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DCCUMENT RESUME ED 330 569 SE 052 079 TITLE The State of Mathematics Achievement in New Hampshire: Me Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NC 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 availab3e directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior 7igh Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS National Assessment of Educational Progress; *New Hampshire; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for tha first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. Th3 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In New Hampshire, 2,568 students in 98 public schools were assessed. This report describes the mathematics proficiency of New Hampshire 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 (curriculUm coverage, amount of homework); delivery of math instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, New Hampshire students had an average proficiency of 273 compared to 261 nationwide. Many fewer students (New Hampshire-17%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics A in NEW HAMPSHIRE The Trial State Assessment. at Grade Eight ?EST MY AVAILABLE 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 tNAEP). is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1969. 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 part 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 carrying out the NAEP project through competitive awards to qualified organiintions. NAEP reports directly to the Commissioner, who is also responsible for providing continuing reviews, including validation studies and solicitaion of public comment, on NAEP's conduct and usefulness. In 1985, Congress created the National Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The hoard is responsible for selecting the subject areas to be assessed, which may include adding to those spevified 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 standanis and procedures for invrstate. 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 free from racial, cultural, gender. or regional bias. The National Assessment Governing Board Richard A. Boyd, Chairman Executive Director Martha Holden Jennings Foundation Cleveland. Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.O.C.F.S. Sarutoga Springs, New York Franck Alexander Associate Superintendent California Department of Education Sacramento, California David P. Battini High School Hi,tory Teacher Cairo-Durham High School Cairo. New York Parris C. Battle Teueher Horace Mann Elementary Sehool Miami. Florida Mary R. Blanton Attorney Cromwell, Porter. Blanton & Blanton Salisbury. North Carolina Boyd W. Boehlje Attorney Gaass, Klyn, & Boehlje lowa Linda R. Bryant Teacher Greenway Middle School Teacher Center Pittsburgh. Pennsylvania Honorable Michael N. Castle Governor of Delaware Carve! State Office Building Wilmington. Delaware Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hartford, Conneeticut Chester E. Finn, Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.C. Michael S. Glade Wyoming State Board of Education Saratoga. Wyoming Christine Johnson Principal Abraham Lincoln High School Denver, Colorado John Lime ley Principal South Colby Fleme..tary Sehool Port Orchard. Washaigton Carl J. Moser Directe... of Sehoo ls 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 Fort Smith, Arkansas Matthew W. Prophet, Jr. Superintendent Portland Oregon School District i'ortland. Oregon Honorable William T. Randall Commissioner 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 Rogotienski Coronado, California Herbert J. Walberg Professor of Education University or Illinois Chicago, Illinois Assistant Secretary for Educational Research and Improvement (Ex-Officio) U.S. Department of Education Washington; D.C. Roy Truby Executive Director. NAGB Washington. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The SUM of 11/1 hematites Achievement in NEW HAMPSHIRE The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement 13nmo V. Manr, 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. Far catering 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 supplits last, write: Education Information Branch Office of Educational Research and Imworament U.S. Department of Education 555 New Jersey Avenue, NW Washington. D.C. 20208-5641 or call 14300424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Comma, Catalog Card Ninnba: 91-61473 ISBN: 043615-14-9 The week upon which this publication is based was perfonned for the National Caner for Education Statistics. Office of Educational Reseatch and Imp:wallas, by Educational Muting Service. Educational Ustins Service is an equal . laflionative action aturbyer, Educational Talks Servico, EIS, and ant registered tradenutrics of Educational Testing Service Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION 7 Overview of the 1990 Trial State Asseirsment 8 This Report 9 Guidelines for Analysis 12 Profile of New Hampshire 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PA RT ONE How Proficient in Mathematics Are Eighth-Grade Students in New Hampshire Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 Levels of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race/Ethnicity 24 Type of Community 27 Parents' Education Level 29 Gender 31 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT Ci lu 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 DeliverecP 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used/ 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics'' 67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 iv THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's hiitory -- a provision authorizing voluntary state-by-state assescrnents on a trial basis, in addition to continuing its primary mission, the national assessinccts that NAEP has conducted since its inception. As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Progam 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 of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in thc. program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT 1 New Hampshire In New Hampshire, 98 public schools participated in the assessment. The weighted school participation rate was 97 percent, which means that all of the eighth-grade students in this sample of schools were representative of 97 percent of the eighth-grade public-school students in New Hampshire. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 0 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 12 percent had an IndMdualized Education Plan (1EP). An 1EP 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 assessmt-nt. The students who were excluded from the assessment because they were categorized as LEP or had an 1EP represented 0 percent and 5 percent of the population, respectively. In total, 2,568 eighth-grade New Hampshire public-school students were assessed. The weighted student participation rate was 95 percent. This means that the sample of students who took part in the assessment was representative of 95 percent of the eligible eighth-grade public-school student population in New Hampshire. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from New Hampshire on NAEP mathematics scale is 273. This proficiency is higher than 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 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. 9 2 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire In New Hampshire, 100 percent of the eigLth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in New Hampshire (17 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric poperties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in New Hampshire performed higher than students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the New Hampshire eightb-grade student population defmed by race/ethnicity, type of community, parents' education level, and gender. In New Hampshire: White students had higher average mathematics proficiency than did Hispanic students. Further, a greater percentage of White students than Hispanic students attained level 300. The results by type of community indicate that the average mathematics performance of the New Hampshire students attending schools in advantaged urban areas was about the same as that of students attending schools in extreme rural areas and areas clas,sified as "other". In New Hampshire, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 28 points higher than that of students whose parents did not graduate from high school. The results by gender show thi there appears to be no difference in the average mathematics proficiency of eighth-grade ina les and females attending public schools in New Hampshire. In addition, there was no difference between the percentages of males and females in New Hampshire who attained level 300. Compared to the national results, females in New Hampshire performed higher than females across the country; males in New Hampshire performed higher than males across the country. THE 1990 NAEP TRIAL STATE ASSESSMENT 3 New Hampshire 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, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information about student achievement. Some of the salient results for the public-school students in New Hampshire are as follows: Less than half of the students in New Hampshire (38 percent) were in schools where mathematics was identified as a special priority. This is a smaller percentage than that for the nation (63 percent). In New Hampshire, 82 percent of the students could take an algebra course in eighth grade for high-school course placment or credit. A greater percentage of students in New Hampshire were taking eighth-grade mathematics (55 percent) than were taking a course in pre-algebra or algebra (43 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Accord;mg to their teachers, the greatest percentage of eighth-grade students in public schools in New Hampshire spent 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 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. 11 4 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire In New Hampshire, 15 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 23 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In New Hampshire, 30 percent of the students never used a calculator to work problems in class, while 32 percent almost always did. In New Hampshire, 35 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. More than half of the students (60 percent) had teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in New Hampshire 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 students who had zero to two types. Some of the eighth-grade public-school students in New Hampshire (17 percent) watched one hour or less of television each day; 7 percent watched six hours Or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. 12 THE 1990 NAEP TRIAL STATE ASSESSMENT 5 New Hampshire ME NATION'S REPORT CARO INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Gcorgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands 4.1 THE 1990 NAEP TRIAL STATE ASSESSMENT 7 New Hampshire This report describes the performance of the eighth-grade public-school students in New Hampshire 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 New Hampshire. Part One describes the mathematics performance of the eighth-grade public-school students in New Hampshire, the Northeast region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in New Hampshire, the Northeast region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the projert'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 instrwnent 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)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(i))) As a result of the legislation, the 1990 NAEP progfam included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The re.ults of the monitoring indicated a high degree of quality and uniformity across sessions. 8 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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 authorized le 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 grade eight. An everview 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 New Hampshire, in the Northeast region, and for the nation. Results also arc provided for groups of students defined by shared characteristics -- race/ethnicity, type of community, parents' education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for New Hampshire are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nationally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAFP program was necessary because the voluntary nature of the Trial State Assessment Program did not guarantee representative national or regional results, since not every state participated in the program. 2 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 9 New Hampshire 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 Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Procedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for New Hampshire. TYPE OF CONLMUNITY Results are provided for four mutually exclusive community types -- advantaged urban, disadvantaged urban, extreme rural, and other -- as defmed below: Advantaged Urban: Students in this group live in metropolitan statistical arms and attend schools where a high proportion of the students' parents are in professional or managerial positions. Disadvantaged Urban: Students in this group live in metropolitan sta.istical 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 metropolitan statistical areas, live in areas with a population below 10,000, and atteA schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defmed 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. i 6 30 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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 I. 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 Noitheast 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 bc to the Southeast. FIGURE 1 I Regions of the Country NE NATION'S REPORT I"Grmir CARD NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Alabama Illinois Alaska Delaware Arkansas Indiana Arizona District of Columbia f Wilda Iowa California Maine Giorgi," Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana New Jersey North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohlo Oklahoma Rhode island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Uta h Washington Wyoming .; 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 11 New Hampshire Guidelines for Analysis This report &scribes and compares the mathematics proficiency of various subpoptilatiora 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 proficiency are based on samples -- rathes 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 sigmficant), 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 1 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 hetween 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 the 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. I S 12 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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 contidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests arc based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined goup (reported in the text) may differ slik,htly 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 result's of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT 13 New Hampshire Profile of New Hampshire EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISMCS Table I provides a profile of the demographic characteristics of the eighth-grade public-school students in New Hampshire, 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 New Hampshire Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS - MO NAEP TRIAL STATE ASSESSMENT Now Hampshire Northeast Nation DEMOGRAPHIC SUBGROUPS Percentage Percentage Percentage Race/Ethnicity White 94 ( 0.6) 80 ( 4.2) 70 ( 0.5) Black 1 ( 0.2) 12 ( 4.2) 16 ( 0.3) Hispanic 2 ( OA) 5 ( 1.2) 10 ( 0.4) Asian 1 ( 0.2) 3 ( 1.1) 2 ( 0.5) American Indian 2 ( 0.2) ( 0.3) 2 ( 0.7) Type of Community Advantaged urban 8 ( 0.5) 23 ( 7.3) 10 ( 3.3) Disadvantaged urban 0 ( 0.0) 8 ( 5.7) 10 ( 2.8) Extreme rural 3 ( 0.6) 14 (10.3) 10 ( 3.0) Other 89 ( 0.8) 55 (11.2) 70 ( 4.4) Parents' Education Did not finish high school 6 ( 0.6) 7 ( 2.2) 10 ( 0.8) Graduated high school 25 ( 0.8) 23 ( 3.3) 25 ( 1.2) Some education after high school 19 ( 0.9) 15 ( 3.0) 17 ( 0.9) Graduated college 46 ( 0.9) 49 ( 5.8) 39 ( 1.9) Gender Male 53 ( 1.1) SO ( 2.1) 51 ( 1.1) Female 47 ( 1.1) SO ( 2.1) 49 ( 1.