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DOCUMENT RESUME ED 330 564 SE 052 074 TITLE The State of Mathematics Achievement in Maryland: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; Nat.'-onal 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 Po"tage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Ma:_hematics Tests; National Programs; Protlem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS *Maryland; National Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational ?rogress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-stat 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 Maryland, 2,794 students in 105 public schools were assessed. This report describes th mathematics proficiency of Maryland eighth-graders, compares their overall performance to students in the Northeast region of the United States and the nation (using data from the NAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, parents' 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 content (curriculam coverage, amount of homework); delivery of mach instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math leirning (e.g., hours of television watched, atsenteeism). On the'NAEP math scale, Maryland students had an average Proficiency of 281-1-tompared to 261 nationwide. Many fewer students (Maryland-14%; U.S.-12%)'-- appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics AWevement in MARYLAND The Trial State Assessment at Grade Eight ron WLAiE U S DEPARTMENT OF EDUCATION OP, p 00 E .11001at Reser( r, AN1 I mprovemer01 CA TIONAL RE SOURCE,S INF ORMAT ION CE NTIT4 E RIC) has Dern reptotlut ed as ,ece,e.A I,orys te perscr, of ofganipt.op or ,gmatng .1 M,rlor hangp% pavp twen PladP 00,P0'00,1. 00,c1,on P,,,nis ot ,e or 0101NonSSIAlpti MINS LUX u meni dC0 not rle,,e$saf000( ,eloresew otfir.,a1 Ok. HI pt,I r ve,hry 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 areias. Since 1989, assessments 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 pan of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAEP 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 canying out the NAEP project through competitive awards to qualified organizations NAEP reports directly to the 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 include adding to those specified by Congress; identifying appropriate achievement goals for each age and grade; developing assessment objectives: developing test specifications: designing the assessment methodology: developing guidelines and standards for data analysis and for 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 selected for use in the National Assessment are fret 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 B4O.C.E.S. Saratoga Springs, New York Franck Alexander Associate Superintendent California Department of Educat on Sacramento. CalifOrnia David P. Battini High School History Teaeher Cairo- Du,ham High School Cairo, New York Parris C. Battle Teacher Horace Mann Eleraeritary School Miami, Florida Mary R. Blanton Attorney Cromwell, Porter. Blanton & Blanton Salisbury. North Carolina Boyd W. Boehije Attorney Gams, Klyn. & Bochlje Pella, Iowa Linda R. Bryant Teacher Greenway Middle School Teacher Center Pittsburgh, Pennsylvania Honorabk Mkhael N. CaMle Governor of Delaware Carve! State Office Building Wilmington, Delaware Honorabk Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hanford, Connecticut Chester E. Finn, Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.C. Mkharl S. Glade Wyoming State Board of Education Saratoga, Wyoming Christine Johnson Principal Abraham 1.incoln 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 President Southern Regional Education Board Atlanta, Georgia Honorable Carolyn Pollan Arkansas House of Representatives Eon Smith. Arkansas Matthew W. Prophet, Jr. Superintendent Portland Oregon School District Portland. Oregon Honorable William T. Randall Coinmissioner of Education State Department of Education Denver, Colorado Dorothy K. Rich 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 Topuzes Attorney Law Offices of Frank Rogoaienski Coronado. California Herbert i. Walberg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and Improvement (Ex-Officioi U.S, Department of Education Washington, D.C. Roy Truby Executive Director, NAGB Washington. D.C, NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement in MARYLAND The Trial State Aeseseament at Grade Eight THE NATION'S REPORT CARO 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 4 US. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Manna 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 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Congress, Catalog Card Number: 91-61478 ISBN: 0-88685-14-9 The work upon which this publication is b.ased was performed for the National Center for Education Statistics, Office of Educational Researth snd Improvement. by Educational Testing Service. Educational Testing Service is an equal opportunity/affirmative action employer. Educational Testing Service, ETS, anda are registered trademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of Maryland 14 EiglIth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Maryland Public Schools? 17 Chapter I. Students' Mathematics Performance 18 Levels of Mathematics Proficiency. 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations Race;Ethnicity Type of Community 27 Parents' Education Level 29 Gender ;1 Content Area Performance THE 1990 NAEP TRIAL STATE ASSFSSMENT 111 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 S. How Are Calculators Used" 60 'Ile 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 Iducational Background 68 Summar). 71 Chapter 7. The Conditions Beyond School that Fad !Rate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Televsion Watched per Day 75 Student Absenteeism 76 Students Perceptions of Mathematics 78 Summary. 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Edi:..anonal Progress ( \AFT), which included -- for the firsi time in the project', history -- a provision authorizing voluntary state-by-state asssments on a trial basis, in addition to continuing its primary mission, the national ac...,:.,,:rients that NAL P has conducted since its inception. As a result of the legislation, the 1990 NMI' 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 tour. eight, and twelve. For the Trial State Assessment, eighth-gade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in Februai-y 1990. The sample was carefully designed to represent the eighth-gade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the progam. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent uf the sessions as part of the quality assurance program desigied to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAB' TRIAL STATE ASSESSMENT 1 Maryland In Maryland, 105 public schools participated in the assessment. The weighted school participation rate was 100 pement, which means that all of the eighth-gade students in this sample of schools were represertative of 100 percent of the eighth-grade public-school students in Maryland. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 1 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 10 percent had an Individualized Education Plan (IFP). 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 andior 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 panicipating in the assessment. The students who were excluded from the assessment because they were categorized as I.EP or had an IEP represented 1 percent and 4 percent of the population, respectively. In total, 2,794 eighth-grade Maryland public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the ehgible eighth-grade public-school student population in Maryland. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from Maryland on the NAEP mathematics scale is 260. This proficiency is no different from that of students across the nation (261). Average proficiency on the NAEP 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 geater 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 NAFP scale. 9 2 "ME 1990 NAEP TRIAL STATE ASSESSMENT Maryland In Maryland, 96 percent of t.h 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 Maryland (14 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 Maryland 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 Maryland eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In Maryland: White students had higher average mathematics proficiency than did Black or Hispanic students but lower mathematics proficiency than did Asian students. Further, a greater percentage of White students than Black or Hispanic 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 Maryland students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural areas, or areas classified as "other". In Maryland, the average mathematics proficiency of eighth-gade public-school students having; at least one parent who gaduated from college was approximately 31 points higher than that of students whose parents did not gaduate from high school. The results by gender show that there appears to be no difference in the average mathematics proficiency of eighth-gxade males and females attending public schools in Maryland. In addition, there .was no difference between the percentages of males and females in Maryland who attained level 300. Compared to the national results, females in Maryland performed no differently from females across the country: males in Maryland performed no differently from males across the country. 0 TUE 1990 NAEP TRIAL STATE ASSESSMENT 3 Maryland 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 supplemented with contextual information about schools, teachers, and students. To gather such information, thc 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 ,inderstanding information about student achievement. Some of the salient results for the public-school students in Maryland are as follows: About three-quarters of the students in Maryland (78 percent) were in schools where mathematics was identified as a special priority. This is a greater percentage than that for the nation (63 percent). In Maryland, 92 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A smaller percentage of students in Maryland were taking eighth-gade mAhematics (38 percent) than were taking a course in pre-algebra or algebra (59 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 eignth-grade students in public schools in Maryland 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 Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 4 THE 1990 NAEP TRIAL sTATE ASSESSMENT Maryland In Maryland, 18 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 21 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 Maryland, 26 percent of the students never used a calculator to work problems in class, while 47 percent almost always did. In Maryland, 59 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. About three-quarters of the students (79 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 Maryland who had four types of 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 fAudents who had zero to two types. Some of the eighthloade public-school students in Maryland (I I percent) watched one hour or less of television each day; 19 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 Mwyland ME NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Asseument of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Umbrian Oregon California Mary Ind Pennwlvania Colorado Mgan Rhode Island Connecticut Ilfnmesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virenia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho_ New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands t.) THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Maryland This repot-. describes the performance of thc eighth-grade public-school students in Maryland and consists of three sections: This Introduction provides background information about the Trial State Assessment and this report. It also provides a profile of the eighth-grade public-school students in Maryland. Part One describes the mathematics performance of the eighth-grade public-school students in Maryland, the Northeast region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Maryland, the Northeast region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congess passed new legislation for the National Assessment of Educational Progress (NMI)), 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 instrument 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 (i)( 2 }(C El) of the General Education Provisions Act, as amended by Pub. L. 100-297 ( 20 (.7.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-gade 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 tenitory. 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 progam. Local district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance progam designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 1. 4 8 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patterned after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that autht ized 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 formal 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 final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in gxade 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-grade public-school students in Maryland, 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 arc presented below. The results for Maryland 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 progxam. 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 natior-1 or regional results, since not every state participated in the progarn. National Council of Teachers of Mathematics, Curriculum and Evahiation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 9 Maryland 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, Hispanic, Asian (including Parific 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 Maryland. TYPE OF COMMUM'IN 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 metropolitar. 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 group live outside metropolitari statistical areas, live in areas with a population below 10,000, and Itend 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, gaduated 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 Maryland 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 region 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. FIGURE 1 I Regions of the Country NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Delaware District al Cokunbia Maine Maryland Massachusetts New Movably. Now Jersey New 'York Pennsylvania Rhode Island Vermont WSW. Alabama Arkansas Florida 000101 Kentucky Loaislana Mississippi Writs Carolina South Carolina Tennessee West Virginia THE 1990 NAEP TRIAL STATE ASSESSMENT liNnele Wiens Iowa Kansas Minassois Missouri Wins& Notth Dakota Okla South Dakota Wisconsin :7 Alaska Adams California Colorado Hawaii Wks Moslissa Nevada Now Mexico Mama Omen Taos Utah Washington Wyoming 11 Maryland Guidelihes 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 subpopulations 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 pzoficiency 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 be 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 group 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 groups, the confidence interval included zero, and thus no difference could be assumed between thc groups. When three or more groups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendix. 4 12 THE 1990 NAEP TRIAL STATE ASSESSMENT filmy land 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 th::, 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 sl.own in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may diffe: 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 rcsults of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NA EP TRIAL STATE ASSESSMENT 13 Maryland Profile of Maryland EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in Maryland, 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 1 I Profile of Maryland Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS NAEP TRIAL STATE ASSESSMENT DEMOGRAPHIC SUBGROUPS Percentage Parconlif$ Percantigoo Racs/EdetkIty White 50 ( 1.5) 80 ( 4.2) 70 ( 0.5) Black 2$ ( 14) 12 ( 4.2) 18 ( 0.3) Hispanic 7 ( 0.8) 5 ( 1,2) 10 ( OA) Asian 4 ( 0.7) 3 ( 1.1) 2 ( 0.5) American Indian 1 ( 0.3) 1 ( 0.3) 2 ( 0.7) Type of Comnamity Advantaged urban 2$ ( 4.0) 23 ( 7.3) 10 ( 3.3) Disadvantaged urban 1$ ( 3.4) 15( 5.7) 10 ( 2.8) Extreme rural 4 ( 1.8) 14 (10.3) 10 ( 3.0) Other 50 ( 4.4) 55 (11.2) 70 ( 4.4) Parents' Education Did not finish high school ( 0.7) 7 ( .2.2) 10 ( 0.8) Graduated high school 27 ( 1.3) 23 ( 3.3) 25 ( 1.2) Some education atter high school 17 ( 0.7) 15 ( 3.0) 17 ( 0.9) Graduated college 43 ( 1.8) 49 ( 5.8) 30 ( 1.9) Gondar Male 51 ( 0.8) 50( 2.1) 51( 1.1) Female 49 ( 0.8) 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 c4tegorized 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 2. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summazizing participation data for Maryland schools and students sampled for the 1990 Trial State Assessment. In Maryland, 105 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in Maryland. TABLE 2 I Profile of the Population Assessed in Maryland EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution Weighted school participation rate after substitution 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 100% 100% 107 2 105 106 EIOHTWORADE PUBLIC-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 were of Li teed 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 ot students assessed 94% 233 115 1% 1% 10% THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Maryland In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 1 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 10 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 1 percent and 4 percent of the population, respectively. In total, 2,794 eighth-grade Maryland public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligible eighth-grade public-school student population in Maryland. lb THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Maryland 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 contains two chapters that describe the mathematics proficiency of eighth-grade public-school students in Maryland. Chapter 1 compares the overall mathematics performance of the students in Maryland 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 defined by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 17 CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from Maly land on the NAEP mathematics scale is 260. This proficiency is no different from that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics 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 14-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 Differences reported are statistically different it 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. 