ( 3.2) 244 ( 3.2)1 KS sa'acksate State 33 ( 4.3) 39 ( 4.7) 28 ( 3.6) 253 ( 32) 252 ( 2.9) 253 ( 3,5) Nation 49 ( 4.6) 45 ( 5.1) 8 ( 2,5) 252 ( 2.8) 257 ( 2.7) Some college State 32 ( 3.6) 38 ( 3.8) 30( 3,1) 264 ( 4.2) 287 ( 3.2) 251 ( 3.7) Nation 51 ( 266 ( 52) 3.1) 42 ( 266 ( 5.1) 3.2) 7 ( *** 2.3) Coder graduate State 27 ( 3,2) 44 ( 3.8) 29 ( 3-5) 273 ( 3.6) 274 ( 2.7) 271 ( 2.9) Nation 48 ( 52) 43 ( 4.4) 11 ( 2.7) 271 ( 2.0) 278 ( 3.0) 285( 4.9)i GENDER Male State 28 ( 3.4) 40 ( 3.7) 32 ( 3.5) 262 ( 2.9) 265 ( 2.5) 262 ( 2.9) Nation SO ( 4.5) 42 ( 4.0) ( 2.1) 261 ( 3.0) 285 ( 3.1) 278 ( 5.3)I Female State 33 ( 3.5) 39 ( 3.4) 28 ( 3.0) 256 ( 3.7) 262 ( 2.7) 256 ( 3.5) Nation 50 ( 4.7) 43 ( 4.7) 7 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 0.0)1 The standard errors of the estimated Statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 111 New York TABLE AlOb I Teachers' Reports on the Use of Mathematical Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT A2 Utast Once a Wtek Lass Than Vice a Weak Now TOTAL State Nation RACE/ETIINICITY wet State Nation Mad( State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Actmtagad urban State Nation Oludvamaged urban State Nat-ln Extrema rural State Nation Maw State Nation Paraantaga and Prallaioncy 13 257 22 254 12 273 17 261 15 940 22 233 18 39 247 7 42 23 *4. 19 237 39 247 22 27 13 272 19 253 Paronnayo and Proficiency Parcenialp and ProliCidireP 2.3) 4.3) 3.7) 3.2) ( 3.1) ( 2.6)1 ( 4.0) ( 3.8)4 ( 2.7) ( *) ( 5.9) ( 5.9)1 ( 10) ( 7.5) ( 3.8) ( 3.4) ( 6.5) ( 2.5) ( 4.1 (14.4) ( 3.5) ( 5.2)1 (11.4) ( 7.5)1 ,4,41 (14.9) ( 4.0) ( 3.8)1 4.3) ( 3.9)1 73 262 09 203 77 272 72 289 84 237 70 241 134 240 55 245 85 52 71 279 63 278 61 240 511 253 76 85 262 80 268 72 263 ( 2.6 ( 1.5 ( 3.01 ( 1.9) ( 3.4) ( 1.3) ( 42) ( 2.1) ( 4.7) ( 3.3) ( 82) ( 2.9) ( 4.8) ( 2.3) ( 7.3) ( 3,8)1 ( 5.8) ( 5.7) ( 9.3) ( 3,7)4 (115) ( 5.8)1 ( ( 3.2) (12.1) ( 7.0)1 (33.1) (14.6) ( 2.8)1 ( 4.3) ( 1.8) ( 5.0) ( 22) 14 ( 2.1) 254 ( 52) ( 2i) 212 ( 8.8)1 11 ( 23) 275 ( 10 ( 2.7) 2118 ( 82)4 2i ( 3.8) 233 ( 4.7)4 8 ( 3.9) 01111 19 ( 4.0) ipomp ( 2.8).) 9 3.9) «11 ( 4.2) 21 ( 9.6) *** 15 ( 9.3) .110 Iht111 20 ( 4.5) 241 ( 8.7)1 2 ( 15) 0 ( 0.0) 8 ( 3.9) *imp ( 2.6) 263 ( 9 ( 3,3) 281 ( 7,1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students), Iif; P-44 112 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE AlOb I Teachers' Reports OD the Use of Mathematical (wntinued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1090 NAEP TRIAL STATE ASSESSMENT At Least Ono a Weak Less Than Ones a Weak Never TOTAL Panenta's and Preldeney Paroentaie and Proadoncy Perestage NW Pralidency State 13 ( 2.3) 73 ( 2.8) 14 ( 2.1) 257 ( 4.3) 262 ( 1.5) 254 ( 519 Nation 22 ( 3.7) 60 ( 3.9) ( 2.6) 254 ( 3.2) 263 ( 1.9) 282 ( 5.9)1 PARENTS EDUCATION IIS non-graduate State 20 ( 4.9) 4,4* 86 ( 5.8) 244 ( 3.3) 14 ( 3.3) van Nation 25 ( 5.6) *44 ( 041 66 ( 7.2) 243 ( 2.2) 9 ( 6.5) *MP ( NS graduate State 13 ( 2.8) ( *141 75 ( 3.3) 254 ( 1.8) 12 ( 2.5) 41 Nation 23 ( 4.8) 70 ( 5.3) 7 ( 2.8) 246 ( 4.0)1 255 ( 2.2) OHM 041 Some college State 11 ( 2.7) **1 TS ( 3.7) 264 ( 2.5) 14 ( 2.7) *Al Nation 18 ( 4.0) 73( 4.3) ( 2.4) 261 ( 4.4)1 269 ( 2.3) Cape graduate State 12 ( 2.4) 74 ( 3.0) 14 ( 2.5) 268 ( 5.4)1 273( 1.9) 273( 7.0)' Nation 20 ( 3.9) 69( 3.7) 11 ( 2.5) 266 ( 3.5)1 274 ( 2.2) 297 ( 4.2)1 GENDER Mato State 13 ( 2.5) 72 ( 3.2) 15 ( 2.5) 260 ( 4.6) 283( 1.7) 259( 6.5) Nation 22( 4.1) 59( 4.1) ( 2.0) 255( 4.1) 265 ( 2.1) 287 ( 7.2)1 Female State 13 ( 2.3) 74 ( 2.8) 13( 2.0) 255 ( 4.8) 261 ( 1.7) 249 ( 6.6) Nation 21 ( 3.6) Se ( 4.2) 10 ( 3.3) 254 ( 3.3) 262 ( 1.9) 278 ( 6.0)! The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 i S THE 1990 NAEP TRIAL STATE ASSESSMENT 113 New York TABLE Alla Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Almost Evary Day Several Times Week About Once a Week or STATE ASSESSMENT Loss TOTAL Percentage and Pro 'dewy Percentage and Proficiency Pettantage and Proeciency State 00 ( 3.5) 31 ( 2.9) 9 ( 1.7) 207 ( 1.9) 254 ( 3.5) 242 ( 4.7) Nation 62 ( 3.4) 31 ( 3.1) 7 ( 1,$) 267 ( 1.8) 254 ( 2.9) 200 ( 5.1)1 RACE/ETHNICITY Milte State 85 ( 4.8) 28 ( 4.1) 7 ( 1.8) 276 ( 1.8) 289 ( 2.5) 253 ( 5.8)1 Nation 64 ( 3.7) 28 ( 3.2) 8 ( 2.3) 272 ( 1.9) 264 ( 3.4) 264 ( 5.4)1 OM* State 53 ( 4.6) 38 ( 4.8) ( 3.2) 243 ( 3.2) 230 ( 4.9)i ( Nation 56 ( 7.7) 244 ( 4.0) 41 ( 7.9) 233 ( 3.9)1 2 ( 1.4) ** ..**) Hispanic State 50 ( 4.8) 37 ( 4.9) 13 ( 2.9) 242 ( 3.2) 234 ( 4.9) ( G") Nation 61 ( 6.8) 32 ( 5.3) ( 2.3) 251 ( 3.1) 240 ( 4.3)1 ( "*) Asian State 59 ( 7.5) ( es») ( ***) ( 444) Nation 03 ( 6.9) 2$4 ( 7.0)1 10 ( 32) *** ( ***) ( 5.1) TYPE Of COMMUNITY Advantaged urban State 79 ( 7.8) 113 ( 5.6) 4 ( 2.7) 281 Nation 63 (15.9) 283 ( 7.3)1 23 ( 52) 14 (14.8) ( .41 Disadvantaged urban State 43 ( 5.9) 44 ( 5.7) 13 ( 42) 247 ( 6.0)1 234 ( 4.8)1 232 ( 5.4)1 Nation 86 (10.7) 31 (11.1) 252 ( 4.7)1 243 ( LOP **It ( Wrenn nral State 37 (14.0) ( 4.1 63 (14.0) *** ***) ( 0.0) OM* 44- Nation 50 (10.6) 268 ( 4.0)1 40 (10.0) 247 ( 7.8)1 10 7.3) 4* ( 1 Other State 85 ( 5.7) 27 ( 4.8) 8 ( 22) 270 ( 2.3) 287 ( 3.2)1 256 ( 6.4)1 Nation 63 ( 3.9) 31 ( 3.5) 8 ( 1.9) 267 ( 2.3) 255 ( 3.1) 257 ( 5.8)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE Al la Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1WO NAEP TRIAL STATE ASSESSMENT Most Every Day Several Times a Week About Ones a Week ar Less TOTAL Peroontage me Preadancof Pommel", Preedoncy Percentage and Prolicioncy State 80(3.5 ) ( 2.9) 9 ( 1.7) 267 ( 1.9) 254 ( 3.5) 242 ( 4.7) Nation 02 ( 3.4) 31(3.1) 7 ( 1.8) 267 ( 12) 254 ( 2.9) 200 ( 5.1)1 PARENTS' EDUCATION NS non-graduate State 52 ( 62) 247 ( 3.3) 41 ( 63) ***) 8 ( 2.4) 6.0.1 Nation 67 ( 5.5) 245 ( 3.2) 27 ( 5.2) 6 ( 2.1) ( **al HS graduate State 57 ( 4.5) 33( 4.1) 10 ( 2.6) 257 ( 2.0) 249 ( 34) Nation 01 ( 4.4) 34 ( 3.7) 8 ( 1.5) 237 ( 2.5) 250 ( La) Sono cottage State 64 ( 4.4) 26 ( 3.6) 8 ( 22) 270 ( 2.4) 255( 4.8) Nation 68 ( 42) 272 ( 2.7) 26 ( 3.7) 2$6 ( £.2) 6 ( 1.9) **) Calk") givduat State 64 ( 3.8) 29 ( 3.2) ( 1.5) 278 ( 2.2) 205 ( 4.6) 252 ( 5.9) Nation 