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages for Race Ethnicity may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know.- Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 2 0 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire SCHOOLS AND STUDENTS ASSFSSED Table 2 provides a profile summarizing participation data for New Hampshire schools and students sampled for the 1990 Trial State Assessment. In New Hampshire, 98 public schools participated in the assessment. The weighted school participation rate was 97 percent, which means that all of the eighth-grade students in this sample of schools were representative of 97 percent of the eighth-grade public-school students in New Hampshire. TABLE 2 I Profile of the Population Assessed in I New Hampshire 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 91% 97% 107 3 4 THE 1990 NAEP TRIAL STATE ASSESSMENT EIGHTH-ORADE PUBUC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups 95% Number of students selected to participate in the assessment 2,922 Number of students withdrawn from the assessment 80 Percentage of students who were of Limited English Proficiency 0% Percentage of students excluded from the assessment due to Limited English Proficiency 0% Percentage of students who had an Individualized Education Plan 12% Percentage of students excluded from the assessment due to Individualized Education Plan status 5% Number of students to be assessed 2,710 Number of students assessed 208 15 New Hampshire In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 0 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 12 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 0 percent and 5 percent of the population, respectively. In total, 2,568 eighth-grade New Hampshire public-school students were assessed. The weighted student participation rate was 95 percent. This means that the sample of students who took part in the assessment was representative of 95 percent of the eligible eighth-grade public-school student population in New Hampshire. 16 THE 1990 NAEP TRIAL STATE ASSESSMENT ME NATION'S REPORT CARO PART ONE How Proficient in Mathematics Are Eighth-Grade Students in New Hampshire 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 NAEP 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 New Hampshire. Chapter 1 compares the overall mathematics performance of the students in New Hampshire to students in the Northeast region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 summarizes the students' overall mathematics performance for subpopulations defmed by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. : THE 1990 NAEP TRIAL STATE ASSESSMENT 1 7 New Hampthire CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-gra& public-school students from New Hampshire on the NAEP mathematics scale is 273. This proficiency is higher than that of students across the natiou (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency NAEP Mathematics Scale 0 200 225 250 275 300 500 Average Proficiency New Hampshire 273 ( 0.8) Northeast 289 ( 3.4) Nation 281 ( 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. a Differences reported are statistically different at about the 95 percent certainty level. This means that with about 9 5 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 2 et 18 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Defmitions of the four levels of mathematics proficiency are 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 levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In New Hampshire, 100 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in New Hampshire (17 percent) and 12 percent in the nation appear to have acquired masoning and problem-solving skills involving fractions, decimals, percnts, elementary geometric properties, and simple algebraic manipulations (level 300). CONTENT AREA PERFORMANCE As previously indicated, the questions comprising the Trial State Assessment covered five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Figure 5 provides the New Hampshire, Northeast region, and national results for each content area. Students in New Hampshire performed higher than students in the nation in all of these five content areas. r. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 New Hampshire FIGURE 3 I Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-step word problems and select the greatest four-digit number in a list. In measurement, these students can read a ruler as well as common weight arid 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 tile algebra dimension, these students can recognize translations of word problems to numerical sentences and extend simple pattern sequences. LEVEL 250 Simple Multiplicative Reasoning and Two-Step Problem Solving Stoi:nts at this level have extended their understanding of quantitative reasoning with whole numbers from additive tO multiplicative settings. They can Solve routine one-Step multiplication and division problems involving remainders and two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to other elementary Nvo-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. 26 20 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire FIGURE 3 I Levels of Mathematics Proficiency (continued) 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 edence 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 number and algebraic understanding to include some properties of exponents. They can recognize scientific notation on a calculator and make the transition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles tt, solve problems. They can find the circumferences of circles and the surface areas of solid figures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirect measurement. These students also can apply their knowledge of the properties of geometric figures to solit oblems, 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. r 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 New Hampshire FIGURE 4 I Levels of Eighth-Grade Public-School 1 Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation freal 1144044 1.^11041 1101.111111.11 140,04 144 0 20 40 ( 0.2) 0 ( 0.5) 0 ( 0.2) 79 ( 1.2) 72 ( 4.8) 64 ( 4.6) 100 ( 0.2) 99 ( 0.6) 97 ( 0.7) 60 80 100 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 1-44). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 22 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire FIGURE 5 I Eighth-Grade Public-School Mathematics Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation DATA ANALYSIS, STATISTICS, AND PROBABILITY ALGEBRA AND FUNCTIONS 0 200 225 250 275 Averap Proficiency 275 ( 1.0) 271 ( 3.1) 2$6 ( 1.4) 272 ( 1.3) 266 ( 4.7) 268 ( 1.7) 272 ( 1.0) 268 ( 3.6) 259 ( 1.4) 276 ( 0.9) 273 ( 3.6) 262 ( 1.8) 271 ( 1.0) 267 ( 3.4) 260 ( 1.3) SOO Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by H-4). If the confidence intervals for the populaUons do not overlap, there is a statistically significant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT 23 New Hampshire CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY The Trial State Assessment results can be compared according to the different racial/ethnic groups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White and Hispanic students from New Hampshire are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Hispanic students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Hispanic students attained level 300. 30 24 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire FIGURE 6 I Average Eighth-Grade Public-School 1 Mathematics Proficiency by Race/Ethnicity MEP Mathematics Scala 200 225 250 275 300 SOO Avaraiia , 1tal New Hampshire White 1,4 0.1t) Hispanic SU 31) Nalhaast White . 274 ( 3.0) Hispanic 16111 Nation White 211 ( 1$) Hispanic X3 ( 2.13) 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 1-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. *** Sample size is insufficient to permit a rehable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 25 New Hampshire THE NATION'S REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARD Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Hispanic RIRSon White Hispanic Nation White Hispanic LEVEL 250 State White Hispanic MPS Ion White Hispanic Nation White Hispanic LEVEL 200 State White Hispanic Region White Hispanic Nation White Hispanic 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 1-4-4). 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. *** Sample size Is insufficient to permit a reliable estimate (fewer than 62 students). 100 26 THE 1990 NAEP TRIAL STATE ASSESSMENT Percentage 18 ( 1.2) 4 ( 3.1) 18 ( 2.5) IS ( 1.5) 3 ( 1.1) 80 ( 1.2) 58 (10.8) 78 ( 4.8) mu, ) 74 ( 1.8) 41 ( 4.5) 100 ( 0.2) 98 ( 2.1) 100 ( 0.0) mut ...) ( 0.4) 93 ( 1.6) New Hampshire TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, extreme rural areas, and areas classified as "other". (These are the "type of ccmmunity" groups in New Hampshire with student samples large enough to be reliably seported.) The results indicate that the average mathematics performance of the New Hampshire students attending schools in advantaged urban areas was about the same as that of students attending schools in extreme rural areas and areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community New Hampshire 1-40101 Advantaged urban 2 ( 16) 1-40114 Extreme rural 278 ( * Other 214 ( 0.8) Northeast Advantaged urban 278 ( 11..0)1 Extreme rural Other 272 3J1) Nation 1-1Pal Advantaged urban 3.88 Iwermi Extreme rural ( 4.1y Other 2111 ( 18) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 27 New Hampshire FIGURE 9 LEVEL 300 State Adv. urban Ext. rural Other Raglan Adv. urban Ext. rural Other Nation Adv. urban Ext. rural Other LEVEL 250 State Mv. urban Ext. rural Other Region Adv. urban Ext. rural Other Nation Mv. urban Ext. rural Other LEVEL 200 Stall Adv. urban Ext. rural Other Region Adv. urban Ext. rural Other Nation Adv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent wrtainty. 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 confident,- intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *'* Sample size is insufficient to permit a rehable estimate (fewer than 62 students). 27 ( 3.3) 24 ( 7.8)1 17 ( 1.1) 22 ( 8.7)1 nem ) 1$ ( 2.6) 26 ( 4.8)1 6 ( 2.3)1 12 ( 1.2) 113 ( 4.2) 81 ( 5.2)1 80 ( 1.2) 12 ( 9.5)1 MUM ( ) 77 ( 4.4) 83 ( 4.6)1 ( 6.2)1 64 ( 23) 100 ( 0.0) 100 ( 0.9)1 100 ( 0/1 100 ( 0.0) *.) 96 ( OA) 100 ( 0.0) 87 ( 2.8)1 97 ( 1.0) 100 28 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In New Hampshire, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 28 points higher than that of students who reported that neither parrnt graduated from high school. As shown in Table 1 in the Introduction, a larger percentage of students in New Hampshire (46 percent) than in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 6 percent for New Hampshire and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School I Mathematics Proficiency by Parents' Education NAEP Alathamatics Scala 0 200 225 250 275 300 500 Averap Proficioncy Aggawwwwwwwwwwwq New Hampshire HS non-graduate $34 2.4) HS graduate 241 ( 1.1) Some college 272 ( 15) N4 College graduate 213 ( 1.1) Northaast HS non-graduate 4.41 HS graduate 218 ( 2.3) P-1111 Some college 2.14 2.4) College graduate $3 4 3.6) Nation HS non-graduate 943 ( 2.0) POI HS graduate 264 ( 14) Some college M( 1.7) College graduate 274 ( 1.6) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1.4.1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 3 :"; THE 1990 NAEP TRIAL STATE ASSESSMENT 29 New Hampshire THE NrON'S REPORT FIGURE Il I Levels of Eighth-Grade Public-School cARD Mathematics Proficiency hy Parents' Education LEVEL 300 slate HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. Ragion HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. 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 I44). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 ( 2.3) ( 1.1) 15 ( 2.4) 25 ( 1.7) ( 2.8) 13 ( 2.7) ( 4.3) 1 ( 0.9) 5 ( 1.5) 12 ( 1.4) ( 12) 57 ( 8.3) ( 2.5) ( 2.4) 06 ( 1.4) mor 12 ( 5.9) 71 ( 4.5) 110 ( 4.6) 37 ( 4.6) 543 ( 2.7) 71 ( 2.6) 7$ ( 2.0) OS ( 2.0) 59 ( 0.7) 100 ( 0.0) 100 ( 0.1) mo, ..) ( 0,0) SO ( 1.4) 00 ( 0.4) Se ( 1.9) 07 ( 0.8) ( 0.7) ( 0.7) 100 3 6 30 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire GENDER As shown in Figure 12, there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in New Hampshire. Compared to the national results, females in New Hampshire performed higher than females across the country; males in New Hampshire performed higher than males across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender NAEP Mathematics Scala 200 225 250 275 300 500 Average Prencioncy New Hampshire Male Female 4111MIIIMIMPIM.M1 273 ( 02) 274 ( 1.3) Northeast Male 270 ( 4.1) P-4.4 Female 21118 ( 3.2) Nation HI Male 282 ( 1.8) NI Female 210 ( 1.3) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-4-4). If the confidence intervals for the populations do not overlap, there is a statistically sigrnficant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in New Hampshire who attained level 200. The percentage of females in New Hampshire who attained level 200 was greater than the percentage of females in the nation who attained level 200. Also, the percentage of males in New Hampshire who attained level 200 was greater than the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASSESSMENT 31 New Hampshire FIGURE 13 I Levels of Eighth-Grade Public-School i Mathematics Proficiency by Gender LEVEL 300 State Male Female Region Mate Female Nation Male Female LEVEL 250 State Mate Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Mate Female Nation Male Female THE NATION'S REPORT mom CARD ipeomm.....y 0 20 40 60 80 Percentage 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 1+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 m this figure because so few students attained that level. 