113 THE 1990 NAEP TRIAL VTATE ASSESSMENT Maryland 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' prnficiency 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. Defmitions of the four levels of mathematics proficiency arc given in Figure 3. It is important to note that the definitions of these levels are based solely on student performance on the 1990 mathematics assessment. The levelsare 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 Maryland, 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 Maryland (14 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 Maryland, Northeast region, and national results for each content area. Students in Maryland performed comparably to students in the nation in all of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 Maryland FIGURE 3 I Levels of Mathematics Proficiency [LEVEL 200 4101=1 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 Simple Multiplicative Reasoning and Two4tep Problem Solving Students at this level have extended their understanding of qurvititative 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 of 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, and 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 analysis, they can complete a 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. C"! 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland 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 of 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 sentences 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 numerical 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 numtvr and algebraic understanding to include some properties of exponents. They can recognize scientific notation on a calculator ancl make the trinsition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles to solve problems, They can find tne circumferences of circles and the surface areas of solid figures. In geometry, they can apply the Pytnagorean theorem to solve problems involi ,ng indirect measurement, These students also can apply their knowledge of the properties of geometric figures to .! 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. (N. P9 x. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 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 0 20 40 so so 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each populauon of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by I-4-4). If the confidence intervals for the populations do rot overlap, there is a statistically significant difference between the populations. 22 THE 1990 NAEP TRIAL STATE ASSESSMENT O ( 0.1) O ( 0.5) 0 ( 0.2) 14 ( 1.2) 16 ( 2.7) 12 ( 1.2) 61 ( 1.8) 72 ( 4.8) 64 ( 1.6) 96 ( 0.5) 99 ( 0.6) 97' ( 0.7) Maryland NE WOWS REPORT FIGURE 5 I Eighth-Grade Public-School Mathematics CARD i Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation , .AT. 0 200 225 250 275 Average Proficiency 264 ( 1.4) 271 ( 3.1) 268 ( 1.4) 258 ( 1.7) 268 ( 4.7) 258 ( 1.7) 258 ( 1.4) 268 ( 3.6) 259 ( 1.4) 260 ( 1.5) 273 ( 3.6) 262 ( 1.8) 263 ( 1.6) 267 ( 3.4) 260 ( 1.3) 300 500 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 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 Maryland 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 Maryland are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black or Hispanic students but lower mathematics proficiency than 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 FIGURE 6 I Average Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity 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 1.4-4). 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 meaa proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 25 THE WOWS REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CMO I Mathematics Proficiency by Race/Ethnicity LEVEL 300 state White Black Hispanic Asian Region White Black Hispanic Asian /teflon White Black Hispanic Asian LEVEL 250 Stall White Black Hispanic Asian RB9km White Black Hispanic Asian Station White Black Hispanic Asian LEVEL 200 state White Black Hispanic Asian N.gan 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 3 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. 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). ( 1.8) 2 ( 0.8) 4 ( 1.4) 44 ( 6.0) 19 ( 2.5) 3 ( 4.1)1 alot .**) 15 ( 1,5) 2 ( 1.3) 3 ( 1.1) 31 ( 6.2)1 76 ( 1.7) 32 ( 3.0) 33 ( 3.8) 90 ( 3.4) 79 ( 4.8) 39 (10.9)1 II *. POI *** 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) SO ( 5.0)1 SO ( 0.4) 91 ( 1.5) Se ( 2.5) SO ( 1.0) 100 ( 0.0) 93 ( 3.0)1 ( *) 99 ( 0.4) ( 3.1) ( 1.8) 97 ( 2.5)1 100 26 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students atteading public schools in advantaged urban areas, disadvaataged urban areas, extreme rural areas, and areas dassilied as "other". (These are the "type of community" groups in Maryland with student samples large enough to be reliably reported.) The results indicate that the avenge mathematics perfonnance of the Maryland students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural areas, or areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathanatics Proficiency by Type of Community 'Wary land Advantaged urban Disadvantaged urban Extreme rural Other Northoist Advantaged urban Disadvantaged urban Extreme rural Other Nation Advantaged urban Disadvantaged urban Extreme rural Other 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 10-4-1). If the confidence interval; for the populations do not overlap, there is a statistically significant difference betw.-mi the populations. ! Interpret with caution the nature of the sample does not allow aocurate 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 FIGURE 9 LEVEL 300 state Adv. urban Disadv. urban Ext. rural Other Re Oen Adv. urban Deady. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other LEVEL 250 Slate Adv. urban Disadv. urban Ext. rural Other Raglan Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban Duch/. uroan Ext. rural Other LEVEL 200 Stat Adv. urban Disadv. urban Ext. rural Other R*011 Adv. urban Disadv. urban Ext. rural Other Nation My. urban Disadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Comm 0 20 40 60 BO Percantag at or Above Proficioncy Lewis The standard 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 I-I-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. *1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 .14 28 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 ( 3.2) 2 ( 1.2)1 7 ( 3.6)1 13 ( 1.6) 21 ( 11.7)1 ( 4.9)1 NEI ( 2.6) 211 ( 4.6)1 7 ( 2.1)1 ( 2.3)1 12 ( 1.2) 77 ( 4.2) 29 ( 5.5)1 ( 4.8)1 63 ( 3.1) 22 ( 9.5)1 (11.9)! sum ( .41 77 ( 4.4) 13 ( 4.6)1 419 5.0)1 ( 6.2)1 66 ( 2.3) ( 0.7) ( 2.9)1 96 ( 2.4)1 IPS ( 0.8) 100 ( 0.0) 93 ( 2.7)1 aaa 99 ( 0.8) 100 ( 0.0) 99 ( 1.5)1 97 ( 2.8)1 97 ( 1.0) Maryland 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 Maryland, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 31 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 Maryland (43 percent) and in the nation (39 percent) had at least one parent who graduated from college. In comparison, the peiventage of students who reported that neitherparent graduated from high school was 7 percent for Maryland and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School Mathematics Proficiency by Parents' Education NAEP Mathematics Scale 200 225 250 275 300 SOO Average Proficiency FIN4 Maryland 115 non-graduate HS graduate Some college College graduate Northeast NS non-graduate HS graduate SOMe co4lege College graduate Nation HS non-graduate HS graduate Some college College graduate The standard errors art 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 1-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. *1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSWNT 29 Maryland Thr NMI HEW. FIGURE 1 1 I Levels of Eighth-Grade Public-School CAM I Mathematics Proficiency by Parents' Education LEVEL 300 State HS non-grad. HS graduate Some conege Cateee grad. Raglan HS non-grad. HS greduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 Slate HS non-grad. HS graduate Some college College grid. Region HS nort-grad. HS graduate Some college College grad. *Won HS non-grad. HS graduate Some college College grad. LEVEL 200 State HS non-grad. HS graduate Some cottage College grad. 9.9k1g1 115 non-grad. HS graduate Some college Gonne grad. Nation HS non-grad. HS graduate Some college Coflage grad. : &.,,,V t'. '1 ,;N . ' ,,. 0 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 ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by O-1-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 it not presented in this figure because so few students attained that level. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 30 THE 1990 NAE? TRIAL STATE ASSESSMENT 4 ( 1.8) 4 ( 1.0) 10 ( 1.9) 26 ( 1.9) wit ( ,) ( 2.8) 13 ( 2.7) 2$ ( 4.3) ( 0.9) ( 1.5) 12 ( 1.4) 21 ( 1.9) ( 4.7) 44 ( 2.4) N ( 3.0) 74 ( 1.8) ***) 92 ( 5.9) 71 ( 4.5) 99 ( 4.6) 37 ( 4.8) 58 ( 2.7) 71 ( 2.6) 79 ( 2 0) 93 ( 2.1) 63 ( 1.2) 99 ( 1.0) 99 ( OS) g ui t ( 0.9) 90 ( 1.4) 69 ( 0.4) 90 ( 1.9) 97 ( 0.8) 99 ( 0.7) 99 ( 0.7) Maryland 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 Maryland. Compared to the national results, females in Maryland gemmed no differently from females across the country; males in Maryland performed no differently from males across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender The standard errors art 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 044). 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 Maryland who attained level 200. The percentage of females in Maryland who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of wales in Maryland who attained level 200 was similar to the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASSESSMENT 31 FIGURE 13 I Levels of Eightb-Grade Public-School i Mathematics Proficiency by Gender LEVEL 300 Stat. Male Female Raglan Male Female Nation Mate Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 Stat Male Female Region Male Female Nation Male Female 0 20 40 100 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 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. Proficiency level 350 is not presented in this figure because so few students attained that level. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 ( 1.3) 14 ( 1.4) 19 ( 3.3) 13 ( 3.8) 14 ( 1.7) 19 ( 1.3) GO ( 1.8) 111 ( 2.2) 72 ( 5.8) 72 ( 4.5) 54 ( 2.0) 54 ( 1.8) IS ( 0.6) N ( 0.7) ( 0.7) 99 ( 0.7) 97 ( 0.9) 97 ( 0.6) Maryland In addition, there was no difference between the percentages of males and females in Maryland who attained level 300. The percentage of females in Maryland who attained level 300 was similar to the peicentage of females in the nation who attained level 300. Also, the percentage of males in Maryland 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 Matyland TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1690 IMP TRIAL STATE ASSESSMENT Ntrabore and OP6/11119119 Geometry Data Analysis, Statistics, and Probability and Functions TOTA1, State Region Nation RACFATHNICITY Mite State Region Nation Rade State Region Nation Hispanic State Region Nation Asian State Region Nation TYPE OF COVIlititiftl Advantaged urban State Region Nation Disadvantaged urban State Region Nation Extreme rural State Region Nation Other State Region Nation Irnalldowy Pollak/ow Powasionai Preislioci PrOldsegi 211v tv 21411 ,16.31 :::(( 2A1 awl 1.4i 2011 1.771 20( 174 202 ( 14) 213 ( 1 22:70 775( 1.4) 271 ( 13) ase( 1 271 ( 1.7) 274 ( 1.1 273 ( 3.1) 272 ( 4.6) 272 ( 279 ( 3.1) 271 ( 3.01 273 ( 14) 267 ( 2.0) 267 ( i 212 ( 1.11) 21311 ( 14 244 ( 2.0 225 ( 2.e) 233( 14) 234 ( 23) 21 2.11. 260 ( 5.4)4 233 ( 94)1 243 ( We 244 ( 111.2)4 242 9.2p 244 ( 3.1) 227 ( 3..t 236 ( 23) 231 ( U) 237 2.7) t) 1 .3:1? 243 ( 3.1) 296 ( 4.2) 440 ( gin 279 ( 11.7)4 24'.1 i iii 222 1 LI 222 1 Ul 236 / le21 244 ( 2.7) 239 ( 3.4) 243 ( 3.2) 238 ( 14) 294 ( 3.7) 222 ( 43) 2641 ( 4.9) 266 ( 4.7) 0411,* ( ed ) 006 ( 0411 ( ***) Re* ( *In 20 ( 51)1 271 ( 13.3); 275 i 54)4 292 ( 8.9)4 2311 36) 274 ( 4.3) 274 ( 4.0) 277 ( 34) 262 ( 63)1 279 f 83)4 275 ( coy 292 ( 64)4 263 ( 3,2)1 231 ( 3.2)4 277 ( 5.2)1 29$ ( 44)1 240 ( 3.7)1 221 ( 41)1 221 ( 231 ( 41)4 251 ( 7.2p 236 (13.6)1 242 (13.5)4 245 (11 A)! 2155( 3.1)1 242 ( 4.9)4 246 ( 3.7)4 247 ( 43)1 254 ( 33)1 4.4 ( 255 (( 54)4 250 ( 2.1)4 253 ( 4ip ( 256 ( 43)1 254 ( 4,2)1 25$ ( 46)1 257 ( 5.0)1 264 2.1) 257 ( 2.9) 250 ( 2.4) 262 ( 2.5) 274 ( 3.7) 265 ( 6.5) 272 ( 3.3) 277 ( 3.9) 200 ( 1.9) 247 ( 24) 250 ( 1.7) 261 ( 2.2) ( 4.2) 273 (10.1)4 277 ( 44)4 230 ( 243 (12.6 247 ( 3.2 255 (2,0)1 444 .41 256 ( 4.8)4 263 ( 2.5) 271 ( 3.4) 231 ( 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. *** Semple size is insufficient to permit a reliable estimate (fewer than 62 students). ft 34 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE 3 I Eighth-Grade Public-School Mathematics (continued) Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT Numbers and Operations aleaterereent Geometry _ Data Ansty.sis ' Statletka, and Pivbabai ly Algebra and Rowans yOTAL, State Region Nation frolidency 264 ( 1.4) 271 ( 11) 239 ( 14) Prifielenay 250 ( 1.7) 200 ( 43) 251 ( 1.7) Prtilkaancy 256 ( 14) 200 ( 34) 200 ( 1.4) Preisis095 24: ( 1.0) PAREN73S EDUCATION NS non-graduate State Region 250 ( 2.9) 4441 237( 3.3) *No ***) 234I (SA) 37(13) .4. Nation 247 ( 2.4) 237 ( 35) 242 ( 240 ( HS graduate State 251 ( 14) 240 ( 2.1) 242 ( 1.4) 240 ( 1.0) Region 200 ( 2.7) 256 ( 5.1) 254 ( 3.2) 264 ( 4.6) Nation 250 ( 11) 248 ( 2.1) 252 ( 15) 263 ( 2.2) Saw college State MO ( 2.1) 256 ( 2.4) 259 ( 1.8) 243 ( 3.5) Region 267 ( 2.3) 261 ( 5.7) 267 ( 3.4) 273 ( 3A) Nahon 270 ( 14) 264 ( 2.7) 262 ( 2.0) 209 ( 2.4) Coleco* graduat State 278 ( 1.6) 272 ( 2.2) 260(14) 274 ( Region 205 ( 31) 279 ( 5.5) 277 ( 3,8) 297 ( 31) Nation 27$ ( 1.8) 272 2.0) 270 ( 15) 271 ( 22) GENDER Maio State 264 ( 1,4) 200 ( 14) 251 ( 14) 201 ( 1,7) Region 272 ( 3M 271 ( 5.9) 209 ( AA) 274 ( 4.1) Nation 206 ( 2.0) 262 ( 2.3) 200 ( 1.7) 202 ( 2.1) Foetal. State 264 ( 1.6) 252 ( 2.2) 258 ( 1.7) 200 ( 14) Region 270 ( 31) 261 ( 4.3) 203 ( 4.1) 273 ( 3.8) Nation 268 ( 1.4) 253 ( 14) 258 ( 1.5) 281 ( 1.9) 11F98499999 2171 :1 1.31 244 ( 11) 242 I 34 24$ ( 254 ( 2.0 263 ( 2 115 ( 24) 292 ( 25) 253 ( 2.2) 275 ( 2.0) 280 ( 35) 273 ( 1.7) 261 ( 1.8) 286 ( 4.1) 200 (14) ( 14) 266 ( 3.7) 200 ( 1,4) The standard errors of the estimated statistics appear m 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 3$ Maryland ME NATION'S REPORT CARD PART TWO Finding 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 supplemented with contextual information about schools, teachers, an,' 'Indents. 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 l'wo of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. I .2 THE 1990 NAEP TRIAL STATE ASSESSMENT 37 Maryland Through the questionnaires wiministered 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' su estions 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 textbooks or worksheets. Also, it is widely recognized that home environment has an enomious impact on future academic achievement. Yet, as shown in Chapters 3 and 7, Irge 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. 38 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland 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 Maryland public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public scho,.)ls' policies and staffing. Some of the salient results are as follows: About three-quarters of the eighth-grade students in Maryland (78 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curtls McKnight, et al., The Underachieving Curriculum Assessing U.S. School Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign, Stipes Publishmg Company, Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Maryland In Maryland, 92 percent of the students could take an algebra course in eighth grade for high school course placement or credit. All of the students in Maryland (100 percent) were taught mathematics by teachers who teach only one subject. Almost all (93 percent) of the students in Maryland 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 Maryland Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Maryland Northeast Nation Percentage of eighth-grade students in public schools that identified mathematics as remising spacial emphasis in school-wide goals and objectives, instruction, in-service training, etc. Percentage of eighth-grade public-school students who are offerod a course in algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are tought by tam:tsars votto teach only mathematics Percentage of eighth-grade students in public schools who are assigned to a nuthamatIcs class by their ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics kutwction par weak flehal 78 ( 22 ( 4.4) 2.1) Pirowdage 45 (18.5) 90 ( 7.3) Povedivis 03 ( 5.9) 78 ( 4.6) 100 ( 0.0) 100 ( 0.0) gi ( 3.3) 93 ( 1.1) 71 (10.1) 53 ( 4.0) 39 ( 3.0) 14 ( 5.5) 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 Malyland CURRICULUM COVERAGE To place students' mathematics proficiency in a cuniculum-related context, it is necessary to examine the extent to which eighth graden in Maryland are taking mathematics courses. Based on their responses, shown in Tabk 5: A smaller percentage of students in Maryland were taking eighth-grade mathematics (38 percent) than were taking a course in pre-algebra or algebra (59 percent). Across the nation, 62 percent were taking eierth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in Maryland who were enrolled in preAlpbra or algebra courses exhibited higher average mathematics proficiency than did those who WC= 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 abk students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Oass I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAVY TN1A1. STATE ASSESSMENT Alar*and Northeast Nation What kind of mathematics class are you Peneetlie Permeda. 041r011111.1 taking this year? WWI Preielancy 31 ( 2.0) 237 ( 1.4) 10111 Pralkiistav 13 ( SA) 230 ( 2.0) snit Preadsol0 e2 ( 2.1) 25114) ( Bgh St-grads maSionsatics Pm-algebra ( 1.4) 111 ( SI) 10 ( 1.9) 291 ( 1.8) 271 ( 0.7)1 272 ( 2.4) ANNIbra 27 ( 1.5) 11 ( SS) 15 ( 1.2) 291 ( 4,7) 297 ( VI) 290 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for eath 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 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Maryland Further, from Table A5 in the Data Appendix:4 About the same pereeniage of females (61 percent) and males (56 percent) in Maryland were enrolled in pre-algebra or algebra courses. In Maryland, 62 percent of White students, 54 percent of Black students, 42 percent of Hispanic students, and 81 percent of Asian students were enrolled in pre-algebra or algebra courses. Similarly, 72 percent of students attending schools in advantaged urban areas, 46 percent in schools in disadvantaged urban areas, 52 percent in schools in extreme rural areas, and 59 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 of eighth-grade students in public schools in Maryland 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 Maryland, 3 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 4 percent of the students in Maryland and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. For every table in the body of the report that Includes estimates 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 Matyland The results by race/ethnicity show that 4 percent of White students, 5 percent of Black students, 3 percent of thymic students, and 9 percent of Asian students spent m hour or more on mathematics homework each day. In comparison, 2 percent of White students, 6 percent of Black students, 3 percent of Ifspanic students, and I percent of Asian students spent no time doing mathematics homework. In addition, 4 percent of students Antall:11g schools in advantaged urban areas, 6 percent in schools in disadvantaged urban OWLS, 0 percent in schools in extreme rural areas, and 6 percent in schools in areas classified as "other" spent an how or more on mathematics homework daily. In comparison, 0 percent of students attending schools in advantaged urban areas, $ percent in schools in disadvantaged urban anas, 0 percent in schools in extreme rural arras, and 3 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teuhers' Reports on the Amount of Thne Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MCI MEP TRIAL STATE ASSESSMENT About how much time do studentS spend on mathematics homework each day? Nene 16 minutes 30 minutes 45 minutes An how or more 114roomiass Pomade. Pireoulags sad awl Prollaioncy Prolatiour Prelleleasy 3 ( 1.1) 237 ( My 0 i 0.01 4.1 f Eli se ( 2.8) 54 (13.2) 4$ ( 42) 252 ( 2.1) 284 ( 4.1)1 258 ( 23) 48 ( 2.5) 35 (12.5) 4$ ( 43) 205 ( 2.2) 270 ( 4.1)1 2011 ( 113) 1 ( 1.2) *MI 4Mbill 9( 2.7) 10 ( 13) 289 ( 5.1) 272 ( 5.7)4 273 ( 5.8)4 «3 (( g 2711 ( SMI 4 ( 0.9) 4 ( 1.3) The standard errors of the estimated statistics appear in arentheles. It can be said with about 95 percent wrtainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. t 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 Maly laird 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 1110 NAEP TRIAL STATE ASSESSMENT Mara land Norihead Nation About how much time do you usually spend each day on mathematics homework? None 15 minutes 30 minutes 46 minutes An how or mere lisessetimp Perm Imp Pima hop Sid ihrillOmer 11101.4, 2 ( 4.3) 4 ( 0.11) *** ( Me 1 ( 11 1 ( 0.1) 111) 251 4 2.4) 30 ( 1.1) 57 ( 3.3) 31 ( 2.0) 250 ( 14) 2N ( 2.4) SO ( 1.11) 38 ( 11) 20.14 32 ( 12) 263 ( 1.8) 2g i 20 ( 1.0) 13 ( OS) 45 ( 2.3) 11 ( 1.0) 267 ( 2.5) 272 ( SA) WS ( 1.9) 9 1 0.1 II ( 1.?) 