61 ( 4.0) 281 ( 2.2) 31 ( 3.9) 2S5 ( 3.1) 8 ( 3.1) 4 ( GENDER Male State 59 ( 3.9) 31 ( 3.0) 10 ( 2.4) 268 ( 2.2) 256 ( 35) 243 ( 5.2)1 Nation 00 ( 3.7) 33 ( 3.4) ( 1.9) 269 ( 2.1) 256 ( 3.6) 261 ( 0.7)1 Female State 81 ( 3.6) 34 ( 3.3) ( 1.4) 265 ( 2.1) 250 ( 4.2) 240 ( 6.4) Nation 65 ( 3.61 26 ( 3.3) ( 2.2) 206 ( 1.8) 253 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT 115 New York TABLE Al lb I Teachers' Reports on lie Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Sweat Times a Week About Cit v a Week Lass than Wesidy TOTAL Panetta's and Proficiency Percentage and Proficiency Pereentage End Proficiency State 43 ( 3.9) 31 ( 2.0) 27 ( 3.4) 200 ( 24) 2511 ( 2.9) 203 ( 3.1) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 260 ( 2.3) 274 ( 2.7) RACE/ETHNICITY Wilts State 46 ( 5.1) 29 ( 3.4) 25 ( 4.2) 212 ( 1.7) 270 ( 2.6) 270 ( 3.2) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 264 ( 2.1) 2/9 ( 2.9) Mack State 39 ( 5.7) 32 ( 54) 29 ( 5,5) 231 ( 3.8)I 240 ( 6.7) 240 ( 3.3) Nation 45 ( 7.5) 31 ( 7.6) 23 ( 8.3) 232 ( 3.1)1 243 ( 2.3)1 248 ( 7.0)1 Hispanic State 3$ ( 5.8) 34 ( 4.3) 29 ( 6.1) 234 ( 3.2)1 227 ( 4.4) 242 ( 4.9)1 Nation 41 ( 7.7) 26 I 5.3) 33 ( 1.5) 242 ( 3.2)1 244 ( 5.1)1 257 ( 2.3)1 Asian State 36 ( 7.8) 26 ( 6.4) ( Nation 37 ( 6.3) ,m) 35 ( 9.7) 27 (10.4) TYPE OF COMMUNITY Advantaged urban State 46 ( $.6) 39 ( 8.4) 15 ( 5.8) 274 ( 4 a)! 272 ( 3.2)1 Nation 59 (13.2) 273 ( 3.4)1 20 ( 6.0) ...) 21 ( 8.2) Disadvantaged urban State 41 ( 8.3) 38 ( 4.1) 22 ( 4.4) 233 ( 3$)1 242 ( 5.2) 24$ ( 8.1)1 Nation 50 (13.9) 22 (11.2) 28 (10.7) 237 ( 2.4)1 258 ( 8.3)i 263 ( 4.1)1 Extreme rural State 14 (19.1) 83 (14.0) ( *41 22 (33.1) Nation 27 (14.3) 49 (12.7) 24 (10.1) 25$ ( 6.7)1 Other State 46 ( 6.8) 23 ( 4.4) 30 ( 5.3) 270 ( 2.0) 285 ( 3.2)1 266 ( 3.8)1 Nation 30 ( 4.4) 3.5 ( 4.3) 38 ( 4.2) 258 ( 3.3) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 121 116 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE Al lb I Teachers' Reports on the Frequency of (cmitinued) i Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10110 NAEP TRIAL Al Least Several Times STATE ASSESSMENT a Week About Once a Week Lass than Weekly TOTAL Parma lap and Pre Wavy al $4 3.8) 236 2.3) Percentage Prelkianay 25631 21 33 ( 3.4) 20:1( 1.3) Perouttage and Pralkdamy 263 3.1 $22 36 274 ( 2.7) Stets Nation PARENTS' EDU0Apon NS nen-graduate State 43 ( 241 ( 6.$) 4.5)1 3$ ( 4.7) 4.**) 22 } 4.2) Nation 35 ( 239 ( 6.0) 3.5) 29 ( 6.3) *pi 30 ( SA) 280 ( 4.5); NS graduate State 41 ( 5.2) 34 ( 3.5) 20 ( 4.7) 2$4 ( 2.9) 252 ( 3.3) 250 ( 44) Nation 35( 5.3) 36 ( 4.5) 30 ( 4.5) 250 ( 3.8) 250 ( 2.7) 263 ( 3.4) Some college State 45 ( 4.5) $2 ( 4.4) 22 ( 3.3) 264 ( 3.2) 200 ( 31) 270 ( 4.7) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.4) 260 ( 2.8) 203 ( 4.2) 278 ( 2.6) College graduate State 43 ( 4.5) 27 ( 3.1) 29 ( 3.9) 272 ( 3.0) 271 ( 4.2) 275 ( 3.7) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Mato State 42 ( 4.2) 31 ( 3.3) 27 ( 4.0) 263 ( 2.9) 200 ( 3.5) 264 ( 3.3) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 261 ( 2.8) 275 ( 3.2) Female State 43 ( 4.1) 30 ( 3.0) 2$ ( 3.1) 258 ( 2.8) 250 ( 2.7) 262 ( 4.0) Nation 34 ( 4.1) ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 22 THE 1990 NAEP TRIAL STATE ASSESSMENT 117 New York TABLE Al2 I Students' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19.0 NAEP TRIAL STATE ASSESSMENT Al Least Once a Week Leas Than Once a Weak Never TOTAL Ritteentage and Priiidency PatitMeage and Pteildency Percentage and Prelidency State 21 ( 1.5) 20 ( 1.4) 56 ( 2.1) 254 ( 2.8) 271 ( 2.1) 281 ( 1.5) Nation 28 ( 2.5) 26 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 281 ( 1.8) RACE/ETHNICITY White State 20 ( 2.1) 24 ( 2.1) 58 ( 2.6) 270 ( 2.1) 279 ( 2.0) 273 ( 1.3) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 268 ( 3-1) 272 ( 1.9) 270 ( 1.7) Mack State 22 ( 2.7) 13 ( 1.7) 84 ( 2.9) 229 ( 3.6) ( 238 ( 3.1) Nation 28 ( 3.0) 24 ( 3.6) 4$ ( 4.7) 234 ( 3.0) 245 1 4.8) 234 ( 3.1) Hispanic State 27 ( 3.4) 13 ( 2.1) 60 ( 3.8) 229 ( 4.1) 239 ( 2.8) Nation 37 ( 52) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) Asian State 21 ( 6.4) 61 ( 7.1) *** ( Mt* ) Nation 28 ( 6.4) ( 32 ( 4.0) 40 ( 6.2) «el TYPE OF COMMUNITY Advantaged urban State 20 ( 3.4) 27 ( 3.9) 53 ( 6.6) 270 ( 3.3)1 287 ( 4.1)1 261 ( 2.7)1 Nation 27 (134) *A..) 33 ( 288 ( 4.5) 5.4)1 40 279 (13.4) ( 3.5)1 Disadvantaged 'Min State 24 ( 2.1) 14 ( 1.8) 63 ( 3.1) 233 ( 4.0) 240 ( 8.2)1 240 ( 3.1)1 Nation 31 ( 5.7) 20 ( 2.8) 49 ( 6.3) 245 ( 4.0)1 267 ( 8.411 246 ( 3.7)! Extreme rural State 22 02.9) 34 ( 9.4) 45 (21.8) Nation 34 (10.8) 27 ( 3.8) 39 (11.6) 249 ( 5.2)! 284 ( 3.5)1 256 ( 6.2)1 Other State 20 ( 2.5) 24 ( 2.6) 56 ( 3.3) 267 ( 3.1) 275 ( 2.2) 268 ( 1.8) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 280 ( 3.3) 264 ( 2.1) 262 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 118 .1 t: THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A 12 I Students' Reports on the Frequency of Small (ccetinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT At Least Once a Weak Lass Than Once a Week Never TOTAL Percentage and Peoliclem Percentage and Madam Percentage and Prciatency State 21 ( 1.5) 20( 1A) 58 ( 2.1) 254 ( 2.8) 271 ( 2.1; 261 ( 1.5) Nation 28 ( 2.5) 28 ( 1.4) 44 ( 2.9) 2$6 ( 2.7) 267 ( 2.0) 201 ( 1.8) PARENTS EDUCATION IfS non-graduate State 26 ( 4.1) 15 ( 2.1) 59 ( 4.2) 244 ( 3.8) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4.5) 242 ( 3.4) 244 ( 3.0) 242 ( 2.7) HS graduate State 19 ( 1.9) 19 ( 2.1) 62 ( 2.9) 244 ( 3.6) 284 ( 3.9) 252 ( 1.9) Nation 28 ( 3.0) 2$ ( 1.8) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some college State 24 ( 2.5) 23 ( 2.4) 53, 3.0) 258 ( 4.0) 272 ( 3.7) 265 ( 2.7) Nation 27 ( 3.9) 27 ( 2.4) 46 ( 3.8) 265 ( 3.6) 268 ( 3.3) 286 ( 2.1) College graduate State 20 ( 2.1) 24 ( 1.9) 56 ( 2.7) 269 ( 3.9) 281 ( 2.4) 272 ( 1.8) Nation 28 ( 3.0) 28 ( 1.9) 44 ( 3.8) 270 ( 2.7) 278 ( 2.6) 275 ( 2.2) GENDER Mate State 21 ( 1.7) 21 ( 1.6) 58 ( 2.2) 255 ( 3.1) 273 ( 2.9) 282 ( 1.7) Nation 31 ( 2.9) 26 ( 1.7) 41 ( 2.9) 259 ( 3.3) 26$ ( 2.6) 262 ( 1.8) Female State 21 ( 2.0) 20 ( 1.6) 58 ( 2.4) 253 ( 3.5) 269 ( 2.3) 259 ( 1.9) Nation 26 ( 2.4) 27 ( 1.6) 47 ( 3.2) 257 ( 2.8) 2136 ( 1.7) 260 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 New York TABLE A13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1999 NAEP TRIAL STATE ASSESSAIENT At Least Once a Week Lass Than Once a Week Never - TOTAL Arrosatage aml Prceo fancy Paraintaps and Pralkiency Paramdago and Proilidancy State 27 ( 1.3) 32I( 12 41 ( 2.0) 254 ( 1.8) 271 ( 1.51 258 ( 1.6) Nation 26 ( 1.8) 31 ( 1.2 41 ( 2.2) 2U ( 2.6) 209 ( 259 ( 1.6) RACE/ETHNICITY White State 23 ( 1.3) 38 ( 1.8) 3$ ( 2.4) 271 ( 2.0) 277 ( 1.3) 272 ( 1.5) Nation 27 ( 1.9) 33 ( 1.6) 40 ( 2.5) 266 ( 2.6) 275 ( 1.8) 268 ( 1.8) Made State 32 ( 3.3) 19 ( 2.3) 49 ( 3.6) 233 ( 3.8) 242 ( 4.4) 236 ( 3.5) Nation 27 ( 3.3) 27 ( 3.2) 48 ( 4.5) 234 ( 3.7) 248 ( 4.5) 232 ( 2.6) Hispanic State 34 ( 3.6) 21 ( 2.1) 45 ( 42) 229 ( 3.6) 252 ( 4.7) 237 ( 2.7) Nation 36 (42) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) Asian State 38 ( 7.0) 41 ( 6.4) 111* ilre Ortri Nation 32 ( 3.7) 30 ( 32) ( &en 38 ( 4.7) v**) TYPE OF COMMUNITY Advantaged urban State 27 ( 2.6) 37 ( 3.6) 37 ( 3.9) 27$ ( 4.5)1 256 ( 2.3)1 277 ( 2.5)1 Nation 36 (10.3) 33 ( 4.8) 32 (11.1) 27$ ( 8.1)1 284 ( 3.2)1 251 ( 5.9)1 Disadvantaged urban State 32 ( 3.5) 23 ( 2.2) 45 ( 4.4) 232 ( 2.7)1 252 ( 4.2)1 236 ( 2.7)1 Nation 35 ( 8.6) 19 ( 2.1) 46 ( 8.4) 249 ( 5.3)1 256 ( 5.7)1 246 ( 4.5)1 Extreme rural State 29 ( 8.1) 58 ( 4.2) 13 ( 5.3) ( Nation 21 ( 3.1) 4,0* 37 ( 4.7) 262 ( 4.7)1 43 ( 5.0) 251 ( 5.2)1 Other State 24 ( '2.0) 36 ( 22) 40 ( 3.1) 266 ( 2.6) 274 ( 1.9) 268 ( 1.9) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 256 ( 2.9) 270 ( 1.8) 280 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 320 r- THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A13 I Students' Reports on the Use of Mathematics (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1060 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency Pennallale and ProlonLY Permute's and Prolklency State 27 ( 1.3) 32 ( 12) 41 ( 2.0) 254 ( 1.8) 271 ( 1.5) 258 ( 1.8) Nation 2$ ( 1.8) 31(1.2) 41 ( 22) 258 ( 2.6) 269 ( 1,5) 259 ( 1.6) PARENTS EDUCATION HI non-graduate State 30 ( 4.1) .4r.) 24 ( *Mr ( 3.0) WS!) 48 ( 240 ( 5.2) 3,1) Nation 27 ( 4.2) 26 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) HS graduate State 25 ( 2.0) 31 ( 2.3) 45 ( 2.9) 245 ( 2.9) 281 ( 2.1) 252 ( 2.5) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some college State 27 ( 2.2) 32 ( 2.4) 41 ( 3.0) 258 ( 4.5) 269 ( 3.4) 296 ( 32) Nation 29 ( 2.6) 3$ ( 2.3) 3$ ( 2.6) 281 ( 3.5) 274 ( 2.2) 283 ( 2.1) College graduate State 25 ( 1.8) 37 ( 1.7) 37 ( 2.3) 288 ( 2.2) 281 ( 2.0) 289 ( 2.4) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.6) 269 ( 3.0) 27$ ( 2.0) 275 ( 2.0) GENDER Mali State 29 ( 1.9) 31 ( 1,7) 40 ( 2.4) 253 ( 2.4) 273 ( 1.9) 262 ( 2.5) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 24 ( 1.5) 33 ( 1.5) 43 ( 2.3) 254 ( 2.1) 209 ( 2.2) 255 ( 2.1) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 288 ( 1,5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 121 New York TABLE A14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Elan Day - Several Times a Week About Caws a Week or Lase TOTAL and Prolkisny Parnentara and Prolealencv Per04111111116 INW State 03 ( 2.4) 2i ( 12) 17 ( 1.7) 264 ( 14) 255 ( 1.9) 248 2.6) Nation 74 ( 1.9) 14 ( 0.6) 12 14) 267 ( 1.2) 252 ( 13) 242 4.5) RACE/ETHNICITY, %Mao State 65 ( 2.9) 20 ( 1.6) 15 ( 2.1) 277 ( 1.5) 269 ( 1.6) 264 ( 2.8) Nation 76 ( 24) 13 ( 0.6) 11 ( 2.2) 274 ( 1.3) 25S ( 22) 252 ( 5.1)1 Black State 54 ( 4.2) 23 ( 2.8) 23 ( 32) 242 ( 3.6) 231 ( 3.0) 228 ( 24) Nation 71 ( 2.8) 15 ( 1.7) 4 ( 3.2) 240 ( 2.9) 232 ( 3.1) 223 ( 8.1) Hispanic State 59 ( 4.8) 21 ( 2.9) 20 ( 3.5) 241 ( 3.0) 235 ( 3.7) 227 ( 3.8) Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) Asian State 73 ( 280 ( 4.9) 0.1)1 14 ( 4.0) 13 ( ( 3.6) .44) Nation 79 ( 289 ( 4.9) 5.0)1 13 ( 3.4) 8 ( ( 2.0) ***) TYPE OF COMMUNITY Advantaged urban State 03 ( 285 ( 5.7) 2.1)1 24 ( 274 ( 2.8) 3.6)1 13 ( 3.7) *4.1 Nation 73 (11.1) 256 ( 4.6)1 13 ( 1.7) 14 (104) DisadVantaged urban State 54 ( 5.1) 22 ( 2.2) 24 ( 3.7) 242 ( 3.8)) 235 ( 4.9)1 233 ( 33)1 Nation 09 ( 2.8) 15 ( 2.5) 15 ( 2.2) 253 ( 3.7)1 243 ( 4.4)1 235 ( 0.5)1 Extreme niral State 89 ( 8.5) 11 ( 0.5) 0 ( 0.0) 274 ( 2.1)1 Nation 08 (113) 203 ( 4.2)1 *gm) 17 ( 6.2) Other State 66 ( 3.4) 19 ( 1.9) 16 ( 2.4) 273 ( 1.8) 264 ( 2.1) 202 ( 32) Nation 75 ( 2.2) 14 ( 1.0) 10 ( 1.9) 267 ( 1.6) 252 ( 2.6) 239 ( 4.3)? The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A14 I Students' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT , Almost Every Day Several Timms a Week Mead Once a Weak ar Lass TOTAL liereentap and Pteaciency Poreentage and Prelldwcy Percentage and Predidong State 63 ( 2.4) 21 ( 12) 17 ( 1.7) 266 ( 1.8) 255 ( 1.9) 248 ( 2.6) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.6) 267 ( 12) 252 ( 1.7) 242 ( 4.5) PARENTS' EDUCATiON Ittl non-graduate State 55 ( 248 ( 6.0) 3.5) 26 ( VIM ( 4.4) *11^1 19 ( 94. ( 4.7) Nation 64, ( 245 ( 3.4) 2.3) 18 ( *4* ( 2.0) ***) 18 ( 3.1) ***) NS graduat State 57 ( 3.8) 24 ( 2.6) 19 ( 2.0) 256 ( 2.6) 251 ( 31) 244 ( 3.7) Nation 71 ( 3.6) 16 ( 1.8) 13 ( 2.8) 258 ( 1.6) 249 ( 3.2) 239 ( 3.4)1 Some college State 62 ( 2.8) 21 ( 2.4) 17 ( 2.4) 271 ( 2.0) 257 ( 3.5) 250 ( 6.0) Nation 80 ( 270 ( 2.0) 1.9) 11 ( 1.2) .44) 9 ( 1.7) College graduate State 67 ( 2.7) 19 1.5) 14 ( 1.7) 277 ( 1.8) 269 ( 2.4) 261 ( 3.9) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 200 ( 2.8) 257 ( 6.4)1 GENDER Mal State 62 ( 2.5) 22 ( 1.4) 15 ( 1.9) 267 ( 2.1) 257 ( 2.5) 251 ( 3.5) Nation 72 ( 2.4) 16 ( 1.2) 12 ( 2.1) 268 ( 1.6) 252 ( 2.5) 242 ( 8.1) Female State 63 ( 2.7) 19 ( 1,6) 1$ ( 1.9) 285 ( 2.1) 253 ( 2.8) 246 ( 3.1) Nation 76 ( 1.8) 13 ( 1.0) 11 ( 1.6) 265 ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 12S THE 1990 NAEP TRIAL STATE ASSESSMENT 123 New York TABLE A 15 1 Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Lust Several