3 S 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 17 ( 1.3) 19 ( 1.6) 19 ( 3.3) 13 ( 3.8) 14 ( 1.7) 10 ( 1.3) 79 ( 1.3) 90 ( 2.3) 72 ( 5.8) 72 ( 4.5) 04 ( 2.0) 84 ( 1.8) 00 ( 0.4) 100 ( 0.2) 96 ( 0.7) 09 ( 0.7) 97 ( 0.9) 97 ( 0.8) New Hampshire In addition, there was no difference between the percentages of males and females in New Hampshire who attained level 300. The percentage of females in New Hampshire who attained level 300 was greater than the percentage of females in the nation who attained level 300. However, the percentage of males in New Hampshire 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. :Y) THE 1990 NAEP TRIAL STATE ASSESSMENT 33 New Hampshire TABLE 3 I Eighth-Grade Public-School Mathematics Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Meas urement - Geometry Data Analysis' Statistics, il and Probabity Algebra and Rmetions TOTAL Proadoncy Proadency MS:Wm Proficiency Pracking State 275 ( 1.0) 272 ( 1.3) 272 ( 1.0) 278 ( 0.9) 271 ( 1.0) Region 271 ( 3.1) 288 ( 41) 208 ( 3.8) 273 ( 3.6) 2137 ( 3.4) Nation 266 14) 258 ( 1.7) 259 ( 1,4) 262 ( 1.8) 260 ( 1.3) RACE/ETHNICITY White State 275 ( 1.1) 273 ( 1.3) 272 ( 1.0) 277 ( 1.0) 272 ( 1.0) Region 275 ( 3.1) 272 ( 4.6) 272 ( 3.1) 279 ( 3.1) 271 ( 3.0) Nation 273 ( 1.6) 267 ( 2.0) 267 ( 1.5) 272 ( 1.8) 288 ( 1.4) Hispanic State Region 257 ( 3.8) Mr* ( Iht *441 255 ( ck 5.5)1 ,3 ( *IN! ( 0.1) INF* ) 252 ( ( 5.9) Nation 248 ( 2.7) 238 ( 3.4) 243 ( 32) 239 ( 3.4) 243 ( 3.1) TYPE OF COMMUNITY Advantaged urban State 280 ( 4.0) 283 ( 5.6) 281 ( 4.6) 281 ( 3.9) 277 ( 2.8) Region 282 ( 6.5)1 279 ( 6.8)1 275 ( 9.6)1 282 ( 8$)1 273 (10.1)1 Nation 283 ( 3.2)1 281 ( 32)1 277 ( 52)1 285 ( 4.8)1 277 ( 4.8)1 Extrema runt State Region 278 ( 5.2)1 **4. 276 ( *1.4 ( 7.0)1 27$ ( 4.3)1 283 ( ( 5.7)1 278 ( 5.5) 1 .44(4*4) Nation 258 ( 4.3)1 254 ( 4.2)1 253 ( 4.5)1 257 ( 5.0)1 256 ( 4.8)1 Other State 275 ( 1.1) 273 ( 1.4) 272 ( 1.0) 277 ( 1.0) 272 ( 0.9) Region 274 ( 3.7) 268 ( 6.5) 272 ( 3.3) 277 ( 3.9) 271 ( 3.4) Nation 266 ( 1.9) 257 ( 2.4) 259 ( 1.7) 281 ( 21) 261 ( 1.7) The standard errors of the estimated statistics appear in parentheses, It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determination of the variability Of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 (i 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Nemo Hampshire TABLE 3 I Eighth-Grade Public-School Mathematics (continued) I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1960 NAEP TRIAL STATE ASSESSMENT Munlb____!!!____and &Warsaw= MeasuremeM Geometry Data Analysis ___,, Statistics, uu Probability Algebra and Function* TOTAL Proficiency Wade lam Proficiency Profidency Pro lidenclf State 27Sf 1.0) 272 ( 1.3) 272 ( 1.0) 276 ( 0.9) 271 ( 1.0) Region 271 ( 3.1) 266 ( 4.7) 2613 3.6) 273 ( 3.6) air ( 3.4) Nation 266 ( 1.4) 258 ( 1.7) 259 ( 1.4) 2e2 ( 1.8) 260 ( 1.3) PARENTS' EDUCATION NS non-graduate State Region Nation 258 ( 2.8) *el 247 ( 2.4) 258 (( 237 ( 3.C) «4) 3.6) 2$9 ( .44 ( 242 ( 2.6) 22) 241.i , **IP ( 240 ( 3.6) *41 3.1) 249 ( 242 ( 3.3) 3.0) NS witduat State 203 ( 1.5) 259 ( 2.3) 259 ( 1.4) 263 ( 1.4) 260 ( 1.3) Region 260 ( 2.7) 255 ( 5.1) 258 ( 3.2) 264 ( 4.6) 254 ( 2.9) Nation 259 ( 1.8) 24$ ( 2.1) 252 ( 1.6) 253 ( 21) 253 ( 2.0) Some coNele State 277 ( 1.7) 273 ( 2.7) 274 ( 1.8) 280 ( 2.1) 274 ( 2.0) Region 267 ( 2.3) 261 ( 5.7) 267 ( 3.4) 273 ( 3.4) 262 ( 2.9) Nation 270 ( 1.5) 264 ( 2.7) 282 ( 2.0) 269 ( 2.4) 283 ( 2.2) Came graduate State 284 ( 1.2) 283 ( 1.6) 281 ( 1.3) 287 ( 1.4) 281 ( 1.4) Region 285 ( 3.8) 279 ( 5.5) 277 ( 3.8) 287 ( 3.5) 280 ( 3.6) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.8) 276 ( 2.2) 273 ( 11) GENDER Male State 275 ( 1.1) 273 ( 1.6) 271 ( 1.0) 276 ( 1.3) 269 ( 1.2) Region 272 ( 3.9) 271 ( 5.9) 289 ( 4.0) 274 ( 4.1) 266 ( 4.1) Nation 286 ( 2.0) 262 ( 2.3) 260 ( 1.7) 262 ( 2.1) 260 ( 1.6) Ringo State 274 ( 1.4) 272 ( 1.8) 273 ( 1.4) 275 ( 1.5) 274 ( 1.5) Region 270 ( 3.1) 261 4.3) 266 ( 4.1) 273 3.6) 268 ( 3.7) Nation 266 ( 1.4) 253 ( 1.6) 258 ( 1.5) 261 ( 1.9) 260 ( 1.4) 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). 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 New Hampshire THE 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, and gut 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 NAM' data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. 1 r) THE 1990 NAEP TRIAL STATE ASSESSMENT 37 New Hampshire Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an enonnous impact on future academic achievement. Yet, as shown in Chapters 3 and 7, 7, -ge proportions of students report having spent much more time each day watching te':vision 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 CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.' This chapter focuses on curricular and instructional content issues in New Hampshire public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: Less than half of the eighth-grade students in New Hampshire (38 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. ' Curtis McKnight, et stl., The Underachieving Curriculum. Assessing U.S. School Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign, IL Stipes Publishing Company, 1987` Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). Li s. THE 1990 NAEP TRIAL STATE ASSESSMENT 39 New Hampshiro In New Hampshire, 82 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Almost all of the students in New Hampshire (93 peicent) were taught mathematics by teachers who teach only one subject. About three-quarters (78 percent) of the students in New Hampshire 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 New Hampshire Eighth-Grade Public Schools PERCENTAGE OF STUDENTS WOO NAEP TRIAL STATE ASSESSMENT New Hampshire Northeast Nation _ Percentage of eighth-grade students in public schools that identified mathematics as receiving special emphasis in school-wide goals and objectives, instruction, in-service training, etc. Percentage of eighth-grade public-school students who are offered a course in algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers WTO teach only mathematics Percentage of eighth-grade students in public schools who are assigned to a mathematics clan by their ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics instruction per week Percentage Percentage Percentage 38 ( 0.7) 45 (164) 83 ( 5.9) 82 ( 1.0) 90 ( 7.3) 78 ( 4.6) 93 ( 0.6) 100 ( 0.0) 91 ( 3.3) 78 ( 1.0) 71 (10.1) 63 ( 4.0) 30 ( 1.1) 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. 5 40 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in New Hampshire are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in New Hampshire were taking eighth-grade mathematics (55 percent) than were taking a course in pre-algebra or algebra (43 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in New Hampshire who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRtAt. STATE ASSESSMENT Nets Hampshire Northeast Nation What kind of mathematics class are you taking this year? Percentage and Pronciency Percentage and Prof Idtmcy Percentage and Pro &limy Eighth-grade mathematics 55 ( 1.3) 53 ( 5.8) 62 ( 2.11 2821 1.0) 259 ( 2.9) 251 ( 1.4) Pre-algebra 28 ( 1.0) 16 ( 3.9) 19 ( 1.9) 280 ( 1.0) 278 ( 6.7)1 272 ( 2.4) Algebra 14 ( 0.9) 18 ( 3.3) 15 ( 1.2) 308 ( 1.6) 297 ( 3.6) 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the 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 New Hampshire Further, from Table AS in the Data Appendix:4 A greater percentage of females (47 percent) than males (39 percent) in New Hampshire were enrolled in pre-algebra or algebra courses. In New Hampshire, 43 percent of White students and 34 percent of Hispanic students were enrolled in pre-algebra or algebra courses. Similarly, 44 percent of students attending schools in advantaged urban areas, 44 percent in schools in extreme mral areas, and 42 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 New Hampshire spent 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes daily. Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix): In New Hampshire, 2 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 3 percent of the students in New Hampshire 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 subpopulauons race ethnicity, type of community, parents' education level, and gender. 42 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire The results by race/ethnicity show that 3 percent of White students and 1 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 2 percent of White students and 2 percent of Hispanic students spent no time doing mathematics homework. In addition, 6 percent of students attending schools in advantaged urban areas, 7 percent in schools in extreme rural areas, and 3 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 0 percent of students attending schools in advantaged urban areas, 0 percent in schools in extreme rural areas, and 2 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire Northeast Nation Percentage and Proficiency Percentage and Proficiency 0 ( 0.0) *I* 1111-11.) Percentage and Proficiency 1 ( 0.3) *" ( 0") 1 About how much time do students spend , on mathematics homework each day? N one 15 minutes 33 ( 0.9) 54 (132) 43 ( 4.2) 265 ( 1.2) 284 ( 4.7)1 256 ( 2.3) 30 minutes 55 ( 1.0) 35 (12.5) 43 ( 4.3) 274 ( 13) 270 ( 4.1)1 266 ( 2.6) 46 minutes 8 ( 0.8) 40 ( 1.9) 293 ( 3.2) 272 ( 5.7)1 An hour or mere 3 ( 300 ( 0.4) 3.4) 3 ( 0.6) ***) 4 ( 278 ( 0.9) 5.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- irle nature of the sample does not allow accurate determination of the variability of this estimated mean profmency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 43 New Hampshire 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 1990 NAEP TRIAL. STATE ASSESSMENT New Hampshire Northeast Nation About how much time do you usually spend each day on mathematics homework? Percentage and Pro Adam Percentage and Proldanq Porcontep nd Prodding, None 5 ( 0.5) 9 ( 0.8) 258 ( 2.7) 251 ( 2.8) 16 minutes 34 ( 12) 37 ( 3-3) 31 ( 2.0) 272 ( 1.3) 269 ( 2.4) 264 ( 1.9) 30 minutes 38 ( 13) 34 ( 2.0) 32 ( 1.2) 277 ( 1,3) 271 ( 6.0) 263 ( 1.9) 45 minutes 15 ( 0.9) 15 ( 2.3) 16 ( 1.0) 275 ( 1.7) 272 ( 8.5) 266 ( 1.9) An hour or more 8 ( 0.6) 12 ( 1.1) 274 ( 2.6) ( 258 ( 3.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each populauon 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). And, according to the students (Table 7 and Table A7 in the Data Appendix): In New Hampshire, relatively few of the students (5 pement) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 8 percent of the students in New Hampshire 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 9 percent of White students and 8 percent of Hispanic students. spent an hour or more on mathematics homework each day. In comparison, 5 percent of White students and 11 percent of Hispanic students spent no time doing mathematics homework. 4.1 44 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire In addition, 9 percent of students attending schools in advantaged urban areas, 16 percent in schcols in extreme rural areas, and 8 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 8 percent of students attending schools in advantaged urban areas, 3 percent in schools in extreme rural areas, and 5 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, compuiation, 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 ot the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. 5 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics. 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 45 New Hampshire 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 cmphasis" -- 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. THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampsidre TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1999 NAEP TRIAL STATE ASSESSMENT New Hampshire Northeast Nation Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Teacher 'emphasis" categories by content areas NUIribillri and Operations Heavy emphasis 30 ( 1.8) 41 ( 6.9) 49 ( 3.8) 289 ( 1.9) 268 ( 2.9) 280 ( 1.8) Little or no emphasis 17 ( 292 ( 1.5) 2.8) 21 rat ( 6.5) ) 15 ( 287 ( 2.1) 3.4) Measurement Heavy emphasis 15 ( 0.9) 32 (11.5) 17 ( 3.0) 261 ( 2.0) 257 (11.7)1 250 ( 5.6) Little or no emphasis 36 ( 1.1) 34 ( 8.3) 33 ( 4.0) 278 ( 2.0) 282 ( 4.8)1 272 ( 4.0) Geometry Heavy emphasis 27 ( 1.4) 48 (11.9) 28 ( 3.8) 272 ( 2.2) 264 ( 6.1)1 260 ( 3.2) Little or no emphasis 25 ( 274 ( 1.2) 2,3) 9- ( 1.9)) 21 ( 264 ( 3.3) 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 16 ( 269 ( 0.8) 3.8) 12 ( 6.1)) 14 ( 269 ( 2.2) 4.3) Little or no emphasis 55 ( 1.5) 46 (10.1) 53 ( 4.4) 276 ( 1.6) 279 ( 5.4)1 261 ( 2.9) Algebra and Ftmetions Heavy emphasis 47 ( 1.9) 52 (11.5) 46 ( 3.6) 284 ( 1.8) 273 ( 8.6)i 275 ( 2,5) Little or no emphasis 24 ( 253 ( 1.3) 1.9) , as.) 20 ( 243 ( 3.0) 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 .1 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included, ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 47 New Hampshire 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: Less than half of the eighth-grade students in New Hampshire (38 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In New Hampshire, 82 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in New Hampshire were taking eighth-grade mathematics (55 percent) than were taking a course in pre-algebra or algebra (43 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. According to their teachers, the greatest percentage of eighth-grade students in public schools in New Hampshire spent 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 New Hampshire, relatively few of the students (5 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 8 percent of the students in New Hampshire 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. t- (...o 48 THE 1990 NAEP TR1.4.L STATE ASSESSMENT New Hampshire CHAPTER 4 yazx 42-3 MIMI UMW!" Ma 11111111111111111 MR 11111111111111 MO IRAN IIMf)SE 8111111111111111111119 :.1111111.11111. .4nomoollIVAII11 UURt IMMO! IIIIIIIR1F.111111111 MERU ONIIIIIMIll MOO MOON 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.6 An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. ° National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). rJ THE 1990 NAEP TRIAL STATE ASSESSMENT 49 New Hampshire From Table 9 and Table A9 in the Data Appendix: In New Hampshire, 15 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 23 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In New Hampshire, 0 percent of students attending schools in advantaged urban areas, 0 percent in schools in extreme rural areas, and 16 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in New Hampshire, 22 percent of students attending schools in advantaged urban areas, 14 percent in schools in extreme rural areas, and 23 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had higher mathematics achievement levels than those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of 1 Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TMAL STATE ASSESSMENT New Hampshire Northeast Nation 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 all the resources I need. I got most of the resources I need. I get some or none of the resources I need. Percentage end Proficiency Percentage Percentage and and Proficiency Proficiency 15 ( 0.8) 26 ( 6.6) 13 ( 2,4) 274 ( 2.1) 271 ( 7.2)1 265 ( 4.2) 61 ( 1.3) 38 (11.7) 56 ( 4.0) 275 ( 0.9) 272 ( 2.9); 265 ( 2.0) 23 ( 1.0) 38 (11.8) 31 ( 4.2) 268 ( 1.6) 274 ( 9,8); 261 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! interpret with caution -- the nature of the sample does not allow accurate dziermination of the variability of this estimated mean proficiency. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.7 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 New Hampshire (57 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics problems in small groups (10 percent). The largest percentage of the students (59 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; some never used such objects (11 percent). In New Hampshire, 55 percent of the students were assigned problems from a mathematics textbook almost every day; 11 percent worked textbook problems about once a week or less. About half of the students (49 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (25 percent). ' Thomas Romberg, "A Common Curnculum for Mathematics," Individual Differences and the Common Curricukim. gghty-second Yearbook of the National Society for the Study of Education (Chicago, IL: University of Chicago Press, 1983). r. r 0 b THE 1990 NAEP TRIAL STATE ASSESSMENT 51 New Hampshire TABLE 10 I Teachers' Reports on Patterns of Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 IMP TRIAL STATE ASSESSMENT New Hanyshirs Northeast Nation Percentage and ProAciency Percentage and Proficiency Percentage and Proficiency About how often do students work problems in small groups? At last once a week 57 ( 1.5) 44 ( 6.4) 50 ( 4.4) 273 ( 1.0) 264 ( 8.0)1 260 ( 22) Less than once a week 33 ( 1.4) 39 ( 8.6) 43 ( 4.1) 274 ( 1.9) 267 ( 5.0)1 264 ( 2.3) New 10 ( 0.7) 17 ( 8.3) 8 ( 2.0) 270 ( 1.7) 277 ( 5.4)1 About how often do students use objects Percentage Percentage Percentage like rulers, counting blocks, or geometric and and and solids? Proficiency Proficiency Proficiency At least once a week 31 ( 12) 270 ( 1.3) 14 ( 5.5) ,-**) 22 ( 3.7) 254 ( 32) Less than once a week 59 ( 1.6) 78 ( 6.8) 69 ( 3.9) 272 ( 1.0) 269 ( 1.6) 263 ( 1.9) Never 11 ( 1.1) 9 ( 3.5) 9 ( 2.6) 262 ( 4.8) 282 ( 5.9)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). r 6,) 52 THE 2990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE 11 I Teachers' Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY .. 1990 NAEP TRIAL STATE ASSESSMENT New Hampshk* Northeast Nation - Percentage and Proficiency Percentage end Proficiency Percentage and Proficiency About how often do students do problems from textbooks? Almost every day 55 ( 12) 57 ( 9.3) e2 ( 3.4) 273 ( 1.4) 276 ( 4.4) 267 ( 1.8) Several times a week 34 ( 1.4) 31 ( 8.3) 31 ( 3.1) 272 ( 1.2) 261 ( 62)1 254 ( 2.9) About once week or less 11 ( 1.2) 13 ( 2.8) 7 ( 1.8) 276 ( 2.0) 260 ( About how often do students do problems on worksheets? Percentage and Percentage and Percentage and Proficiency Proficiency Proficiency At least several times a week 49 ( 13) 53 (113) 34 ( 3.8) 270 ( 1.1) 282 ( 4.5)1 256 ( 2.3) About once a week 26 ( 1A) 32 ( 8.2) 33 ( 3.4) 272 ( 1-2) 270 ( 3.4)1 280 ( 2.3) Less than weekly 25 ( 12) 200 ( 2.4) .44) 32 ( 3.6) 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 is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. **s Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 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 compa.res the responses of the students to Close of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT 53 New Hampshire COLLABORATING IN SMALL GROUPS In New Hampshire, 33 percent of the students reported never working mathematics problems in small groups (see Table 12); 32 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1100 NAEP TRIAL. STATE ASSESSMENT New Hampshire Northeast Nation Percentage and Proficiency Percentage imd Proficiency Percentage and Ihreficioncy How often do you work in small groups in your mathematics class? At least once a week 32 ( 1.1) 27 ( 6.7) 26 ( 25) 274 ( 1.2) 260 ( 4.8)1 258 ( 2.7) Lass than once a week 35 ( 1.1) 22 ( 2.6) 211 ( 1.4) 276 ( 1.4) 271 ( 5.0) 267 ( 2.0) Now 33 ( 1.0) 51 ( 7.0) 44 ( 2.9) 271 ( 1.3) 273 ( 4.8) 261 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. Examining the subpopulations (Table Al2 in the Data Appendix): In New Hampshire, 43 percent of students attending schools in advantaged urban areas, 44 percent in schools in extreme rural areas, and 33 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 32 percent of White students and 38 percent of Hispanic 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 (33 percent and 32 percent, respectively). 54 THE I990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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: Less than half of the students in New Hampshire (37 percent) never used mathematical objects; 30 percent used these objects at least once a week. Mathematical objects were used at least once a week by 17 percent of students attending schools in advantaged urban areas, 41 percent in schools in extrtme rural areas, and 29 percent in schools in areas classified as "other". Males were more likely than femal mathematics classes at least once respectively). In addition, 30 percent of White students used mathematical objects es to use mathematical objects in their a week (33 percent and 27 percent, students and 27 percent of Hispanic at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS A) AVERAGE MATHEMATICS PROFICIENCY 1 1900 NAEP TRIAL STATE ASSESSMENT New Hampshire Northeast Nation How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class7 Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency At least once a week 30 ( 0.9) 30 ( 4.3) 23 1.8) 272 ( 15) 265 ( 6.9) 258 ( 2.6) Less than once a week 33 ( 0.9) 30 ( 3.2) 31 ( 1.2) 276 ( 1.4) 277 ( 3.9) 269 ( 1.5; Never 37 ( 1.0) 40 ( 4.8) 41 ( 2.2) 273 ( 1.4) 266 ( 3.9) 259 ( 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 1- 2 standard errors of the estimate for the sample. C THE 1990 NAEP TRIAL STATE ASSESSMENT 55 New Hampshire MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in New Hampshire who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table Al4 in the Data Appendix): About three-quarters of the students in New Hampshire (72 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 81 percent of students attending schools in advantaged urban areas, 84 percent in schools in extreme rural areas, and 71 percent in schools in areas classified as "other". TABLE 14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL STATE ASSESSMENT New Hampshire Northeast Nation How often do you do mathematics 1 problems from textbooks in your mathematics class? Almost every day Several times a week About once a week or less Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency 72 ( 1.4) 72 ( 5.3) 74 ( 1.9) 276 ( 1.0) 275 ( 3.7) 267 ( 1.2) 15 ( 0.7) 14 ( 1.6) 14 ( 0.8) 268 ( 1.7) 261 ( 4.5) 252 ( 1.7) 13 ( 1.3) 14 ( 4.3) 12 ( 1.8) 267 ( 1.5) 249 ( 7 A)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. 61 56 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire And, for the frequency of worksheet usage (Table 15 and Table AlS in the Data Appendix): Less than half of the students in New Hampshire (43 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 29 percent of students attending schools in advantaged urban areas, 41 percent in schools in extreme rural areas, and 46 percent in schools in areas classified as "other". TABLE 15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1990 MAEP TRIAL STATE ASSESSMENT New Hampshire Northeast Nation ..._ How often do you do mathematics problems on worksheets in your mathematics class? Percentage and Proficiency Percentage and Proficiency Parcontage and Proficiency At least several times a week 43 ( 1.3) 44 ( 5.9) 38 ( 2.4) 271 ( 0.9) 261 ( 3.8) 253 ( 2.2) About once a week 27 ( 0.9) 22 ( 1.8) 25 ( 1.2) 272 ( 1.6) 268 ( 3.6) 261 ( 1.4) Len than weeidy 30 ( 1.0) 34 ( 6.5) 37 ( 2.5) 279 ( 1.9) 282 ( 4.3)1 272 ( 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 er of the estimate for the sample, ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. THE 1990 NAEP TRIAL STATE ASSESSMENT 57 New Hampshire TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS , 1990 NAEP TRIAL STATE ASSESSMENT New Itampshirs Northeast Nation Patterns of classroom instruction Percentage of students who work mathematics problems In smaN groups At least once a week Less than once a week Never Percentage of students vMo use objects like nders, counting blocks, or geometric solids At least once a week Less than once a week Never f t Materials for mathematics instruction Percentage of students who use a mathematics textbook Almost every day Several times a week About once a week or less Percentage of students who US& a mathematics worksheet At least several times a week About once a week Less than weekly Percentage Percentage Percentage Students Teachers Students Teachers Students Teachers 32 ( 1.1) 57 ( 1.5) 27 ( 6.7) 44 ( 6.4) 28 ( 23) 50 ( 4.4) 35 ( 1.1) 33 ( 1.4) 22 ( 2.8) 39 ( 8.6) 28 ( 1.4) 43 ( 4.1) 33 ( 1.0) 10 ( 0.7) 51 ( 7.9) 17 ( 6.5) 44 ( 2.9) 8 ( 2.0) 30 ( 0.9) 31 ( 12) 30 ( 4.3) 14 ( 5.5) 28 ( 1.8) 22 ( 3.7) 33 ( 0.9) 59 ( 1.6) 30 ( 3.2) 78 ( 6.8) 31 ( 12) 69 ( 3.9) 37 ( 1.0) 11 ( 1.1) 40 ( 4.8) 9 ( 3.5) 41 ( 22) 9 ( 2.6) Percentage Percentage Percentage Students Teachers Students Teachers Students Teachers 72 ( 1.4) 55 ( 1.2) 72 ( 5.3) 57 ( 9.3) 74 ( 1.9) 62 ( 3.4) 15 ( 0.7) 34 ( 1.4) 14 ( 1.6) 31 ( 8.3) 14 ( 0.8) 31 ( 3.1) 13 ( 1.3) 11 ( 1.2) 14 ( 4.3) 13 ( 2.8) 12 ( 1.8) 7 ( 1.8) 43 ( 13) 49 ( 1.3) 44 ( 5.9) 53 (11.3) 38 ( 2.4) 34 ( 3.8) 27 ( 0.9) 26 ( 1.1) 22 ( 1.8) 32 ( 8.2) 25 ( 1.2) 33 ( 3.4) 30 ( 1.0) 25 ( 1.2) 34 ( 6.5) 15 ( 4.6) 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 t 2 standard errors of the estimate for the sample. 58 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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 New Hampshire (57 percent) worked mathematics problems in small groups at least once a week; relatively few never worked in small groups (10 percent). The largest percentage of the students (59 percent) used objects like rulers, counting blocks, or geomettic shapes less than once a week, and some never used such objects (11 percent). In New Hampshire, 55 percent of the students were assigned problems from a mathematics textbook almost every day; 11 percent worked textbook problems about once a week or less. Abo,,t half of the students (49 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (25 percent). And, according to the students: In New Hampshire, 33 percent of the students never worked mathematics problems in small groups; 32 percent of the students worked mathematics problems in =all groups at least once a week. Less than half of the students in New Hampshire (37 percent) never used mathematical objects; 30 percent used these objects at least once a week. About three-quarters of the students in New Hampshire (72 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. Less than half of the students in New Hampshire (43 percent) used worksheets at least several times a week, compared to 38 percent in the nation. LL' THE 1990 NAEP TRIAL STATE ASSESSMENT 59 New Hampshire CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computeis -- 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.5 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. 8 National Assessment or Education41 Progress, Mathematics Objectives 1990 Assessment (Princeton, NI: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evalliation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire Table 17 provides a profile of New Hampshire eighth-grade public schools' policies with regard to calculator use: ln comparison to 33 percent across the nation, 38 percent of the students in New Hampshire had teachers who allowed calculators to be used for tests. About the same percestage of students in New Hampshire and in the nation had teachers who permitted unrestricted use of calculators (21 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of New Hampshire Policies I on Calculator Use PERCENTAGE OF STUDENTS MO NAEP TRIAL STATE ASSESSMENT New Hama*. Northeast Nation Percentage of eighth-grade students in public schools whose teachers permit the unrestricted use of calculators Percentage of eighth-grade students in public schools whose teachers permit the use of calculators for tests Percentage of eighth-grade students in public schools whose teachers report that students have mass to calculators owned b øa school Percentage Percentage Percentage 21 ( 1.3) 20 (11A) 18 ( 3.4) 38 ( 1.4) 14 ( 9.2) 33 ( 4.5) 89 ( 0.9) 28 ( 8.2) 56 ( 4.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. GE; THE 1990 NAEP TRIAL STATE ASSESSMENT 61 New Hampshire THE AVALLARILITY OF CALCULATORS In New Hampshire, most students or their families (99 percent) owned calculators (Table 18); however, fewer students (51 percent) had teachers who explained the use of calculators to them. Fmm Table A18 in the Data Appendix: In New Hampshire, 50 percent of White students and 64 percent of Hispanic students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (51 percent and 51 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 1900 NAEP TRIAL STATE ASSESSMENT New Hampshire Northeast Naiion _ Perosedap and Preilkkoecy 90 ( 0.3) 274 ( 0.9) ( 0.3) es. ( Perceniop and Proficiency Percentage and Proficiency 98 ( 0.7) 209 ( 3.3) 2 ( 0.7) *** ( .) Percentese one Proficiency Percentage and Proficiency 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( 31) Percentage and Proficiency Do you or your family own a calculator? Yes No Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes SI ( 1.2) 30 ( 4.0) 49 ( 2.3) 272 ( 1.1) 25$ ( 4.3) 258 ( 1.7) No 49 ( 1.2) 70 ( 4.0) 51 ( 2.3) 27$ ( 1.2) 274 ( 39) 299 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each poptdation of interest, the value for the entire population is within ± 2 standard errors of the estimate for Mt sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 6" 62 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire THE USE OF CALCULATORS As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment, students Ar asked how frequently (never, sometimes, almost always) they used calculators 1, Norking problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In New Hampshire, 30 percent of the students never used a calculator to work problems in class, while 32 percent almost always did. About one-quarter of the students (22 percent) never used a calculator to work problems at home, compared to 27 percent who almost always used one. About half of the students (47 percent) never used a calculator to take quizzes or tests, while 17 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 1990 NAEP TRIAL STATE ASSESSMENT New Hampshirs Northeast Nation Percentage and Pro Waxy Percantage and Prat:Jena Percentage and Milt:fancy How often do you use a calculator for the following tasks? Working problems in class Almost always 32 ( 1.3) 40 ( 4.0) 48 ( 1.5) 286 ( 1.2) 255 ( 3.9) 254 ( 1.5) Never 30 ( 1.1) 39 ( 8.0) 23 ( 1.9) 281 ( 1,4) 282 ( 2.2) 272 ( 1.4) Doing problems at home Almost always 27 ( 1.0) 30 ( 3.3) 30 ( +.3) 270 ( 1.3) 284 ( 5.8) 281 ( 1.8) Never 22 ( 1.0) 22 ( 2.5) 19 ( 0.9) 276 ( 1.7) 275 ( 2.3) 283 ( 1.8) Taking quizzes or tests Almost always 17 ( 1.1) 23 ( 3.3) 27 ( 1.4) 265 ( 1.9) 256 ( 5.6) 253 ( 2.4) Never 47 ( 1.3) 45 ( 5.1) 30 ( 2.0) 281 ( 1.3) 284 ( 2.1) 274 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. 6 c' THE 1990 NAEP TRIAL STATE ASSESSMENT 63 New Hampshire 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 iLotructions 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 :alculator 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 State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they wen: presented. (2; 64 iHE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: About the same percentage of students in New Hampshire weir in the High group as were in the Othes group. About the same percentage of males and females were in the High group. In addition, 48 percent of White students and 49 percent of Hispanic students were in the High group. TABLE 20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT New Hampshire Northeast Nation "Calculator-use" group Percentage and Pre Selena Percentage and Palk:ken Percentage and Pro &km/ High 48 ( 1.5) 44 ( 2.5) 42 ( 1.3) 279 ( 1.3) 279 ( 3.8) 272 ( 1.6) Other 52 ( 1.5) 58 ( 2.5) 58 ( 1.3) 206 ( 1.2) 263 ( 2.9) 255 ( 1.5) The standard errors of the estimated statisfics 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. 