12 ( 1.1) *we ( o) 251I ( 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. "1* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). And, according to the students (Table 7 and Table A7 in the Data Appendix): In Maryland, 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, 9 percent of the students in Maryland 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 8 percent of White students, 9 percent of Black students, 6 parent of Hispanic students, and 17 percent of Asiisin. students spent an hour or more on mathematics homework each day. In comparison, 4 percent of White students, 4 percent of Black students, 6 percent of Hispanic students, and 1 percent of Asian students spent no time doing mathematics homework. 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland In addition, 8 percent of students attending schools in advantaged urban areas, 12 percent in whools in disadvantaged urban areas, 10 percent in schools in extreme rural areas, and 8 percent in schools in areas classified as "other" spent an hour or molt on mathematics homework daily. In comparison, 2 percent of students attending schools in advantaged urban areas, 5 percent in schools in disadvantaged urban areas, 8 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, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement.' 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 Mathemaucs, Curriculum and Evaluation Standards for School lvfathematks (Reston, VA: National Council of Teachers of Mathematics, 1989). 5 0 THE 1990 NAEP TRIAL STAT.6 ASSESSMENT 45 Maryland 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 Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 5 46 THE 199O NAEP TRIAL STATE ASSESSMENT Maly land TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11180 MAE? TRIAL STATE ASSESSMENT Mandand Northeast Nadon 41/ Teacher "emphasis" categories by Paraeaalas sal Pareaalseil aid Ileramaa. content areas Prallaimay *nears and Operations Heavy emphasis 35 ( 2.6) 41 (6.9) 41 ( ( 1.0) 20I ( 2A) 240 ( 13) Little or no emphasis 24 ( 2.1) 21 ( 6.5) 15 ( 2.1) 298 ( 2.3) «a* ( 287 ( 3.4) Manumitting Heavy emphasis 21 ( 2.8) 32 (113) 17 ( 3.0) 237 ( 3.9) 257 (111)1 250 ( SA) Little Of no emphasis 37 ( 22) 34 ( 11.3) 33 ( 4.0) 278 ( 3.1) 292 ( 4.5), 272 ( 4.0) Oaontatry Heavy emphasis 22 ( 23) 44 (11.9) 28 ( 3.8) 254 ( 3.1) 264 ( 13.1)I 260 ( 3.2) Little Of ITO emphasis 30 ( 22) 9 ( 1.9) 21 ( 3.3) 264 ( 2.7) ( 264 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 14 ( 2.0) 12 ( 6.1) 14 ( 2.2) 257 ( 4.5) *41 269 ( 4.3) Little Of r10 emphasis 57 ( 23) 48 (10.1) 53 ( 4.4) 265 ( 2.1) 279 ( 5.4)1 261 ( 2.9) Algebra and Functions Heavy emphasis 51 ( 2.4) 52 (11.5) 443 ( 3.6) 283 ( 2.3) 273 ( 0.6)1 275 ( 2.5) Little or no emphasis 22 ( 2.0) 14 ( 6.6) 20 ( 3.0) 232 ( 2.8) 4.44. 243 ( 3.0) The standard errors of the esumated 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 "Moderate emphasis" category is itot 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 permita reliable estimate (fewer than 62 students). 5 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 47 Maryland SUMMARY Although many types of mathematics learning can take place outside of the school environment, there 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 Maryland (78 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Maryland, 92 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A smaller percentage of students in Maryland were taking eighth-grade mathematics (38 percent) than were taking a course in pre-algebra or algebra (59 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 Maryland 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. In Maryland, 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, 9 percent of the students in Maryland 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 Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 48 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland CHAPTER 4 yazx 1118.11111111 1111111111111 WRNS SU 111111111.11 is 11111111M114/11111 MOIIII111111111111111111111 11111111111111. MU AIM URMA -4neuall asta urawipm peas m.smes ism sumo 411111111111111111111111111 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 arc 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. ° National Council of Teachers of Mathematics, Professional Standarcis for the' Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Maryland From Table 9 and Table A9 in the Data Appendix: In Maryland, 18 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 21 percent of the students were taught by teachers who got only some or nem of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Maryland, 12 percent of students attending schools in advantaged urban areas, 3 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 17 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in Maryland, 17 percent of students attending schools in advantaged urban areas, 53 percent in schools in disadvantaged urban areas 15 percent in schools in extreme rural areas, and 17 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 izathematics 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 NAEP TRIAL STATE ASSESSMENT Which of the following statements is true about how well supplied you are by your school system with the instructional materials and other resources you need to teach your class', I get ad the resources I need. get most of the resources I need. I gat some or none of the ri Ayres I need. Percentage Percentage Percentage and and and Pre/Wein Proficiency Prilideacy 18 ( 2.5) 28 ( 6.6) 13 ( 2.4) 269 ( 2,8) 271 ( 7.2)1 263 ( 42) 61 ( 3.4) 38 (11.7) 56 ( 4,0) 264 ( I.9) 272 ( 2.9)1 2e5 ( 2.0) 21 ( 2.8) 36 (11.8) 31 ( 4.2) 243 ( 3.2) 274 ( 9.8)1 261 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It ean be said with about 95 percent ,...rtitinty 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 determinauon of the variability of this estimated mean proficiency. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland P ATTERNS IN CLASSROOM INSTRUCTION Research in education and cggnitive 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: More than half of the students in Maryland (56 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics problems in small groups (8 percent). The largest percentage of the students (67 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; some never used such objects (1 I percent). In Maryland, 57 percent of the students were assigned problems from a mathematics textbook almost every day; 10 percent worked textbook problems about once a week or less. About half of the students (47 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (23 percent). ' Thomas Romberg, "A Common Curriculum for Mathematics," Individual Difierences and the Common Curriculum Eighty.second Yearbook of the National Society for the Study of Education (Chicago, IL: University of Chicago Press, 1983). r o t)c.) THE 1990 NAEP TRIAL STATE ASSESSMENT 51 Maryland TABLE 10 I Teachers' Reports on Patterns of Mathematics I Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT About how often do students work problems in small groups? AI least once a week Less thin once a week Never About how often do students use objects like rulers, counting blocks, or geometric solids? Al least once a week Less than once a week Now fronamemp Pairsolop Olortomiage and Ind and Pralidency NW PrOkihma, 36 ( 3.3) 30 ( 44) 260 ( 2.7) at 1 88:3 260 ( 2.2) 36 ( 52) 43 ( 4.1) 262 ( 2.3) 2:11 1.01, 264 ( 23) 6 ( 2.2) 264 ( 3.2)4 17 ( IS) " ( 1 II ( 2.0) 277 ( 54)4 Percentage Percentap Perceatage and and end Prolickstcy Preficioncy Proadincy 22 ( 254 ( 2.4) 3.0) 14 ( ivit 5.5) ***) 22 ( 254 ( 3.7) 32) 67 ( 2.4) 78 ( 6.8) es ( 3.9) 261 ( 1.6) 269 ( 1.6) 263 ( 1.9) 11 ( 2.0) 9 ( 3.5) 9 ( 2.6) 262 ( 5.0) 252 ( 5.9)i 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). 5 7 52 THE 1990 NAEF TRIAL STATE ASSESSMENT Maryland TABLE 11 I Teachers' Reports on Materials for I Mathematics instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY NAEP TRIAL STATE ASSESSMENT Maryland Northeast Madan About how often do students do problems Paraudaga Parasainge lad floorseidap from textbooks? iketifiesig 67 ( 33) 267 ( 2.0) 2511 1 WA*** 67( 270 2r1 63) ( 4.4) and arlikkadd ( 3.4) 207 ( 16) 31 ( 3.1) 254 ( 2.11) Almost every day Several tines a wash Aland once a *web or less 10 ( 11 131 2.11) ( 1.8) 247 ( 4.1) 0.21 200 ( 5.1)4 About how often do students do problems on worksheets? Penmentage Parawdag. and Parasahe and Praidatcy Proddefflay Madam Al least several limes a week 47 ( 2.5) 53 (11.3) 34 ( 3.0) 257 ( 2.5) 262 ( 4.5)! 250 ( 2.3) About owe a week 29 ( 3.1) se ( 8.2) 33 ( 3.4) ( 3.2) 270 ( 3.4)4 260 ( 2.3) Less than weekly 23 2.8) 15 ( 4.6) 32 ( 3.6) 262 ( 3.4) ) 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 interest, the value for the entire population it within ± 2 standard errors of the estimate for the sample. 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). 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 t3 those of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT 53 Maayland COLLABORATING IN SMALL GROUPS In Maryland, 42 percent of the students reported neves working mathematics problems in small groups (sec Table 12); 30 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 1 Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ISSO NAEP TRIAL STATE ASSESSMENT Maryland Northeast Nation How often do you work in small groups in your mathematics class? At WM moo a week Lass than once a weak Now Parma. Pidolimpay Poisods. PrAliciessy 30 ( 2.1) 27 ( 8.7) 25 ( 2.2) 210 ( 4.1)I 21 ( 1.4) 22 ( 2.1) ( 2.9) 271 ( 5.0) 42 ( 2.3) 51 ( 7.8) 2$8 ( 1.8) 273 ( 4.8) Peramitapp tJLsir 2$ 256 1 2111 20 ( 1.4) 2457 ( 2.0) 44 ( 24) 281 ( CO) 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. I 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 Maryland, 34 percent of students attending schools in advantaged urban areas, 37 percent in schools in disadvantaged urban areas, 22 percent in schools in extreme rural areas, and 28 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 27 percent of White students, 36 percent of Black students, 38 percent of Hispanic students, and 32 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 (29 percent and 32 percent, respectively). 5 9 54 THE. 1990 NAEF TRIAL STATE ASSESSMENT Maryland 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 A 13 in the Data Appendix summarize these data: About half of the students in Maryland (46 percent) never used mathematical objects; 23 percent used these objects at least once a week. Mathematical objects were used at least once a week by 23 percent of students attending schools in advantaged urban areas, 21 percent in schools in disadvantaged urban areas, 17 percent in schools in extreme rural areas, and 21 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 (26 percent and 20 percent, .espectively). In addition, 21 percent of White students, 26 percent of Black students, 28 percent of Hispanic students, and 23 percent of Asian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11100 NAEP TRIAL STATE ASSESSMENT Maryland Northeast Nation How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Percentage and Proadency Partentaga end ProOdency Percentage and Pralkiency At least one* a Week 23 ( 1.4) 30 ( 4.3) 28 ( 1.8) 252 ( 2.0) 265 ( 6.2) 256 ( 2.6) Less than once a week 31 ( 1.1) 30 ( 3.2) 31 ( 1.2) 267 ( 1.6) 277 ( 3.9) 2651( 1.5) Never 46 ( 1.7) 40 ( 4.8) 41 ( 2.2) 260 ( 2.0) 266 ( 3A) 256 ( 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 foi. the entire population is within ± 2 standard errors of the estimate for the sample. C THE, 1990 NAEP TRIAL STATE ASSESSMENT 55 May d MATERIAIS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in Maryland 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 A 14 in the Data Appendix): More than half of the students in Maryland (62 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 59 percent of students attending schools in advantaged urban areas, 59 percent in schools in disadvantaged urban areas, 83 percent in schools in extreme rural areas, and 64 percent in schools in areas classified as "other". TABLE 14 I Students' Reports on the Frequency of Mathemafics Textbook Use L11100 NAEP TRIAL STATE ASSESSWNT PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY How often do you do mathematics problems from textbooks in your mathematics class? Perants. and Proficiency Pertents. estO Proficiency Ihrosnlapo era Proficiency Mosul every day 62 ( 2.2) 72 ( 5.3) 74 ( 1.9) 266(1.8) 275 ( 3.7) 247 ( 1.2) Several times a week 22 ( 1.1) 14 ( 1.8) 14 ( 0.8) 256 ( ) 281 ( 4.5) 252 ( 1.7) Mad once a week or less 18 ( 1.7) 14 ( 4.3) 12 ( 1.8) 247 ( 2.2) 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. EU 56 ThE l99 e, NAEP TRIAL STATE ASSESSMENT loyhved And, for the frequency of worksheet usage (Table 15 and Table A 15 in the Data Appendix): About half of the students in Maryland (47 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 49 percent of students attending schools in advantaged urban areas, 41 percent in schools in disadvantaged urban areas, 20 percent in schools in extreme rural areas, and 48 percent in schools in areas classified as "othtr". TABLE 15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 RAEP TRIAL STATE ASSESIMAENT Maryland Northeast Nation How often do you do mathematics problems on worksheets in your mathematics class? Peramisis and finolkienay parawitage sag Prollekssay At least several tknes a week 47 ( 2.0) 44 ( 5.9) 258 ( 1.4) 281 ( 3.5) About once a week 2. ( 12) 22 ( 1.6) 283 ( 22) 2135 ( 39) Less than weedy 27 ( 2.1) 34 ( 8.5) 287 ( 2.7) 252 ( 4.3)1 Perimifigo ant linelldsmay 38(24) 233 ( 22) 25 ( 12) 231 ( 1.4) 37 ( 2.5) 272 ( 14) 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 ac, 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. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1900 NAEP TINAL STATE ASSESSMENT Patterns of classroom Instruction Nom 11990 eivissits TiltadlerS Peressfaga Teachers Pereents. 1188818914 Tudors Percentage of students who wort ina0tematics problems In small groups At least once a week 30 ( 2.1) 58 ( 3.3) 27 ( 6.7) 44 ( 6.4) 28 ( 2.5) 50 ( 4.4) Less than once a week 28 ( 1.4) 36 ( 3.2) 22 ( 2.8) 30 ( 8.6) 28 ( 1.4) 43 ( 4.1) Never 42 ( 2.3) ( 2.2) 51 ( 7.9) 17 ( 6.5) 44 ( 2.9) 8 ( 2.0) Percentage of students voho use objects like ruff's, counting Mocks, or geometric solids At least once a week 23 ( 1.4) 22 ( 2.4) 30 ( 4.3) 14 ( 53) 28 ( 1.8) 22 ( 3.7) Less than once a week 31 ( 1.1) 67 ( 2.4) 30 ( 3.2) 78 ( 6.8) 31 ( 1.2) 89 ( 3.9) Never 48 ( 1.7) 11 ( 2.0) 40 ( 4.6) 9 ( 3.5) 41 ( 2.2) 9 ( 2.6) Materials for mathematics instruction Percentage MON' Towbars Percentage Studants Teachers Pamentaga Siudints Ur:awn Percentage of students Mx, use a mathematics textbook Almost every day 62 ( 2.2) 57 ( 3.2) 72 ( 5.3) 57 ( 9.3) 74 ( 1.9) 62 ( 3.4) Several times a week 22 ( 1.1) 33 ( 3.0) 14 ( 1.6) 31 ( 6.3) 14 ( 0-6) 31 ( 3.1) About once a weak or less 16 ( 1.7) 10 ( 1.7) 14 ( 43) 13 ( 2.8) 12 ( 1.8) 7 ( 1.8) Percentage of studants who use a mathematics wodesheet At least several times a week 47 ( 2.0) 47 ( 2.5) 44 ( 5.9) 53 (11.3) 38 ( 2.4) 34 ( 3.8) About once a week 26 ( 1.2) 29 ( 3.1) 22 ( 1.8) 32 ( 8.2) 25 ( 1.2) 33 ( 3.4) Less than weekly 27 ( 2.1) 23 ( 2.6) 34 ( 6.5) 15 ( 4.0) 37 ( 2.5) 32 ( 3.6) 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. 3 58 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland 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 mathematics 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: More than half of the students in Maryland (56 percent) worked mathematics problems in small groups at least once a week; relatively few never worked in small groups (8 percent). The largest percentage of the students (67 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and some never used such objects (11 percent). In Maryland, 57 percent of the students were assigned problems from a mathematics textbook almost every day; 10 percent worked textbook problems about once a week or less. A hout half of the students (47 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (23 percent). And, according to the students: In Maryland. 42 percent of the students never worked mathematics problems in small groups; 30 percent of the students worked mathematics problems in small groups at least once a week. About half of the students in Maryland (46 percent) never used mathematical objects; 23 percent used these objects at least once a week. More than half of the students in Maryland (62 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. About half of the students in Maryland (47 percent) used worksheets at least several times a week, compared to 38 percent in the nation. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Mao, land 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. 