Times a Week About Once a Week LIMS Than Wukty TOTAL Parentage end Proficiency Percentage and Pratt:16M Perseedage and Prelicieney State 41 ( 2.4) 22 ( 1A) 38 ( 2.3) 256 ( 2.0) 263 ( 1.9) 265 ( 2.2) Nation 38 ( 2.4) 25 ( 1.2) 37 ( 2.5) 253 ( 2.2) 261 ( 1.4) 272 ( 1.9) RACE/ETHNICITY Wt. State 42 ( 3.0) 23 ( 1.6) 36 ( 3.0) 289 ( 1.3) 215 ( 1.6) 278 ( 2.5) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 262 ( 2.5) 269 ( 1.5) 277 ( 2.0) Black State 45 ( 4.7) 22 ( 3.1) 33 ( 3.4) 231 ( 3.2) 238 ( 3.3) 243 ( 3.8) Nation 48 ( 3.8) 32 ( 2.7) 20 ( 3.1) 232 ( 4.3) 241 ( 2.9) 241 ( 4.4) Hispanic State 38 ( 3.0) 22 ( 2.3) 40 ( 3.6) 233 ( 3,9) 239 ( 3.7) 240 ( 3.0) Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 238 ( 3.9) 247 ( 3.3) 248 ( 3.3) Asian State 34 ( 5.6) ***) 20 4.6) ( VIM ) 46 ( 8.0) Nation 32 ( 5.1) ( *411 17 ( 3.5) *4. ( 51 ( 5.9) TYPE OF COMMUNITY Advantaged urban State 48 ( 6.0) 24 ( 3.8) 28 ( 6.9) 276 ( 3.6)1 281 ( 4.5)! 289 ( 3.8)1 Nation 50 ( 9.0) 19 ( 4.9) 31 ( 9.3) 271 ( 3.3)1 299 ( 5..q)3 Disadvantaged urban State 44 ( 5.1) 20-( 2.7) 36 ( 3.9) 234 ( 4.0)1 237 ( 4.2P 245 ( 4.0)1 Nation 37 ( 5.8) 23 ( 3.6) 41 ( 6.7) 240 ( 4.8)1 253 ( 4.1)1 255 ( 4.2)1 Extreme rural State 24 ( 9.2) 39 ( 9.0) 38 (17.6) 0*4(44*) Nation 42 (10.1) 30 ( 4.4) 28 ( 7.5) 249 ( 4.0)1 258 ( 3.4)1 267 ( 7.3)! Other State 40 ( 3.7) 21 ( 1.6) 32 ( 3.6) 266 ( 1.8) 270 ( 2.3) 273 ( 3.0) Nation 36 ( 2.9) 26 ( 1.2) 38 ( 2.9) 252 ( 3.0) 261 ( 2.1) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. II* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I r`t 124 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A15 I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week About Onc a Week Less Than Wee Idy TOTAL Percentage and Prof Mem Percentap tad Pradency Percentage and Proficiency State 41 ( :4.4) 22 ( 1.4) 30 ( 2.3) 256 ( 2.0) 263 ( 1.9) 205 ( 2.2) Nation 38 ( 2.4) 25 ( 1.2) 37 ( 2.5) 253 ( 2.2) 261 ( 1.4) 272 ( 1.9) PARENTS' EDUCATION NS non-graduate State 36 ( 5.1) 24 ( 4.5) 41 ( 52) 242 ( 3-5) 11.1111 ( 240 ( 3.6) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 243 ( 2.7) 253 ( 2.6) 1111 graduate State 43 ( 3.2) 22 ( 22) 34 ( 2.7) 249 ( 2.5) 257 ( 2.9) 255 ( 2.8) Nation 40 ( 3.2) 29 ( 22) 32 ( 3.6) 247 ( 2.7) 256 ( 2.5) 262 ( 2.2) Some college State 45 ( 3.1) 20 ( 1.7) 35 ( 3.0) 260( 3.0) 263 ( 3,9) 271 ( 3.4) Nation 34 ( 3.4) 26 ( 22) 40 ( 3.5) 259 ( 2.3) 2891 2.6) 271 ( 2.6) College graduate State 41 ( 2.8) 22 ( 1.6) 36 ( 3.0) 267 ( 2$) 277 ( 2.6) 278 ( 2.8) Nation 38 ( 2.6) 22 ( 1.5) 41 ( 2.6) 264 ( 2.6) 273 ( 2$) 265 ( 2.3) GENDER M. State 40 ( 2.3) 25 ( 1.5) 35 ( 2.4) 257 ( 2.4) 266 ( 2.1) 207 ( 2.5) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2,7) 263 ( 2.3) 274 ( 2.4) Female State 43 ( 3.0) 20 ( 1.6) 37 ( 2.6) 256 ( 2.4) 259 ( 2.6) 203 ( 2.5) Nation 37 ( 2.5) 25 ( 1$) 38 ( 2.6) 253 ( 2.1) 259 ( 1.8) 209 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire ;_opulation is within -t 2 standard errors of the estimate for the sample. *** Sample size is insutTicient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 New York TABLE A18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL !STATE ASSEVIMENT Owt a Caktiator Teacher Explains Calculator Use Yes No Yes No l TOTAL Pavenieg and Prodeiem Percentage and Preflafeneg Percentage and Proficiency Percentage and Proficiency State 96 ( 0.5) 4 ( 0.5) 36 ( 22) 84 ( 22) 282 ( 1.3) 236 ( 4.8) 257 ( 1.1) 283 ( 1.4) Nation 97 ( 0.4) 3 ( 0.4) 49 ( 2.3) 51 ( 23) 263 ( 1.3) 234 ( 3.8) 258 ( 1.7) 266 ( 1.5) RACE/ETHNICITY White State 99 ( 0.3) 2 ( 0.3) 36 ( 2.9) 64 ( 2.9) 274 ( 1.0) 271 ( 1.4) 275 ( 1.3) Nation 96 ( 270 ( 0.3) 1.5) 2 ( ( 0.3) .41 48 286 ( 2.6) ( 1.8) 54 ( 273 ( 2.6) 1.8) Stub State 93 ( 237 ( 2.0) 2.7) 7 ( 2.0) ( «el 35 231 ( 3.0) ( 2.9) 65 ( 239 3.0) 2.8) Nation 93 ( 14) 7 ( 1.5) 53 ( 4.9) 47 ( 4.9) 237 ( 2.8) ( "`) 235 ( 3.8) 239 ( 2.7) Hispanic State 91 ( 1.6) 9 ( 1.0) 37 ( 4.1) 83 ( 4.1) 238 ( 2.7) 235 ( 3.9) 239 ( 2.4) Nation 92 ( 1.2) 8 ( 12) 63 ( 4.3) 37 ( 4.3) 245 ( 2.7) ( ) 243 ( 3.4) 245 ( 2.9) Asian State 99 ( 281 ( 1.4) 5.0)1 1 ( 1.4) 32 ( 5.7) .44) 68 ( ( 5.7) **a) Nation 99 ( 282 ( 0.9) 5.3)1 1 ( ( 0.9) 52 ( 4.8) 4$ ( 44-4 ( 4.8) TYPE OF COMMUNITY Advantaged urban State 99 ( 0.5) 1 ( 0.5) 35 ( 3.4) 65 ( 3.4) 281 ( 2.2)1 279 ( 3.3)1 282 ( 2.9)1 Nation 99 ( 1.0) 1 ( 1.0) 45 (12.2) 55 (12.2) 281 ( 3.8)1 4" ( 444) 278 ( 2.5)1 285 ( 6.4)1 Disadvantaged urban State 92 ( 1.3) 8 ( 1.3) 39 ( 4.9) 61 ( 4.9) 239 ( 2.6) 235 ( 4.0)1 241 ( 3.0)1 Nation 94 ( 1.2) 6 ( 1.2) 53 ( 7$) 47 ( 7.5) 250 ( 3$)1 4" ( 247 ( 4.1)1 251 ( 3.6)1 Extreme rural State 95 ( 276 ( 3.9) 2.4)1 5 ( 3.9) 40 (12.3) +41.) ea (12.3) Nation 96 ( 257 ( 1.3) 3.9)1 4 ( 4 1.3) 42 251 ( 8.7) ( 4.8)1 58 ( 261 ( $.7) 4.4)1 Other State 98 ( 0.4) 35 ( 3.5) 65 ( 3.5) 270 ( 1.5) 267 ( 1.9) 271 ( 1.7) Nation 97 ( 0.5) 3 ( 0.5) 50 ( 2.7) 50 ( 2.7) 263 ( 1.7) 233 ( 5.4) 258 ( 2.1) 266 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 -tandard errors of the estimate for the sample. ! Interpret with cauLion -- the nature of the sample does not sllow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). .I3i 126 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE AM Students' Reports on Whether They Own a (continued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IOust 1900 NAEP TRIAL STATE ASSESSMENT a Calculator Teacher Explains Calculator Use , Yes No Yes 1 No i TOTAL. Percentage Pereentap and and Pnoliciency Pre deism Pereentage d Praidency State 96 ( 0.5) 4 ( 04) 35 ( 262 ( 1.3) 226 4.8) 257 ( Nation 97 ( 0,4) 3 0.4) 40 ( 2.3 263 ( 1.3) 234 3.8) 258 ( 1.7 PARENTS EDUCATION MS non-graduate State 80 ( 3.1 11 ( 3.11 5.0S.41 242 ( 2.6) ( 24421 [ Nation 92 ( 243 ( 1.6) 2.0) 8 ( 1.6) 444) 53 ( 4A 242 ( 2.9) NS graduate State 95 ( 1.3) 5 ( 1.3) 30 ( 3.3 254 ( 1.7) *Mt ( *41 253 ( 2.5 Nation 07 ( 0.0) 3 ( 0.6) 54 ( 3.01 255 ( 1.5) 252 ( 1.9) Some college State 98 ( 265 ( 0.8) 2.0) 2 ( .0. 0.8) ....) 