7 t) THE 1990 NAEP TRIAL STATE ASSESSMENT 65 New Hampshire SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessafy 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 emph nized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 38 percent of the students in New Hampshire had teachers who allowed calculators to be used for tests. About the same percentage of students in New Hampshire and in the nation had teadiers who permitted unrestricted use of calculators (21 percent and 18 percent, respectively). In New Hampshire, most students or their families (99 percent) owned calculators; however, fewer students (51 percent) had teachers who explained the use of calculators to them. In New Hampshire, 30 percent of the students never used a calculator to work problems in class, while 32 percent almost always did. About one-quarter of the students (22 percent) never used a calculator to work problems at home, compared to 27 percent who almost always used one. About half of the students (47 percent) never used a calculator to take quizzes or tests, while 17 percent almost always did. 7 1 66 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has become an issue of increasing importance to fedend, state, and local governments. As part of their effort to improve the educational process, policymakers 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 New Hampshire, 35 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 stud, ts across the nation. More than half of the students (60 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of the student , weir taught by mathematics teachers who were certified at the highest level available in their states. Many of the students (80 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). 7 2, THE 1990 NAB? TRIAL STATE ASSESSMENT 6 7 New Hampshire TABLE 21 I Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 11110 NAEP TRIAL STATE ASSESSMENT Nay H ampshire Northeast Nation 111MMM. Percentage of students whom mathematics teachers reported having the 'Wowing dowses Perowntage Perantage Perosatige Bachelor's degree iA) 46 (15.0) 50 ( 42) Master's or specialist's degree 34 ( 1.4) 54 (15.0) 42 ( 42) Doctorate or professional degree 1 ( 0.1) ( 0.0) 2 ( 1.4) Percentage of students whose mathematics teachers have the following Ines of teaching certificates that are recognized by New Hampshire No regular certification 4 ( 0.5) 0 ( 0.0) 4 ( 12) Regular certification but less than the highest available 38 ( 1.4) 19 (11.5) 29 ( 43) Highest certification available (perManent Or long-term) 00 ( 1.4) Si (11.5) 06 ( 42) Percentage of students whose mathematics teachers have the following types of teaching certificates that are recognized by New liampshire Mathematics (middle school or secondary) 80 ( 1.5) 89 ( 3.7) 84 ( 2.2) Education (elementary or middle school) 16 ( 1.4) 8 ( 3.8) 12 ( 2.6) Other 3 ( 0.5) 4 ( 3,7) 4 ( 1.5) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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. THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire Teachers' responses to questions concerning their uzdergraduate and graduate fields of study (Table 22) show that: In New Hampshire, 44 percent of the eighth-grade public-schml 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 New Hampshire (20 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and I Graduate Fields of Study PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire Northeast Nation , What was your undergraduate major? Mathematics Education Other IWhat was your graduate major? Mathematics Education Other or no geaduate levet study Percentage Percentage Percentage 44 ( 4.1) 44 ( 9.2) 43 ( 3.9) 42 ( 12) 34 ( 8.0) 38 ( 3.8) 15 ( OA) 22 ( 8.1) 22 ( 3.3) Percentage Percentage Percentage 20 ( 1.3) 22 ( 9.7) . 22 ( 3.4) 31 ( 1.5) 42 ( 5.2) 38 ( 3.5) 49 ( 1.3) 37 ( 4.5) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 69 New Hampshire Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In New Hampshire, 69 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-semice education dedicated to mathematics or the teaching of mathemalies. 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 New Hampshire (3 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 19110 NAEP TRIAL STATE ASSESSMENT New Hampshire 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 hours 18 hours or more Percentage Percentage Percentage 3 ( 0.3) 25 ( 7.0) 11 ( 2.1) 28 ( 1.5) 37 ( 4.1) 51 ( 4.1) 69 ( 1.4) 38 ( 8.4) 39 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 5 70 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement." Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be.1' In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In New Hampshire, 35 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. More than half of the students (60 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In New Hampshire, 44 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 New Hampshire (20 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. '° Archie E. Lapointe, Nancy A. Mead, and Gary W. Philhps, A World of Differences. An International Assessment af Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). 11 Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The Slate of Mathematics Achievement: NAEP's 1990 Assessment of the Nation and the Trial Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). r ,71, THE 1990 NAEP TRIAL STATE ASSESSMENT 71 New Hampshire In New Hampshire, 69 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 whc) spent at least that much time on similar types of in-service training. Relatively few of the students in New Hampshirt (3 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. 77 72 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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' anitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, eacouragement, and participation in student learning experiences are powerful influences. Together, teachers and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment and mathematics proficiency, students participating in the Trial State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education. THE 1990 NAEP TRIAL STATE ASSESSMENT 73 New Hampshire AMOUNT OF READING MATERIALS IN ME 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 newspapas, 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 _ 1990 NAEP TRIAL STATE ASSESSMENT Sow tiamoshirs Northeast Nation , , 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 Thro typos Four types Pave*. Preikieney Penentive and Pralkiany Permits. and Palideacy 12 ( 0.6) 13 ( 2.0) 21 ( 1.0) 201 ( 2.1) 262 ( 244 ( 2.0) 27 ( 13) 31 ( 2.7) 30 ( 1.0) 271 ( 1.4) 264 ( 2.9) 258 ( 13) 01 ( 1.3) 541 ( 3.7) 48 ( 1.3) 277 ( 12) 278 ( 4.3) 212 ( 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 New Hampshire reveal that: Students in New Hampshire who had all four of these types of materials in the home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire About the same percentage of Hispanic students had all four types of these reading materials in their homes as did White students. About the same percentage of students attending schools in advantaged urban areas as in extreme rural areas and areas classified as "other" had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Trial Stre 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 100 MAEP TRIAL STATE ASSESSMENT Now Nairnshire Northeast Nation Percentage and Proficiency Percentage and Proficiency Percentage and Pro lickincy How much television do you usually watch each day? One hour or loss 17 ( 0.9) 12 ( 1.3) 12 ( 0.8) 282 ( 1.9) 277 ( 4.4) 269 ( 2.2) Two hours 20 ( 1.1) 21 ( 2.3) 21 ( 0.9) 278 ( 1.7) 278 ( 3.1) 266 ( 12) Throe hours 24 ( 02) 23 ( 1.2) 22 ( 0.8) 274 ( 1.6) 271 ( 3.5) 265 ( 1.7) FMK to nifil hours 25 ( 0.9) 28 ( 2.6) 28 ( 1.1) 268 ( 1.2) 296 ( 4.1) 260 ( 1.7) Six hours or more 7 ( 0.7) 15 ( 3.3) 16 ( 1.0) 255 ( 3.0) 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. oC 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 75 New Hampshire From Table 25 and Table A25 in the Data Appendix: In New Hampshire, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Some of the eighth-grade public-school students in New Hampshire (17 percent) watched one hour or less of television each day; 7 percent watched six hours or more. A greater percentage of males than 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, 6 percent of White students and 24 percent of Hispanic students watched six hours or more of television each day. In comparison, 18 percent of White students and 8 percent of Hispanic 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 New Hampshire, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in New Hampshire (39 percent) did not miss any school days in the month prior to the assessment, while 22 percent missed three days or more. In addition, 22 percent of White students and 36 percent of Hispanic students missed three or more days of school. 76 THE 1990 NAEP TRIAL STATE ASSESSMENT New Ramps Itire Similarly, 30 percent of students attending schools in advantaged urban areas, 24 percent in schools in extreme rural areas, and 21 percent in schools in areas classified as "other" missed three or more days of school. TABLE 26 1 Students' Reports on the Number of Days of 1 School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NW TRIAL STATE AS4OSMENT New Hempen We Northeast Nation ...... How many days of school did you miss last month? One or two days Three days or more Ilarcentage and Praadenay 39 ( 12) 279 ( 0.9) 39 ( 1.3) 276 ( 12) 22 ( 1.2) 261 ( 1.6) Paraantage Panuntsp and and Madam* Proficiency 43 ( 22) 275 ( 3.6) 37 ( 3.1) 271 ( 2.6) 21 ( 3.0) 255 ( 5.5) 45 ( 1.1) 205 ( 1.6) 32 ( 0.9) 200 ( 1.5) 23 ( 1.1) 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 esfunate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 77 New Hampshire STU NIS' 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 asked if ttiey agreed or disagreed with five statements designed ti 'icit their perceptions of mathematics. These included statements about: Personal experience with mathematics, including students' enjoyment of mathematics and level of confidence in their mathematics abilities: I like mathematics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Alnwst all people use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is usefid for solving everyday problems. A student "perc:Ttion index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly agree" were given a value of 1 (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value .1 3. Each student's responses were averaged over the five statements. The students were then assigned a perception index according to whether they tended to strongly agree with the statement- (an index of I), tended to agree with the statements (an index of 2), oi tended to be undecided, to disagree, or to strongly disagree with the statements (an in.lex of :7). Table 27 provides the data for the students' attitudes toward mathematics as defined by their perception index. The following results were observed for New Hampshire: Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecide,i, disagree, strongly disagree" category. About one-quarter of the students (29 percent) were in the "strongly agree" category (perception index of 1). This compares to 27 percent across the nation. Smile of the students in New Hampshire (19 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). 12 National Council of Teachers of Mathematics, Curricutum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). S 78 THE 1990 NAEP TRIAL STATE ASSESSMENT New Ifampshire TABLE 27 1 Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAUE MATHEMATICS PROFICIENCY 1990 NAEP 1 ttIAL STATE ASSESSMENT Maw Hs1iks Ncrth.ast Nation Penman. aa9 Proloiaity Penunlige Orogaisecy P4reenisap and Student 'perception Index" groups Strongly agree 29 ( 13) 20 ( 4.9) 27 ( 1.3) ("perception index" of 1) 213( 1.5) 276 ( 5.0)1 271 ( 1.9) Wes 52 ( 1.4) 53 ( 3.0) 49 ( to) ("perception Index" of 2) 273 ( 0.9) 270 ( 4.5) 202 ( 12) Undecided, disagree, sWongly disagree 19 ( 1.2) 21 ( 3,3) 24 ( 12) ("perception index" of 3) 200 ( 1.5) 201 ( 5.8) 251 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a Oositive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. Tne data related to out-of-school factors show that: Students in New Hampshire 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 materials. This is similar to the results for the nation, where students who had all four types of .11Rterials showed higher mathematics proficiency than did students who had aro to two types. 84 THE 1990 NAEP TRIAL STATE ASSESSMENT 79 New Hampshire Some of the eighth-grade public-school students in New Hampshire (17 t) watched one hour or less of television each day; 7 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Less than half of the students in New Hampshire (39 percent) did not miss any school days in the month prior to the assessment, while 22 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 (29 percent) were in the "strongly agree" category Mating to students' perceptions of mathematics. Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. SO THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire ME 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 Educat1uz91 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 incomph te black (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimi7ing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The fvst 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. S THE 1990 NAEP TRIAL STATE ASSESSMENT 81 New Hampshire The blocks were then assembled into assessment bookl,ets 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 WIT given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required approximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every c.ther block in one booklet. Sevest 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 SCUi011 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 f rogram were developed using a broad-based consensus 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 1). 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 (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on students' performance on the set of mathematics items they received. IRT provides a common scale cn which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This common scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. National Assessment of Educational Progress, Mathematics Objectives' 1990 Assessment (Pnnceton, NJ: Educational Testing Service, 1988). 