3 National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princvton, NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Currkulum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 60 TILE 1990 NAEP TRIAL STATE ASSESSMENT Table 17 pmvides a profile of Maryland eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 30 percent of the students in Maryland had teachers who allowed calculators to be used for tests. About .the same percentage of students in Maryland and in the nation had teachers who permitted unrestricted use of calculators (19 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of Maryland Policies on Calculator Use PERCENTAGE OF STUDENTS NAEP TRIAL STATE ASSESSMENT Maryland Northeast Nation Percentage of eighthlrade students in public 3ch001s whose teachers permit the unrestricted uee of calculators Percentage of elghth-grade students in public schools whose teachers permit the use of calculators for tests Percentage of eighth-grade students in public schools whose teachers report that students have motto to calctdators owned by the school Ponaudaps Parcentage Pavaa logs 19 ( 21) 20 (11.8) 11 ( 34) 30 ( 33) 14 ( fa) 33 ( 4.5) 77 ( 2.5) 20 ( 1.2) 56 ( 4.0) 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 1990 NAEP TRIAL STATE ASSESSMENT 61 Maryland THE AVAILABILITY OF CALCULATORS In Maryland, most students or their families (98 percent) owned calculators (Table 18); however, fewer students (51 percent) had teachers who explained the use of calculators to them. From Table A 18 in the Data Appendix In Maryland, 52 percent of White students, 49 percent of Black students, 59 percent of Hispanic students, and 45 percent of Asian students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (49 percent and 53 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 MAP TRIAL STATE ASSESSMENT Mar Oahe Northeast Nation Do you or your family own a calculator? Does your mathematics teacher explain how to use a calculator for mathematics problems? The Perim lionmigs. Amp law am *ad and Pro Now aillehmay Pre Odom 08 ( 0.3) OS ( 0.1) 251 ( 1.5) 200 ( 3.3) 2 ( 0.3) 2 ( 0.7) ) ( 203 ( 1.3) 3 ( 0.4) 234 (Si) Parcenta. Parasols. PareamOMIP and Preicishoy Preldlow Prelistaict 61 ( 13) 4 49 ( 2.3) 250 ( 1.5) 21°8 41 258 ( 1.7) 40 ( 19) TO ( 4.0) 51 ( 2.3) 264 2.0) 274 ( 3.0) 201 ( 13 ) The standard errors of the estimated statistics appear in parentheses. It can be aid with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the esUrnate for the sample. 6** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 13 7 THE 1990 NAEP TRIAL STATE ASSESSMENT Aft ilyland 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 slcills and content. As part of the Trial State A33CSSMent, studr were asked how frequently (never, sometimes, almost always) they used calculak... 3 for working problems in class, doing problems at home, and tstking quizzes or tests. As reported in Table 19: In Maryland, 26 percent of the students never used a calculator to work problems in class, while 47 pacent almost always did. Some of the students (18 parent) never used a calculator to work problems at home, compared to 35 percent who almost always used one. Less than half of the students (36 percent) never used a calculator to take quizzes or tests, while 22 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 1950 NAEP TRIAL STATE ASSESSMENT MarOand Northeast Nation How often do you use a calculator for the Porconlese aid Partalatta. Porceolage end end following tasks? Proficiency Prolicioney Proficiency Working problems in class Almost always 47 ( 1.4) 40 ( 4.0) 48 ( 1.5) 248 ( t5) 255 ( 3.9) 254 ( 1.6) Never 28 ( 1.7) 39 ( 8.0) 23 ( 1.9) 275 ( 2.0) 282 ( 2.2) 212 ( 1.4) Doing problems at home Almost always 3S ( 1.4) 30 ( 3.3) ( 1.3) ( 1A) 284 ( 5.8) ;.01 ( 1.8) Never 18 ( 1.0) 22 ( 2.5) 19 ( 0.9) 271 ( 2.2) 275 ( 2.3) 263 ( 1.6) Taking quizzes or tests Almost always 22 ( 1.0) 23 ( 3.3) 27 ( 1.4) 247 ( 2.0) 258 ( 5.8) 253 ( 2.4) Never $8 ( 1.8) 45 ( 5.1) 30 ( 2.0) 275 ( 1.5) 284 ( 2.1) 274 ( 1.3) dr 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. r3 THE 1990 NAEP TRIAL STATE ASSESSMENT 63 Maryland 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 question 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 Stat- 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 gyoups:, 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 1990 NAEP TRIAL STATE ASSESSMENT The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in Maryland were in the High group than were in the Other group. A smallex percentage of males than females were in the High group. In addition, 50 percent of White students, 38 percent of Black students, 37 percent of Hispanic students, and 58 percent of Asian students were in the High group. TABLE 20 Students' Knowledge of Using Cal.mlators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 10110 NAEP TRIAL STATE ASSESSMENT Maryland Northeast I- Nation "Calculator-use group Nigh Pertentapp Pwaintap Parana. and owl and PEW 'okay Meek lacy Preadiency 48 ( 1.2) 272 ( Le) 54 ( 1.2) 252 ( 4.7) 44 ( 2.5) 279 ( SA) 58 ( 2.5) 283 ( 2.0) 42 ( 1.3) 272 ( 1.8) 54 ( 1.3) 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 ± 2 standard errors of the estimate for the sampk. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 MaPyland SUMMAR Y 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, 30 percent of the students in Maryland had teachers who allowed calculators to be used for tests. About the same percentage of students in Maryland and in the nation had teachers who permitted unrestricted use of calculators (19 percent and 18 percent, respectively). In Maryland, most students or their families (98 percent) owned calculators; however, fewer students (51 percent) had teachers who explained the use of calculators to them. In Maryland, 26 percent of the students never used a calculator to work problems in class, while 47 percent almost always did. Some of the students (18 percent) never used a calculator to work problems at home, compared to 35 percent who almost always used one. Less than half of the students (36 percent) never used a calculator to take quizzes or tests, while 22 percent almost always did. 71 66 THE 1990 NAEP TRIAL Sl'ATE ASSESSMENT Maryland 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, poficymakers have reexamined existing methods of educating and certifying teachers.9 Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In Maryland, 59 percent of the students were being taught by mathematics teachers who reported having at kast a master's or education specialist's degree. This compares to 44 percent for students acioss the nation. About three-quarters of the students (79 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 (87 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). 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 TABLE 21 I Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 11190 NAEP TRIAL STATE ASSESSMENT Manotand Northeast Mien Percentage cif students when mathematics teachers reported having the Mowing degrees Bachelor's degree Master's or specialist's degree Doctorate or professional degree Percentage at students when methemadce teachers have the kerning twee at teaching certiOcatee lhat ars recognized by Maryland No regular certification Regular certification but less than the highest available Highest certification available (permanent or long-term) Percentage of students whose mithanuttics teachers have the followIng byes of teaching certificates lhat are recognized by Mandand Mathematics (middle school or secondary) Education (elementary or middle school) Other pineal. *mew 415: 14 I Eli a ( flonolaile Al 3 ( 17 ( 79 ( 17 ( 10 ( 3 ( 1.2 S.01 2.1 1.91 10 11.5 111 11 3Sf 3. 11 4 3.7 4 ( 211( 33 ( 114 42 ( 4 1.2 43 4.3 ( 2.2) 2.3) ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 9$ 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,. 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. 3 68 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland Teachers' responses to questions concemaing thek undergraduate and graduate fields of study (Table 22) show that: In Maryland, 47 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. Some of the eighth-grade public-school students in Maryland (19 percent) were taught mathematics by teachzrs 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 I Graduate Fields of Study PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Maryland Northeast Nation Whet was your undergraduate major? MattwmatIcs Education Other What was your graduate major? Mathematics Edwation Other or no graduate Wel study Perdeita. Percintige Pereentage 47 ( 3.4) ( 3.4) 14 ( 1.9) 44 ( 9.2) 34 ( 8.0) 22 ( 8.1) 43 ( 34) 35 ( 3.8) 22 ( 3.3) Percentage Parcentage Percentage 19 ( 24) 52 ( 3.3) 29 ( 2.15) 22 ( 9.7) 42 ( 8.2) 31 ( 44) 22 ( 34) 38 ( 3..5) 40 ( 3A) 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 Moyiand Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that In Maryland, 47 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. Relatively few of the students in Maryland (6 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 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS NAEP TRIAL STATE ASSESSMENT Maryland I. Northeast 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 Nal 1$ hotrs or more Percentage ParsOntage Pim:entails 25 7.0) 11 ( 2.1) 47 ( 3.2) 37 4.1) 51 ( 4.1) 47 ( 3.0) 31I IA) ( 3.8) The standard errors of the estimated StatistieS 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 Maryland 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." 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 Maryland, 59 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. About three-quarters of the students (79 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 Maryland, 47 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergxaduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in Maryland (19 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. I° Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Dilferences An International Assessment of Mathematics and Science (Princeton. NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). 1' Ina VS. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement NA EP's 1990 Assessment of the Nation and the Thal Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 71 Maryland In Maryland, 47 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 h A teachers who spent at least that much time on similar types of in-service training Relatively few of the students in Maryland (6 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 Maryland 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. e 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Matykind AMOUNT 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 Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1NO NAEP TRIAL STATE ASSESSMENT Marb4and Northeast Does your family have, or receive on a regular basis, any of the following items: more than 25 books, an encyclopedia, newspapers, magazines? Zwo to two typos Throe typos Fotr typos Parasols. Panddlego Parsurtage and and and Praildeney Prailicimoy Priaddow 17 ( 0.41) 13 ( 2.0) t' ( 1.0) 243 ( 1.1) 252 ( Si) 244 ( 2.0) 31 ( 0.9) 31 ( 2.7) 30 ( 1.0) 255 ( 13) 20 ( 23) 256 ( 1.7) 52 ( 12) 50 ( S.?) 41 ( 1.3) 270 ( 1.5) 275 ( 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 ± 2 standard errors of the estimate for the sample. The data for Maryland reveal that: Students in Maryland 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 '.esults for the nation, where students who had all four types of materials vhowed higher mathematics proficiency than did students who had zero to two types. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT A smaller percentage of Black and Hispanic students and about the same percentage of Asian students had all four types of these reading materials in their homes as did White students. A greater percentage of students attending schools in advantaged urban areas than in disadvantaged urban areas or areas classified as "other" and about the same percentage of students in schools in advantaged urbanaim as in extreme rural areas 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 NAEP TRIAL STATE ASSESSMENT Percents. and Proficiency Permits. end Prelicieney Percents. end Proficiency How much television do you usually watch each day? Otis hour or less 11 ( 04) 12 ( 1.3) 12 ( 04) 277 ( 3.5) 277 ( 4.4) NG ( 22) Two hours 20 ( 0.9) 21 ( 2.3) 21 ( 0.9) 272 ( 2.2) 27$ ( 3.1) HS ( 1.8) Three hours 21 ( 0.7) 23 ( 11) 22 ( 0.3) 205 ( 1.7) 271 ( 3.5) 205 ( 1.7) Four to See hours 30 ( 1.0) 23 ( 2.8) 23 ( 1.1) 257 ( 1.5) 2011( 4.1) 280 ( 1.7) Slx hours or more 19 ( 0.9) 18 ( 3.3) 18 ( 1.0) 240 ( 1.4) 254 ( 5.5)1 245 ( 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. 80 THE 1990 NAEP TRIAL STATE ASSESSMENT 75 Maryland From Table 25 and Table A25 in the Data Appendix: In Maryland, 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 Maryland (11 percent) watched one hour or less of television each day; 19 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, 12 percent of White students, 34 percent of Black students, 22 percent of Hispanic students, and 8 percent of Asian students watched six hours or more of television each day. In comparison, 13 percent of White students, 5 percent of Black students, 8 percent of Hispanic students, and 23 percent of Asian students 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 Maryland, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in Maryland (37 percent) did not miss any school days in the month prior to the assessment, while 27 percent rnissed three days or mow. In addition, 26 percent of White students, 30 percent of Black students, 30 percent of Hispanic students, and 13 percent of Asian students missed three or more days of school. 76 THE 1990 NAEP TRiAL STATE ASSESSMENT Maryland Similarly, 19 pacent of students attending schools in advantaged urban areas, 36 percent in schools in disadvantaged urban areas, 24 percent in schools in extreme rural areas, and 27 percent in schools in areas classified as "otha" missed three or more days of school. TABLE 26 I Students' Reports on the Number of Days of i School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1SSO MEP TRIAL STA i ,r, ,1= .. , CSSUENT anolmik. How many days of school did you miss last month? Parawilip an* Prolkisew 37 ( 1.1) 205 ( 1.7) Poromerse end Prifkimoi 43 ( 22) 273 ( 3.6) Parma. Prallfagy 411( 1.1) 205 ( 12) Nona Ono or two days 36 f 04) 37(3.1 ) 32 ( 0.9) 264 ( 1.5) 271 ( 22) 2115 ( 12) Throe days Of Mr. 27 ( 1.0) 21 ( 3.0) 23 ( 1.1) 250 ( 1.5) 255 ( 5.5) 250 ( 12) 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. 62 THE 1990 NAEP TRIAL STATE ASSESSMENT 77 Maryland DENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not only to master essential skills and concepts but also to develop confidence in their mathematical abilities and to value mathematics as a discipline." Students were askeo if they ?greed 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 exper:ted relevance to future work and life requirements: Almost all people use mathematics in their lobs; 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 problems. A student "7erception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly agee" were given a value of I (indicating very positive attitudes about the subject), those who responded "agree' were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a lalue of 3. Each student's responses were averaged over the five statements. The students were then assipped a perception index according to whether they tended to strongly agne with the statements (an index of 1), tended to agyee with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statements (an index of 3). Table 27 provides 'he data for the students' attitudes toward mathematics as defined by their perception inde%. The following results were observed for Maryland: Average mathematics proficiency was lowest for students who were in the "undecided, disagme, strongly disagree" category. A..,ut onequarter of the students (30 percent) were in the "strongly agree" category (perception index of I) This compares to 27 percent across the nation. Some of the students in Maryland (20 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagyee" category (perception index of 3). 1 2 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). E3 78 THE 1990 NAEP TRIAL STATE ASSESSMENT ') Maryland TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 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. I Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiemy. 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 incremed value placed on educational achievement, among other desirable outcomes. The data related to out-of-school factors show that: Students in Maryland who had four types of :eading materials (an encyclopedia, newspapers, magazines, and more thaa 25 books) at home showed higher mathematics proficiency than did studtmts with zero to two types of materials. This is similar to the resalts for tli. nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT 79 Maryland Some of the eighth-grade public-school students in Maryland (11 percent) watched one hour or less of television each day; 19 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 Maryland (37 percent) did not miss any school days in the month prior to the assessment, while 27 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 (30 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was lowest for students who were in the "undecided, disabree, strongly disagree" category. rLJU 80 THE 1990 NAEP TRIAL STATE SSESSMENT Mwy land 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 were 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 Educaii'mal Testing Service. The development of the Trial State Assessment Program benefitted 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 program. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incorwlete 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 BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT 81 Maryland The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete eacn 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 consety as process, as described in the introduction to this report.' 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 I). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once 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 gave various responses to each cognitive and background question. Item response theory (1RT) 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. 1RT provides a common scale 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. N anon& Assessment of Educational Progress, Minhematics ()Neal s 1990 Assessment (Princeton, NJ: Educational Testmg Service. 1988). tr7 82 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland 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. Measurement 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, and comri1d^ir7ate 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 abfe 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 This content area focuses on data representation and analysts across all 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 tor gathering data, the visual exploration ot data, and the development and evaluation of arguments based on data analysis. Algebra and Functions 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. 88 THE I49O NAEP TRIAL STATE ASSESSMENT 83 Maryland FIGURE A2 I Mathematical Abilities The following three categories of mathematical abilities are not to be COnstruec' 3 hierarchical. For example, problem solving involves interactions between conceptual knowledge an. iirocedural 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 they 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 definitions: 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 involvirig concepts in mathematical settings. Such understandings are essential to performing procedureS in a Meaningful way and applying them in problem-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 inherent in problem settings. Procedural knowledge includes the various ntimerical 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, arid perform noncomputational Skills such as rounding and ordering. [problem Solving .1 In problem solving, students are required to use their reasoning and analytic abilities len they encounter new situations. Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, rlata, models, and relevant mathematics; generate, extend, and modify procedures; use reasoning e., spatial, inductive, deductive, statistical, and proportional); and judge the reasonableness and correctness of solutions. t,14 84 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland A scale ranging from 0 to 500 was created to report performance for each content arca. Each content-area scak was based on the distribution of student performance 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 levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection Li 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 define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics items .fr im the 1990 assessment that discriminated well between adjacent levels. The criteria fo 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. fl 0 THE 199U NAEP TRIAL STATE ASSESSMENT 85 Maryland 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. Each of 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.' 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 educaional 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 the use of various instructional approaches. Because of the nature of the sampling for the Trial State Assessment, the responses to the mathematics teacher questionnaire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 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 twelfth-grade national assessment. (11 86 THE 1990 NAEP TRIAL STATE ASSESSMENT FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 A-7 Coif 0 Tomb GeV 0 liatrWr lab 7. lathe ltai Wee Who those all the are dm eel thew &Hawn loads et bath ao shoos there. If the I& Nth bas with dee hued of bath thaw& whoa Iwo wt0 bath the fewest belle la Of 410 The boo we* the lanais bah 41 The boa mg the getit belle 71te bee iosir the nab& bath 41D Yam co' t fah. EXAMPLE 2 DOM OF MU PIO= AT FARAWAY MAMS nois Wossi Caps dile Wink Oft,* Loom Otepheit O. How arty bathe a *awe were picked ow Tbscadayi tro 51 CD 60 40 70 CD 10 CD 90 410 1 datit know, Grade 4 Overall Percentage Correct: 73% Percentage Correct for Anchor Levels: 2§11 222 3§2 65 91 100 Grade 4 Overall Percentage Percentage Correct 21:2 zfa 75 Ql fl2 Grade Overall Percentage Percentage Correct ZO2 ZCIQ 76 87 Correv-, for Anct;,, RQ 100 Correct: 89% for Anchor Levels: 222 96 100 Mwyland FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) ILevel 250: Simple Multiplicative Reasoning and Two-Step Problem Solving EXAMPLE 1 7. What is the value of a + 5 when a ai 3 t Answer. EXAMPLE 2 KAM CUM SLIWZY MU= Grad. 8 Overall Percentage Cermet 75% Percentage Correct for Anchor Levels: 222 224 MI 224 28 59 95 se Geo el 1 Kat hasseis' Grade $ NOW Percentage Correct 73% Percentage Correct for Ancbor Levels: 11 SO Tags 222 attil 242 2314 Tee uWe gm shows the Mob We =icy ei kW coke. Ca sit rank 21 as 92 92 lebew, loge a rink srsok so Women she deem io the sablt. Label each pen el dee cede ipeph wish she Nam be* Wm. Ded you use she cliculeset ea this geese kat 0 Wm ON. EXAMPLE 3 6. Kackkeo u peckete baocbstis law boxes. Each box holds basebelh. Sbs hes 24 balk WIluclo istimbrz uncatee will help ha Ifni oxe how nucy holm she will sued; cp 24 6 - oh 24 + 6 41, 24 + 6 0 co 24 Id 6 0 CD clon"; know. Grade 5 Overall Percentage Correct 77% Percentage Coned for Anchor Levels: 222 224 22R 37 71 95 100 88 TIM 1990 NAM' TRIAL &TAM ASSESSMENT Masyland FIGURE A3 I 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 1 Which el the Wow* shows the wok fiiinme4 tie above muses ever she hrher a) EXAMPLE 2 le she RAJ owe that e dem is *NW. a of !I kes leaf Se wyeesewsed by s eceie sesisl 3 1.neku hen. U the ewe seek is wok bone IS tea ligh %void be rtewtoesued hi model hew way bass Med CSaa 4 IP 7 e V ress wee she setchtbsist est Ws we/0W CI Yee Cs No THE 1990 NA131$ TRIAL RATE AssEssiENT Grade 8 Overall Percentage Correct 80% Percentage Correct for Anchor Levels: 221 Zig RI Mg 33 49 n 90 Grade 12 Overall Percentage Correct 75% Percentage Correct tor Anchor Levels: ZOQ 48 79 05 Grade 8 Overall Percentage Correct 59% Percentage Correct tor Anchor Levels: 222 222 ZIQ af2 17 48 88 99 BEST COPY AVAILABLE 89 Maryland FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability EXAMPLE 'I 110, (141 asthma 16-17 mkt us the isi1iaws4 patios at ase.hautss 0 2 16. III doh rori of gloaturcs is studious& bow sass am k Ike EXAMPLE 2 17. 1.1p1ala low you found vuut ialwa theitiOa /6, Manx Grade 8 Overall Percentage Correct 34% Percentage Correct for Anchor Levels: 224 214 222 2:20 13 19 53 88 Grade 12 Overall Percentage Correct: 49% Percentage Correct for Anchor Levels: 222 214 222 212 22 48 90 Grade 8 Overall Percentage Correct: 15% Percentage Correct for Anchor Levels: 224 2/2 222 212 1 4 28 74 Grade 12 Overall Parcentage Correct 27% Percontag Correct for Anchor Levels: 22/ 2§2 MQ 3 22 74 5 90 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland SCHOOL CHARAC1ERIS11CS 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 reLvived 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 scale-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 NAEP) arc subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like almost all estimates based on assessment measures, N AEP's total group and subgroup proficiency estimates are subject to a second source of uno-n-tainty, 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 the assessment questions -- or the entire set of questions -- somewhat different estimates of total gr-oup and subgroup proficiency might have been obtained. 11us, a second source of uncertainty arises because each student was administered a subset of the total pool of questions. fl9 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 Mapy land ln 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 ef 'mates 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 background 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 of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inferences about the population. The use of confidence Litervals, based on the standard errors, provides a way to make inferences about the populati,.m means and proportions in a manner that reflects the uncertainty associated with th, sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence interval for the corresponding population qua.ntny. This means that with approximately 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 samph; 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 Mterval for the population quantity would he 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 he constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 lercent). For extreme percentages, confidence mtervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals arc quite complicated. I 92 THE 1990 NAEP TRIAL. STATE ASSESSMENT Mao land 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 students' mathematics teachers to questions in the mathematic3 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 ptoficiency than students who reported spending IS minutes or less? To answer the question posed above, one begins by comparing 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 homewoik is higher, 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 average proficiency of the groups in the sample. Remember that the intent is to make a statemelit about the tntire population, not about the particular sample that was assessed. The data from the sample are used to make inferences 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 gioups 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 manner in which the standard error for an individual gmup mean or proportion is used, the standard error of the difference can he used to help :-.4etermine 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. ci THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Maryland 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 particular state's public sibools. 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 4 2.0 Male 255 2.1 The difference betweeil the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is N12.02 + 2.12 = 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 draw the conclusions that are presented. If a statement appears in the repon indicating that a particular group had 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 included 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 significant 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 c)f thi, difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSM:AT Maryland 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 significance is being performed. However, in each chapter of this report, many different 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 enor is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount 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 errors -- should be interpreted cautiously. Further details concerning procedures for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for goups defined 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 Urban, 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 sufficienly high to permit accurate estimation of proficiency and/or background variable results. As a result, data are not provided for the subgroups with very small sample sizes. 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. 1.00 TfiE 1990 NAEP TRIAL STATE ASSESSM ENT 95 Maryland 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 population in the state or tenitory, divided by the standard deviation of the proficiency in the total population. If the true difference between subgroup and totai group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to cletxt such a difference with a probability of .8. Further details about the prxedure for determining minimum sample size appear in the Trial State Assessment technical report. Desci ling 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 degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in questio, . 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. Percntage Description of Text in Report I p = 0 None 0 < p ... 10 Relatively few 10 < p .s. 20 Some 20 < p .s. 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 79 About three-quarters 79 < p ....s. 89 Many 89 < p < 100 Almost all p = 100 All in 96 THE 1990 NAEP TRIAL STATE ASSESSMENT c*,; Maryland 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 corresponding data for each level of the four reporting subpopulations race/ethnicity, type of community, parents' education level, and gender. 1n2 THE 1990 NAEP TRIAL STATE ASSESSMENT 97 Maryland TABLE A5 I Students' Reports on the Mathematics Class 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP 'TRIAL Eighih-grade STATE ASSESSMENT blaihmatics Pre-algebra , .. TOTA1. and 'ffelhollaney lid friagiargt State ti 24 22 ( 23t 2$1 ( 291 Nation 92 2.1 10 ( I 15 .1.2 lescramem 291 1.4 ( 2.4 200 ( 2.4) WM. State 34 3.3) 32 ( 1.6) 30 ( 1.7) 240 ( 13) 272 ( 1.2) 290 ( 1.7) Nation 50 ( 2.5) 24) 17 ( 13) 25a ( 1.8) 271 (2.2) 300 ( 23) Slack State 44 ( 3.5) 33 ( 21 ( 23) 222 ( 2.0) 240 ( 2.1 205 ( 2.5) Nation 72 ( 4.7) ( 3.0 9 ( 2.2) 232 ( 3.4) 241 ( 8.4) *If ( Hispanic State 2211531 1041 31 ( 3.9) t ) 11 ( IN* 23) 010111 Nation TS ( 4.4) 13 3.9) 6 ( 1 3) 240 ( 2.4) 1114. 441.1 44* ( 4+1 Asian State 27 ( 33) ( *In 54 ( ( 4.7) .41 Nation 32 ( OS) ( *en 21 ( 6.5) ( .11 41 ( ( 7.4) .41 TYPE OF COMMUNITY Advantaged urban Staie 22 ( 33) 35 ( 3.4) 37 ( 3.5) 245 6.5) 267 ( 4.1)1 301 ( 4.0) Nation 56 269 ( 04) ( 2.5)1 22 ( 7.9) 04* 21 ( I. ( 4.4) 4.) Disadvantaged urban State 49 6.9) 20 ( 11.4) 20 ( 3.0) 221 3.3)1 235 ( 5.2)1 261 ( 6.3)1 Nation 65 ( 6.0) 14 ( 3.3) 240 ( 4.0)1 ( INN) 267 ( 4.2)1 Extreme rural State 45 ( 5.0) a.** ( .) 26 ( 4.9) ( *01 25 ( 2.2) Nation 74 ( 4.5) 14 ( 5.0) ( 2.2) 249 ( 3.1)1 ( Other State 30 ( 3.2) 33 ( 2.5) 26 ( 2.2) 23a ( ts) 263 ( 2.5) 293 ( 3.2) Nation ( 2.2) 20 ( 2.1) ( 1.4) 251 ( 2.0) 272 ( 2.6) 294 ( 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 interest, the value for the entire population is within 2 standard errors of the estimate fbr 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 sariple 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 C 3 98 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE AS I Students' Reports on the Mathematics Class (continued) i They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IIMO NAEP TRIAL STATE AMMO= I P9Sb1 Algebra /2/is State Nation fmacimmensat NS non-radiate State Nation KS graduate State Nation Some colkno State Nation CoNsge "'JAW. State Nation M. State Nation Fonda State Nation fria000141 OS ( 234 ( 41.411 77( 3.7 241 ( 2.1) 51 ( 2.9) 232 ( 1.5) 70( 2.6) 249 ( 1.9) 35 ( 3.1) 244 ( 2.8) 00 ( 3.1) 257 ( 2.1) 26 ( IX" 243 ( 53 259 ( 1.5) 40 ( 2.1) 239 ( 1.6) 63 ( 2.1) 252 ( 1.6) 35 ( 24) 235 ( 1.7) 61 ( 2.6) 251 ( 1.5) am. Inelkimmicv ( 14) 221 ( 13) 19 ( 1.9) 272 24) CM Pallokief 27 ( 13) 201 ( 1.7) 15 ( 1.2) 229 ( 2.4) 2$ ( 2.9) 15 2.9) ".. "434 131 *a* ***) 3 } 1.1; 29 ( 2.3) IS ( 1.6) 255 ( 2.6) 211 ( 32) it ( 3.4) ( 1.1) 263 ( 3.5) 277 5.2) 35 ( 2.5) ( IA) 262 ( 2.1) 282 ( 2.7) 21 ( 2.9) 15 ( 1.9) 270 ( 2.8) 295 ( 3.2) 34 ( 1.9) 96 ( 2.1) 200 ( 1.8) 300 ( 1.9) 21 ( 2.3) 24 ( 1.7) 278 ( 2.1) 303 ( 2.3) 32 ( 1.7) 24 ( 1.4) 262 ( 1.9) 294 ( 2.2) 18 ( 1.8) 16 ( 12) 275 ( 2.9) 299 ( 2.5) 32 ( 1.7) 29 ( 1.8) 261 ( 2.0) 28a ( 1.6) 20 ( 2.3) 15 ( 1.7) 200 ( 3.0) 293 ( 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. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ** Gample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Maryland TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Moe 15 Minutes 30 Minutes 46 Minu tes An HOW or Men TOTAL State Nation Pareselays pipra~ fartonlaia ivanioNNIs illemago and SPA IIM MI IN Povadimay PfeadMilif PNIMOIMCV Ikalleanat firf*iersi 3 ( 1.1) NO ( 23) 4 2$) 4 tt 4 1 237 ( 7.13, 232( 2.1) 220 &I V3 1 1 0.3) 43 ( 4.2) 43 HI 10 1 41 0.2 v.. 1 25$ ( 23) Me 272 VS 5.1 RAMETHNICITY Mtn. State 2 ( 0.7) 42 2.1) 44 2.0) 1.3) is? ( ( ') 261 1.6) 279 23) 302 4.2) Nation I ( 0.3) 30 4.5) 43 s.v, 11 2.4) 41 0.11s "4 ( 444) 293 22) 270 ( 5.7) 277 73)4 279 33 Mack State I ( 2.4) 32 ( 4.0) 30 ( 3.8) 7 ( 2.0) 229 ( 23) 241 ( 54) 444) Nation 1 ( 0.7) 55 ( 7.6) 40 ( 07) 3 ( 1.2) 2 ( 0.4) 444 ( 4") 232 ( 3.1) 2411 ( 53) ) ( Hispanic State 3 ( 1.5) 41 ( 52) 4$ ( 4.7) 5 ( 1.7) 3 ( 14) 235 ( 4.9) 242 ( 3.8) *** V") ( 441 Nation 14.1 48 ( 7.8) 34 ( 5.6) 13 ( 2.9) 2.1) ( *4) 245 ( 3.0)1 251 ( 4.2)1 ( ( Asian State 1 ( 1.3) 27 ( 8.8) 47 ( 7.1) 15( 4.0) 9 ( 3.5) ( 444) Nation 0 ( 0.0) 29 ( 7.8) 37 ( 6.6) 10 ( 34) 24 (10.2) 4" ( 44.4) ( 444) 444 ( 44.0 ) 444 ( 444) ( TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged trban State NatiOn Extreme nral State Nation Other State Nation 4" ( 1 ( 0.9) .44 .4) 5 ( 2.5) 444 ( .4) 0 ( 0.0) 444 ( "4) 0 ( 0.0) "4 ( 4") 0 ( 0.0) 44 .4) 3 ( 2.5) 4" ( 444) ( 0.4) 4.) 34 ( 5.8) 282 ( 8.9)1 01 (11.3) 273 ( 3,1)1 24 ( 5.3) 219 ( 3.7)1 41 (12.8) 238 ( 2.1)1 83 (20.4) 444 .44) 08 (14.9) 253 ( 5.4)1 42 ( 5.7) 253 ( 3.1) 37 ( 4.3) 256 ( 3.1) 52 ( 8.2) 265 ( 44)1 32 (OA) .4) 50 ( 0.0) 235 ( 44)1 38 ( 9.4) 253 ( 9.0)1 *!: 129414 14 (10.9) 0*4(44*) 42 ( 4.0) 205 ( 2.8) 49 ( 5.1) 285 ( 25) 10 ( 2.6) 296 (11.4)1 5 ( 3.4) 0411* 441) 6 ( 3.1) 4 ( 1.8) 444 ( 0 ( 0.0) 444) a ( 2.1) *44(44.4) 12 I 5-9) 044 ( .4) 0 0.0) 844 .4) ( 5.0) ( .4) ( 1.111) 295 ( 64)1 10 ( 2.4) 278 ( 5.0)1 10 ( 8.2) .44 ( 444) 0 ( 0.0) ( 4") 10 ( 7.3) *44(4*. ) ( 3.0) 4 ( 1.1) 282 (11.8)4 The standard errors of the estimated statistics appear in pa:entheses. 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 ti2e is insufficient to permit a reliable estimate (fewer than 62 students). 1r5 100 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE A6 (continued) Teachers' Reports on the Amount of Time Students Spent on Mathematics How work Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT I None 15 Minutes 30 Mimeos 45 Minutes An How or More TOTAL itavoodana and firalidanny 3 ( 1.1) 227 ( 7.1)4 1 ( 0.3) illowoodags and Pftliolancy 30 ( 2.3) 252 ( 2.1) 43 ( 4.2) 256 ( 2.3) Ilevantega and *Odom 46(2.5) 265 ( 2-2) 43 ( 4.3) 200 ( 2.5) State Nation EDUCATION ../MTS' RS non-graduate State 2 ( 1.5) 50 ( 5.8) 44 ( 5.3) grerilt imrs) 231 3.8) 4.1) Nation ( 0.8) 49 240 8.3) ( 2.8) 40 245 8.1) 3.7) NS graduate State 5 ( 1.4) 44 ( 4.1) 41 ( 3.41) ( *En 242 ( 2.6) 249 ( 2.7) Nation (. 0.5) 43 ( 5.2) 249 ( 3.1) 44 ( 258 ( 58) 2.7) Some college State 3 ( 1.4) 39 ( 3.5) 45 ( 3.6) ( ***) 259 ( 2.7) 264 ( 34) Nation ( 0.9) 44 ( 5.4) 43 ( 5.6) coøgi cirlduats 4060 hHI. ) 265 ( 2.6) 270 ( 3.6) State 2 ( 1.1) 35 ( 2.7) 48 ( 2.6) ( 211 ( 2.9) 270 ( 2.8) Nation 0 ( 0.3) 40 ( 4.7) 44 ( 4.1) ( "41 265 ( 25) 277 ( 3.0) GENDER M. State 3 ( 1.1) 43 ( 3.1) 43 ( 2.7) ( ***) 252 ( 23) 268 ( 2.1) Nation ( 0.3) 44 ( 4.4) 43 ( 4.3) ( "41 257 ( 2.9) 268 ( 2.9) Female State 3 ( 1.2) 35 3.0) 49 ( 2.7) ( 251 ( 2.4) 263 ( 2.7) Nation 1 ( 0.4) 41 ( 4,4) 43 ( 4.7) 255 ( 23) 264 ( 2.8) Peroordaip Paranalaga and and Prodolancy PralidaacY 2 ( 1.0) ( *en 1 .7) ***) 5 ( 1.3) 11+1Ir ) 9 ( 3.1) MI* ( 441 3 ( 1.9) ( *toil ( 2.1) 10 ( 302 ( ( 287 ( 7 ( 290 ( 9 ( 273 ( 8 ( 267 ( t1 ( 272 ( 4 1.3) 273 .10 4 0.9) 271 5.1)1 2 ( 1.1) ( 4 (1.3) 5 ( 1.8) ORM ( 3 ( 1.0) ( vow) 5 ( 1.7) 4 ( 1.0) 1.3) ***) 1.3) *ft ( 16) 52) 4 ( 4.0," 2.3) 5 ( 6.1)1 1.1) 4 ( 8.4) *44. 1.9) 5 ( 7.3)1 279 ( 1.5) 5 ( 4.9) ipe ( 2.0) 4 ( 5.7)1 ( 111EMIIMM=0MIMI11110 The standard errors of the estimated statistics appr:ar in parentheses. It can be said with about 95 percent certainty that, for etch population of interest, the vii'Lie for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with Laution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficienq. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1r6 THE 1990 NAEP TRIAL STATE ASSESSMENT 101 TABLE A7 I Students' Reports ou the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1160 NW TRIAL STATE ASSESSINENT Nano 15 UMW* XI Minutes U thuds* An Hour ar Sono TOTAL State Nation MgraMMIM State Nation Stack State Nation Hispanic State Nation Asian State Nation mg OF COMMUNITv Advsataged urban State Nation Disadvantaged State Nation Extreme rural State Nxtion Other State Nation 0.11 4 it 251 ( 4.1 ( 14 251 ( 3A) 4 1.11 7 1.51 ( 1.8) 12 ( 1.8) vs* I .441 1 1.0) .fro. 4 2.0) oh* ( ran 2 ( 01) $ ( 2.5) 5 ( 25) 12 ( 3.7) to* ( ein $ ( 1.9) .90.) ( 2.3) ( .") 4 ( 0.7) 4 441 ( 1.0) 250 ( 3.11) 1.1 :3: 1.2 1 16i 0. .4 12 1611.0 263 1.6 e ( I 42 ( 270 ( 1 33( 24 370 (1.8) 31(4J) ne (2.1) NI 2.5) 241 3.0) 97 ( 3.1) 240 ( 3.5) 27 ( 3.0) 245 ( 25) 15 ( 33) 404 ( 441 22 ( 4.8) *4* ( 444) 35 270 2.2 22 1 270 2.1 241 2 ID 23 237 23 30 ( 26) 290 ( 42) 30 ( 2.6) 248 ( 3.4) 45 ( 5.5) *** 444) 31 ( 5.0) 444 441 11 ( 222 15 277 13 ( 240 ( 1$ ( 240 ( 17 241 ( 22 ( *44 ( 18 ( 444 200 12 ; sal 0.9 2.4 0.91 22 1.3) ( 274 ( 11 2/1 ( ( 21) t35 23) 16 3.0) 232 2.01 6 ( IMO ( 2.1) 14 ( 4.3) 26) 444) 17 3.9) 441 25 *4.4 34 ( 2.9) 41 ( 2.4) 15 ( 1.7) 275 ( 3.7) 278 ( 4.6) 201 ( 4.9) 41 (124) 31 ( OA) 12 ( 3$) 278 ( 3.0)1 200 ( 45)1 "" ( ) 37 ( 3.0) 35 ( 3.0) 12 ( 2.2) 231 ( 3.6)1 235 ( 5.2)1 ( ".) 24 ( $.3) 31 ( 3.0) 20 ( 1.9) 253 ( 4.9)1 247 ( 4.7)1 250 ( 4.8)1 3$ ( OA) 34 ( IA) 10 ( 3.7) .44 ( .....) ) e.b ( ) 36 ( 4.6) 3i ( 2.9) 16 ( 3.8) 200 ( 3.5)1 255 ( 5.1)1 I** ( "e) 42 ( 1.8) 34 ( 1.4) 12 ( 12) 200 ( 2.3) 213 ( 3.3) 205 ( 3.4) 30 ( 14) $2 ( 1.3) 15( 1.1) 263 ( 2.3) 264 ( 2.3) 267 ( 2.1) 1.1 3.1 ( 1.4) 7 3.4) 12 1.2) 44* 441 14 2.2) *a* 10 ( 25) ( 2.7) «F. ( 6 ( 0.9) 202 ( 42) 13 ( 1.1) 258 ( 3.5) .m The standard errors of the estimated si4istics 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). 