34 ( 265 ( 3.3, 2.7) Nation OS ( 268 ( 0.9) 1.8) 4 ( 0.9) .41 48 ( 265 ( 32 2.4 o Nage graduate State 99 ( 0,4) ( 0.4) 33 ( 2S 274 ( 1.4) 268 ( 2.5 Nation 99 ( 02) ( 0.2) 48 ( 2.6 pENDER 275 ( 1.6) is ( RIM) 268 ( 2.2) Male State 97 ( 0.6) 3 ( 0.6) 38 ( 2.6) 263 ( 1.5) 259 ( 2.2) Nation 97 ( 264 ( 0.5) 1.7) 3 ( 0.5) ..) 51 ( 256 ( 2.6) 2.1) Female State 96 ( 0.8) 4 ( 0.8) 36 ( 2.3) 261 ( 1.5) 255 ( 1.9) Nation 97 ( 0.5) 3 ( 04) 47 ( 2.5) 262 ( 1.3) 4" ( .4 ) 258 ( 1.7) Perim bp and Pre Wow 2.2 283 1.1 51 2.11 WM 1.5 58 243 3.3 47 243 2.5 61 ( 3.3) 254 ( 2.2) 258 ( 2.0) 06 ( 33) 265 ( 2.1) 52 ( 3.2) 26$ ( 2.2) 87 ( 2.5) 278 ( 1.8) 54 ( 2.6) 280 ( 13) 64 ( 2.6) 265 ( 12) 49 ( 22) 299 ( 2.1) 64 ( 23) 261 ( 1.9) 53 ( 2.5) 263 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 New York TABLE A19 I Students' Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVEPAGE MATHEMATICS PROFICIENCY . 1990 NAEP TMAL STATE ASSESSMENT , Working Pro Idiom kt Class Doing Problems at Nome - Taking Quizzes or Tests Almost Always - I Ne ex Almost Always Never - Almost Always I Never - TOTAL Percentage and Proficiency Percentage sad Miaow Percentage and Proticiency Percentage and Mildewy Percentage and Proficiency Percentage end Proficiency State 40 ( 1.2) 38 ( 1.8) 29 ( 1.3) 24 ( 1.1) 21 ( 1.3) 44 ( 1.4) 247 ( 1.6) 277 ( 1.6) 251 ( 1.8) 273 ( 2.2) 242 ( 2.0) 279 ( 13) Nation ( 1.5) 23 ( 1.9) 30 ( 1.3) 19( 0.9) 27 ( 1.4) 39 ( 2.0) 254 ( 1.5) 272 ( 1.4) 281 ( 1.8) HO ( 1.8) 253 ( 2.4) 274 ( 1.3) RACE/ETHNICITY Mite State 33 ( 14) 44 ( 2.2) 28 ( 1.2) 26 ( 1.5) 18 ( 1.2) 52 ( 1.7) 281 ( 1.4) 233 ( 1.7) 264 ( 1.5) 280 ( 2.3) 258 ( 2.3) 283 ( 1.5) Nation 48 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 25 ( 1.8) 32 ( 2.3) 282 ( 1.7) 278 ( 1.3) 270 ( 1.7) 269 ( 2.3) 263 ( 2.8) 279 ( 1.2) Black State 55 ( 2.7) 24 ( 2.8) 32 ( 2.4) 17 ( 2.0) 34 ( 3.7) 2$ ( 2.8) 230 ( 2/) 258 ( 2.7) 233 ( 3.8) *NI ( 4111.11 ) 228 ( 3.5) 257 ( 2.9) Nation 57 ( 3.2) 20 ( 3.9) 31 ( 2.9) 18 ( 1.9) 38 ( 3.3) 24 ( 3.1) 232 ( 2.4) 249 ( 4.0) 233 ( 3.3) 248 ( 5.5) 230 ( 3.8) 251 ( 4.1) Hispanic State 49 ( 3.8) 2$ ( 2.7) 32 ( 3.6) 22 ( 2.3) 27 ( 3.7) 29 ( 3.0) 231 ( 3.2) 254 ( 18) 229 ( 3.0) 254 ( 6.1) 229 ( 3.5) 258 ( 2.7) Nation 51 ( 2.9) 18 ( 3.5) 26 ( 3.2) 21 ( 2.1) 28 ( 2.7) 22 ( 3.1) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1) 237 ( 3.2) 258 ( 4.2) Asian State 29 ( 5.1) *** ) 56 ( 8.8) 26 ( 5.9) 35 ( ft* ( 6.5) V** ) ( 61 ( 6.8) ***) Nation 29 ( 5.8) ) 11,44/ 041.4 ( ) TYPE OF COMMJNITY Advantaged urban State 29 ( 2.8) 48 ( 4.1) 25 ( 2.1) 27 ( 3.1) 14 ( 2.2) 57 ( 3.8) 287 ( 2.7)1 288 ( 2.3)1 270 ( 4.0)1 282 ( 3.4)1 ( ***) 299 ( 2.0)1 Nation 51 ( 5.4) 23 (10.7) 32 ( 0.1) 15 ( 2.4) 31 ( 3.8) 28 ( 9.8) 270 ( 4.7)i *** ( ***) 274 ( 4.911 ( ") 281 ( 711)' 285 ( 4.2)1 Disadvantaged urtan State 48 ( 3.2) 29 ( 4.9) 32 ( 3.6) 22 ( 3.0) 26 ( 33) 31 1 3.5) 227 ( 2.7) 259 ( 3.4)1 228 1 2.5)1 256 ( 5.1)1 226 ( 1.8)1 261 2.8)i Nation 52 ( 3.1) 22 ( 4.5) 30 ( 3.3) 24 ( 2.3) 27 ( 2.9) 27 1 4.8) 241 ( 3.8)1 259 ( 5.4)1 240 ( 52)1 254 ( 4.8)1 240 ( 4.9)1 283 5.0)1 Extreme nral State 32 ( 2.0) 44 (13.2) 40 ( 4.4) 25 ( 6.5) 14 ( 1$) 55 6.3) ( .44) ) *it* ( VIM ) *Me { *Re ) MY. ) Nation 4$ ( 7.4) 29 ( 6.5) 20 ( 2.5) 23 ( 3.9) 24 ( 6.6) 37 8.3) 24$ ( 4.3)1 268 ( 8.1)1 *** ( ') 263 ( 4.4)1 " ( 270 4.0)1 Other State 37 ( 1.6) 42 ( 2.4) 29 ( 1.5) 24 ( 1.5) 20 ( 1.8) 49 1.9) 256 ( 2.0) 280 ( 2.1) 281 ( 2.2) 279 ( 2.1) 251 ( 2.9) 281 1,6) Nation 48 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1.8) 29 ( 2.1) 254 ( 2.1) 272 ( 1,8) 283 ( 2.3) 263 ( 2.8) 253 ( 2.7) 275 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 3 es,tj 128 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A 19 I Students' Reports on the Use of a Calculator (continued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Wimidng Prabi" Is in Class Doing Problems at Home Taking Quizzes or Tests Almost Always Never Almost ys Alwa I Never Almost Always Never _ TOTAL Percentage ind Proficiency Patentee* and Proficiency Percentage and Proficiency Percenteg* and Proficiency Percentags end Proficiency Percentage and Proficiency State 40 ( 3e ( 1.8) 29 ( 13) 24 ( 1.1) 21 ( 1.3) 44 ( 1.4) 247 ( 1.8 ) 277 ( 1.6) 251 ( 1.8) 273 ( 2.2) 242 ( 2.0) 279 ( 1.3) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 ( 1.4) 90 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) PARENTS EDUCATION HS non-graduate State Nation 56 ( 237 ( 54 ( 4.7) 3.1) 3.3) 2$ ( 44* ( 19 ( 3.7) 3.8) 37 ( 238 ( 26 ( 3.7) 3.7) 3.1! 18 ( 4 t 22 ( 3.2) 4.,e) 2.8) 28 ( ( 32 ( 3.1) 441 36) ( 24 ( 32) ( 2.3) 244 ( 3.8) 244 ( 4.2) 237 ( 2.3) 251 ( 4.6) KS graduate State 43 ( 2.5) 35 ( 2.7) 32 ( 1.9) 25 ( 2.4) 24 ( 2.3) 42 ( 2.9) 244 ( 2.7) 264 ( 22) 249 ( 2.7) 259 ( 2.8) 241 ( 3.2) 266 ( 1.7) Nation $2 ( 2.5) 20 ( 2.4) 29 ( 1.9) 18 ( 1.5) 26 ( 1.8) ( 2.2) 249 ( 1.4) 265 ( 2.7) 250 ( 2.4) 258 ( 2.4) 248 ( 2.8) 265 ( 2.0) Some college State 38 ( 2.8) 42 ( 2.8) 25 ( 2,5) 24 ( 2.0) 20 ( 2.9) 48 ( 2.5) 251 ( 2.8) 278 ( 2.8) 255 ( 3.0) 279 ( 4.1) 241 ( 4.5) 281 ( 2.3) Nation 48 ( 2.8) 26 ( 2.8) 28 ( 2.0) 20 1.0) 28 ( 2.4) 35 ( 2.5) 258 ( 2.1) 272 ( 2.5) 267 ( 3.0) 268 ( 3.2) 255 ( 3.8) 275 ( 2.0) College graduate State 34 ( 1.8) 43 ( 2.3) 28 ( 1.8) 26 ( 1.7) 18 ( 1.7) 50 ( 2.0) 256 ( 2.0) 287 ( 2.1) 259 ( 2.8) 258 ( 2.5) 249 ( 3.1) 288 ( 1.9) Nation 4$ ( 1.9) 25 ( 2.4) 33 ( 234 18 ( 1.4) 26 ( 1.8) 33 ( 2.7) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 268 ( 2.8) 285 ( 2.0) OENDER Mal* State 40 ( 1.5) 36 ( 1.8) 30 ( 1.8) 23( 1.4) 20 ( 1.7) 42 ( 1.8) 251 ( 1.9) 279 ( 1.9) 251 ( 2.5) 275 ( 2.4) 242 ( 2.4) 281 ( 1.7) Nation 50 ( 1.7) 20 ( 2.0) 29 ( 16) 19 ( 1.3) 27 ( 1,5) 20 ( 2.1) 255 ( 1,9) 275 ( 2.2) 264 ( 2.8) 283 ( 2.5) 256 ( 3.0) 277 ( 1.9) Female State 39 ( 1.8) 40 ( 2.2) 2$ ( 1.6) 24 ( 1.4) 22 ( 1.8) 45 ( 1.8) 243 ( 2.0) 274 ( 22) 250 ( 2.1) 272 ( 2.9) 241 ( 2.5) 277 ( 1.8) Nation 48 ( 2.0) 28 ( 2.1) 32 ( 1.8) 18 ( 1.2) 27 ( 1.8) 33 ( 2.1) 252 ( 1.7) zsa ( 1,8) 259 ( 1.7) 283 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 New York TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL "Caku "Calculator-Use" STATE ASSESSMENT 140 later-Use" Grew Other Group , _ TOTAL Parcontass and Prono Paraentas anti Prolialancy State 40 ( 1.1) 54 1.1) 209 ( 1.4) 252 1.8) Nation 42 ( 1.3) 5$ 1.3) 272 ( 1.6) 255 ( 1.5) RAWETNNICITy Mite State 51 ( 1.3) 49 ( 1.3) 278 ( 1.4) 267 ( 1.6) Nation 44 ( 1.4) 56 ( 1.4) rek 277 ( 1.7) 263 ( 1.7) State 37 ( 3.3) 63 ( 3.3) 245 ( 2.9) 230 ( 3.0) Nation 37 ( 3.4) 63 ( 3.4) 24$ ( 3.9) 231 ( 3.0) Hispanic State 37 ( 2.8) 63 ( 2.8) 242 ( 3.3) 232 ( 3.0) Nation 36 ( 42) 04 ( 4.2) 254 ( 4.6) 238 ( 3.0) Asian State 50 ( 7.9) 50 ( .4* ( 7.9) Nation 50 ( 4.8) 50 ( «. 4.8) .44) TYPE OF COMMUNIVY Advantaged urban State 50 ( 3.4) 50 ( 3.4) 289 ( 1.6)1 272 ( 2.6)1 Nation 50 ( 3.8) 50 ( 3.8) 288 4.9)1 275 ( 4.4)1 Disadvantaged urban State 42 ( 2.3) 56 ( 2.3) 245 ( 2.9)1 232 ( 2.4) Nation 38 ( 4.2) 62 ( 4.2) 262 ( 5.6)I 244 ( 3.9)1 &drams nevi a lite 56 ( 4.9) 44 ( 4.9) ght ( *44 ) Nation 39 ( 5.6) 61 ( 5.6) 209 ( 4.4): 246 42)1 Other State 49 ( 1.7) 51 ( 1.7) 276 ( 1.7) 263 ( 2.2) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with abotn 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A20 I Students' Knowledge of Using Calculators (continued) PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ MO NAEP TRIAL "Cats:dater-Use" STATE ASSESSMENT High Group Other "Calculator-Us*" Group . . TOTAL Percentage and Preliciency 46 ( 1.1) 280( 1.4) 42 ( 1.3) 272 ( 1.6) Percentage and Prefidency ( 1.1) 252 ( 1.6) 58 ( 1.3) 255 ( 1.5) State Nation PARENTS EDUCATION 141 non-graduate State .44 .61 00 ( 239 ( 4.1) 3.0) Nation 34 ( 3.3) 86 ( 3.3) 248 ( 4.4) 242 ( 2.4) HS graduate State 45 ( 2.1) 55 ( 2.1) 259 ( 2.5) 247 ( 2.3) Nation 40 ( 2.2) 80 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some cafes" State 43 (2.7) 57 ( 2.7) 272 ( 2.4) 257 ( 2.8) Nation 48 ( 22) 52 ( 2.2) 277 ( 2.6) 258 ( 2.5) Co Naga graduate State 51 ( 2.2) 49 ( 22) 283 ( 1.7) 263 ( 2.3) Nation 4413 ( 2.0) 54 ( 2.0) 282 ( 2.1) 286 ( 1.9) GENDER &tale State 44 ( 1.8) 56 ( 1.8) 270 ( 2.0) 254 ( 2.1) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 48 ( 1.7) 52 ( 1.7) 268 ( 1.8) 250 ( 2.2) Nation 45 ( 1.8) 55 ( 1.8) 2e9 ( 1.7) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. "1' Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 New TABLE A24 I Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY i 1990 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Upes Four Types TOTAL Peranntage and Pnd Macy Panoantap and Pralialanty Pannntaga mad Pratiancy State 21 ( 1.2) 29 ( 1.0) 1.4) 243 ( 2.4) 258 ( 1A) 1.2) Nation 21 ( 1.0) SOf 1.0) 4411 1.3) 244 ( 2.0) 254 ( 1.7) 272 ( 1.5) RACE/ETHNICITY White State 12 ( 1.0) 27 ( 1.2) 62 ( 259 ( 2.9) 268 ( 1.3) 278 ( 1.2 Nation 16 ( 1.1) 29 ( 1.3) 54 ( 1.5 251 ( 2.2) 268 ( 1.5) 278 ( 13) Black State 27 ( 2.4) 38 ( 95 ( 3.1 232 ( 3.0) 234 ( 2.9 242 ( 391 Nation 31 ( 1.9) 30 ( 22 33 ( 2.4 232 ( 3.2) 233 ( 3.9) 245 ( 3,3 Hispanic State 42 ( 2.1) 29 ( 2.3) 29 230 ( 3.8) 238 ( 3.2) 248 2.8 Nation 44 ( 3.0) 30 ( 2.4) 26 2.3 237 ( 3.4) 244 ( 4.3) 253 ( 2.4 Asian State 42 ( 5.4) 28 4.4,* ( 4.1) 30 4.9) Nation 28 fro* ( 13.0) 38 4.2) TYPE Of COMk4UAITY_ Advantaged urban State 10( 14) 24 ( 2.7) 08 ( 3.8) ( 276 ( 4.0)1 284 ( 2.2)1 Nation 13 ( 36) ( *41 26 ( 2.1)) 51 ( 267 46) ( 3.6)1 Disadvantaged urban State 35 ( 2.4) 34 ( 2.1) 31 ( 1.9) 226 ( 2.9)1 238 ( 2.2) 252 ( 3.9) Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.6) 243 ( 2.9)1 247 ( 3.7)1 257 ( 4.9)1 Extrama rural State 8 ( 3.9) *el 58 ( 7A) Nation 4" 4.9) *v.) 33 253 ( 3.2) ( 4.3)1 50 263 ( 5.1) ( 5.6)1 Other State 16 ( 1.7) 2$ ( 1.5) 58 ( 2.3) 260 ( 3.1) 263 ( 1.9) 276 ( 1.6) Nation 22 ( 14) 30 ( 1.3) 48 ( 1.5) 244 ( 2.6) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 137 132 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A24 I Students' Reports on Types of Reading (continued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types FOX Typos _ TOTAL Pareentap and liondiciancy Pantentage and ProliMency Parandasa and Prollicioney State 21 (12) 29 ( 1.0) SO ( 1.4) 243 2.4) 256 ( 1.4) 271 ( 1.2) Nation 21 1.0) 30 ( 1.0) 46 ( 1.3) 244 ( 2.0) 256 ( 11) 272 ( 1.5) PARENTS' EDUCATIOR HS non-graduate State 48 ( 3.4) 27 ( 3.1) 239 ( 3.5) ( Nation 47 ( 4.0) 2$ ( 3.0) 25 ( 26) 240 ( 3.4) 243 ( 3.3) 248 ( 3.3) HS graduate State 22 ( 2.4) 34 ( 2.0) 44 ( 2.7) 244 ( 3.1) 249 ( 3.0) 259 ( 2.1) Nation 26 ( 22) 33 ( 1.9) 40 ( 13) 246 ( 2.2) 253 ( 2.7) 260 ( 2.1) Some coilege State 17 ( 2.4) 31 ( 2.6) 52 ( 2.6) 4,41 296 ( 3.4) 273 ( 2.4) Nation 17 ( 1$) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1,0) College graduate State 12 ( 1.3) 14- 63 ( 1.5) 251 ( 3.7) 2 280 ( 1.5) Nation 10 ( 0.8) : 62 ( 2.0) 254 ( 2.8) 269 280 ( 1.8) GENDER Male State 20 ( 1.4) 29 ( 1.5) 50 ( 1.6) 245 ( 2.8) 257 ( 2.0) 273 ( 1.7) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Female State 22 ( 1.6) 29 ( 1.4) 49 ( 2.0) 242 ( 2.9) 255 ( 2.1) 269 ( 1.6) Nation 22 ( 1.2) 29 ( 1.4) 49 ( 1.9) 244 ( 2.2) 258 ( 1.9) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with abvut 95 percent certainty that, for each population of interest, the value for Ow entire population is within ± 2 standard errors of the estimate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 3 S THE 1990 IsiAEP TRIAL STATE ASSESSMEN 133 New York TABLE A25 Students' Reports ou the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT , One Hour or Loss Two NOM Three Hours Four to Sy* Hairs - SW Hours or Mor TOTAL Percentage and Prolkiency Percentage end Proficiency Percentage and Pro Wend Pimento. and ProficioncY Penedo. and Plvackincy tate 12 ( 0.6) 20 ( 0.6) 22 ( 1.0) 29 ( OA) 17 ( 1.0) 271 ( 2.2) 273 ( 2.0) 265 ( 1.7) 257 ( 1.5) 242 ( 2.3) Nation 12 ( 0.8) ( 0.9) 22 ( 0.8) 28 ( 1.1) 16 ( 1.0) 269 ( 2.2) 268 ( 1.8) 265 ( 1.7) 200 ( 1.7) 245 ( 1.7) RACE/ETHNICITY 'Mite State 13 ( 0.9) 25 ( 0.9) 25 ( 12) 27 ( 1.0) 10 ( 0.8) 278 ( 2.4) 282 ( 2.0) 272 ( 1.5) 269 ( 1.7) 261 ( 2.2) Nation 13 ( 1.0) 23 ( 1.2) 24 ( 1.1) 27 ( 1.4) 12 ( 1.2) 276 ( 2$) 275 ( 22) 272 ( 1.9) 267 ( 1.7) 253 ( 2.6) Black State ( HI* ( 12) 114-1111 13 ( /sm. ( 2.3) 44.1 13 ( .44 12) 31 ( 237 ( 2.7) 3.1) 37 232 ( 2.5) ( 3.5) Nation 6 ( 0.8) 13 ( 1.7) 17 ( 2.1) 32 ( 1.8) 32 ( 2.2) ( 239 ( 7.0) 239 ( 5,0) 239 ( 4.0) 233 ( 2$) Hispanic State 10 ( 1.5) ***) 10 ( 1.6) 18 ( 2.3) 36 ( 239 ( 2.2) 2.2) 26 232 ( 2.5) ( 4.2) Nation 14 ( ( 2.4) ***) 20 ( 245 ( 2.5) 3.2) 19 ( 242 ( 2.1) 5.6) 31 ( 247 ( 3.1) 3$) 17 236 ( 1.7) ( 3.8) Asian State 22 ( 5.4) 24 ( 4.3) 19 ( 5.0) 7 ( 3.4) 111t4 ( 4144 ) *44(4e*) ( Nation 18 ( 5.0) 0-**) 24 ( 4.2) ( as.) 22 ( 3.1) 23 ( ( 4.7) 13 *** ( 4.0) ( ***) TYPE Or COMMUNITY Advantagod urban State 24 ( 3.3) 25 ( 3.0) 26 ( 2.8) 8 ( 2.3) 286 ( 3.0)1 280 ( 3.5)1 273 ( 3.9)1 Nation 18 ( ( 1.4) 44.) 