1r7 102 THE 1990 NAEP TRIAL STATE ASSESSMENT Matyland TABLE A7 I Students' Reports on the Amount of Time They (c(Intinued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11=1. 11110 NAEP TRIAL STATE ASSESSMENT Nene 16 Minutes 30 Minutes 46 Minutes Art Hour or taro TOTAL State Nation PARrinvjEstsigat NS nen-gratkiata State Nation HI graduate State Nation Sanwa cottage State Nation CeSege graduate State Nation GENDER M. State Nation Female State Nation $4661112910 0340.111110, iiid lid WiUIuii liV01011MSV 0 2.3) 17 ( gm.) 0 I 1.21 10 ( 1.7) 246 ( 4.2) ea* 41 3 011) 9 ( 1.2) 3 ( 0.4) 4144. 4141 7 ( 0.9) 265 ( 3.6) 5 ( 02) 242 ( 3,8) 11 ( 1.1) 3 ( 0.6) ( 0.9) 246 ( 4.1) 24.1 2354/ 4 240 ( 4.0) 44 ( 1.9) 247 ( 2.0) 3$ 2.2) 259 ( 32) 42 ( 24) 264 ( 2.3) 30 ( 2.7) 200 ( 3.0) 33 ( 1.7) 273 ( 2.1) 31 ( 34) 275 ( 2.0) 42 ( 14) 26) ( 16) 34 ( 2.4) 264 ( 2.4) 35 ( 1.4) 257 ( 1.8) 28 ( 2.0) 263 ( 1.5) 29 ( 2.6) $4 44 ( 2.6) 31 ( 2.0) 20 ( 2.5) 31 ( 1.9) 254 ( 2.4) 35 f 2.5) 213 ( 2.9) 33 ( 2.1) 220 ( 2.6) 39 ( 1.3) 275 ( 2.4) 31 ( 2.0) 275 ( 2.5) 33 ( 1,5) 205 ( 23) 29 ( 1.3) 266 ( 2.4) 39 ( 1.3) 262 ( 2.0) 35 ( 1.7) 260 ( 2.0) .1 I :141) 12 2.2) ***) 15 1.4) 24 4.) 10 1.0 220 2.9) 12 ( 13) Ho) 14 ( 1,8) 274 ( 15) 15 ( 1.0) 279 ( 3.1) 10 ( 12) 271 3.2) 12 ( 0.9) 264 ( 3$) 1$ ( 1.2) 205 ( 3.0) 13 ( 1.1) 270 ( 3.4) 17 ( 1.0) 267 ( 2.4) ( 0.7) 259 ( 4.9) 11 ( 14) 2211 ( 4.1) 261 (4.8) 13 1.3) $ 0.9) 258 ( 3.3) 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. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 113 THE 1940 NAEP TRIAL STATE ASSESSMENT 103 TABLE AS I Teachers' Reports on the Emphasis Given To i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY and 11188 NAEP TRIAL Operations ifeastreassnt Geometry STATE ASSESSMENT Heavy Emphasis Utile or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation ANEMIC-la State Nation Sad( State Nation Hbpanie State Nation Aslan State Natio(' TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged State Nation Extreme rural State Nation Ottw State Nation Possidepo Favinitne Pare400.4 Pircomik. 046111$0.00 end one an0 Proisiony riveciersay Pra 041401v restakaxw Miaow 294:1 230 ( 15 267 3.4 49 3.3 15 2.1 2.3 32 ( 25) 261 ( 1.5) 48 ( 3.7) 287 ( 22) 43 ( 4.11) 233 ( 2.11) 54 ( 7.9) 243 ( 43) 42 ( 4.9) 230 ( 3.1) 47 ( el) 246 ( 4.6) 17 ( 4.0) 32 ( 93) Is. ( 441 21 ( 2.8) 258 ( 3.1) 28 (13.0) .4* ( ***) 51 ( 9.8) 228 ( 3.0)3 48 (12.1) 255 ( 3.3)4 41 0.7) 444, 53 (12.4) 257 ( 7.1y 97 ( 4.0) 252 ( 3.1) 52 ( 4.1) 260 ( 2.3) Off 3.0 17 3.0 250 ( 19 ( 2.5) 257 ( 33) 14 ( SA) 259 ( 6.9)1 27 214 4.6 25 7.4 223 ( asp 27 $4) *11 141 23 ( 4.1) ( V 2711 2721 40 ( 2111103 27/ ; 31 ( 248 ( 23 ( 233 23 ( 41* ( 34 ( 235 ( 3.1 4.0 2.2) 416.7i 4.3; 4.2) 4.7) 5.7) 4.1)1 4.3) 53) 44)4 254 2.1 26 3.8 203 3.2) 24 ( SA) 244 4421 216 13 19 ( 3.2) 232 ( 4.2) 33 ( 7.9) 242 ( 5.6$ 21 4.1) .$4 orte) 27 ( 6.3) .11(m) 45 ( vfro. 27 ( 42 ( 301 ( 16 (( 15 9 ( ** 18 ( VIka 6 ( * ( 20 290 ( 16 ( 266 ( 0.7) 5.2) 4.2) 4.6)i 4.2) *41 34) *MI ) 4.0) «Hi) 4.1) 1+1 3.8) *41 2.4) 3-3) 2.7) 3.6) 10 *** 23 *** 12 246 9 K. 40 2311 238 41 44.6 20 251 16 253 ( 3.4) *in ( 5.8) ( *a) ( 2.7) ( 5.3p ( 7.0) .44) (11.3) 11a4 ( imp (11.5) *NI 40) ( 3.4) ( e.cv ( 3.9) ( 7.1$ SS 44 IN* 53 289 40 .0* 22 ( 245 ( 21 ( ( 23 ( *14(0*1 32 (11.7) 2455 ( 34 ( 2110 ( 34 ( 270 ( ( 6.4) ( 3.9) ( 4.9) 3.7) 8.5) ( *fr.) 8.2) 8.3)4 6.5) 444) ftly 44) 4.4) 5.3) 4.6) 12 34 17 403 38 267 22 224 33 244 39 9 *** 20 200 26 283 ( 3.6) ( 9.2) ( 441 ( 4.1) ( 5.4$ ( 9.4) ( toy ( 7.3) ( 5.1$ (11.6) ( 3.2p (10.5) *44) ( 0.1) ( 4.3) ( 4.3)4 ( 4.6) ( 31) 1111~06114 Praktimay IP 2.71 284 &4) 21 3.3 310 ( 2.2 26 ( 2.6) 2411 2.8) 273 (5.8) 22 34) 34 ( 3.3) 235 ( 3.1) 24 ( 7.3) 239 ( 4.7$ 26 ( 4.8) elm, *el 16 ( 5.5) 14 ( 6.5) *gm) 41 ( 5.3) 260 ( 5.0y 13 ( 3.2) 4,44, ***) 26 ( 5.4) 234 1 6.1)1 27 (10.2) *44 ( 16 ( 7.9) ( 5.7) 263( 5.1) 05 *on 27 ( 3.4) 24 ( 4.3) 2 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percen' 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). 104 11 9 THE 1990 NAEP TRIAL STATE ASSESSMENT Metyland TABLE A8 I Teachers' Reports on the Emphasis Given to (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAN TRIAL STATE ASSESSMENT Numbers and Operations Messoroment Geometry Hoosivy Emphasis I Uttie or No Emphasis Heavy I Emphasis Me or No Emphasis Heavy Emphasis Little or No Emphasis State Nation maitnimfinim IM nen-graduate State Nation 1M graduate State Nation Same *Mega State Nation college graduate State Nation 2CLER lisle State Nation Female State Nation l*/**101r Prneetim .reZsuiv 4. 210 40 $02 PeumWelle Pir2010202 ail and 11Wielmoy MirelManov 04 2.1 *1 sr 2.7 12 292 227 2711 2.1 wi 3.2 4.1 17 39 26 31 21 3.3 14 297 344 910 272 210 32 IMP 5.4 40 81/44 14 ( 3.1 24 ( 33) 29 4.2) 24 ( 5.3) 2.7) 22 " . , ,... , 4., ...., ( ...) ... ...) 7 1 2.11 .11 .634 2 v./ .r. 1 v./ 2, tii 231 SA 41 25 27 1 23) )241 LI 25( 3.1) 241 2.3 202 $.5 2241 4,2 242 ( 3.2) IRS 4.1 11 2.$ 17 $S 3211 ti 2? i 4.5) 34 ( 5.1) 250 2.9 "'a ( ***) 251 ( 2.1 25S 4.7 225 ( 4.2) 246 ( 4314 40 ( 22 ( 3.0) 24 34 ( 3.0) 24 ( 2.2 33 247 ( 4.0) 2441 1,0 1? ( SS) 274 ( 4.0) 252 ( U II 2/771 II 47 4.4 12 2.7 119 ( 54) 27 1 5.0 23 4.1) 205 23) 294 ( 4.9 ". ( "e) 279 ( 4.5) 222 ( 4.8 270 4.7) 27 ( 24) 34 ( 3.1) It ( 2.3) 46 ( 3.1) 21 ( 2.0) 16 ( 2.7) 254 ( 23) 204 ( 22) 252 ( 54) 292 ( 3.2) 263 ( 4.2) 279 ( 23) 44 ( 4.1) 19 ( 2.4) 18 ( 33) 37 ( IA) 28 ( 3.4) 21 ( 2.9) 289 ( 25) 296 ( 3.4) 164 ( 7.2)1 283 ( 3.8) 270 ( 35) 290 ( OA) 38 ( 2.9) 23 ( 2.3) 22 ( 2.8) 36 ( 2.6) 23 ( 24) 30 ( 2.2) 249 ( 1.9) 293 ( 3.0) 243 ( 282 3.4) 3.2) 284 ( A ( 4.1) 14 ( 2.1) 17 ( 3.3 32 3.9) 29 4.1) 20 ( 3.3 261 ( 2.5) 257 ( 4.4) 258 ( 0.7 275 4.8) 263 3.1) 266 ( 66 34 ( 2.5) 25 ( 2.3) 20 ( 23) 38 ( 3.1) 21 ( 3.0) 29 ( 2.6) 2045 1 4.4) 294 ( 2.3) 231 ( 5.1) 275 ( 3.3) 253 264 ( 3.3) 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 3.9 23 ( 3.5) MO ( 2.0) 286 ( 3.3) 241 ( 6,4) 20 ( 4.1) 256 3.3 203 ( 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 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). 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Maryland TABLE AS I Teachers' Reports on the Emphasis Given To (030tinued) I Specific Mathematics Content Areas PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 180 NAEP TRIAL STATE ASSESSMENT Dmta Malys* SUMO* and Probability Algebra and Rinctione Heavy E ,priasis Lift le or No Emphasis vy Emphasis URI* or No Emphasis TOTA11 State Nation fialaMILKL.1 TY SNO State Nation Slack State Nation Hispanic State Nation Aldan State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extrema rural State Nation Other State Nation f72 ( 3.6 13 ( 14 ( 2.4 270 ( 4.1) 233 ( 7.0 15 ( 444) 14 3.4 14 3.5) 15 ( 4.1) .01 14 ( 3.3) 34 ( OLT) ( *di ( 2.0) ( 11 i 0.5) 17 ( 8.5) *4.,) 19 ( 0.4) 1111. 4I-111 5 ( 3.5) *" "1 5 ( 5.4) 10 ( 3.4) 205 ( 40)1 15 ( 22) 267 ( 4.7) vs 43) 59 2.9) 53 5.0) 2/1 ( $A) $3 NI 225 44) 53 $.2) 50 ( 4.8) 248 ( 4.4 240 ( 4.4 51 15 ( 03 50 ( 5.6) .as(.as) 257 50 264 54 235 94 (114) 230 ( 82)t 75 (15.7) 253 ( 6.7)1 05 (16.0) 254 ( 54 ( 3.5) 264 ( 3.2) 53 ( 52) 200 ( 34) 211 40 42 ( 21$ SA 44 311 7.1 48 ( SS) 257 ( 40)1 301 ( 3.1 74 ( 81 32) 84 3.9) 290 10.4) 41 ( 74)1 290 ( 0.4) 45 ( 5.0)1 250 ( ( 4.1) ( ( 7.0 ( ( SA) ( 6.3)4 53(112) 254 ( 03)1 361{ n 4.0) *i 93 0.1) & MI ( **41) 52 ( 4.0) 265 ( 3.0) 47 4.3) 275 ( 2.5) $44.4s 21!..1i2 3.1 21111 eel 221 2.2), 27 Oa 21: 1xi 1 ( 3.1) dkel ( Oa* ( 15 ( 2. 250 *** .01 VI 5,3 21 ( 0.2) 21$ ( 4.4)1 20 ( 9.4) 241 5,0)4 42 111.0i 44 227 3.3) 23 3.5) 17 3.3) 245 ( 4.4)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 may not total 100 percent because the "Moderate emphasis" category 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). 106 i.1 THE 1990 NAEP TRIAL STATE ASSESSMENT Malyland TABLE A8 I Teachers' Reports on the Emphasis Given To (wntinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 18410 NAEP TRIAL STATE ASSESSMENT Theta Me lysio, Statiatke, and Probability Algebra and Arnotiona Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation PARENTS' EDUCATION HS non-graduate State 14 ( 3.8) 57 ( 4.8) 37 ( 4.3) Nation 9 ( 3.0) 236 ( 6.1) 53 ( 7.7) i 441 29 ( 5.2) 240 ( 8.2) 441. ( dill HS graduate Nation 17 ( 3.7) S4 ( SA) 44 ( 4.8) 281 ( (LOY 247 ( 2.11) 205 ( 15) Soma collage Nation 13 ( 2.5) 57 ( 5.8) 411 ( 4.8) 11 Wends. Prolido02 14 ( 2.0) 257 ( 4.6) 14 ( 22) 2118 ( 4.3) .011016111010 Pirgeleata mut Prelidtray Prefolsoy Prilkilsocy 37 ( 2.5) 205 ( 2.1) 53 ( 4.4) 281 ( 2.8) 51 ( 2.4) 233 ( 2.3) 22 241 2441 21 20 ( 2.0i 243 ( $.0) COMM! glildUats State 12 ( 2.1) 60 ( 2.7) $2 ( 2.4) 263 ( 51) 2W ( 2.5) 292 ( 2.8) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 282 ( 4.5) 275 ( 3.8) 238 ( 3.0) GENDER Male State 13 ( 1.9) 50 ( 2.6) 49 ( 2.3) 24 ( 2.2) 258 ( 4.5) 268 ( 2.3 282 ( 2.0) 231 ( 3.3) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 31) 275 ( 51) 260 ( 3.5) 276 ( 3.2) 243 ( 3.0) Female .... State 14 ( 2.4) 55 ( 3.0) 54 ( 2.8) 19 ( 2.0) 257 ( 5.9) 265 ( 2.4) 285 ( 2.3) 234 ( 3.1) Nation 18 ( 2.4) 53 ( 4.5) 48 ( 3.8) 18 ( 2.9) 263 ( 4.4) 262 ( 21) 274 ( 2.7) 244 ( 3.9) 36 ( 5.7) 4001, 29(BJ 30 ( 3.3) 225 ( 3.2) 23 ( 3.9) 239 ( 3.4) 18 ( 2.3) 242 ( 5.3) 17 ( 3.1) «Hi 16 ( 1.6) 241 ( 5.3) 18 ( 2.4) 249 ( 4.0) 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 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 107 Maryland TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1100 MEP TRIAL I OM NI Me NOSOUreel I 1 0111 Most of Ito I Oat Same or Nene of STATE ASSESSMENT Need Resources I Need the Itesources I Need fl121eic State Nation White State Nation Mack State Nation Newer* State Naton Aldan State Nation TYPE OF COMMUNITY AdvantagA titan State Nation Ofeadvataged 'sew State Nation Extreme nraI State Nation Other State Nation 3.1) 278 2.9) 11 2.5) 275 35)4 13 ( 2.3) 245 (3.1) 18 4.2) 241 (5.3)4 10 OM Me 23 ( 7.15) 240 ( 7.1)1 ( *Al 1 0 5.0) 12 4.41 200 ( 4A)I 31 ( 0.2) 272 ( 8.5)4 3 ( 2.2) 10 ( 0.0) *SO ( el 440 ( 2 ( 2.6) *el 17 ( 3.7) 281 ( 4.9)1 11 ( 2.3) 265 ( 3.9)1 Peopembp am8 licalidowe 88 ( 273 ( 1.$ SO ( 4.8 270 ( 2.3) 82 ( 4.7) 942 ( 2.8) 52 ( 8.8) 242 ( 2.4) 85 ( 4.4) 244 ( 3.5) 44 ( 4.9) 250 ( 2.9) 03 ( 5.0) 294 ( 5.3)I 37 ( 7.7) ( ) 71 ( 4.0) 277 ( 4.0) 50 ( 3.9) 203 ( 1.3)1 44 (13.4) 241 ( 4.4)1 40 (13.1) 251 ( 5.4)1 85 (17.5) 253 3.8)1 54 114) 280 8.8)1 ea ( 4.7) 253 ( 29) 53 ( 5.4) 284 ( 2.1) 933331040 9193ismy 224 32 $i 4.2 201 (2.9) 15 ( 2.7) 287 ( 30 ( 28? ( 35 ( 4.8) 33 ( 7.2) 258 ( 4.9) 2.4 1121 34 7.7) 244 ( 3.0)1 17 ( 4.4) 114* G111 44 (12.7) 17 ( 4.7) 213 ( 4.7)1 53 (14.1) 224 ( 1.6)1 50 (143) 253 ( 5.5)1 15 (174) 43 (10.3) 257 ( 5.0)1 17 ( 3.7) 25.2 ( 33)t 31 1 5.8) 283 ( 4.2) S. The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proft6ency. *** Sample size it insufficient to permit a reliable estimate (fewer than 62 students). 1 3 108 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TABLE A9 I Teachers' Reports on the Availability of (vantinwd) I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO 'MEP TRIAL I Oet All the Reeources I I Get Most of the I Oat Sem or None of STATE ASSESSMENT Need Reeewces I Need the Reseurose I Need TOTAL aN2 Prifisleacv 12 21 aM PrelloNNICY 61(3.4) State 394 ( Nation ..111 24.1i 295 ( 2.0 MINTS' EDUCATION NS non-graduate State 18 ( 3.6) 51 ( 8.2) Va. ( Nen 245 ( 4.6) Nation ode 2.6) .41 54 244 ( 5.7) ( 2.7) NS graduate State 18 ( 2.3) 80 ( 4.3) 254 ( 5.0) 250 ( 19) Nation 10 ( 23) 54 ( 43) 253 ( 4.8)I 258 ( 13) Some college State 19 ( 3.7) 50 4.7) 267 ( 34) 268 2.0) Nation 13 ( 3.3) 0.4,) 62 ( 200 4.3) ( 2.5) College graduate State 19 ( 2.8) 81(2.4) 261 ( 2.2) 275 ( 2.3) Nation 15 ( 2.9) 5$ 4.9) 278 ( 5.4)1 276 ( 2.2) GENDER M. State 17 ( 24) 61 ( 3,4) 208 ( 3.2) 285 ( 2.0) Nation 13 ( 2.6) 57 ( 4.0) 264 ( 5.0)1 265 ( 2.6) Female State 18 ( 2.6) 61 ( 3.6) 209 ( 3.3) 263 ( 2.2) Nation 13 ( 2.4) 55 ( 4,4) 200 ( 3.9) 264 ( 2.0) Panmodop itea1600662 33 0.2) $6 83) 243 ( 3.5)I 24 ( 232 ( SS ( 4.0 256 ( 2.6 22 3.7) 245 4.5) 25 4.1) 287 ( 3.6) 17 ( 2.7) 202 ( 4.11) 30 ( 5.1) 273 ( 3.7) 22 ( 2.3) 240 ( 33) 30 ( 4.0) 264 ( $3) 21 ( 3.0) 244 ( 3.2) 32 ( 4.7) 257 ( 3.0) 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. ! 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 309 Maryland TABLE Ala I Teachers' Reports on the Frequency of Small i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1800 NAER TRULL STATE ASSESSMENT Al Least Once a Week Less Than Once a Week Never TOTAL. Illirawease and Proloisecy Pereentaer and Prolkieney Penmauloge and 11Prvildony State 58 ( 290 ( 2.7 30 ( 262 2.3 ( 284 ( 3.2 Nation $0 ( 4.4 43 4.1 ( 2.0 240 ( 2.2) 284 2.3 277 ( 5.4)4 EEMnp_il4 TY White State 51 ( 4.0) 9$ ( 3.6) 10 ( 3.2) 275 ( 2.6) 273 ( 270 ( 3.3)4 Nation 49 ( 4.6) 43 ( 4.5 ( 2.3) 285 ( 2.7) 271 ( 2.2 285 ( 4.9)1 Black State 61 ( 4.8) 237 ( 3.4) 34 ( 4.5) 239 ( 2.5) 5 ( 1.9) Nation 47 ( 8.1) 4$ ( 7.0) 9 ( 4.1) 240 ( 3.4) 235 ( 4.0) ( * ) Hispanic State 68 ( 4.4) 28 ( 4.6) 237 ( 3.4) 04.0) ( Nation 64 ( 7.2) 32 ( 6.9) 4 ( 1.4) 248 ( 2.5) 247 ( 6.3)1 ( "*) Aston State 88 ( 7.5) 3 , 2.4) 291 ( 52)1 Nation 80 ( 8.2) ***) 37 ( 7.9) 04* ( 0.411 4 ( 2.7) **) TYPE Of COMMUNITY Advantaged urban State 67 ( 8-5) 30 ( 8.3) 3 ( 2.0) 278 ( 4.9) 278 ( 5.6)4 Nation 39 (22.9) 41 (17.9) 20 (12.2) 273 ( 6.0)4 *iv ett Disadvantaged urban State 78 ( 6.1) 23 ( 5.9) I ( 0.7) 234 ( 5.2)1 230 ( 4.5)4 Nation 70 (11.7) 248 ( 4.8)! 21 ( 9.0) 249 ( 3.7)1 6 ( 8.5) 4-4. .44) Extrame rural State 25 (17,9) *44) 44 (14.5) G.111 31 (27.8) *eV ( *41 Nation 35 (14.8) 56 (17.1) 9 ( 0.6) 255 ( 5$)1 258 ( 5.9)1 Other State 43 ( 5.6) 48 ( 6.1) 11 ( 4.4) 259 ( 4.3) 263 ( 2.8) 267 ( 3.9)1 Nation 50 ( 4.4) 44 ( 4.5) ( 1.8) 260 ( 2.4) 264 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated natistics 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 stie is insufficient to permit a reliable estimate (fewer than 62 students). 115 110 THE 1990 NAEP TR. .L STATE ASSESSMENT Marykurd TABLE Al Oa 1 Teachers' Reports on the Frequency of Small (coniinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSAIENT At Least Once a Week Lees Trian Once a Weak Never 12161 State Nation fammiumeansai iss nonipsdusts State Nation 118 graduate State Nation Peamalles aid Prelkisioy ( $.3) SOO f 10 ( 4.4 2.0 ( 2.2 53 ( 236 ( 3.7 00 ( 0.4 244 ( 32) 56 ( 4.1) 24301 262 ( 2.8) Sonia coNege State 53 ( 4.2) 202 ( Nation 51 ( 5.2 200 ( 3.1 College graduate State 58 ( 3.9) 275 ( 3.0) Nation 40 ( 52) 271 ( 2.6) OENDIR M. State 54 ( 34) 261 ( 2.7) Nation 50 ( 44) 261 ( 3.0) Female State 56 ( 3.5) 259 ( 3.0) Nation 50 ( 4.7) 2$9 21) .4ENENImmowww,. fleystags wd firdawnst as 3.2 202 2.31 43 4.1 204( 2.3) 36 ( 8.0) 30 ( ts) 244 ( 3.2)4 36 ( 3.7) 250 ( 45 ( 5.1) 257 ( 2.7) 30 ( 4.0) 204 ( 3.0) 42 ( 5.1) 288 ( 3.2) 30 ( 3.6) 273 ( 2.8) 43 ( 4.4) 270 ( 3.0) 36 ( 3.3) 261 ( 2.7) 42 ( 4.0) 2t 3.1) 35 ( 3.2) 254 ( 2.5) 43 ( 4.7) 263 ( 2.1) Pennidaga wid Preidency 1 2.2) 204 1.2)4 $ 2.0) 217 6/4)1 11 i 4.1) .44) 1 ( 1.4) ( 9 ( 3.1) 250 ( 4.1)1 $ ( 2.5) 400004) 9 ( 2.6) *do .4,4) 7 ( 2.3) 4.40. 444) ( 2.0) 260 ( 4.8)1 11 ( 2.7) 285 ( 4.9)1 ( 2.4) 267 ( 3.5)1 ( 2.1) 274 ( 5.3)1 ( 2.2) 260 ( 39)1 ( 2.1) 275 8.0)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. '0" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 14,8 THE 1990 NAEP TRIAL STATE ASSESSMENT 111 Maryland TABLE AlOb I Teachers' Reports on the Use of Mathematical Objects PERCENTAGE OF STUDENTS AND AWRAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT AI Least Ow* a Week Lau Than Once a WaML New TOTAL. Pommia. kolitismy 22 ( 2.4 3.0 254 ( 22 3.7 ( 254 ( 10 ( 2.7) 267 ( 13) 17 ( 4.0) 261 ( 18)1 25 13) 23$ 2.5) 22 5.9) 233 5.9)t 31 ( SI) 44 0,4) 30 ( 74) 247 ( 3.8) 18 ( 4.7) Pois02011 awl PnOkilearv 2:71-1 1!6i41) 69 2.0) 272 ( 1.9) 12(4.2) 285(2.1) 05 3.8) 230 2.9) 70 6.3) 241 ( 2.9) 62 ( 5.3) 242 ( 3.0) 55 ( 7.3) 245 ( 34)1 58 ( LS) State Nation NACVETNNICITY Wt. State Nation Black State Nation hispanic State Nation Asian State 294 ( 4.3)4 Nation 42 ( 8.5) ***) 52 5.7) *al TYPE OF COMMUNITY Advantaged Lathan State 17 ( 5.3) 55 ( 5.7) 271 ( 62)1 277 ( 4.4) Nation 23 (14.4) 83 (114) ( INN) 27$ ( 54)1 Disaclvalgagad urban State 17 ( 4.4) 71 ( 5.4) ( Me) 232 ( 4.5)1 Nation 39 (11.4) 59 (12.1) 247 ( 7.5)1 253 ( 7.0)4 Extreme rural State 11 ( 1.8) 7$ (10.1) 24$ ( 2.3)1 N. ,en 27 (14.9) 55 (146) 262 ( 2.8)1 Other State 22 ( 4.1) 09 ( 4.0) 247 ( 3.6)1 264 ( 2.4) Nation 19 ( 4.3) 72 ( 5.0) 253 ( 34)1 263 ( 2.2) ParOmeisse 11 2112 212 220 4,5) 12 2.3) 10 2.7) 25$ ( 5.2)4 244 ( 5. 10 ( $ ( 19 *an 7 ( 2.3) .04,41 7 2.5) *by ( 041 15 ( 3.8) *** 4.21 1$ ( 5.0) 293 ( 7.4)1 15 ( 9.3) ( dim.) 11 5.1) *** 2 1.8) ( ON) ( 2.4) 281 ( 9.4)1 ( 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 pronciency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 112 I THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE AlOb Teachers' Reports on the Use of Mathematical (cCIntinlied) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT At 411/111 Once a Week _ Loss Than Once a Week New TOTAL Poramtert ani Volishingt Pandata. ad Prelideacy Parvadais wd Prididady State 22 ( 24) 97 ( 24) 11 ( 2.0) 234 ( 3.0) 291 ( 1.8) 2$2 ( 90) Nation 22 ( 3.7) $9 ( 3.9) 9 ( 2.6) 254 ( 3.2) 213 ( 1.9) 2$2 ( 5.9)1 PARENTS' EVOCATION ttS non-gracluate State 4. 70 ( 244 ( 4.3) 3.3) 7 ( 23) Nation 25 ( 5.6) 93 ( 243 ( 7.2) 2.2) ( ".) HS graduate State 24 ( 9.0) 70 ( 2.9) ( 1.4) 239 ( 2.4) 247 ( 1.9) Nation 23 ( 248 C 4.8) 4.0)1 70 ( 255 ( 5.3) 2.2) 7 ( 2.8) Some calve State 22 ( 3.1) 89 ( 3.5) 10 ( 2.41 256 ( 9.3) 264 ( 2.8) Nation 18 ( 261 ( 4.0) 4.4)4 73 ( 269 ( 43) 2.3) 9 ( 4* ( 2.4) 4 ) College graduate State 21 ( 2.7) 04 ( 2.8) 16 ( 2.?) 268(3.6) 274 ( 2.4) 293 ( 5.?) Nation 20 ( 3.9) 69 ( 3.7) 11 ( 2.5) 266 ( asp 274 ( 22) 297 ( 4.2)1 GENDER M. State 23 ( 2.8) 67 ( 2.7) 10 ( 20) 253 ( 3.5) 202 ( 2.0) 282 ( 58) Nation 22 ( 4.1) 69 ( 4.1) ( 2,0) 255 ( 4.1) 285 ( 2.1) 287 ( 7,2)1 Fan*, State 21 ( 23) 67 ( 2.5) 12 ( 2.2) 254 ( 3.1) 200 ( 2.1) 261 ( 5;9 Nation 21 ( 3.5) 09 ( 42) 10 ( 3.3) 254 ( 3.3) 262 ( 1.9) 278 ( 6.0)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 113 Marylead TABLE Alla I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 110 MAEP TRIAL TATE ASSEISMENT Muni Ever)/ MY Swami Times a Week AIS" an" /1444/44". Las TOTAL State Nation amil 4100114isami affigniagn White State Nation Medi State Nation Moat* State Nation ,Aelan State Nation TYPE Qf (IMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation edriNTIO nrat State Nation Other State Nation a? 271 i 01 04 S. 22 I 97.7 02 ( 251 3.1 36°41 I 3,7 81 1 0.1 $3 ( 7.0) sot 83 ( 0.0) 204 ( 7.0$ 41 ( 1.5) 244 (0,5) 03 15.0) 211$ ( 7,3)4 33 ( 7.7) 240 ( 5.5)1 08 (10.7) 252 ( 4.7)4 I** **11) 30 50 10.41) 201I ( 4.0)1 241 2.2) 53 (Si) 3.0) 207 ( 2.3) $41 IN $ $47 4 1 11 7 is 204 IM 5.1g 11.1 2.0) 3.4) 20 32) 34) 37 ( 5.2) 233 ( 3.2) 41 ( 7.2) 223 ( 3.0)4 25 234 5.4) 4.5) 32 5.3) 240 ( 4.3)4 31 ( 7.0) ( 10 ( 3.2) ( ***) 42 ( 0.5) 274 ( 5.1)1 23 ( 52) *** Ion) 34 ( 7.8) 224 ( 4.2)4 31 (11.1) 243 ( 8.0)1 42 (214) *** 40 (10.0) 247 ( 74)1 24 ( 3,9) 255 ( 4.3)1 31 ( 3.5) 255 ( 3.1) & ( 1.7) 24: ( 411 204 $.4 14 ( 1.9) 223 ( 5.1) 2 ( 1.4) so* ( *41 15 ( 5.4) 041 ( 2.3) ".) 10 Le) le 441 ( 5.1) ( 441 9 ( 3.8) ( 14 (144) 13 ( 4.4) 4 ( 2.2) ye.) 2 ( 2.0) ( "e) 10 7.3) WM fel ( 2.8) 242 ( 5.2)1 8 ( 1.9) 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. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "is Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 1 (I THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE Alla I Teachers' Reports on the Frequency of (continued) I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1880 MAEP TRIAL STATE ASSESSMENT , Most Every Day Sweral Times a Week A Mout Mee a Week er Lem BM!, State Nation IlisEinuardmi NS non-graduate State Nation HS graduate State Nation Sane °Mop State Nation College graduate State Nation GENDER M. State Nation Female State Nation NS I 4; .4. 