25 ( 4.3) 21 ( 1.6) 4,41.) 30 ( 4.3) *44) 6 ( 2.0) ( 41 Disadvantaged State 9 ( 0.5) 13 ( 1.6) 20 ( 2.1) 33 ( 1.9) 25 ( 2.2) 251 ( 5.4)1 242 ( 3.6)1 237 ( 2.3)1 227 ( 2.0) Nation ( 4.) 17 ( 250 ( 3.1) 4.0)1 19 ( 255 ( 2.1) 5.0)1 34 ( 251 ( 2.4) 42)1 20 238 ( 3.2) ( 4$)1 Extreme rural State 13 ( 2.8) 30 ( 9-2) 28 ( 7.4) 7 ( 3.7) 11.441. ( *HI ) ( 40414 161.1 Nation 14 ( oho. 3.3) 23 ( 2.0) 26 ( 256 ( 2.7) 3.6)1 4,-*1 Other State 13 ( 0,9) 24 ( 1.2) 23 ( 1.1) 28 ( 1.4) 12 ( 1.3) 272 ( 3.1) 278 ( 2.4) 272 ( 2.1) 267 ( 1.5) 253 ( 2.7) Nation 12 ( 1.0) 21 ( 1.0) 23 ( 1.2) 27 ( 1.2) 17 ( 1.4) 268 ( 2.6) 2es ( 2.3) 265 ( 2.1) 259 ( 21) 248 ( 2$) Thz standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 13 (t) 134 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A25 I Students' Reports on the Amount of Time Spent (cmtinued) i Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT Ono Hour or Loss Two How-.1 _ Dim Hours Pow to Flvo Hours Six Hairs or Mors TOTAt. Pomo lege and Proficiency 12 0.6) 271 2.2) 12 (0.0) 200 r 2.2) 10 ( 2A) 12 ( 2.2) 44* ( 11 ( 1.3) .04* 41 8 ( 1.0) 249 ( 4.7) 10 ( 1.5) IMO ( din 10 ( 1.4) *0* ( *44 ) 14 ( 1.1) 282 ( 3.6) 17 ( 1.3) 282 ( 2.6) 10 ( OA) 271 ( 4.3) 11 ( 0.9) 264i ( 3.3) 14 ( 1.1) 271 ( 2.8) 14 ( 1.1) 209 ( 2.8) Percentego and Pre liciency 20 ( 0.1) 273 ( 2.0) 21 f 0.9) 263 ( 1.6) 12 ( 3.1) et* 1111 20 ( 3.1) in* ( «Al 15 ( 1.5) 261 ( 32) 17 ( 1.4) 257 ( 2.5) 21 ( 2.0) 232 ( 3.8) 25 ( 2.4) 275 ( 2.7) 24 ( 1.3) 283 2.3) 22 ( 1.6) 280 ( 2.5) 20 ( 12) 276 ( 3.0) 22 ( 1.2) 207 ( 2.6) 21 ( 1.1) 271 ( 2.7) 20 ( 1.3) 269 ( 2.2) Poreadep and Pro Adam 22 ( 1.0) 265 ( 1.7) 22 ( OA) 205 ( 1.7) 23 ( 4.3) .4.41 21 ( 2.5) 22 ( 2.0) 257 ( 3.0) 23 ( 2.0) 259 ( 3.2) 23 ( 2.0) ( 3.6) 23 ( 2.8) 269 ( 35) 22 ( 1.4) 280 ( 24) 23( 1.1) 277 ( 22) 22 ( 1.4) 267 ( 2.8) 22 ( tO) 267 ( 22) 22 ( 12) 263 ( 2.1) 23 ( 1.4) 264 ( 1.5) Paroestage and Pra lidency 29 0.9) 257 15) 25 1.1) 200 ( 1.7) 32 ( 4.0) 25 ( 2.9) 244 ( 3.2) 31 ( 2.3) 249 ( 2.9) 32 ( 2.3) 253 ( 2.5) 30 ( 2.1) 200 ( 2.3) 25 ( 2.2) 267 ( 2.5) 25 ( 1.5) 269 ( 2.0) 25 ( 15) 270 ( 2.4) 30 ( 1.3) 255 ( 1.9) 25 ( 1.3) 262 ( 2.1) 28 ( 1.3) 255 ( 2.1) 21 ( 15) 258 ( 4.9) Paromiage and Prefedency 17' ( 1.0) 242 ( 2.3) 16 ( 10 ) 245 ( 12) 23 ( 3.7) ( vas 17 ( 1.8) 240 ( 3.0) 19 ( 1.6) 246 ( 3.0) 18 ( 2.2) 14 ( 1.5) 242 ( 3.4) 15 ( 1.4) 249 ( AA) 12 ( 1.1) 25$ ( 3.2) 19 ( 1.3) 247 ( 2.5) 17 ( 1.5) 248 ( 2.5) 15 ( 1.4) 237 ( 3.2) 15 ( 1.2) 241 ( 2.2) State Nation PARENTS EDUCATION HS non-grixtuato State Nation HS graduate State Nation Some college State Nation College graduate State Nation GENDER Mat* State Nation Female State Nation The standard enors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest. the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 140 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 New York TABLE A26 I Students' Reports on the Number of Days of i School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY STATE ASSMIMENT [70 NAEP TRIAL None One or Two Days Throe Days or Mors , TOTAL. Pareantaga and Prod.:Ma Paraentap and ProNdancy Percentage and Prolidangy State 41 ( 1.1) 30 ( 1.0) 29 ( 1.3) 267 ( 1.4) 263 ( 1.6) 252 ( 2.0) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.6) 266 ( 1.5) 250 ( 1.9) RACE/ETHNICITY State 42 ( 1.4) 31 ( 1.2) 2. ( 1.3) 277 ( 1.6) 274 ( 1.5) 296 ( 1.4) Nation 43 ( 1.2) 34 ( 1.2) 23 ( 1.2) 273 ( 1.8) 272 ( 1.7) 258 ( 2.1) Black State 37 ( 2.3) 28 ( 2.1) 35 ( 2A) 241 ( 3.3) 241 ( 3.7) 229 ( 3.6) Nation 56 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 36 ( 3.4) 28 ( 2.3) 30 ( 4.3) 244 ( 3.6) 242 ( 3.3) 231 ( 3.5) Nation 41 ( 3.3) 32 ( 2.2) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) Asian State 54 ( ( 5.2) *41 ( ***) 18 ( .4* ( 3.9) Nation 62 ( 287 ( 5.6) 4.7)1 27 ( 1". ( 5.3) 44.) 11 ( 4.9) ** ) TYPE OF COMMUNITY Advantaged urban State 42 ( 2.9) 31 ( 1.8) 27 ( 2.4) 283 ( 3.4)1 266 ( 2.6)1 272 ( 2.8)! Nation 47 ( 284 ( 2.3) 4.4)1 38 ( 279 ( 2.6) 4.5)1 15 ( *44 ( 3.7) 441 Disadvantaged urban State 37 ( 2.6) 28 ( 1.6) 35 ( 2.6) 247 ( 4.7)1 238 ( 3.5) 232 ( 2.4)1 Nation 42 ( 3.3) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 256 ( 4.2)1 236 ( 6.3)1 Extreme rural State 61 (11.2) 20( 2.1) 19 (12.4) ( RN) Nation 43 ( 4.4) 32 ( 4.2) 25 ( 3.9) 257 ( 4.1)1 264 ( 5.8)1 +11r ( *al Other State 42 ( 1.8) 33 ( 1.5) 25 ( 1.4) 273 ( 1.7) 270 ( 1.9) 264 ( 1.8) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 266 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors or the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 141 136 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A26 I Students' Reports on the Number of Days of (continued) I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None Ons or Two Days TM* Days or Mors MAL State Nation PARENTS' EDGCATIOR NS non-graduate State Nation ICS graduate State Nation Some college State Nation College graduate State Nation GENDER Maia State Nation Famaia State Nation Parvantasa and Walkaway 41 1.1) 207 1A) 45 1.1) 205 1.6) 34 30 245 3$ 258 43 255 38 207 40 270 48 279 51 275 42 288 47 206 40 265 43 284 Pareentas aid Pentialancy Parco000 sod ProliMmIcy 30 1.0) 20( 203 IA) 252 ( 2.0 32 04) 23 ( 1.1 206 ( 1.5) 250( 1.9 ( 3.5) 20 ( ~ ( 3.4) ..b.) 38 235 ( 32) 2. ( 3.1) 38 ( 3.0) 249 ( 3.3) 237 ( 2.7) 30 ( 2.1) 32 ( 2.3) 253 ( 2.8) 240 ( 2.1) 31 ( 1.9) 27 ( 2.0) 257 ( 2.8) 249 ( 2.4) 33 ( 2.6 28 ( 3.3) 268 ( 2.7 258 ( 1.8) 37 ( 1.8 23 ( 3.0) 271 ( 2.5) 253 ( 1.9) 30 ( 1.8) 24 ( 2.0) 275 ( 2.1) 284 ( 1.6) 33 ( 1.2) 18 ( 2.1) 277 ( 1.7) 285 ( 1.6) 31 ( 1.3) 27 ( 2.2) 28$ ( 2.2) 253 ( 1.6) 31 ( 1.4) 22 ( 2.0) 207 ( 2.1) 250 ( 1.6) 30 ( 1.6) 31 ( 1.8) 282 ( 2.5) 251 ( 1.4) 32 ( 1.1) 25 ( 2.3) 288 ( 1.7) 250 3.3) SI) 3.5) 3.1) 2.7) 3.2) 1.9 ( 2.4) ( 2.1 ( 3.5 ( 1.6 ( 3.1) ( 1.6 ( 2.8 ( 1.3 ( 3.1 ( 1.8) ( 2.9) ( 1.4) ( 2.8) ( 1.7) ( 2.4) ( 1.3) ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 142, THE 1990 NAEP TRIAL STATE ASSESSMENT 137 New _York TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Strom ly Agra* _ Agree Undecided, Disagese, Strongly Mario TOTAL Penile Isle and !widow Penientage and Preldersw Percenties and ProlciencY State 27 ( 1.0) 511 1.1) 22 ( 1.0) 289 ( 1.7) 262 ( 1.5) 252 ( 1.7) Nation 27 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 252 ( 1.7) 251 ( 1.8) RACE/ETHNICITY Milts State 27 ( 1.4) 51 ( 1.2) 25 ( 12) 281 ( 1.4) 274 ( 1.4) 264 ( 1.6) Nation 26 ( 1.6) 45 ( 1.3) 26 ( 1.5) 279 ( 2.0) 272 ( 1.8) 257 ( 2,0) Black State 33 ( 3.3) 47 ( 3.7) 20 ( 2.6) 243 ( 3.6) 237 ( 3.1) 226 ( 3.8) Nation 32 ( 2.5) 52 ( 2.3) 10 ( 1.9) 247 ( 4.1) 233 ( 3.3) 227 ( 4.2) Hispanic State 24 ( 3.0) 54 ( 3.5) 22 ( 2.8) 250 ( 42)1 238 ( 2.7) 228 ( 3.8) Nation 24 ( 23) 43 ( 2.6) 28 ( 2,1) 257 ( 5-5) 244 ( 2.2) 236 ( 3.8) Asian State 28 ( 1,. ( 4.6) on 48 ( ...... ( 5.3) 4,44) 24 ( -.4. ( 3.9) ......1 Nation 29 ( 5.5) 53 ( 5.6) 17 ( 4.9) *Ire () *** ( ***) *44 *41 OF COMMUNITY .TYPE Advantaged urban State 26 ( 22) 51 ( 1.9) 23 ( 1.3) 286 ( 3.5)! 282 ( 2.1)1 271 ( 2.7)1 Nation 17 ( er 1 3.2) ......) 55 ( 280 ( 2.4) 4.1)! 28 ( ...... 4.2) Disadvantaged urban State 28 ( 1.9) 51 ( 2.6) 21 ( 2.3) 248 ( 3.4)1 239 1 2.9) 227 1 3.7)1 Nation 26 ( 2.9) 48 ( 2.9) 26 ( 3,2) 260 ( 5.8)1 249 ( 4.0)1 240 ( 4.5)1 Extrem neat State 26 ( 4,-4- ( 0.1) *oil 55 ( 44.. ( 4.9) 4.4,) 19 ( ..... ( 8.3) .....) Nation 34 ( 2.8) 49 ( 2.2) 17 ( 1.4) 270 ( 3.9)1 252 ( 4.1)1 *I,* ( **) Other State 26 ( 1.8) 51 ( 1.5) 23 ( 14) 278 ( 1.9) 269 ( 1.9) 261 ( 1.9) Nation 27 ( 1.4) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 260 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with shout 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 4 3 138 THE 1990 NAEP TRIAL STATE ASSESSMENT New York TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 MEP TRIAL. STATE ASSESSMENT Stroll dy Agri* Mins Undecided, Disagra., Strongly Disagros TOTAL. Porcontago and Proliciancy Percentage and Proficiency Porcontags mid State 27 ( 1.0) 51 ( 1.1) 22 ( 1.0) ( 1.7) 262 ( 1.5) 252 ( 1.7) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 12) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) PAR_PiTS' EDUCATION KS non-graduate State 25 ( 3.5) 53 ( 3.3) 22 ( 4.0) 244 ( 2.6) .... ( .....) Nation 20 ( 2.6) 50 ( 3.3) 30 ( 3.6) 243 ( 2.6) 238 ( 4.3) HS graduate State 27 ( 2.1! ifil ( 2.5) 25 ( 22) 25$ ( 2.6) 255 ( 2.7) 244 ( 2.5) Nation 27 ( 2.1) 47 ( 2.3) 26 ( 2.0) 262 ( 2.7) 255 ( 2.3) 245 ( 2.4) Solna wiles* State 24 ( 22) 52 ( 3.0) 23 ( 22) 274 ( 3.0) 265 ( 2.3) 255 ( 4.0) Nation 28 ( 2.5) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 25$ ( 32) Collage graduate State 31 ( 1.7) 49 ( 1.6! 20 ( 1.4) 278 ( 2.4) 274 ( 1.9) 267 ( 2,5) Nation 30 ( 2.3) 51 ( 1.6) 19 ( 1.8) 280 ( 2.4) 274 ( 2.2) 208 ( 2.5) GENDER Male State 2$ ( 1.4) 50 ( 1.6) 21 ( 1.4) 270 ( 1.9) 264 ( 2.0) 254 ( 2.0) Nation 28 ( 1,5) 48 ( 12) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Amat State 26 ( 1.4) 51 ( 12) 23 ( 1.3) 267 ( 2.6) 200 ( 1.8) 251 ( 2.5) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 269 ( 2.1) 262 ( 1.6) 252 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, aud reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing service (Ers), Wedat, and National Computer Systems (NO). Tie program benefitted from the contributions of hundreds of isfividuals at the dee and local levels Gammon, Chief State School Officers, State and District Test Directoa, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Finally, and mod importantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (CCSSO) for its considerable contributiosis to the program, especially its =anapaest of the National Amassment Pluming Project. That project resulted in the mathematics framework and objedives for the amemment and recommendations about reporting the results of the program. In particularove note the sipfficant contributions of Ramsay Selden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Commktees of the National Assessment Planning Project. The Trial State Assessment was funded through NOM, in the Office of Educatiooll Research and Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raid Garza worked closely and coliegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people from school cristricts, colleges and universities, and State Education Agencies worked tirelessly to help ET'S staff develop the assessment and a framework for interpreting the resuks. Under the NAEP contract to ETS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by Jolm Mazzeo, with consultatioo from Eugene Johnson and Donald Rock John Barone managed the data analysis activitieg Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, teat development; David Holism, the fiscal aspects; and Stephen Koffier, state services. Sampling and data collection activities we carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zithack. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based c4.3 lt chuacteristics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution test and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report John Mazzeo oversaw the analyses for this report John Ferris, David Freund, Bruce Kaplan, Edward Keck, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowie:, Laura McCamley, and Craig Pizauti Debra Kline coordinated the effocts.of the data analysis staff. Stephen Kegler wrote the text for the report. Kent Ashworth was responsible for coordinating the cover design and final printing of this report Special thanks are also due to many individuals for their invaluable assistance in reviewing the reports, especially the editors who improved the text and the analysts who checked the data. US. GOVERNMENT PRINTING OPTICE : I991 0 - 233415 QL 3 (13K.. 143