27 55 31 011* 11(42) 252 ( 23 151 ( 4.4 257 ( 2.$1 10 ( 4.1) 207 ( 3.1) OS ( 4.2) 272 ( 2.7) 57 ( 3.4) 262 ( 2.3) 91 ( 4.0) 291 ( 2.2) 57 ( 32) 267 ( 2.1) 90 ( 9.7) 2212 ( 2.1) 57 ( 3.8) 288 ( 2.3) 85 ( 3.5) 206 ( 14) 33 SA) 24124 22 250 ( 2.61 30 3.4) 211020 SI 254 ( 52 35 ( 3.5) 24$ ( 4.1) $1 ( 3.0) 205 ( 3.1) 33 ( 2.6) 257 ( 33 ( 34) 216 ( LS) 34 ( 3.5) 254 ( 34) 26 ( 3.3) 253 ( 24) 10 ( 1.7) 250 ( 43) ( 14) 211 ( 5.7)1 9 ( 1.6) 243 ( 5.04 7 C 22) *an The standard errors of the estimated statistics appear in parentheses. It can be said with &built 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. 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). .1 f." 0 THE 1990 NAE.P TRIAL STATE ASSESSMENT 115 Mary/old TABLE Al lb I Teachers' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1160 NAEP TRIAL At Least Several Timm STATE ASSESSMENT a Week About Once a Weak Lass then Weekly rirosidade ml Poillickary 47(22) 257 ( 2.5) 54 ( $.8) 256 ( 2.3) Peron's. and Prof/dam 211 2131 23 200 Permeells end Praiisacd ( ( 3.2 I $4 2: 23 ( ( 34 f 23 274 2.7 state Nation RACE/ETNNICITY Mite State 47 2.9) 30 ( 3.1) 23 ( 2.9) 266 ( 2.5) 261 ( 2.6) 275 ( 33) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.6) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Madc State 46 ( 42) 29 ( 4.9 25 ( 4.2) 234 ( 2.7) 242 ( 3.2 238 ( 62) Nation 45 ( 7.5) 31 ( 7.6 23 ( 63) 232 ( 3.1)4 243 ( 2.3144 243 ( 7.0)1 Hispanic State 52 ( 5-2) 27 ( 4.7 21 4.6) 233 ( 4.2) VI* 4111 Nation 41 ( 7.7) 26 ( 5.3 33 ( 7.5) 242 ( 3.2)1 244 ( 5.1)I 257 ( 2.3)1 Asian State .44 ( 25 ( 7.1 044 ( 41Nlit 19 ( 5.0) ( Nation 37 ( 6.3) 44 ( 041 27 .44 (10.4) TYPE OF COMMUNITY Advantaged urban State 55 ( OA) 32 ( 6.9) 13 ( 3.7) 271 ( 5.3) 266 ( 5.5)4 293 ( 6.0)1 Nation 59 113.9) 273 ( 3.4)1 20 ( 6.0) ( 214 ( 8.2) ( 4 Disadvantaged urban State 4$ ( 7.2) 37 ( 7.6) 230 ( 4.3)1 237 ( 7.8)1 Nation 50 (13.9) 22 (112) 28 (10.7) 237 ( 24)1 25$ ( 8.3)1 263 ( 4.1)1 Wren* rural State 25 (20.8) 87 (22.9) 94-IP 250 ( 65)I Nation 27 (14.3) ( .41 49 (12.7) 258 ( 6.7)4 24 (10.1) ( *On Other State 44 ( 4.8) 32 ( 4.9) 25 ( 42) 256 ( 3.4) 266 ( 4.3) 265 ( 38)1 Nation 30 ( 4.4) 35 ( 4.3) 38 ( 4.2) 256 ( 3.3) 259 ( 2.11) 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 w..th 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). 1 116 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TABLE Al lb I Teachers' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAEP TRIAL STATE ASSESSMENT At Least Savant Tina a Weitt About Once WomeL Lass than Weeidy f- lEfilt State Nation MinalLgeircaneN NS neniraduato State Nathan NS graduate State Nation time cellege State Nation colloge graduate State Natim OENDER Makt State Nation Female State Nation PrellOmor 20 ( 4.5) i 19 (8.3) ( 3.2 1M4 2.41 36 5.3 Aso( 3A) 27 ( 949 ( 36 ( 2$0 ( 3.03) 3.3) 4.5) 2.7) 41 ( 3A) 2.0) 33 4.7) 210 2A) 47 ( 3.0) 203( 1,1) 36 ( 3.11) 264 ( 2A) ( 2,8) 25? ( 2.8) 35 ( 4,1) 257 ( 3.2) 41 2.9) 27 ( 2.7) 34 ( 4.1) 254 ( 2.1) IS ( 4.0) 272 ( 5.1) 32(4.0) 206 ( 4.2) 32 ( 3.7) 211 ( 3.4) 32 ( 3.4) 271 ( 2.4) 28 ( 3.1) ( 3.3) 35 ( 3.6) 261 ( 2.1) 30 ( 3.4) 285 ( 3.7) 32 ( 3.7) 258 ( 2.3) Perisaisp and Oviagiony 33 274 2.7 29( 5.3) 014 441 341( SA) 250 ( 4.5$ 27 3.9) 247 3.3) 30 4.1) 203 3.4) 23 ( 2.3 205 ( to) 3$ ( 4.1) 278 ( 2.8) 21 ( 2.9) 260 ( 4.3) 33 ( 3.5) 269 ( 2.9) 24 ( 2.8) 204 ( 3.3) 31 ( 3.5) 275 ( 3,2) 23 ( 2.8) 260 ( 4.2) 34 ( 4.1) 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 ample. ! Interpret with caution - the nature of the ample 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 Maryland TABLE A 12 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAEP TRIAL STATE ASSEUMENT AI Liss* Oesso a Week Lass Than One a Wink Now _ 12/ft State Nation 1100111111120 White "1":1111111.4 11110d1041 au Ls to sa( Li) State 37 ( 2.4) 273 ( 2.5) Nation 27 ( 2.9) 2N ( 3.1) Maack State 30 3.14) 230 1.9) Nation 24 3.0) 234 ( 3.0) Hispanic State 36(31) 230 (3.1) Nation 37 ( 5.2) 242 ( 3.9) Asian State 32 8.6) OM *44) Nation 26 ( 8,4) TYPE OF COMMUNITY Advantaged urban State 34 ( 5.7) 276 ( 4$)1 Nation 27 (131) 114411 DisadVantaged urban State 37 ( 3.7) 234 ( 3.6)! Nation 31 ( 5.7) 245 ( 4.0)1 Extreme nrral State 1111he 11114 Natism 34 (101) 249 ( 5.2)1 Other State 2$ ( 3.3) 253 ( 3.5) Nation 27 ( 2.8) 200 ( 3.3) 30 1.5) 271 22 1. 272 ( 1 22 ( 13) 244 ( 3.7) 24 ( 35) 245 ( 4.2) 27 ( 3.7) *IMP ft4M1 22 ( 3.8) 250 ( 3.4) 20 ( 59) 32 4.1) **11 33 ( 3.9) 2411 ( 4.1)I 33 ( 4.5) 203 548 1$ ( 2.9) 444) 20 ( 25) 267 ( 6.4)1 30 ( 4.4) *en 27 ( 3.111) 264 ( 3,5)1 27 ( 208 ( 2. 26 ( 284 ( 2.1) 00 1.9 0 3.4 44 27 23444 i4. 234 ( V 42 ( SS 43) 231 240 2.8 41 5.0 33 ( 5.7) 1 ( 12/ ***) 33 ( 41) ( 4.6)1 40 (134) 279 ( 3,5)1 45 ( 4.8) 229 ( 4.4)1 49 ( 0.3) 245 ( 3.7)1 4 ( 5,3) .44) 30 (11.8) 250 ( 0.2)1 44 ( 3.6) 204 C 24) 45 ( $4) 232 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "*" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 118 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TABLE Al2 I Students' Reports on the Frequency of Small (continued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1800 NMP TRIAL STATE ASSESSMENT At Least Once a VIM Lm Than Once a Meek Never TOTAL Proventaipe and Pnilidency Pagoda. and Prellakticy eirroside. and Prilkilescy State ( 2.1) 28 ( 1.4) 42 ( 2.2) 256 ( 2.2) 269 ( 2.3) 256 ( Nation 20 ( 2.5) 28 ( 1A) 44 ( 2.9) 256 ( 2.7) 207 ( 2.0) 241 ( 13) PARENTS EDUCATION RS non-graduate State 27 ( 4.3) 24 ( 3.3) 4$ ( 4.9) 044 242 ( 3.5) Nation 29 ( 4,5) 29 ( 3.0) 42 ( 4.5) 242 ( 3.4) 244 ( 3.0) 242 ( 2.7) HS graduate State 30 ( 2.8) 26 ( 1.6) 43 ( 3.0) 240 ( 2.5) 250 ( 2.5) 249 ( 2.3) Nation 26 ( 3.0) 28 ( 1.6) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Soma maga State 30 ( 23) 20 ( 2.3) 45 ( 3.1) 258 ( 2.3) 268 ( 3.4; 263 ( 3.3) Nation 27 ( 3.9) 27 ( 2.4) 48 ( 3.8) 265 ( 3.6) 268 ( 3.3) 206 ( 2.1) Colags graduatt State 31 ( 2.7) 30 ( to) 39 ( 2.8) 274 ( 2.8) 254 ( 2.7) 26. j 2.3) Nation 28 ( 3.0) 23 ( 1.9) 44 ( 3.6) 270 ( 2.7) 273 ( 2.8) 275 ( 2.2) GENDER Mato State 32 ( 2.0) 28 ( 1.5) 40 ( 2.2) 257 ( 2.2) 271 ( 2.7) 258 ( 1.9) Nation 31 ( 24) 28 ( 1.7) 41 ( 2.9) 250 ( 3.3) 208 ( 2.8) 282 ( IA) Female State 22 ( 2,5) 27 ( 1.8) 44 ( 2 7) 250 ( 2.6) 267 ( 24) 257 ( 2.4) Nation 26 ( 2.4) 27 ( 1,8) 47 ( 3.2) 257 ( 24) 206 ( 1.7) 200 ( 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 populahon is within ± 2 standard errors of the estimate for the sample. *IPS Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 24 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Masykad TABLE A 13 I Students Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAV TRIAL STATE ASSESSMENT At Least Om a Weak Lass Than Once a We* - Saver 14at mid **111101141411 110101101111. NMI .1401161011, State art 1.1) Nation le I 1.4 2$7 $1 1.2 22041 41 2.2 SS$ ( 2111 1.5 aft ( tej BfigaiMISM Mike State 21 ( 1.6) 34 1.5) 4e. 2I)) 201 ( 23) 277 1.7) 273 Nation 27 ( 1.3) 33 14) 40 2.5 ( 2.8) 275 ( 1.6) 28$ ( 1.$ "Neck State 22 ( 2.4) 27 ( 1.5) 4$ ( 2.5) 232 ( 2.3) 242 ( 2.5) 237 ( 21) Nation 27 ( 3.3) 27 ( 3.2) 40 ( 4.5) 234 ( 3.7) 244 ( 4.3) 232 ( 2.6) Hispanic State 21 ( 4.3),) 211 ( 3-3) ( *el 44 2319 ( 4.3) ( 3.0) Nation 34 i 4.2) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4,3) 240 ( 1.2) Asian State 23 ( 44) ow.) 26 ( 4.4) wow* ( «on 50 ( 6.0) Nation 32 ( 3.7) 30 ( 3,2) 0,14. ( ( TYPE QF COMMUNITY Advantaged urban State 23 ( 34) 34 ( 3.2) 43 ( 4.0) 271 ( 5,4)1 221 ( 3.5) 277 ( 4.9) Nation 30 (10.3) 33 ( 4.8) ...2 (11.1) 378 ( 6.1)? 214 ( 3.2)1 261 ( 5,141 Disadvantaged urban State 21 ( 3.3) 23 ( 24) 56 ( 4.8) 224 ( 4.1)1 242 ( 5.7)1 232 ( 4.1)1 Nation 35 ( 6.6) 12 ( 2.1) 48 ( 6.4) 249 ( 5.3)1 256 ( 5.7)1 242 ( 4.8)! Edreme rurai State 17 ( 9.1) ( *ill 31 ( *4,4, ( 6.2) 441 52 *** 13.1) ..) Nation 21 ( 3.1) 37 ( 4.7) 43 ( 5.0) ( ....) 252 ( 4.7)4 251 ( 5.2)1 Other State 21 ( 1.9) 32 ( 1.7) 47 ( 24) 251 ( 3.3) 265 ( 2.2) 264 ( 2.9) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 250 ( 2.0) 270 ( 14) 200 ( 2.2) -,.... The standard errors of the estimated statistiC4 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 simple. ! 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 ti 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Matyland TABLE A13 1 Students' Reports on the Use of Mathematics (c(mtinued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TAAL STATE ASSESSMENT At Least Once a Week Lau Than Once a Week New TOTAL State Nation POWNT1' EDUCATION non-raduate State Nation NS graduate State Nation Some coNegs State Nation College Gpiaduate State Nation GENDER Maki State Nation Renate State Nation a Ont001011116 3.0) 27 4.21 237 3.0 23 ( 2.1) 241 ( 2.0) 27 ( 2.7) 250 ( 2.4) 24 ( 1.9) 252 ( 2,4) 29 ( 29) 201 ( 3.5) 22 ( 11) 205 ( 2.9) 30 ( 2.5) 262 ( 3.0) 26 ( 1.6) 252 ( 2.1) 32 ( 2.0) 254 ( 2.9) 20 ( 1.6) 253 ( 3.0) 25 ( 2.0) 257 ( 3.0) 26 ( 3,2) 49 20 ( 2.7j *44 47 253( 3.5) 240 25$ ( 2.7) 3 SO 2.3 1 ( 2.4) 45 3.3 253 3.1 29 ( 19) 252 .4 ( 2) 31 ( 2.1) 46( 2.6) no ( 2.6) 2434 274 ( 2.2) .3) * 24) 3 36 ( 2 ) 203 2.1) 34 ( 1.?) 44 ( 24) 276 ( 2.0) 32 ( 2.0) IS 275 2.3) 2.6) 2711 ( 2.2) 27$ 2.0) 4 32 ( 14) 200 ( 1i) 30 ( 1.5) 271 ( 2.1) 30 ( 1.3) 206 ( 1.9) 31 ( 14) 206 ( 1.5) 42 ( 19) 203 ( 2.4) 30 ( 2,2) 2001 19) 50 ( 2.0) 256 ( 2.1) 25744 2.6191 The standard errors of the estimated statistics appear in parentheses. It can be said with rbout 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 Maryland TABLE A 14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Almost Every Day IleverM noes a Weak About Ones a Weak or Use TOTAL and Prollicium PoismIsms anti permealle mut Prellekswey State 621 2.2) 22 ( 16 ( 1.7) 200 tit) 2$6 ( 1.7 247 ( 2.2) Nation 74 I 1.93 14 ( 0.6 12 ( 1.6) 267 ( 1.2) 262 ( 1.7) 242 ( 4.5) RACE/ETHNIC1TY Mite State 66 ( 2.7) 20 ( 1.4) 15 ( 2.1) 278 ( 1.7) 267 ( 2.1) 2110 ( 2.4) Nation TO ( 2.5) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 2.2) 252 ( 5..ty Black State 61 ( 3.0) 23 ( 1.6) its( 2.0) 240 ( 2.6) 237 ( 2.8) 227 ( 3.0) Nation 71 ( 2.8) 15 ( 1.7) 14 ( 3.2) 240 ( 2.9) 232 ( 3.1) 223 ( OA)4 Hispanic State 48 ( 5.2) 23 ( 3.3) 24 ( 4.0) 242 ( 3.6) O.* ( 41.* 41N114 ) Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3,4) Aslan State 63 ( 6.2) 299 ( 3.6)1 26 ( 5.4) 11 ( 3.8) Nation 79 ( 4.9) 289 ( 5.0)1 13 ( 3.4) ( 441 -** fel TWE OF COMMUNITY Advantaged urban State 59 ( 4.4) 24 ( 25) 17 ( 3.7) 282 ( 4.6) 271 ( 4.7) 207 ( 32)1 Nation 73(11.1) 13 ( 1.7) 14 (10.4) 266 ( 4.6)1 ( Disadvantaged urban State 59 ( 5.3) 23 ( 3.3) 18 ( 4.5) 235 ( 4.7)1 235 ( 4.2)1 220 3.6)1 Nation 69 ( 2.8) 15 ( 2.5) 15 ( 21) 253 ( 3.7)1 243 ( 4.4)1 235 ( 6.5)1 Wiwi. rural State 83 ( 6.8) 14 ( 4.1) 3 ( 2.8) 257 ( 1.7)1 Nation 66 (11.3) 17 ( 8.2) 263 ( 4.P)l *IP/ Other State 64 ( 4.1) 20 ( 2.0) 1 6 ( 2.4) 267 ( 24) 255 ( 3.0) 246 ( 34)1 Nation 75 ( 22) 14 ( 1.0) 10 ( 1.9) 267 ( 1.6) 252 ( 2.6) 239 ( 42)1 The standard errors of the estimated statistics appecr 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. 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). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TABLE A14 I Students' Reports on the Frequency of ("mtillued) I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ MO NAEP TRIAL About Once a Week or STATE ASSESSMENT Nowt Every Day Several Them a Week Less Mak State Nation featatuesansm NI nen-graduate Slate Nation HI rackets State Nation Some caller State Nation College graduate State Nation OEM M. State Nation Female State Nation 01 S,A) SO. 2.3) 50 ( 2.1) 251 ( 2.1) 71 ( 3.9) 955 ( 1.6) 66 ( 3.0) 299 ( 24) 270 ( 1.2) 64 ( 2.4) 279 ( 2.1) 17 ( 2.7) 279 ( 1.6) ( 2.3) 216 ( 1,9) 72 ( 24) 261 (1.5) 64 ( 24) 295 ( 2.0) 76(1.5) 225 ( 1,3) 22 ( 3.51 12 *l 21 ( 1.2) 245 ( 2.6) 19 ( 1.1) 249 ( 3.2) 19 2.0) 220 SA 11 1.2) *4,1 23 ( 1.5) 266 ( 2.4) 13 ( 0.9) 260 ( 2.6) 23 ( 1.5) 258 ( 2.1) 16 ( 1.2) 252 ( 2.5) 20 ( 12) 257 ( 2.3) 13 ( 1,0) 250 ( 2,5) "919999.191/ 969 fhWilkolf 20 ( 2.5) 12 ( 3.11 .14,1 20 2.1) 235 2.9) 13 2.6) 229 ( 3.4)4 1$ ( 2.3) 2St ( 4.0) 9 ( 1.7) 13 ( 1.8) 258 ( 2.7) 10 ( 2.3) 257 ( 8.4)1 16 ( 1.8) 24$ ( 2.6) 12 ( 2.1) 242 ( 6.1) 16 ( 1.9) 246 ( 2.8) 11 ( 1.8) 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 ± 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 si2e is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Matyktid TABLE MS Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1090 MAEP TRIAL At Least Swami Tbnas STATE ASSESSMEKT a Weak Maui Ome a Weak Lisa run Vaaalety TOTAL State Nation MULEINAM State Nation Mack State Nation Hispanic State Nation Asian State Nation TYPE Of C94111UNITY Advantaged urban State Nation Disadvantaged urban state Nation Extreme nral State Nation Other State Nation Paresidap an$ Maim 21$ ( 25$ ( 22 31(24 47 ( 42 ( 2.7) 207 ( 14) 35 1 2.2) 222 ( 2.5) 42 ( 2.5) 234 2.2) 4$ 3.1 232 4.3) ) 53 ( 4.0) 232 ( 3.3) 44 ( 4.1) 23$ ( 3.9) 47 ( 5.1) 41, 32 ( 5.1) or** ( 49 ( 3.3) 272 ( 3.9) 50 ( 6.0) 271 ( 3.3)1 41 ( 4.1) 229 ( 4.9)4 37 ( 5.5) 240 ( 4.5)4 20 ( 1.0) 42 (10.1) 249 ( 4.0)1 48 ( 33) 255 ( 2.5) 30 ( 2.9) 252 ( 3.0) Proislaw 275 2.3 222 1.5 24 1.3 SO In 2 41 li 24) 23$ ( 2.7 20 ( 22 ( 2. 20 I iii III M 241 ( 2.9 221 ( 4.4) .«3 1 .31 25 ( 3,4 eta i 111 32 247 ( 3.3 241 ( 3.3) 24 ( 4.0) 20 ( 1144. ( OM) 004 ( ?I'hil 17 ( 3.5) 51 ( 5.9) .. ( ....) 40, ( .*) 29(2.1) 275 ( 5.4)4 19 ( 4.9) ( 28 ( 2.8) 235 ( 4.6)1 23 ( 30) 253 ( 4.1)1 32 ( 9.0) *el 30 ( 4.4) 250 ( 34)4 23 ( 10) 223 ( 3.1) 22 ( 1.2) 2131 ( 2.1) 22 201 5.2 $1 943 209 ( 53)1 31 ( 22) 234 ( 5.3)1 41 ( 0.7) 255 ( 4.2)1 4 ( 9.4) 44.) 23 I 7.5) 207 ( 7.3)1 24 34 272 13) SI 20) 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). 124 JA. THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TABLE A15 I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1010 NAEP TRIAL STATE ASSESSMENT At Least Sew* Times1- a *sok Meta Once a Week Loss Than Weeidy _ TOTAL Peratalaga and ProildancY 47 ( 2.0) 255 ( 14) 36(24) 253 ( P4410110. Prelledanay 26(12) 253 ( 2.2) 25 ( 1.2) 261 ( 1.4) Pantionago aid Pralklesay 207 2.7) 37 15) 272 ( 1.9) State Nation PARENTS' EDUCAT10141 145 non-waduate State 49 ( 240 ( 5.1) 2.8) 20 04* 2.6) «in 31 ( 5.3) qmpe) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 23S ( 3.1) 243 ( 2.7) 253 ( 2.8) NS graduate State 48 ( 2.7) 25 (2.0) 26 ( 2.9) 245 ( 1.9) 246 ( 2.1) 241 ( 8.8) Nation 40 ( 3.2) 29 22) 32 ( 3.6) 247 ( 2.7) 256 ( 2.5) 262 ( 22) Sam collage State 48 ( 2.8) 27 ( 1.0) 26 ( 3.1) 257 ( 2.3) 208 ( 2.8) 209 ( 4.4) Notion 34 ( 3.4) 26 ( 2.2) 40 ( 3.6) 259 ( 2.3) 289 ( 2.8) 271 ( 2.8) College graduate State 45 ( 22) 2e ( 1.7) 29 ( 2.0) 267 ( 2.0) 276 ( 32) 263 ( 2.0) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 273 ( 2.3) 285 ( 2.3) GENDER Mato State 51 ( 2.0) 25 ( 12) 25 ( 1.9) 258 ( 1.5) 261 ( 2.5) 270 ( 3.0) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 2e3 ( 23) 274 ( 2.4) Fong* State 43 ( 22) 27 ( 1.5) 30 ( 2.5) 255 ( 1,8) 264 ( 2.7) 264 ( 3.1) Nation 37 ( 2.5) 25 ( 1.5) 38 ( 2.6) 253 ( 21) 25S ( 1.8) 269 ( 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. *** Sample size it insufficient to permit a reliable estimate (fewer than 62 students). 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 Maryland 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 MO NAEP TRIAL STATE ASSESSIIENT Om a Calotdator Teacher Explains Calculator Use Yes 4 _ No .. Yes I No , State Nation MIZMISILU *Me State Nation State Nation Hispanic State Nation Asian State Nation TYPE OF C9MMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme neat State Nation Other State Nation persome. reakikeer firt I Jitf 97 0.4 3 ( 0.41 0.3 13) 234 ( as(0.2) 273 MI 0.3 270 ( 1.5 93 ( 0.7) 231 ( 2.1) 93 ( 1.5) 231 t 2.3) 94 1.7) 230 2.4) 92 1.2) 245 2.7) 90 ( 1.1S) 292 ( 3-7) 99 ( 0.8) 282 ( 5.3)1 ite ( 0.5) 277 3.7) tO) 281 ( 2,8)1 08 ( 1.4) 233 ( 3.9)1 94 ( 1.2) 250 ( 3.5)1 ( 1.6) 258 ( 24)1 90 ( 1.3) 257 ( 3.2)1 ae ( OA) 282 ( 2.3) 97 ( 0.5) 263 ( 1.7) 1 ( .44 2 03 4 ( 0.7) .44 ( 441 ( 1.5) .40 ( .44) ( 1.7) 11 ( 1.2) .44 ( ( ".) ( ***) ( IrtrIt ( ( .0 44* ( *el 4 ( 1.4) 4.4 6 ( 1.2) .44 ( 41 4 ( 1.8) .44) 4 ( 1.3) 4 ( .41 2 ( 0.4) ( 3 ( 0.5) 233 ( 54) Praiskisql Illsresalse INWINkm,/ a 111 as 1.1 ass 1.5) 52 ( 21) 270 ( 1.7) 48 ( 21) 2e. ( 1.$) 49 ( 3.1) 238 ( 1.7) 53 ( 44) 228 ( 3.8) 59 ( 4.1) 238 ( 3.1) 63 ( 4.3) 243 ( 3.4) 45 ( 5.9) .041 52 ( 4.8) ( 441 50 ( 4.3) 274 ( 3.7) 45 (12.2) 276 ( 2.5)1 42 ( 41) 232 ( 3.7)1 53 ( 75) 247 ( 4.1)t 09 ( 0.5) 281 ( 3.8)1 42 ( 8.7) 251 ( 41)1 4$ ( 3.2) 258 ( 2.4) 50 ( 2.7) 258 ( 2.1) 4$ ( 2.1) 279 ( 11) 54 ( 21) 273 ( 1.1) ( 3.1) 23411 ( 3-4) 47 ( 4.0) 230 ( 2.7) 41 ( 4.1) 243 ( 3.6) 37 ( 4.3) 245 ( 24) 55 ( 5.9) ...) 43 ( 4.8) 414 ( *AO ) 201 4.8) 55 12.2) 50 4.3) 265 ( 6.4)4 58 ( 49) 234 ( 4.6) 47 ( 7 .5) 231 ( 3.6)1 31 ( 9.5) 58 ( 8.7) 261 ( 44)1 52 ( 32) 225 ( 2 7) 50 ( 2.7) 288 ( 2.0) The standard errors of the ettimated 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. 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). 126 131 THE 1990 NAEP TRIAL STATE ASSESSMENT " 17 TABLE A18 entS S.' ..eports on Whether They Own a (cmtinued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE All$EUMENT Om a Oakidator , Teacher DOAN Ca Mutat" Use Yes , 1_ No Yes No illamiesses ase igiak state Nation Eammingm IN nemgraduate State Nation NS graduate State Nation Some college State Nation Coliege graduate State Nation 9E1414R Male State Nation female State Nation 65(0.3) 201(tS) 07 ( CA) AO 2113 (IA) 234 244 OS 1.1) 02 1.6 j 1 21 ....) 2 1 1.1) 243 ( 3.0 5$ ( 53 ( 243 ( 2.0 242 ( 266 ( 1 .5 247 ( rt ( 0.0 OWN ( INN ..? f ...) 3 ( 253 ( 14 245 ( 1 54 ( 3.0 53 ( 9? ( 03) 95 ( 02) 2 ( 0.6) 263 ( 12) ... ( 44.) 95 ( 0.9) 4 ( 0.9) 265 ( 14) *** ( "*) 09 ( 0.3) 1 ( 11.3) 274 ( 1.7) .44 ( ...) 99 ( 02) 1 ( 0.2) 275 ( 12) .... ( .4.1 91 262 ( 0.5) ( 1.6) 2 ( ( 0.5) .41 97 ( 204 0.5) ( 1,7) ( 0.. ( 04) 95 261 ( 0.3) 1.6) 2 ( .44 0.3) ...) 07 ( 0$) 3 ( 0.5) 212 ( 12) ( 50 ( 2.11) 203 ( 2.2) 45 ( 3.2) 205 ( 2.4) 49 ( 2.1) 271 ( 2.0) 46 ( 2.6) 201 ( 2.2) 53 ( 1.7) 251 ( 14) 51 ( 2.6) 251 ( 2.1) 49 2.4) 200 ( 14) 47 ( 2.5) 251 ( 1.7) 2444411 43 $43 2U 2.0 249 2.2 4$ 30 47 262 2.6) 260 2.2) 50 2.11) $2 3.2) 51 ( 2.1 277 2.4 54 ( 2.61 ( 200 ( 1.9) 47 ( 1.7) 266 ( 2.1) 49 ( 2.6) 209 ( 2.1) 51 ( 2.4 262 ( 2.5 53 ( 2.5 2.3 ( 1.6 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 127 TABLE A19 I Students' Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROfICIENCY 1900 NAEP TRIAL STATE ASSESSMERT Working Problems in Class Doing Pro(lems al Homo Taking QuIzzas or Tests Almost Always ',ever Almost Always Never Almost Always Never TOTAL State Nation RACEIETHNICITY White State Nation Mack State Nation Hispanic State Nation As lan State Nation TYPE Of COMMUNITY Advantaged uhan State Nation Disattvantagad urban State Nation Extrema rtral State Nation Other State Nation Parventie pannatage Parma es Parambo Mereentage Paramte. mod aid and and and Praia Way Pro lidew Pracksicy Pesioknoy linsidsmay Pralkiamy 47 1.4) 26 1.7) 35 ( 1.4) 18 ( I 249 275 2.0) 255 ( 1.4) 271 2.2 48 1.5 23 1.9) 30 ( 1.3) 19 254 ( 15 272 1.4) 281 ( 1.8) 283 1.11 42 ( 1.13) 20 ( 2.2) 34 ( 1.5) 20 ( 1.2) 282 ( 11) 234 ( 1.9) 238 ( 1.8) 279 ( 2.2) 48 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 202 ( 1.7) 278 ( 1.3) 270 ( 1.7) 289 ( 2.3) 54 ( 2-3) 23 ( 2.3) 39 ( 1.9) 18 ( 1.6) 230 ( 1.9) 253 ( 3.4) 232 ( 2.2) 250 ( 3.9) 57 ( 3.2) 20 ( 3.9) 31 ( 2.9) 18 ( 1.9) 232 ( 24) 249 ( 4.0) 233 ( 3.3) 248 ( 5.5) 56 ( 17) 14 ( 2.7) 35 ( 4.0) 10 ( 2.2) 236 ( 3.2) ( 238 ( 4.5) "" ( ***) 51 ( 2.9) 18 ( 33) 28 ( 3.2) 21 ( 2.1) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1 ) 40 ( 4.5) 33 ( 5.1) 34 ( 4.3) 21 ( 4.7) It «NI *** ( *41 35 ( 8.3) 29 ( 5.8) 30 ( 8.3) 23 ( 4.4) 0,04) *44 ( HMI ) Re. ( MN') 43 ( 3$) 283 ( 4.3) 51 ( 5.4) 270 ( 4.7$ 49 ( 2.8) 223 ( 2.8)4 52 ( 3.1) 241 ( 3.8)4 443 ( 7.4) .41 40 ( 7.4) 248 ( 4.3)4 47 ( 2.2) 248 ( 2.3) 48 ( 1.9) 254 ( 2.1) 28 ( 4.3) 288 ( 5.3)4 23 (10.7) ( 28 ( 3.2) 252 ( 54) 22 ( 43) 259 ( 5.4)4 22 ( 6.8) 29 ( 6.5) 288 ( 8.1y 30 ( 2.9) 278 ( 2.8) 22 ( 2.0) 272 ( 1.8) 36 ( 271 ( 32 ( 274 ( 37 ( 227 ( 30 ( 24$ ( 38 ( 20 ( 4411 ( 33 ( 254 ( 32 ( 263 ( 22 247 27 253 1.0 2.0 1.4 24 36 270 30 274 1.8 1.5 2.0 1.3 18 ( 1.2) 41 ( 2.0) 203 ( 2.3) 283 ( 1.7) 25 ( 1.6) 32 ( 2.3) 283 ( 2.8) 279 ( 1.2) 31 ( 1,8) 29 ( 2.5) 231 ( 2..) 253 ( 25) 38 ( 3.3) 24 ( 3.1) 230 ( 3.6) 251 ( 41) 21 ( 3.3) 22 ( 3.2) ( "4) "4"` ( ***) 213 ( 2.7) 22 ( 3.1) 237 ( 3.2) 256 ( 4.2) 11 ( 3.4) 44 ( *RR 5.7) se..) 23 ( 5.8) 443 ( 41A) *** ( 444 ROM ( *if* ) 34) 3.7) 6.1) 4.9)1 2.7) 3.7)1 3.3) 52)4 7.5) .44) 2.5) ***) 2.3) 2.4) 1.7) 2.3) 18 ( 2.1) 287 ( 4.5)4 15 ( 2.4) ( .41 18 ( 1.8) *am. ( 24 ( 2.3) 254 ( 4.ey ( 23 ( 3.9) 263 ( 44)4 19 ( 1.8) 271 ( 3.2) 115 ( 1.1) 283 ( 2.8) 21 ( 267 ( 31 ( 281 ( 30 ( 223( 27 ( 240 ( 20 ( 24 ( cum, 20 ( 245 ( 27 ( 253 ( 2.8) 5.2)4 3,8) 7.6); 2.2) 3.1)4 2.9) 4.9)1 4.8) 8.8) 1.5) 2.9) 1.8) 2.7) 39 ( 290 ( 211 ( 285 ( 32 ( 253 ( 27 ( 283 ( 36 ( 37 ( 270 ( 40 ( 277 ( 29 ( 275 ( 4.7) 3.5) 9.8) 4,2)1 3.4) 3.8) 4.3) 5.0)4 3.4) 8.3) 4.0)1 2.5) 2.3) 2.1) 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). 123 3 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TABLE A19 I Students' Reports on the Use of a Calculator (continugd) 1 for Problem Solving or Tests PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE A3521311111T working Clan Problones in Doing Probisms AO Homo Toldng QuIzzos or Toes Almost Always Never Almost Atways Never Almost Always Never TOT State Nation 2811211 jaMEN NS noniraduste State Nation NS graduate State Nation Setae college State Nation College Indiana State Nation WPM Mae State Nation Female State Nation krao PiromMose Peretallisi Pqrsonble ANI em ad awl es 201 242,2102v. 7104122141, P740,002.14f PaillMenar P4020m2g 14141244122 A 144 ar. 11 36 IA 16 1 22 1.0 22 1.2) , SO 1.4 271 2.2 347 2,0 270 1.5 42 14 -...a to 12 19 0.9 27 1.4 30 2.01 SU i 272 14 MN Li 20 1.4 222 2.4 274 14 57 ( 33 191 titt 21 SI) 19 ( 31) lee I E!) 20 3.0) 237 ( 2.0 241 42) *". ( ") .... *Di 54 ( 3.5 191 WI) 33 3.1) 22 ( 22) 32 i 11.51 24 3.2) 240 ( 2.31 ( ) 244 ( 3.2) 244 ( 4.2) 237 ( 2.3 251 4.5) $0( 2.0) 22 ( 12 114 2.1) 16 ( 1.7 24 ( 2.0) 34 ( 2.0) 210 ( 2.2 242 2.2) 257 ( 3-0 224 ( 2.0) 261 ( 1.0 82 2.5) 20 ( 2.4 29 12) 16 ( 1.5 28 ( 12) 27 ( 2.2 20 14) 205 ( 2.7 350 2.4) 255 ( 2.4 248 ( 2.5) 205 ( 2.0) 4 ( 2.4) 28 ( 3.1) St ( 3.0) 19 ( 2.0) 22 ( 1.9) 35 ( 3.0) 254 ( 2.4) 274 ( 257 ( 2.5) 274 ( 3.0) 254 ( 32) 273 ( 2.0) 4 ( 2.5) 20 ( 2.41 Vi ( 2.0) 20 ( 1.9) 26 ( 2.4) 95 ( 2.5) 255 ( 2.1) 272 ( 2.5 26? ( 3.0) 206 ( 3.2) 255 ( 3.5) 275 ( 2.0) 40 ( 11) 30 1 2.5) 35 ( 11) 10 ( 14) 20 ( 1.5) 40 ( 2.8) 259 ( 2.0) 255 ( 22) NO ( 1.0) 252 ( 21) 250 ( 3.1) 245 ( 1.7) 45 ( 1.9) 25 ( 2.4) 33 ( 2.0) 18 ( 1.4) 2$ ( 1.5) 33 ( 2.7) 285 ( 1.7) 254 ( 1.5) 274 ( 22) 276 ( 2.5) 246 ( 2.6) 285 ( 2.0) 51 ( 1 0 23 ( 12 35 ( 1.5) 17 1.1) 21 ( 1.1) 32 ( 1.7) 250 ( 11 278 2.7 258 ( 1.8) 273 21) 248 ( 2.3) 279 ( 1.9) 50 ( 1.7 20 2.0 29 ( 1.8) 19 1.3) 27 ( 1.5) 2$ ( 2.1) 256 ( 4.9 275 2.2 264 ( 2.5) 265 ( 2.5) 258 ( 2.0) 277 ( 1.9) 42 ( 30 ( 1.8) 33 ( 1.7) 20 ( 1.3) 23 ( 1.5) 41 ( 1.9) 247 ( 2.0 273 ( 2.1) 253 ( 1.9) 299 ( 2.7) 247 ( 21) 273 ( 1.7) 48 ( 2.0 28 ( 2.1) 32 ( 1.8) 1$ ( 1.2) 27 ( 1.8) 33 ( 2.1) VA I 1.7) 2$9 ( 1.8) 259 ( 1/) 283 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated ttstistics 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 "Sornettnies" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). V? 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO *UP TMAL STATE ASSESSMENT - High "Cakulater-Use" Onto - Other "Caiodater-Uete Snap TOTA1. State Nation mamma %Mite State Nation Slack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged when State Nation Disadvantaged urban State Nation Extreme rurai State Nation Other State Nation Oralhisi afti *3 1.3 272 1 50 ( 1 261 ( 44 ( 1.4 277 ( 1. 33 ( 2.3) 246( 24) 37 ( 3.4) 2411 ( 3.2) 37 ( 33) 36 42) 25,4 ( 44) SS ( 42) SO 1 Se 14 SP V) 22 231 ( 232 2.4 63 111.4 63 ( 3.7 231 ( 4.1 64 ( 4.2 XS ( 3.0 42 ( 4.2) .. t .4,41 50 ( 4.8) 30 i 4.04 SO ( 2.1) 50 ( 2,1) 267 ( 3.3) 270 ( 4,1) 50 ( 3.8) 50 ( 3.8) 2$$ ( 4,9)1 275 ( 4.04)1 30 ( 2445 ( 4.1) 4.5)I ( zra 4.1) 44)4 38 ( 4.2) 02 ( 4.2) 262 ( 5.6)1 244 ( 3.2)1 $3 ( *44 ( 2.5) 0141 67 ( 2.5),) 39 ( 5.8) 81 ( 54) 282 ( 4,4)1 248 ( 4$)1 48 ( 11) 54 ( 1.7) 272 ( 2.7) 264 ( 2.e) 42 ( 1.4) 51 ( 1.4) 271 ( 1.2) 256 ( 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 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. *1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TABLE A20 I Students' Knowledge of Using Calculatois (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO MAO TRIAL STATE ASSESSMENT M. "Cacti lator-Uee" Group "Calculator-the" Group :TOTAL ferassease irraaelmoy Peramise and Preaciesscy State 46( 12) 14(1.2) 272 ( 252 1. Nation 42 ( 12) 51 ( 13 272 ( 1.6) 255 ( 1$) IsiiRENTS' EDUcATION HI non-graduat State 41 ( 4,6) 50 ( 4.6) ...., ( ) 296 ( 3.7) Nation 34 ( 3.3) 66 ( 3-3) 2411 ( 4.4) 242 ( 2.4) NS graduat State 90 ( 2.4) 61 ( 2.4) 256 ( 2.3) 240 ( 2.1) Nation 40 ( 22) 00 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some college State 47 ( 3.0) 53 ( 3.0) 270 ( 2.4) 256 ( 3.4) Nation 46 ( 22) 52 ( 22) 277 ( 2.6) 258 ( 2$) College graduate State 51 ( 1.7) 50 ( 1.7) 264 ( 2.1) 265 ( 2.0) Nation 48 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER Mai* State 42 ( 1.5) 58 ( 1.5) 274 ( 1.7) 254 ( 1.9) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 50 ( 1.8) 50 ( 1.8) 271 ( 2.0) 250 ( 2.1) Nation 45 ( 1.8) 55 ( 1.8) NO ( 1.7) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. I: 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 esthnate for the sample. **8 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE. ASSESSMENT 131 TABLE A24 I Students' Reports on --Y s of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11441 NAD TRIAL *TATE A9444INAINT Zero le rive Typos lTw Tss Fear Twos TOT State Nation legliMINEM VMS, State Nation Mak State Nation Hispanic State Nation Asian State Maks) 1236-V-021MIM Att41 Inialed tem State Nation INsadvastaged urban State Nation Wrong rind State Nation Othor State Nation 1001... r) 31.0111321 233 43 4: 237 SA 2 1 31 19 44 24 5.0 44 10 ( 1.4) 257 ( 52)4 14 ( Si) lopts ( 243 2 224 340$ 24 2.3) 32 32) .9)1 *al 14 SA) 17 4.9) IN* 14 ( 1.0) 244 ( 2.4) 22 ( 1.5) 244 ( 2.4) SS I 215 35 1% 111 223 41 244 43) 30 i.;1 24 ( 4.2) 33 ( del 271 ( 27 ( 20 ( 2.1 97 ( 2.0) 232 ( 4.0) 31 ( 2.3) 247 ( 3.7)4 ow. 5.4) 243" tit 250 ( 2.7 31 ( 30 ( 1.3 259 ( 2.2) 341 I'l 33 l O 3.3) 43 IA S al 347) 233 2A) 34 3.7) 30 23) .41 54 (4.1) 34 (4.2) *el 243 ( 3.2 41 ( 4.9 03 ( 237 ( SQI SE ( ti) 247 52p 257 4.9)1 37 &I) 43 (10.1) *b. «41 50 5.1) 243 ( 5.4)1 $1 ( 1.5) 210 2.7) 272 1.7) 44 1.5) The standard wort 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. *** Sampli size is insufficient to -rn tit a reliable estimate (fewer than 62 students). 132 I 7 THE 1990 NAEP TRIAL STATE ASSESSMENT Merykutd TABLE A24 I Students' Reports on Types of Reading (cmtinued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MOO MAEP TRIAL. STME ASSESSMENT Zero to Two Typos Theo Typos Four TVpos 12161 State Nation IMEittiniangi 14S non-graesito State Nation KS grackiato State Nation Sem collage State Nation College graduate State Nation GENDER M. State Nation Rotate State Nation 340 47"I 20 243 244: 20 1 1 240 ( 21 30 2.2 1143 ill 34 '1 253 fla 33 14 3110 1,1 1 1 347 ( 251 ( 4.0 17 I 111.141 NO 202 2 32 1 30 3.1) 274 1 $1 St 11 ( 12) 10 ( 1.0) 20 ( 12) $4 ( 14) 252 ( SS) 202 ( P.3) 10 ( 0.4) 21I ( 1.4) 279 ( 02 ( 2.0 254 ( 2A) 209 ( 3.5) MOO ( 1.41 17 ( 1.0) .1 51 ( 245 ( 2.4) k.... , .'.' 1) S1 ( 44) 270 i* 21 ( 115) 44 14 244 ( 23) 250 ( 2.1) 273 2.0 2.5) 254 ( t.9 30 ( 53 1.7) 41 ( 2 til ( 1.1) 22 ( 1.2) 29 ( IA 270 1 49 14 244 ( 2.2) 254 ( 14) 270 1.7 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, far each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the tam*. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 133 Maryland TABLE A25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1690 NAEP TRIAL STATE ASSEILIMENT Ono Hoar ar Laos 1Wo Hours - Three 'lours Fair to Flve Hours _ II Ix Hours or Mors TOTAL state Nation SACEXTHNOTY nite State Nation Mack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation 04eadvas Asgard urban State Nation Extreme rural State Nation Other State Nation OM Wisp sod Pragadwg, freillobeav Sollidspor sit Pnitiessi SkrollidsowS 277 SS) 11 OA) 2/2°1 °Q1 11 10f 16 208 12) 2es 1.4 SOS ( 13 20D ( 1.7 243 ( 12 0.6) 21 22 QS 26( 1.1 240 18 1 13 263 13 276 5 9 ( 24 ( ( 2.6 290 ( ( 1.0 23 ( ( 2.5) 275 ( ( 1.0) 10 ( ( ") 244 ( ( 0.6) 13 ( 1.3) 2.2) 1.2) 2.2) 1.3) 9.1) 1.1) *** ( --I no ( 7.0) 8 ( 1.7) 211 ( 3.1) *Ilir I tel i 1 14 ( 2.4) ... 20 i 2.5) ( "*) 245 ( 3.2) 23 ( 3.8) 23 ( 4.7) .44 ( 16 ( 5.0) 24 ( 4.2) 16 ( 1.6) 294 ( 5.9) 18 ( 1.4) ***) ( 1 A) *4-.) 10 ( 3.6) vii.) 14 ( 3.3) 10 ( 1.3) 273 ( 5.1) 12 ( 1.0) 266 ( 2.6) 24 ( 2.5) 286 ( 2.7)4 25 ( 4.3) ***) 14 ( 2.0) .44 ( 17 ( 3.1) 250 ( 4.0)1 20 ( 2.3) 41. van 19 ( 2.6) 18 ( 1.4) 271 ( 4.0) 21 ( 1.0) 2es ( 2.3) 24 ( 1.1) 27 ( 1.3) 273 ( 1.9) 270 ( 1.61 24 ( 1.1) 27 ( 1.4) 272 ( 1.9) 297 ( 1.7) 15 ( 1.2) 38 1.1) 240 ( 3.1) 239 2.5) 17 ( 2.1) 32 1.6) 236 ( 5,17.1) 239 ( 4.0) 20 ( 3.4) ( o) 30 .4 * ( 4.0) «A ( ) 19 ( 2.1) 31 ( 3.1) 242 ( 5.6) 247 ( 3.5) 15 ( 3.2) 28 ( 4.5) ( 22 ( 3.1) 23 ( 4.1) 4141 444 'en 22 ( 1.2) 26 ( 273) 277 ( 3.1) 270 ( 4.5) 21 ( 1.0) 30 44* ( 4.3) .4..) 15 ( 1.6) 33 ( 2.1) 233 ( 6.0)4 19 ( 2.1) 34 ( 2.4) 255 ( 5.0)4 251 ( 4.7)1 20 ( 4.1) 2$ ( SA) ( *dr* ***) 2$ ( 2.0) ( *el as ( 2.7) 256 ( so)4 21 ( 1.4) 32 ( 1.6) 265 ( 2.7) 290 ( 2.1) 23 ( 1.2) 27 ( 1.2) 255 ( 2.1) 259 ( 2.2) 12 ( 1.0) 253 ( 2.4 12 ( 1.2 253 ( 2.11) 34 ( 2.0) 232 32 2.2 233 2.5 22 ( 2.9) ( ) *** 17 ( 1.7) 236 ( 3.8) ( 2.2) yr** ( 13 ( 4.0) *** 11 ( 2.1) 244 ( 4.4)4 6( 2.0) 31 ( 2.6) ns ( 2.6)1 20 ( 3.2) 236 ( 4.5)1 21 ( 3.1) ( *on 10 ( 3.6) oimi) 20 ( 1.3) 244 ( 2.4) 17 ( 1.4) 248 ( 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). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Marylaid TABLE A25 I Students' Reports on the Amount of Time Spent (wntinued) i Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1NO NAEP TRIAL STATE ASSEUVENT . One Hour or Lees 1Wo Howe _ Three Nam For to Flve Sours litx Nous or More TOTAL State Nation finisamsmse NS non-graduate State Nation NS graduate State Nation Soma college State Nation Wisp graduate State Nation WEE Male State Nation Female State Nation ONO 1.0) 20 ( Si) ( *el Veropollp, iimpro 'Med It 1.0) 12 14) 1$ ( 1.4) SIS(IsS) 2s1 2.6) 234 2.4) ( 1.0) 17 14) 23 2.0) 249 ( 4.7) 257 ( 2.4) 2119 3.2) 10 ( 14) .01 19 ( 2.1) 276 ( 3.4) 22 ( 297 1.6) 3.2) 10 1.4) 24 ( 2.4) 23 ( 2.4) *41 275 ( 2.7) 204 ( 14 ( 1.3) 24 ( 1.4) 22 ( 1.1) 293 ( 3,5) 244 2.6) 273 ( 2.0) 17 ( 1.3) 22 1.4) 23 ( 1.1) 292 ( 2.4) 240 (2.5) 277 ( 2.2) ( 0.8) 19 ( 12) 22 ( 1.1) 275 ( 4.7) 274 3.1) 264 ( 1.9) 11 ( 0.8) 22 1.2) 22 ( 1.0) 208 ( 3.3) 207 2.6) 267 ( 22) 13 ( 1-0) 21 ( 1.3) 19 ( 1.0) 278 ( 3.5) 271 ( 2.5) 265 ( 2.7) 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 208 ( 2.8) 208 ( 2.2) 264 ( 1.8) 14104110111/ trellokier $17 14 10 3. 0 241 2.0 1.1 10 246 1 1.7) 31 ( 2,T) 24(' SA) ( *In 20 ( 244 ( 3.2) ** 0111 1.6 23 ( 1.7) 246 232 ( 2.2) 32 2.3 19 ( 1.6) 253 ( 2.5 248 ( 3,0) ( 2.1) 17 1.7) 200 3.3 245 3.4) 2$ ( 2.2 14 ( 1.5) 207 ( 2.5 242 ( 3.4) 20 ( 1.1 14 ( 1.3 287 ( 1.7 248 ( 2.8 25 ( 1.5 12 ( 1.1) 270 ( 2.4 255 ( 3.2) 31 (1.3) 19 ( 1.1) 258 ( 1.7) 242 ( 2.1) 26 ( 1.3) 17 ( 1.5) 262 ( 2.1) 246 ( 2.5) 28 ( 1.4) 1$ ( 1.1) 250 ( 2.1) 237 ( 2.1) 28 ( 1.0) 15 ( 1.2) 258 ( 1.9) 24/ ( 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Maryland TABLE A26 I Students' Reports on the Numbu of Days of 1 School Missed PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 13110 NAEP TRIAL !TAT Meal/MUT E , Nano - Ono or Ivo Days - Throe Days or Mors TOTAL flowligt aid Proidomer State 208 1.1 Nation 45 1.1 1.$ BeEEIHNICI TY White State 35 ( 1.4) 273 ( 1.7) Nation ( 1.2) 273 ( 1.41) Slack State 37 ( 2.0) 343 ( 2.4) Nation 56 ( 3.1) 240 ( 3.2) Hispanic State 31 3.5 241 ( 4.0 Nation 41 ( 3.3 245 ( 4.8 Asian State 50 ( 4.0) 29$ 3-9) Nation 82 SA) 257 ( 4.7)1 TYPE OF COMMUNITY Advantapd urban State 44 ( 2.3) 281 ( 4.2) Nation 47 ( 2.3) 2e4 ( 4.4)4 Disadvantaged urban State 34 ( 2.7) 2341 ( 4.2) Nation 42 ( 3.3) 254 ( 3.7)1 Extreme rural State 40 ( *-0,.. ( 2.2) .H.,.) Nation 43 ( 4.4) 257 ( 4.1)4 Other State 35 ( 1.7) 265 ( 24) Nation 45 ( 1.3) 265 ( 2.2) 272 ( 1. ( SO ( 22 St ( 1.2 23 lag SO $4} 1.2) M 2.1 21 1.2 33 ( 13 23 2 340 4.1 224 ( 2 3 24 *+4 2 32 ( 2.2) 2 31 27{ ~ 2.6) 250 ( 3.3) 235 ( 3.1) *44 ( .41 tl? 211 ( 4.6) 27 es*11 ( ( 2.6 37 ( 31 le ( 18) 271( 4.0 211 ( *A) 15 ( 3.7) 279 ( 4.5)1 owe ( ....) 30 ( 23) Se ( 34) 25$ ( 4.2)1 )4 2.7) 3.6$ 21( 1.3) 232 6.3 32 235 ( 3.1$ 30( 3.7) 24 ( 3.9) ( ***) 114* ( ihIn 32 ( 4.2) 25 ( OM 204 ( 5.2p ..... ( ...k.) 37 ( 1.4) 27 ( 1.4) 265 ( 2.4) 251 ( 3.5) 32 ( 1.1) 23( 1.1) 26( ( 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 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. 8" Sample size is insuffident to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE A26 I Students' Reports on the Number of Days of (continued) I school missed PERCENTAGE Of STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT None One or Two Days Uwe* Days or Mors TOTAL Pore Wags aid Peratatios Pilatimar 03490110, State $7 ( 1.1) 214 ( 1.7) 250 1.41 Nation 45 ( 1.1) 32 tai 33 1.1 ffifinn:lareinall 205 ( 14) SO 14) 250( 1.0 NS non-graduate State 281 31 34 (31) 33 ( 3.5) 144 *Mb 232 ( Nation 30 ( 3.2) 20 ( 35 ( 3.5 245 ( 3.0) 249 ( 3.31 237 ( 3.1 KS graduate State 1.9) 35 ( 14 31 ( 1.1) 253 2.1) 250 ( 2.2 235 ( 14) Nation 43 2.1) 31 ( 1.91 27(13 ) 235 2.0) 257 ( 24) 249 ( 2.4) Some college State 34 2.0) 30 ( 2.0) 30 ( 22) 263 2.8) 281(2.3) 257 ( 3.9) Nation 40 1.3) 37 ( 115) 23 ( 1.0) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) Collor graduat State 41 ( 14) 38 1.5) 21 ( 1.5) 277 ( 2.1) 275 2.0) 207 ( 2.7) Nation 51 ( 1.6) 33 12) 16 ( 1.3) 275 ( 2.1) 277 1.7) 206 ( 3.1) GENDER M. State $0 ( 1.4) 35 ( 1.3) 26 1.3) 206 ( 2.0) 262 ( La) 252 ( 14) Nation 47 ( 1.6) 31 ( 1.4) 22 1.4) 206 ( 2.0) 207 ( 2.1) 250 ( 2.8) Fen" Stet: 34 ( 1.4) 38 ( 14) 26 1.4) 206 ( 2.1) 265( 1.7) 248 2.3) Nation 43 ( 1.4) 32 ( 1.1) 25 ( 1.3) 204 ( 23) 286( 250 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable fltirnate (fewer than 62 students). 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 Maryland TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1100 MEP TRIAL STATE ASSESSMENT Sir= Mt/ Al Imo AI Pim Undecided, Disagree, Strongly Disagree TOTAL State Nation RACE/ETHNICITY State Nation Slack State Nation Hispank State Nation liall State Nation TYPE OF COMMUNITY Advantaged intan State Nation Disadvantaged urban State Nation Extreme ruraI State Nation Other State Nation Poniumbe and 27 ( 1.1) 27$ ( 1.9) 28 ( 1.8) 279 ( 2.0) 35 2.0) 245 2.4) 32 2$) 247 4.1) 28 ( 2.7) ea* 24 ( 2.5) 257 ( 5.5) S$ ( 47) ( .61 29 ( 5$) ( sin 31 ( 2.4) 2645 ( 3.4) 17 ( 3.2) 32 ( 2.8) 241 ( 5.0)4 24 ( 2.9) 260 ( 5.6)4 31 ( 1.4) 34 ( 2.8) 270 ( 3.9)1 31 ( 1.6) 267 ( 2.1) 27 ( 1.4) 271 ( 2,4) lisramdap and IlivasINEW 62 ( 1.1) 274 ( 1.6) 4$( 1.3) 272 ( 1.8) 47 ( 1.9) 238 ( 2.3) 52 ( 2.3) 233 ( 3.3) $3 ( SA) 237 ( 3.5) 41 ( 2.0) 244 ( 22) 49 ( 5.1) 53 ( 5.8) ( ire') 53 ( 2.2) 274 ( 3.5) 55 ( 2.4) 280 ( 4.1)1 50 ( 3.0) 232 ( 4.5)1 4$ ( 2.9) 244 ( 4.6)1 41 ( 3.4).) 411 ( 2.2) 252 ( 4.1)1 491 241 ( 2.8 48 ( 1.2 263 ( 22) floremisp owl 20 ( 250 2.0 24 1.2 251 16) 20 ( 1.1) 202 ( 2.3) 26 ( 1.5 257 ( 2.0 16 ( 1.5) 227 ( 26) 16 ( 16) 227 ( 4.2) 21 ( 2.9) *4* ( Nal 20 ( 2.1) 236 ( 3.4) 13 ( 2.1) gomit 17 ( 4.9) 16 ( 1.8) 250 ( 6.4) 28 ( 4.2) 18 ( 2.4) MI* ( *In 26 ( 32) 240 ( 44)1 *41 17 ( 1,4) ( 20 ( 1.2) 254 ( 3.2) 25 ( 1.4) 250 ( 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. 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). 143 131 THE 1990 NAEP TRIAL STATE ASSESSMENT Maryland TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT ... 611'0R9V Agree _ Arse , Undecided, Disagree, "ma* Memo TOTAL Perientige Mildew 207 27 1.3 271 12 31 ( 3.1 ( .44 20 ( 2.0) .44) 26 ( 1.6) 253 C 2.7) 27 2.1) 262 21) 30 22) State Nation PARENTS' !VOCATION NS non-graduate State Nation NS graduals State Nation Soma colter State 260 ( 3.1) Nation 20 ( 2.5) 274 ( 3.1) College graduate State 32 ( 1.6) 260 ( 2.1) Nation 30 ( 2.3) 2$0 ( 2.4) GENDER M. State 30 ( 1.3) 267 ( 2.1) Nation 2$ ( 1.5) 273 ( 2.3) Amato State 30 ( 1.2) 208 ( 2.0) Nation 26 ( 1.7) 209 ( 2.1) Pamstall awl Ihreadesmw 100,0***911 and foralisiow 3111 11 1502° $(.1 49 1 24 ( 1.2 202 1.7 251 ( 1.$ 49 3.2) 246 3.9) 50 3.3) 243 ( 2.9) 49 ( 2.0) 24$ ( 2.2) 47 ( 2.1) 255 ( 23) 53 ( 2.4) 264 ( 2.2) 47 ( 2.4) 267 ( 1.9) 50 ( 13) 274 ( 1.9) 51 ( 1.0) 274 ( 2.2) 51 ( 1.2) 281 ( 1.0) 48 ( 1.2) 263 ( 2.0) 51 ( 1.3) 261 ( 2.0) 50 ( 1.7) 262 ( 12) 20 ( 3.1? **a 30 ( 3.11) 231 ( 4.3) 24 ( 1.9) 240 ( 2.6) 24 ( 2.0) 245 2.4) 17 ( 1.7) 251 ( 3.7) 25 ( 1.6) 251 ( 32) 1$ ( 1.0) 264 2.8) 19 1.8) 206 ( 2.5) 20 ( 1.0) 251 ( 2.3) 24 ( 1.4) 251 ( 2,4) 20 ( 1.1) 249 ( 2$) 25 ( 1.9) 252 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 9$ perctent cxrtainty 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 ituufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and 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 (ETS), Westat, and National Computer Systems (NCS). The pmgram benefitted from the contautions of hundreds of individuals at the state and local levels Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Finally, and most 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) far its considerable contributions to the program, especially its management of the National Assessment Planning Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In particular, we note the significant contributions of Ramsay Se !den, Director of the State Education Assessment Center for the CCSSO and the members of the Steering. Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational 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 Gornian, Maureen Treacy, and Raul Garza -- worked closely and collegially 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 districts, colleges and universities, and State Education Agencies workcd tirelessly to help ETS staff develop the assessment and a framework for interpreting the results. 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 John Mazzeo, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspectg Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffier, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and procescing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zaback. 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 on its characteristics 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 text 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 Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koffier wrote the text for the report. Kent Ashworth was responale 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. 1 U.S. GM:CRAB:NT PRINTING orrics : 1991 0 - 293-275 QL MK. 19/