82 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire FIGURE Al I Content Areas Assessed Numbers and Operations This content area focuses on students' understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-world situations, as well as computational and estimation situations. Understanding numerical relationships as expressed in ratios, proportions, and percents Is emphaSiZed. Students' abilities In estimation, mental computation, use of calculators, generalization of numerical patterns, and verification of results are also included. INleasuret7mt This content area focuses on students' ability to describe real-world objects using nurbcrs. Students are asked to identify attributes, select appropriate units, apply measurement concepts, and communicate measurement-related ideas to others. Questions are included that require an ability to read instruments using meVic, 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, voiume, capacity, and angles are also included in this content area. Geometry This content area focuses on students' knowledge of geometric figures and relationships and on their skills in working with this knowledge. These skills are important at all levels of schooling as well as in practical applications. Students need to be able to model and visualize geometric figures in one, two, and three dimensions and to communicate geometric ideaS. In addition, students should be able to use informal reasoning to establish geometric relationships. Data Analysts, Statistics, and Probability This content area focuses on data representation and analysis 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 for gathering data, the visual exploration of 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. S THE 1990 NAEP TRIAL STATE ASSESSMENT 83 New Hampshire FIGURE A2 I Mathematical Abilities The following three categories of mathematical abilities are not to be construed a. Jrarchical. For example, problem solving involves interactions between conceptual knowledge and prt. _Mural skills, but what Is considered complex problem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. 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; knew 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 involving 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 numerical algorithms in mathematics that have been created as tools to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncomputational skills such as rounding and ordering, IProblem Solving In problem solving, students are required to use their reasoning and analytic abilities Whe, I they encounter new situations. Problem solving includes the ability to recognize and formuIrte problems: determine the sufficiency and consistency of data; use strategies, data, models, and relevant mathematics; generate, extend, and modify procedures; use reasoning (i.e., spatial, inductive, deductive, statistical, and proportional): and judge the reasonableness and correctness of solutions. Scl 84 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire A scale ranging from 0 to 500 was created to report performance for each content area. Each contentarea scale 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 of tour 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 rtudents performed at the extreme ends of the scale. Any attempts to defme 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 frw. the 1990 assessment that discriminated well between adjacent levels. The criteria for F Alecting these "benchmark" items were as follows: To defml 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 percentl 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. 90 THE 1990 NAEP TRIAL STATE ASSESSMENT 85 New Hampshim 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 skins. 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 Assesanent, questionnaires were given to the mathematics teachers of assessed studeats and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and 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 reprsent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade stantions 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. 91 Si1 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Sim* Additive Reesonkg and Problem Solving with Whole Plumbers EXAMPLE 1 Sinn 4111 Nat 1110 l=" T. Win hal dm kap boa. 0 in ors ana aid Ens elhases bah at lob s dim slawa Nita lb ant Ms IA* ea We Ink ensta. wait Ina tan is fawn k le 0 Its boa mak Xs mai bit 11abanwloishopilbeh 0 TM ballint atMkt kb asir's EXAMPLE 2 11004111 EX MIT MOD AT !WAWA!' MIMS OM Mos led lbw Dips legs lant COMP lasso 0400 0. lbw any bow al news ware *SW as Ilarraise IS O 60 0 70 0 SO O 90 I deal Icaser. 9 2 Grads 4 Omni Percentage Correot 7316 Percentage Correct for Mahar Levels: 221 200 10C1 es 91 WO Grade 4 Orwell Percentage Carer* 6614 Percentage COMO for Anchor Lemur Z120 75 91 100 Grade 8 Overall P rcentage Correct On Pereentage Correct for maw Lamas: ace Ma 220 2610 78 87 98 100 New Ilampthire FIGURE A3 I (continued) Example Items for Mathematics Proficiency Levels LAW 250: Simple Multiplicative Rmoning and Two-Step Problem Solving EXAMPLE 7. What is the value of a + 5 when n 3? EXAMPLE 2 The salis Arm aim dm Mali of a way el kik who. Os ths dock below, sake a difek mob le ammo es dm. is dm Wk. Laki ode pus el dig glide paplb wish she mom aim Did Tao au dor cakulasst es Oil gandon? 14* 0 No EXAMPLE 3 4. Maim is podoig bask* km boom lack Mos hal44 4 lowsbals. has 14 b.& WU& tarist rostaict will bap fat Hod ow4 bow nay haw A* will Nog cp 14 0 C110 24 4.6.0 24+40 24 xias 0 (1) 1 km's kaow. 88 Grads 8 Moran Paroattlago coast 78% Prconfaos Correct for Anchor Urals: Ail MO Ma 210 28 09 95 96 Grade 8 Ovorail Paroantaga correct 7314 Paroanlago Conn! for Anchor Laval*: 220 2110 Me 21 88 92 92 Grads 8 Oarall Paroontage comet 71% Poroontao Wilmot for Anchor Levels: 2131 MI WI 37 71 95 100 ME 1990 NAEP TRIAL STATE A.VIESSMENT New Hampshire FIGURE A3 I Example Items for Mathematics Proficiency Leveis (continued) Laval 300: Reasoning and Problem Solving Woking Fractions, Dadma Panunts, Elomantary Gaunstrio Properties, and Simple Algebraic Manipulations EXAMPLE 1 Inkb d t. haliwas shags as ma d awe. the aim tames me thoikes Ii EXAMPLE 2 sb. rows Ow ciao is ow ha kat is skisartal Mr auk isadd I litho 1w4.11144 ore mak is a been U liii wooli be nimaisi by a mok goal bar mos Indio takeW ii ea V Doi ris ma t akosisat Ibis swab& O 0 No &ads OveraN Percentage Caned: 80% Percentage Coned far Pactior Lively acs us MO 33 49 77 90 Grade 12 Owe* Percenlage Comet 75% Percentage Coma for Anchor LOWS: 2111 2311 MI 46 76 as Grade 8 Omal Percentage Comet 59% Percentage Comet for Anchor Leak.% MO 222 ars MR 17 48 88 99 BEST COPY AVAILABLE FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) 1 Level Reasoning and Problem Solving invoking Geomairic ileletionehlpeo Algebraic Equal**, and Beginnim Statistics and Probability EXAMPLE 'I R 4122281m 14-172shresh2 ialireieg pavan el ilist-ligwom S 2 It It: =1 dim-00mb maims& boy *NY eau Ira im a. 0 100 10i 0 1211 0 200 0 201 EXAMPLE 2 It. Explain bow yor food ma mower so patio I& Mawr Grade 8 Oacall Percentage Correct 34% Percentage Coned for Maher Lavoie: 121 1111 13 19 MI 88 Grade 12 Oman Percentage Correct 40% Percentage Correct for Moho/ Lewis: 202 221 21211 22 48 90 Grade 8 Overall Percentage Correct 15% Poroentege Correct for Manor unots: atig MI 1 4 2$ 74 Grade 12 Oswalt Pmentage Correct 27% Percentage Correct for Anchor Laves: 21X1 &IQ MI 3 22 74 o 90 'ME 1990 NAEP TRIAL STA= ASSESSMENT New Hampshire SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAE13'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) are 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, NAP's total group and subgroup proficiency estimates are subject to a second source of uncerainty, 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 "Efferent, but equally appropriate, set of the assessment questions -- or the entire set of questions -- somewhat different estimates of total group and subgroup proficiency might have been obtained. Thus, a seeond source of uncertainty arises because each student was administered a subset of the total pool of questions. 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 New Hampshire in addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving variour responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of =certainty 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 popuiation. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population means and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence buena! for the corresponding population quantity. This means that with approximately 95 pescent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire populat;on 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 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. 92 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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 usuahy spend each day on mathematics homework? Still other subgroups are defined by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As an example, one migh; be interested in answering the question: Do students who reported spending 45 minutes or more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spending 15 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 homework is higher, one may be tempted to conclude that that group does have higher achievement than the group wholvorted 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 rtatement about the entire 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 cliff:rent. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard error of the difference between the groups -- is obtained by taking the square of earl 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 group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups ± 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between groups in the population. If the interval does not contain zero, the difference between groups is statistically significant (different) at the .05 level. THE 1990 NAEP TRIAL STATE ASSESSMENT 93 New Hampshire As an example, suppose that one were interested in deteminiag whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard arors for females and males were as follows: Group Average Proficiency Standard Error 1 Female 259 2.0 Male 255 , 2.1 1 The difference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is ,/ 2.0' + 2.1' = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference 2 standard errors of the difference = 4 ± 2 (2.9) = 4 * 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. lf 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 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 diffetence beween 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. Converiely, 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 tense, only appropriate whtn the statistics being compared come from independent samples. For certain comparisons in t,he report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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 inteival 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. If one 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 met/sod -- was used in the analyses described in this report to fonn 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 descxibed 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 etrors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the 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 en-ors 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 groups Oefmed 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 P ural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and/or 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. 100 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 New Hampshire The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question ard the average proficiency for the total eighth-grade public-school population in the state or territory, divided by the standard deviation of the proficiency in the tc :al population. If the true difference between subgrorlp and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical report. Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the niles used to select them are shown below. Percentage Descdption of Text in Report p = 0 None 0 < p 5 10 Relatively few 10 < p 5. 20 Some 20 < p 5 30 About one-quarter 30 < p 5 44 Less than half 44 < p 5 55 About half 55 < p 5 69 More than half 69 < p S 79 About three-quarters 79 < p 5 89 Many 89 < p < 100 Almost all 13 = 100 All , 96 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire 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/ethniciv, type of community, parents" education level, and gender. 162 THE 1990 NAEP TRIAL STATE ASSESSMENT 97 New Hampshire TABLE AS I Students' Reports on the Mathematics Class 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pre-algebra Algebra TOTAL Percentage and Proficiency Percentage and /Proficiency Percentage and Proficiency State 55 ( 1.3) 28 ( 1.0) 14 ( 0.9) 282 ( 1.0) 280 ( 1.0) 306 ( 1.0) Nation 82 ( 2.1) 19 ( 1.9) 15 ( 12) 251 ( 1.4) 272 ( 2.4) 290 ( 24) RACE/ETHNICITY Vatite State 55 ( 1.4) 28 ( 1.1) 15 ( 1.0) 262 ( 1.0) 280 ( 1.0) 309 ( 1.6) Nation 59 ( 2.5) 21 ( 2.4) 17 ( 1.5) 259 ( 1.6) 277 ( 2.2) 300 ( 2.3) Hispanic State 62 ( .44 ( 7.1) Nation 75 ( 4.4) 13 ( 3.9) 240 ( 2.4) TYPE OF COMMUNITY Advantaged urban State 51 ( 262 ( 3.2) 2.7) 26 ( 287 ( 3.8) 1.8) 17 5,3) ***) Nation 55 ( 9.4) 21 ( 4.4) 289 ( 2.5)1 ( "") Extreme rural State 54 ( 8.4) *Iry 28 ( 7.9) **) Nation 74 ( 4.5) 249 ( 3.1)1 14 ( 5.0) 7 ( 4,4,4 ( 2,2) Other State 56 ( 1.4) 28 ( 1.1) 15 ( 1.0) 202 ( 0.7) 281 ( 1.2) 307 ( 1.6) Nation 81 ( 2.2) 20 ( 2.1) 18 ( 1.4) 251 ( 2.0) 272 ( 2.8) 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 -I 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 a.) 98 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE AS I Students' Reports on the Mathematics Class (continued) i They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL ASSESSMENT , hth-grade EigSTATE Mathematics _ Pre-algebra [ Algebra TOTAL State Nation PARENTS EDUCATION non-grad.!fla State Nation 14$ graduate State Nation Some college State Nation College graduate State Nation OENDLK Male State Nation Female State NatIOn and Pod Idiocy 55 ( 1.3) 262 1,0) 62 ( 2.1) 251 ( 1.4) 81 ( 3.9) 251 ( 3.2) 77 ( 3.7) 241 ( 2.1) 67 ( 2.8) 255 ( 1.4) 70 ( 2.6) 249 ( 1.9) 54 ( 2.4) 26$ ( 2.0) 60 ( 3.1) 257 ( 2.1) 44 ( 1.43 269 ( 1.2) 53 ( 259 ( 1-1+) 58 ( 1.6) 262 ( 1.1) 83 ( 2.1) 252 ( 1.6) 52 ( 1.8) 261 ( 1.4) 61 ( 2.6) 251 1,5) Percentage and Proidency Peromplago and preildency 28 ( 1.0) 14 0.9) 260 ( 1.0) 306 1.t3) 19 ( 1.9) 15 1.2) 272 ( 2.4) 291, ( 2.4) 13 ( 3.2) 5 ( 2.1)1 13 ( 3.4)) 3 ( 1.1) *41 24 ( 2.1) 7 ( 1.1) 273 ( 2.2) 15 ( 2.4) ( 1.1) 2019 ( 3.5) 277 ( 5.2) 31 ( 2.5) 13 ( 1.7) 279 ( 2.0) 300 ( 2.8) 21 ( 2.9) 15 ( 1.9) 276 ( 2.8) 295 ( 3.2) 32 ( 1.7) 21 ( 1.6) 284 ( 12) 313 ( 1.8) 21 ( 2.3) 24 ( 1.7) 27$ ( 2.8) 303 ( 2.3) 26 ( 1.3) . 13 ( 1.2) 281 ( 1.3) 309 ( 2.2) 18 ( 1.8) 15 ( 1.2) 275 ( 2.9) 299 ( 2.5) 31 ( 1.5) 16 ( 1.5) 279 ( 1.4) 307 ( 2.0) 20 ( 2.3) 15 ( 1.7) 269 ( 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 nu , not total 100 percent because a small number of students reported taking other mathematics courses. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 99 New Hampshire TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Nom 15 Minutes 30 Minutes 45 Minutes An Hour or Moro TOTAL Percentage and Pro Odom 2 ( 0.5) 41 1 ( 0.3) I* $410) 2 ( 0.5) IIP4* ( *41 ( 0.3) .0* ( 2 ( 13) ( "4) ( 1 ( 0.0) *** ( *") 0 ( 0.0) a" ( "a) 2 ( 0.6) 4" ( 4) ( 0.4) 4" ( ") Percentage and Preiciena 33 ( 0.9) 265 ( 1.2) 43 ( 4,3) 256 ( 2.3) 33 ( 1.0) 285 ( 1.2) 39 ( 4.5) 266 ( 2.2) 30 ( 6.9) 46 ( 7.6) 245 ( 3.0)1 10 ( 1.0) ) 61 (11.3) 273 ( 3.1)1 15 ( $.3) 68 (14.9) 253 ( 5.4)1 33 ( 1.1) 266 ( 1.4) 37 ( 4.3) 256 ( 3.1) Percentage and Pre Adana 55 ( 1.0) 274 ( 1.3) 43 ( 4.3) 266 ( 2.6) 54 ( 0.9) 274 ( 1.4) 45 ( 5.1) 270 ( 2.7) 86 ( 8.9) *0* ( ***) 34 ( 8.6) 251 ( 4.2)1 75 ( 4.7) 284 ( 8.0) 32 ( 8.6) ( 4,4) 81 (10.8) ( 14 (10.9) 54 ( 1.0) 274 ( 1.3) 49 ( 5.1) 265 ( 2.5) Percentage ind Preectency 8 ( 0.8) na ( 3.2) 10 ( 1.9) 272 ( 5.7)1 8 ( 0.8) 294 ( 3.2) 11 ( 2.4) 277 ( 7.8)1 1 ( 0.2) 13 ( 2.9) **) 9 ( 6.7) *** ef ) $ ( 3.4) 1111 ) 17 ( 4.4) *44(4*4) 8 ( 5.6) 8 ( 0.7) 291 ( 3.6) 10 ( 2.4) 276 ( 8.6)1 Percentage and ProlIciency 3 ( 0.4) 300 ( 3.4) 4 ( 0.9) 278 ( 5.1)1 3 ( 0.3) 4 ( 0.9) 279 ( 5.8)1 ( 0.7) 444 ( "a) 7 ( 2.1) ( 0.0) 4" ( 4") 10 ( 7.3) 4" ( 4") 4 ( 1.1) 282 (11.6)1 State Nation LA=V4ICITY Vntite State Nation Hispanic State Nation TYPE OF COMMUNITY Advantagod urban State Nation Extramo rural State Nation Othar State Nation The standard errors of the estimated statistics appear 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. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficmcy. *** Sample sae is insuSicient to permit a reliable estimate (fewer than 62 students), r 100 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A6 (continued) Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT _ None 15 Made* 30 Mind's 46 Motes An Nour or Moro TOTAL Percentage and Proficiency 2 ( 0.5) ( 0.3) ( 4 ( 2.2) ( 1 ( 0.8) ikes. ..**) 2 ( 0.7) 1 ( 0.5) ( °°41 1 ( 0.9) ( q.t.) 1 ( 0.3) 0.0 ( 0.0) .441 1 ( 0.5) ( *0.) ( 0.4) ( `.°) Percentage and Proficiency 33 ( 0.9) 205 ( 1.2) 43 ( 4.2) 250 ( 2.3) fa*. ( 111-11141) 49 ( 8.3) 240 ( 2.8) 34 ( 2.5) 252 ( 3.3) 43 ( 5.2) 249 ( 3.1) 33 ( 2.2) 270 ( 1.9) 44 ( 5.4) 265 ( 2.6) 31 ( 1.3) 273 ( 1.3) 40 ( 4.7) 265 ( 2.5) 34 ( 1.3) 265 ( 1.5) 44 ( 4.4) 257 ( 2.9) 31 ( 1.3) 265 ( 1.8) 41 i 4.4) 255 2.3) Percentage and Proficiency 55 ( 1.0) 274 ( 1.3) 43 ( 4.3) 266 ( 2.6) 48 ( 4.6) 257 ( 2.8) 40 ( 6.1) 246 ( 3.7) 59 ( 2.6) 263 ( 1.8) 44 ( 5.8) 268 ( 2.7) 51 ( 3.1) 277( 2.1) 43 ( 5.8) 270 ( 3.6) 54 ( 1.7) 283 ( 1.5) 44 ( 4.1) 277 ( 3.0) 55 ( 1.2) 274 ( 1.6) 43 ( 4.3) 268 ( 2.9) 54 ( 1.5) 273 ( 2.0) 43 ( 4.7) 264 ( 2.8) Percentage and Proficiency 8 ( 0.8) 293 ( 3.2) 10 1.9) 272 ( 5.7)1 4 ( 1.8) .4. 6 ( 1.7) ( 9 ( 3.1) 9 ( 1.6) EN. ( *It ) 7 ( 2.1) ( 10 ( 12) 302 ( 3.5) 11 ( 2.3) 287 ( 6.1)1 6 ( 0.9) 292 ( 3.8) 9 ( 1.9) 273 ( 7.3)1 10 ( 1.2) 294 ( 4.3) 11 ( 2.0) 272 ( 5.7)1 Percentage and Proficiency 3 ( 0.4) 30( ( 3.4) 4 ( 0.9) 278 ( 5.1)1 1 ( 0.4) 004(04) 4 ( 1.3) «a. 1 1 ( 0.4) 040(40*) 3 ( 1.0) 4*) 3 ( 1.1) **Hi ( 4 ( 1.0) INA ( ***) 4 ( "°) 3 ( 0.5) °°° ( °°°) 5 ( 1.3) 279 ( 7.7)1 3 ( 0.6) ( 4.°) 4 ( 0.9) 000 ( °°°) State Nation PARENTS EDUCATION NS non-graduate State Nation 115 graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statistics ai.pear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, ti.o 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 stze is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 101 New Hampshire TABLE A7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT NOM 16 Maxilla 30 Masan 45 Minutes An Hotr or More TOTAL Percentage end Prole:ion Percentage and Preacioncy Percentage and firsliciency Percentap and Proficiency Perceniege and Plonciency State 5 ( 0.5) $4 ( 1.2) 98 ( 1.5) 15 ( 0.9) ( 0.6) 258 ( 2.7) 272 ( 1.3) 277 ( 1.3) 275 ( 1.7) 274 ( 2.6) Nation 0 ( 0.8) 31 ( 2.0) 32 ( 1.2) 18 ( 1.0) 12 ( 1.1) 251 ( 2.8) 264 ( 1.9) 263 ( 1.0) 266 ( 1.9) 258 ( 3.1) RACE/ETHNICITY Mita State 5 ( 0.5) 34 ( 1.3) 39 ( 1.6) 14 ( 0.9) 9 ( 0.6) 258 ( 2.8) 272 ( 1.3) 278 ( 1.3) 275 ( 2.1) 274 ( 2.6) Nation 10 ( 1.0) 33 ( 2.4) 32 1 1.3) 15 ( 0.9) 11 ( 1.3) 258 ( 3.4) 270 ( 19) 270 ( 2.1) 277 ( 2.2) 268 ( 3,3) Hispanic State 11 ( *44 5.5) 29 ( 7.7) 37 ( ( 8.3) 15 ( 4,44. 4.8)1 ( 3.7) Nation 12 ( 1.6) 27 ( 3.0) 30 ( 2.3) 17 ( 2.1) 444 141 248 ( 3.8) 248 ( 3.4) 241 ( 4.3) ( 1141 TYPE OF COMMUNITY Advantaged urban State ( 2.0) 25 ( 1.2) 37 ( 2.0) 21 ( 3.5) 9 ( 1.9) ( 291 ( 5.8) Nation 8 ( 2.5) 41 (12.5) 278 ( 3.0)1 31 ( 280 ( 6.6) 4.8)1 12 ( 3.3) 4.**) ( 044 ( 3.4) Extreme nraI State 3 ( ( 1.5) ***) 22 ( ( 7.4) 38 ( Oh) 444 ( 23 ( 5.7) 4.41 144 ( **1 Nation a ( 2.3) 36 ( 4.6) 31 ( 2.9) 18 ( 3.8) ( 2.7) 260 ( 3.5)1 255 ( 5.1)1 Other State ( 0.5) 3$ ( 1.5) 39 ( 1.7) 14 ( 0.9) 8 ( 0.7) 259 ( 2.9) 273 ( 1.2) 277 ( 1.2) 275 ( 2.3) 275 ( 2.9) Nation 9 ( 1.0) 30 ( 1.8) 32 ( 1.3) 15 ( 1.1) 13 ( 1.1) 250 ( 3.8) 263 ( 2.3) 264 ( 2.3) 287 ( 2.1) 258 ( 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 enure 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 insuficient to permit a reliable estimate (fewer than 62 students). r 102 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A7 I Students' Reports on the Amount of Time They (continued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 16 Wades 30 Minutes 45 Minutes An Hour or Mare I TOTAL Percentage and Wedding Percentage and Proadincy Porientage and Pleading Pareentap and Pleading Penmen* and Preadoney State 5 ( 0.5) 34 ( 1.2) 38 ( 1.5) 15 ( 0.9) 8 ( 0.6) 258 ( 2.7) 272 ( 1.3) 277 ( 1.3) 273 ( 1.7) 274 ( 2.6) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 16 ( 1.0) 12 ( 1.1) 251 ( 2.8) 264 ( 1.9) 263 ( 1.9) 266 ( 1.9) 258 ( 3.1) PARENTS EDUCATION HS noniraduate State 7 ( ( 22) 36 ( 11.111, ( 3.6) fen 319 ( 4.1) *1.1 11 ( ire* 2.5) 8 ( ( 2.4) Nation 17 ( 3.0) 26 ( 3.3) 34 ( 4.4) 12 ( 2.5) 10 ( 22) 246 ( 4.0) 246 ( 2.6) ( 95 graduate State 8 ( 1.5) 3$ ( 2.2) 34 ( 2.4) 12 ( 1.8) 9 ( 1.3) ( 262 ( 2.1) 268 ( 1.9) 257 ( 3.9) 250 ( 2.9) Nation 10 ( 1.7) 33 ( 2.2) 31 ( 1.9) 16 ( 1.4) 11 ( 1.5) 246 ( 4.2) 259 ( 3.2) 254 ( 2.4) 256 ( 2.8) 244 ( 3.4) Some college State 5 ( 1.4) 37 ( 2.5) 36 ( 2.6) 15 ( 1.5) 7 ( 1.0) 276 ( 2.3) 278 ( 2.0) 273 ( 2.9) Nation 9 ( 1.2) 30 ( 266 ( 2.7) 3.0) 36 ( 286 ( 2.1) 2.6) 14 ( 274 ( 1.8) 3.5) 11 ( ( 1.5) .441 College gtaduate State 3 ( 0.5) 29 ( 1.8) 42 ( 2.4) 17 ( 1.8) 9 ( 1.1) ( e") 280 ( 1.4) 284 ( 1.7) 286 ( 3.0) 290 ( 3.7) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Male State 7 ( 0.8) 38 ( 1.8) 36 ( 1.8) 12 ( 1.0) 7 ( 0.8) 259 ( 3.5) 272 ( 1.3) 278 ( 1.8) 274 ( 31) 273 ( 4.0) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1A) 255 ( 3.9) 264 ( 2.8) 266 ( 2.4) 265 ( 3.0) 258 ( 4.1) Female State 2 ( 0.4) 29 ( 1.5) 41 ( 2.1) 18 ( 1.5) 10 ( 1.2) 271 ( 2.1) 276 ( 1.7) 276 ( 2.6) 274 ( 3.6) Nation 7 ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 246 ( 4.1) 263 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 7t 2 standard errors of the estimate for the sample, "4 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 r S THE 1990 NAEP TRIAL STATE ASSESSMENT 103 New Hampshire TABLE AS I Teachers' Reports on the Emphasis Given To i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Numban and OpaUons M.wsmsM Goometry ..-- Heavy Emphasis Little or No Emphasis Heavy Emphasis I LAM, or No Emphasis Heavy Emphasis I Little or No Emphasis TOTAL Perm lap and Pra Seism 96 ( 1.8) 269 ( 1.9) 49 ( 3.8) 260 ( 1.8) 36 ( 2.0) 269 ( 2.0) 48 ( 3.7) 267 ( 2.2) 38 ( 9.1) 47 ( 8.7) 246 ( 4.6) 49 ( 7.3) 289 ( 4.7) 28 (1/.^% 21 ( 3.9) 53 (12.4) 257 ( 7.1)1 36 ( 1.7) 269 ( 2.1) 52 ( 4.1) 280 ( 2.3) Ponuntsge and Proeciancy 17 ( 1.5) 292 ( 2.8) 15 ( 2.1) 287 ( 3.4) 17 ( 1.5) 293 ( 2.9) 16 ( 2.4) 239 ( 3.5) 12 ( 4,4) ...) 8 ( 2.2) ...) 10 ( 1.4) 0.4 ( 4 16 ( 4.2) 0.1 49 (11.8) ( 3.6) 17 ( 1$) 293 ( 2.6) 16 ( 2.7) 286 ( 3.6) Poroontap and Pro Odom 15 ( 0.9) 261 ( 2.0) 17 ( 3.0) 250 ( 5.6) 15 ( 0.9) 262 ( 2.3) 14 ( 3.4) 259 ( 6.9)1 25 ( 5.1) 23 ( 4.1) .. ) 12 ( 6.1) ) 9 ( 7.0) ...) 29 (13.3) 04.1 ( 4.9) 14 ( 0.9) 264 ( 2.7) 16 ( 3.9) 253 ( 7.1)1 Porosity* and Pra ackncy 36 % 1.1) 278 ( 40 33 ( 4.0) 272 ( 4.0) 38 ( 1.2) 279 ( 2.0) 36 ( 4.7) 277 ( 4.3) 23 ( 6.4) 34 ( 5.8) 255 ( 44)1 25 ( 2.5) ( 40 ( 8$) ...) 41 ( 8.2) 4...) 32 (11.7) 265 ( 9.1)1 40 ( 1.3) 276 ( 2.1) 34 ( 5.3) 270 1 4.3) Parent'. and Pro Seism 27 1.4) 272 2.2) 28 3.8) 260 ( 3.2) 27 ( 14) 272 ( 24) 27 ( 44) 265 ( 3.3) 33 ( 8.0) *IN ( ***) 27 ( 6.8) 22 ( 6.6) 38 ( 9.4) 267 ( 4.0)1 51 ( 9.1) 9 ( 6.1) ..) 22 ( 1.6) 273 ( 2.5) 28 ( 4.0) 200 ( 3.9) Piranha. and Pcsidency 2$ ( 274 ( 2.3 21 ( 3.3 264 ( 5.4) 25 ( 1.2) 274 ( 2.3) 22 ( 3.4) 273 ( 5.8) 21 ( 5.9) ...) 16 ( 5.5) ( ...) 24 ( 3.9) ( ***) 13 ( 3.2) ...) 26 ( 5.8) ( 16 ( 7.9) 27 ( 1.4) 273 ( 2.0) 24 ( 4.3) 2e5 ( 5.7) State Nation RACE/ETHNICITY Whit. State Nation ttlIpanle State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extrema rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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 ertimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE AS I Teachers' Reports on the Emphasis Given to ("mtinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10110 NAEP TRIAL STATE ASSESSMENT lumbers and Operations Measurement Deometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage and Proficiency Percentage and Proficiency Percents., and Profs lona Percentage and Preachment Pavanes., and Mac fancy Percentage and Peek fancy State 36 ( 11) i7 ( 1.5) 15 ( 0.0) 35 ( 1.1) 27 1.4) 2$ ( 12) 209 ( 19) 292 ( 2.5) 261 ( 2.0) 278 ( 2.0) 272 2.2) 274 ( 2.3) Nation 49( 3.8) 15 ( 2.1) 17 ( 3.0) 33 ( 4.0) 28 3.8) 21 ( 3.3) 200 ( 1.8) 287 ( 3.4) 250 ( 5.8) 272 ( 4.0) 200 ( 3.2) 266 ( 5.4) PARENTS EDUCATION 148 non-graduate State 41 ( 5.1) 7 ( 1.4) 9*9(9*9) 20 ( 3.8) *re.) 28 ( 4.9) 3$ ( 4.9) 441 20 ( 4.1) ..) Nation 00 ( 251 ( 6.9) 3.4) ( 2.3) .411 22 ( 5.3) 2$ ( 4** ( 5.3) 32 ( IMO ( 6.3) It4/111 20 ( 6.7) HS graduate State 39 ( 2.6) 12 ( 1.9) 17 ( 1.7) 36 ( 2.4) 27 ( 2.5) 24 ( 2.0) 288 ( 2.0) 272 ( 8.1) 250 ( 4.5) 263 ( 4.0) 259 ( 2.9) 256 ( 3.7) Nation 55 ( 4.8) 11 ( 2.8) 17 ( 3.9) 27 ( 5.0) 27 ( 4.5) 24 ( 5.1) 259 ( 29) 9,11 ( 941 251 ( 6.1)1 253 ( 4.7)1 255 ( 4.2) 246 ( 4.8)1 Some college State 41 ( 3.4) 16 ( 2.4) 34 ( 2.9) 32 ( 3.1) 27 ( 2.3) 275 ( 3.5) 274 ( 4.2) 277 ( 4.4) 289 ( 3.4) Nation 47 ( 4.4) 17 ( 3.3) 12 ( 2.7) 39 ( 5.5) 27 ( 5.0) 23 ( 4.1) 265 ( 2.8) 284 ( 4.1)1 ( 279 ( 4.5) 262 ( 4.8)1 270 ( 4.7) College spliduate State 31 ( 2.1) 23 ( 1.7) 14 ( 1.2) 39 f, 1.3) 24 ( 1.7) 26 ( 1.5) 278 ( 2.3) 300 ( 3.2) 271 ( 3.8) 291 ( 2.8) 280 ( 2.7) 288 ( 3.0) Nation 44 ( 41) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 28 ( 3.4) 21 ( 2.9) 269 ( 2.8) 298 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 8.4) GENDER Male State 36 ( 2.5) 16 ( 1.7) 13 ( 1.4) 37 ( 1.8) 28 ( 2.0) 25 ( 1.6) 270 ( 2.1) 289 ( 4.5) 287 ( 3.6) 276 ( 2.5) 271 ( 2.5) 270 ( 3.0) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 281 ( 2.5) 287 ( 4.4) 258 ( 6.7) 275 ( 4.8) 263 ( 3.8) 266 ( 6.8) Female State 36 ( 2.3) 18 ( 1.9) 17 t 1.2) 35 ( 1.7) 26 ( 2.0) 26 ( 2.2) 267 ( 2.4) 29$ ( 2.3) 257 ( 2.5) 280 ( 3.0) 272 ( 2.7) 278 1 2.6) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 3$ ( 4.3) 27 ( 3.9) 23 ( 3.5) 260 ( 2.0) 286 ( 3.3) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 263 ( 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 A 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 4. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 105 New Hampshire TABLE A8 I Teachers' Reports 'Ai the Emphasis Given To (continued) i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE AIATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Data AA. fits, Statistics, and Probability Algebra and Ploctions Heavy Emphasis 4 Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 16 ( OA) 55 ( 1.5) 47 ( 1.9) 24 ( 13) 209 ( 3.8) 276 ( 1.6) 284 ( 1.8) 253 ( 1.9) Nation 14 ( 2.2) 53 ( 44) 46 ( 3.6) 20 ( 3.0) 209 ( 4.3) 251 ( 2.9) 275 ( 2.5) 243 ( 3.0) RACE/ETH 'CITY white State 15 ( 0.8) 56 ( 1.5) 46 ( 1.9) 24 ( 1.3) 270 ( 4.0) 277 ( 1.7) 284 ( 1.8) 254 ( 1.9) Nation 14 ( 2.4) 53 ( 5.0) 48 ( 4.2) 18 ( 2.8) 270 ( 4.1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) Hispanic State 15 ( 5.7) ***) 46 ( 9.6) ..) 004 ( *) Nation 15 ( 4.1) 441 56 t 6.3) 246 ( 4.4) 48 ( 5.9) 257 ( 4.0)1 18 ( 4.2) .44) TYPE OF COMMUNITY Advantaged urban State 64 (10.3) 62 ( 3.8) 15 ( 4.4) 2119 ( 8.8)1 287 ( 8.3) Nation 11 ( 6.6) 65 (19.4) 284 ( 7.4)1 41 ( 8.9) 298 ( 7.9)1 16 ( 5.3) ***) Exfrme rtral State ( 3.0) 39 ( 8.3) 58 ( 9.2) 27 ( 3.5) *A* ( *41 4.44/ Nation 85 (16.9) 254 ( 8.7)1 33( 8.1) *4.4. ( 44.1 42 (16.0) 241 ( 5.9)1 Other State 12 ( 1.0) 59 ( 1.8) 44 ( 2.1) 27 ( 1.6) 275 ( 3.9) 274 ( 1.4) 285 ( 1.9) 254 ( 1.9) Nation 15 ( 2.9) 53 ( 5.2) 47 ( 4.3) 17 ( 3.3) 267 ( 4.7) 200 ( 3.4) 276 ( 2.8) 245 ( 4.4)1 The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 perant 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). lii 106 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE AS I Teachers' Reports on the Emphasis Given To (continued) I Spr:ific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Utile or No Emphasis TOTAL Peramtage and *a Salem Parandage and rmolidency Pareentaid and Pro Many Percientage and Prsdideney State 16 ( 0.8) IP5 1.5) 47 ( 1.9) 24 ( 1.3) ( 3.8) 2141 1.6) 264 ( 1,8) 253 ( 1.9) Nation 44 ( 2.2) 53 4.4) 46 ( 3.6) 20 ( 3.0) 209 ( 4,3) 251 ( 2.9) 275 ( 2.5) 243 ( 3.0) PARENTS' EDUCATION NS non-graduate State 24 (( 2.11) 51 ( 245 ( 4.5) 5.9) 30 ( 4.9) its.1 36 ( 5.0) Nation 9 ( 3.0) se..) 53 ( 240 ( 7.7) 6.2) 28 ( ( 5.2) 641 29 ( 6.9) KS graduat State 10 ( 1.7) 55 ( 2.5) 38 ( 3.3) 31 ( 1.8) 265 ( 3.8) 259 ( 3,1) 272 ( 2.6) 243 ( 2.5) Nation 17 ( 3.7) $4 ( 5.4) 4.4 ( 4.8) 23 ( 3.9) 261 ( 6.0)I 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Sone college State 15 ( 2.9) 54 ( 2.9) 45 ( 42) 24 ( 3.3) 279 ( 3.6) 285 ( 3.2) 260 ( 4.0) Nation 13 ( 2,5) 4.4.1 57 ( 270 ( 5.8) 3.7) 48 ( 278 ( 4.8) 3.0) 17 ( 3.1) College graduat State 14 ( 1.0) 57 ( 1.9) 4. ( 2.0) 19 ( 12) 279 ( 2.8) 289 ( 1.9) 2fi 1.9) 262 ( 2.9) Nation 15 ( 2.4) 53 ( 4.4) 3.9) 18 ( 2.4) 282 ( 4.5) 275 ( 3.5) 288 ( 3.0) 249 ( 4.0) GENDER M. State 15 ( 1.4) 56 ( 22) 43 ( 1.8) 28 ( 1.4) 274 ( 3.7) 273 ( 2.1) 281 ( 2.0) 253 ( 2.5) Nation 13 ( 2.2) $4 ( 4.7) 44 ( 4.1) 22 ( 3.0) 275 ( 5.8) 260 ( 3.5) 276 ( 3.2) 243 ( 3.0) Female State 16 ( 1.0) 54 ( 1.8) 51 ( 2.4) 20 ( 1.9) 264 ( 4.9) 278 ( 2.2) 287 ( 2.2) 254 ( 2.3) Nation 10 ( 2.4) 53 ( 4.5) 48 ( 3.6) 18 ( 2.9) 263 ( 4.4) 262 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages may not total I DO percent because the "Moderate emphasis" category is not included. Interpret with caution the nature of the sample does not allow accurate determinItion of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a rehable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 107 New Hampshire TABLE A9 I Teachers' Reports on the Availability of i Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19130 NAEP TRIAL I Get All the Resources I I Oft Most of the I Get Some or None of STATE ASSESSMENT Need Resources I Need the ROSOUrCOS I Need TOTAL Pencentaga and Madam* Porcentaga and Prodiciancy Parental@ and Prolicionew State 15 ( 0.8) 61 ( 1.3) 23 ( tO) 274 ( 2.1) 275 ( 0.9) 268 ( 1.6) Nation 13 ( 2.4) 56 ( 4.0) 31 ( 42) 265 ( 4.2) 205 ( 2.0) 261 ( 2.9) RACE/ETHNICITY White State 15 ( 0.8) 62 ( 1.3) 23 ( 1.0) 276 ( 2.2) 275 ( 0.9) 268 ( 1.7) Nation 11 ( 2.5) 58 ( 4.6) 30 ( 4.6) 275 ( 3.5)1 270 ( 2.3) 267 ( 3.3) Hispanic State 20 ( 5.7) ( d1.1 114 ( «Al Nation 23 ( 7.6) 44 ( 4.9) 34 ( 71) 246 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 TYPE OF COMMUNITY Advantaged urban State 0 ( 0.0) 78 ( 5.5) 22 ( 5.5) ( 280 ( 2.8) *0* ( Nation 38 ( 9.2) 59 ( 6.9) 3 ( 3.1) 272 ( 8.5)1 288( 1.3)1 Extrema rural State 0 ( ( 0.0) 88 (14.5) 4-.11 14 (14.5) Nation 54 (10.4) 43 (10.3) ( *441 260 ( 8.8)1 257 ( 5.0)1 Other State 16 ( 0.9) 61 ( 1.5) 23 ( 1.2) 277 ( 2.3) 275 ( 1.1) 268 ( 1.4) Nation 11 ( 2.9) 58 ( 5.4) 31 ( 5.6) 265 ( 3.9)1 264 ( 2.1) 263 ( 4.2) 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). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE I Teachers' Reports on the Availability of ("mtinued) 1 Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL I Oat All the Resources I I Get Moot of the I Got Sum o. Sono a STATE ASSESSMENT Need Rosoircas I Need the Natourcos I Need TOTAL State Nation PARENTS' EnuCATIoN and Prallakow 1$ GI) 274 2.1) 13 2.4) 265 ( 4.2) 12 ( 3.2) cm& uril }2.6) ***) NS non-graduate State Nation RS graduate State 15 ( 441., 13) Nation 10 ( 2.5) 253 ( 4.8)1 Some cottage State 13 ( ale 1.4) Mil Nation 13 ( 3.3) College graduate State 18 ( 1.1) 28$ ( 2.5) Nation 15 ( 2.9) 270 ( 5.4)1 GENDER M. State 15 ( 1.1) 273 ( 2.5) Nation 13 ( 2.8) 264 ( 5.0)I Renato State 18 ( 1,2) 275 ( 3.1) Nation 13 ( 2.4) 268 ( 3.9) and lasNalsacy 01 ( 275 0.9 50 4.0 205 2.0 51 ( 4.0) 253 ( 3.4) 54 ( 5.7) 244 ( 2.1) 50 ( 2.1) 263 ( 1.5) 54 ( 4.9) ZS. ( 1.9) 00 ( S.3) 275 ( 2.0) o2 ( 4.3) 209 ( 2.5) 64 ( 1.7) 264 ( 13) 50 ( 4.9) 270 ( 2.2) 01 ( 1.6) 274 ( 1.2) 57 ( 4.0) 205 ( 2.6) 62 ( 1.8) 275 ( 1.3) 55 ( 4.4) 204 ( 2.0) LaNdosai . i 100 91 4.2 281 ( 2i 243 ( 3.5 11 20 ( 2.0) 251 ( 2.1 35 ( 4.91 250 ( 2.0 20 ( 3.0) 275 ( 2.3) 25 ( 4.1) 207 ( 31) 19 ( 1.1) 276 ( 1.9) 30 ( 5.1) 273 ( 3.7) 24 ( 1.3) 200 ( 1.9) 30 ( 4.0) 264 ( 3.3) 22 ( 12) 269 ( 2.5) 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). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 New Hampshire TABLE Al Oa I Teachers' Reports on the Frequency of Small 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Per0MINISID and fralidency dieramtimid Prelkiency Percenties and Pralidency State 57 t5) 33 ( 14) 10 ( 0.7) 273 tO) 274 ( 1.9) 270 ( 1.7) Nation 50 44) 43 ( 4.1) 8 ( 2.0) 240 ( 2,2) 284 ( 2.3) 4,0 277 ( $.4)1 RACE/ETHNICITY White State 57 ( tip 34 ( 1.5) 10 ( 0.7) 274 ( 1.1) 274 ( 1.9) 270 ( 2.0) Nation 49 ( 4.9) 43 ( 4.5) ( 2.3) lifspardc 285 ( 2.7) 271 ( 22) 285 ( 4.9)1 State TO ( 7.8) ( 23 ( 13.9) .4 7 ( 4.3) Nation 84 ( 72) 248 ( 2.5) 32 ( 13.9) 247 ( 8.3)I 4 ( 1.4) ( .41 TYPE OF COMMUNITY Advantaged urban State 54 ( 5.2) ( 6.5) 8 ( 5.7) 277 ( 0.0) 293 ( 4.8) Nation 30 (22.9) .41 41 (17.9) 273 ( 8.0)! 20 (12.2) ( IMO ) Extreme rtraI State 82(3.1) ( 441 18 ( 3.1) ( *el 0 ( 0.0) 4.411) Nation 35 (14.8) 56 (17.1) 9 ( 9.8) 255 ( SS)! 258 ( 5.9)1 Other State GO ( 1.8) 29 ( 1.8) 11 ( 0.8) 273 ( 1.0) 274 ( 1.7) 272 ( 1.7) Nation 50 ( 4.4) 44 ( 4.5) a ( 1.a) 200 ( 2.4) 264 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insuffic,ent to permit a reliable estimate (fewer than 62 students). 110 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE Al Oa I Teachers' Reports on the Frequency of Small (continued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1M10 NAEP TRIAL STATE ASSESSMENT At Least Once a Weak Lea Than Once a Week Never TOTAL and Preekianni Poroentage and Preadency Parcentage and Prolidancy State 57 ( 1.5) 33 ( 1.4) 10 ( 0.7) 273 ( 1.0) 274 ( 1.9) 270 ( 1.7) Nation 50 ( 4.4) 43 ( 4.1) ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 5.4)1 PARENTS' EDUCATION NS non-graduate State 50 ( 5.7) 37 ( 4.7) 13 ( 3.1) 255 ( 2.4) ( Nation 00 ( 244 ( 6.4) 32) 39(65) 244 ( 3.2)4 1 ( ( 1.4) «61 $3 graduate State 58 ( 259 ( 3.3) 1.9) 32 ( 262 ( 2.8) 2.9) 9 ( 1.4) vo.1 Nation 49 ( 4.8) 45 ( 5.1) 6 ( 2.5) 252 ( 2.8) 257 ( 2.7) Some coilege State 53 ( 270 ( 2.6) 1.6) 35 ( 276 ( 2.9) 2.3) 11 ( ( 1.5) .41 Nation 51 ( 5.2) 42 ( 5.1) 7 ( 2.3) 266 ( 3.1) 268 ( 32) Canoga graduate State 59 ( 1.8) 32 ( 1.7) 9 ( 1.0) 282 ( 1.5) 215 ( 1.9) 277 ( 2.1) Nation 46 ( 52) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 276 ( 3.0) 285 ( 4.9)4 GENDER Mate State 58 ( 2.1) 32 ( 1.9) 10 ( 0.9) 272 ( 1.3) 273 ( 22) 269 ( 3.5) Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 265 ( 3.1) 276 ( 5.3)4 Female State 56 ( 2.0) 35 ( 1.9) 9 ( 1.2) 273 ( 1.3) 274 ( 2$) 272 ( 3.8) Nation 50 ( 4.7) 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.6)! The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. **8 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 6 THE 1990 NAEP TRIAL STATE ASSESSMENT Ill New Hampshire TABLE MOb I Teachers' Reports on the Use of Mathematical i Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - _ 1990 NAEP TRIAL STATE ASSESSMENT At Lust Once a Weak Lass Than Once a Weak Never _. TOTAL State Nation RACVETHNICITY Palfellataila and Preekiancy 31 ( 1.2) 2701 1.3) 22 ( 3.7) 254 ( 32) 31 ( 1.3) 271 ( 1.5) 17 ( 4.0) 261 ( 3.8)1 49 ( 81) ( 39 ( 7.5) 247 ( 3.8) 10 ( 2.9) ( 011111 23 (14.4) ( e ) 48 ( 8.5) .4. ( 27 (14.9) ( 31 ( 1.4) 271 ( 1.5) 19 ( 4.3) 253 ( 3.9)1 Percentage and Preaching 59 ( 1.6) 272 ( 1.0) fia ( 3.9) 263 ( 1.9) 59 ( 1.7) 273 ( 1.0) 72 ( 4.2) 269 ( 2.1) 39 ( 6.2) ( 55 ( 7.3) 245 ( 3.8)! 72 ( 3.1) 284 ( 5.0) 63 (11.5) 278 ( 5.6)1 37 (I0.8) 65 (14.6) 262 ( 2.8)1 57 ( 1.9) 273 ( 1.1) 72 ( 5.0) 263 ( 22) Percentage and Proficiency 11 ( 1.1) 282 ( 4.8) ( 2.8) 282 ( 5.9)1 10( 1.1) 253 ( 5.3) 10 ( 2.7) 288 ( 6.2)i 12 ( 5.0)*) ( 2.6) vel 11 ( 2.3) «fr) 15 ( 9.3) 17 ( 6.0) ( 3.9) fgrib ( 4,11 11 ( 1.2) 280 ( 5.1) 9 ( 3.3) 281 ( 7.1)1 Mt. State Nation HIspanIc State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extreme nut State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of thl estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate dee 'nation of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a estimate (fewer than 62 students). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE AlOb I Teachers' Reports on the Use of Mathematical (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Weak Lau Than Once a Wash Never TOTAL Percentage and Prolidency Percentage and Proficiency Perainiage and Proficiency State 31 ( 1.2) 59 ( 1.6) 11 ( 1.1) 270 ( 1.3) 272 ( 1.0) 282 ( 4.8) Nation 22 ( 3.7) 09 ( 3.9) 9 ( 2.6) R54 ( 3.2) 263 ( 1.9) 282 ( 5,9)1 PARENTS' EDUCATION NS non-graduate State 35 ( *v. 4.9) 53 ( 251 ( 5.0) 3.8) 13 ( 3.7) VT1 Nation 2$ ( 5.6) «HI 86 ( 243 ( 7.2) 2.2) 9 ( 8.5) .4* HI graduate State 32 ( 2.1) 262 ( 2.3) 60 ( 258 ( 22) 2.1) 8 ( 1.6) .04) Nation 23 ( 4.8) 70 ( 5.3) 7 ( 2.8) 248 ( 4.0)1 25$ ( 22) Scow Whim@ State 32 ( 2.4) 56 ( 2.8) 12 ( 1.8) 273 ( 2.6) 276 ( 1.6) *Mt ( *41 Nation 18 ( 4.0) 73 ( 4.3) 9 ( 2.4) 261 ( 4.4)1 269 ( 2.3) ( ".) Collage graduat State 29 ( 1.6) 60 ( 1.7) 11 ( 1.1) 278 ( 1.8) 282 ( 1.3) 298 ( 3.3) Nation 20 ( 3.9) 89 ( 3.7) 11 ( 2.5) 266 ( 3$)1 274 ( 2.2) 297 ( 4.2)1 GENDER Male State 33 ( 1.6) 58 ( 1.9) 9 ( 1.4) 272 ( 1.7) 271 ( 1.3) 278 ( 6.4) Nation 22 ( 4.1) 89 ( 4.1) 8 ( 2.0) 255 ( 4.1) 265 ( 2.1) 287 ( 7.2)1 Female State 29 ( 1.7) 59 ( 2.0) 12 ( 1.3) 269 ( 1.9) 273 ( 1.7) 286 ( 4.9) Nation 21 ( 3.6) 89 ( 4.2) 10 ( 3.3) 254 ( 33) 262 ( 1.9) 27$ ( 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. '1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 I s THE 1990 NAEP TRIAL STATE ASSESSMENT 113 New Hampshire TABLE Alla I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT . Almost Every Day Several Tkass a Week About Om* a Weak or Less . TOTAL Paraeatage and Maim& Petromiego am. Pralkimy State 65 14 273 1.4 272 1.2 Nation 32 SA 31 3.1 267(1.8) 254 2.91 RACE/ETHNICITY Wt. State 55 ( 1.4) 34 ( 273 ( 1.4) 273 ( 1.2 Nation 64(3.7) 25 ( 3.2 272 ( 1.9) 264 ( 34 Hispanic State' 47 4111* ( 8.6) **II) 34 did* 3.5) Nation 61 ( 6.6) 32 5.3) 251 ( 3.1) 240 ( 4.3)1 TYPE OF COMMUNITY Athcantaged titan State 87 266 4.6) ( 5.9) 8 ( 3.3) 441 Nation 63 283 (15.9) ( 7.3)1 23 52) *iv) Extreme rural State 45 et. (10.7) ( 10 ( 39) ttyl Nation 50 (109) 40 (10.0) 268 ( 4.0)1 247 ( 7.8)1 Other State 52 ( 1.4) 37 ( 1.8) 273 ( 105) 273 ( 1.1) Nation (fa ( o.9) 31 ( 3.5) 267 ( 2.3) 25S ( 3.1) Poresataip and Pieloisocy 11 ( 276 ( ( 1.11 200 ( 5.1)I 10 ( 1.2) 2.0) $ 2.3) 264 SAN 1$ 7.7) 111 ( «et) ( 5.7) *gm 14 (14* e. 45 ( 9.2) ( 0,41 10 ( 73) 10 ( 1.4) 274 ( 2.1) 6 ( 1.9) 257 ( 5.8)1 The standard errors of the estimated statistics appear in parentheses lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for t,he 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). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE Al la I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Weak or Lees TOTAL and Pewlistsocy ant Prekleacy Pimento's end Preliciency state 55 12) 34 ( 11 1.2) 273 1.4) 2/2 ( 12 278 ( 2.0) Nation 82 3.4) 31 ( 3.1 7 (1.8) 267 ( 1.8) 254 ( 2.9) 260 (5.1)1 1.111htSAMI KS non-graduate State 53 ( 4.6) 40 ( 5.0) 7 ( 2.9) 251 ( 3.4) Olt* ( Nation 87 ( 245 ( 5.5) 3.2) 27 ( 5.2) *sit) ( IMP* ( 2.1) NS graduate State 55 ( 2.2) 258 ( 1St) 37 286 ( 2.2) ( 2.1) 8 ( 1.5) 04 ( «pi Nation 61 ( 4.4) 34 ( 3.7) ( 1.5) 257 ( 2.5) 250 ( 2.9) ( 1141 Some collgit State 56 ( 275 ( 2.5) 2.2) 33 276 ( 2.9) ( 2.7) 10 ( 444 ( 2.0) 444) Nation 68 ( 42) 26 ( 3.7) 8 ( 1.9) collage graduate 272 ( 2.7) 258 ( 51) State 55 ( 2.0) 32 ( 2.0) 13 ( 1.6) 235 ( 1.8) 279 ( 1.2) 282 ( 2.2) Nation 61 ( 4.0) 31 ( 3.9) ( 3.1) 281 ( 2.2) 265 ( 3.1) GENDER Male State 54 ( 1.9) 36 ( 2.3) 11 ( 1.7) 272 ( 1.6) 272 ( 1.1) 275 ( 2.9) Nation 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2.1) 256 ( 3.8) 261 ( 6.7)1 Female State 57 ( 1.8) 32 ( 1.9) 11 ( 1.3) 273 ( 1.9) 273 ( 1.9) 277 ( 2.7) Nation 65 ( 268 ( 3.6) 1.8) 28 ( 253 ( 3.3) 2.5) 7 ( ( 2.2) 0.0) 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. I 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). 12 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 115 New Hampshire TABLE Alibi Teachers' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Al Lauf Sawaral Tann a Week About Once Weak Lass than Wasedy TOTAL, Parceabge and 9rallicisacar Peroantarr ard Pounding, Peroadaga and Prolkiancy State 49 ( 1.3) 2e( 25 ( 12) 270 ( 1.1) 272 ( 12 290 ( 2.4) Nation 34 ( 3.8) 33 ( 32 ( 3.6) 256 ( 2.3) ( 23) 274 ( 2.7) RACE/ETHNICITY Whits State 49 ( 1.3) 26 ( 1.1) 25 ( 12) 270 ( 1.1) 272 ( 1.4) 281 ( 2.4) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Hispanic State 53 ( 7.3) 28 ( 7 2) 19 ( 6.2) OF* Vail Nation 41 ( 7.7) 26 ( 5.3) 33 ( 7.5) 242 ( 3.2)1 244 ( 5.1)1 257 ( 2.3)1 TYPE Of COMMUNITY Advantaged urdan State 31 ( 7.1) 15 ( 8.3) 53 ( 8.1) 71-41* 4.01) 288 ( 7.1) Nation 59 (13.9) 273 ( 34)1 20 ( 8.0) at.* 21 ( 8.2) sim) Extreme rural State 27 ( 7.4) eg. I ***) 39 ( 7.1) *44 ( 34 ( 6.8) 4..4) Nation '..11 (14.3) *** 49 (12.7) 258 ( 6.7)1 24 (10.1) Other State 52 ( 1.4) 2$ ( 1.2) 19 ( 1.2) 271 ( 1.2) 271 ( 1.3) 282 ( 1.6) Nation 30 44) 35 ( 43) 36 ( 4.2) 256 ( 3.3) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated gatittICS 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). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE Al lb I Teachers' Reports on the Frequency of (cmtinued) i Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week. Less than Weeldy TOTAL Percentage and Ptak:Jena Percentage and ProRdency Percentage and Preedenny State 461 ( 1.3) 26 ( 1.1) 25 ( 1.2) 270 ( 1.1) 272 ( 1.2) 280 ( 2.4) Nation 34 (3.8) 33 ( 3.4) 32 ( 3.8) 250 ( 2.3) 200 ( 2.3) 274 ( 2.7) PARENTS EDUCATION $5 nen-gracluate State 44 ( 5.7) 28 f 4.7) 30 ( 4.0) HI* ) Nation 35 ( 8.0) 29 ( 8.3) 38 ( 6.9) 239 ( 3.5) 250 ( 4.5)1 143 graduat State 48 ( 2.6) 29 ( 2.1) 24 ( 2.3) 258 ( 2.7) 259 ( 1.9) 265 ( 2.5) Nation 35 ( 5.3) 38 ( 4.5) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 263 ( 14) Some college State 47 ( 3.4 28 ( 2.9) 25 ( 2.4) 271 ( 2.2) 278 ( 2.6) 284 ( 2.8) Nation 33 ( 4.7 32 ( 4.0) 35 ( 4.1) 280 ( 2.8) 268 ( 4.2) 278 ( 2.8) Cottage graduate State 51 ( 1.8) 24 ( 1.4) 25 ( 1.7) 279 ( 1.3) 282 ( 1.9) 292 ( 2.9) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 284 ( 2.8) 271 ( 2.4) 289 ( 2.9) GENDER Mal State 48 ( 1.8) 29 ( 1.7) 23 ( 1.5) 270 ( 1.5) 270 ( 1.6) 279 ( 3.0) Nation 35 ( 4.1) 35 ( 3.8) 31 ( 3.5) 257 ( 3.2) 261 ( 2.8) 275 ( 3.2) Female State SO ( 1.8) 23 ( 1.4) 27 ( 1.8) 209 ( 1.7) 274 ( 2.2) 281 ( 2.7) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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 117 New Hampshire TABLE A 12 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Rorer TOTAL Percentage Pestentage and and Proficiency Proficiency Percentage and Proficiency State 32 ( 35 ( 1.1) 33 ( 1.0) 274 ( 1.2 276 ( 1.4) 271 ( 1.3) Nation 28 ( 2.5 25 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 241 ( 1.8) RACEIETHNICITY Whitt State 32 ( 1.2) 35 ( 1.1) 33 ( 1.1) 275 ( 1.4) 276 ( 1.4) 272 ( 1.3) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 268 ( 3.1) 272 ( 1.9) 270 ( 1.7) Hispanic State 38 ( 8.0) 27 ( 8.8) 34 ( 7.4) ( OM/ Nation 37 ( 5.2) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) TYPE OF COMMUNITY Advantaged urban State 43 278 ( 8.3) ( 2.9)1 32 ( 277 ( 8.8) 4,8)1 25 *44 ( 6.0) ( *41 Nation 27 (13.9) 33 ( 4.5) 40 (134) ( **It) 286 ( 5.4)1 279 ( 3.5)1 Extram rural State ( 4.**) 2$ ( 6.6) *4-.) Nation 34 (10.8) 27 ( 3,8) 39 (11.6) 249 ( 5.2)1 264 ( 3.5)1 256 ( 6.2)1 Mar State 33 ( 1.1) 33 ( 1.2) 34 ( 1.2) 273 ( 1.3) 278 ( 14) 271 ( 1.4) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 264 ( 2.1) 262 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, :or each population of interest, the value for the entire population is within ± 2 standard errors of the e4timate for the sample. ! Interpret with caution -- the nature of the 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 New Hampshire TABLE Al2 I Students' Reports on the Frequency of Small (continued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Al Least Once a Week LOSS Than Ones a Weak Now TOTAL Pareentags aid Pindoimcy Peramitas Parepals. and rad PrOICIOICY Prollakscol State 32 ( 1.1) 35 1.1 33 0 274 ( 1.2) 278 14 271 1.3 Nation 2$ ( 2.5) 28 14) 44 2.9 258 ( 2.7) 267 ( 2.0) 261 1 PARENTS' EDUCATION 11$ non-graduate State 30 3.3) ..**) 44 ( 254 ( 4.7) 4.3) Nation 29 ( 4.5) 29 3.0) 42 ( 4.5) 242 ( 3.4) 244 ( 3.0) 242 ( 2.7) 11.1 graduate State 27 ( 1.9) 36 ( 2.4) 37 ( 2.4) 200 ( 2.4) 206 ( 2.0) 280 ( 2.2 Nation 2$ ( 3.0) 28 ( 16) 43 ( 3.4 251 ( 3.7) 261 ( 2.6) 2$2 ( 1.7) Some college State 32 ( 26) 35 ( 3.0) 34 ( 2.4) 279 ( 2.3) 278 ( 2.0) 274 ( 2.7) Nation 27 ( 3.9) 27 ( 2.4) 285 ( 3.6) 268 ( 3.3) 286 ( 2.1) College graduat State 37 ( 1.6) 34 ( 1.4) 29 ( 1.2 282 ( 2.0) 285 ( 1.6) 282 1.8 Nation 28 ( 3.0) 28 ( 1.9) 44 ( 270 ( 2.7) 278 ( 2.8) 275 ( 2.2 GENDER M. State 32 ( 1A) 35 ( 1.8) 33 ( 1.3) 275 ( 1.7) 275 ( 1.9) 270 ( 1.7) Nation 31 ( 2.9) 28 ( 1.7) 41 ( 2.9) 259 ( 3.3) 268 ( 2.8) 262 ( 1.8) Female State 33 ( 1.4) 34 ( 1.5) 33 ( 1.8) 274 ( 2.0) 270 ( 1.4) 272 ( 1.8) Nation 28 ( 2.4) 27 ( 1.8) 47 ( 3.2) 257 ( 2.8) 200 ( 1.7) 260 ( 14) 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students) THE 1990 NAEP TRIAL STATE ASSESSMENT 119 New Hampshire TABLE A 13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT At Least Once a Wasik Less Than Ones a Weak New TOTAL State Nation RACEJETNAHCIrf White State Nation Hispanic State Nation TYPE OF commutert Advantagod urban State Nation Extrome rural State Nation Other State Nation Pardentage and Proadency 30 ( 04) 272 1.5) 24 1.8) 254 2.6) 30 ( 0.9) 273 ( 1.5) 27 ( 1.9) 266 ( 2.6) ( 38 ( 4.2) 241 ( 4.6) 17 ( 3.6) dm. ( 36 (10.3) 278 ( 6.1)1 41 (10.4) 21 ( 3.1) *44 ( 14011) 29 ( 0.9) 273 ( 1.3) 27 ( 2.0) 258 ( 2.9) ansatags and Praldency 33 0.9) 270 31 1.2 ail 1.5 33 ( 0.9) 270 , 1.5) 33 ( 1.0) 275 ( CO) 28 ( 0.1) 4.0. ( 23 ( 2.0) 253 ( 4.3) 40 ( 5.0) 279 ( 4.7) 33 ( 4.8) 284 ( 3.2)1 32 ( 8.2) *** 37 ( 4.7) 262 ( 4.7)1 33 ( 1.0) 276 ( 1.5) 31 ( 1.4) 270 ( 1.8) Perosidage and Pralidency 37 ( 1.0) 279 ( 1.4) 41 ( 2.2) 259 ( 1.8) 37 ( 1.0) 274 ( 11.4) 40 ( 2.5) 268 ( 1.8) 45 ( 02) 444 ( 444) 40 ( 4.0) 240 ( 1.9) 42 ( 4.3) 204 ( 0.3) 32 (111) 281 ( 5.9)1 27 ( 9.4) ( ) 43 ( 5.0) 251 ( 52)1 38 ( 1.0) 273 ( 1.4) 41 ( 2.4) 200( 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. I 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 insuMcient to permit a reliable estimate (fewer than 62 students). .1 r. 5 120 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A13 I Students' Reports on the Use of Mathematics (continuul) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRIAL. STATE ASSESSMENT At Least Once Week Less Than Once a Week New TOTAL, Percentage WWI Proildency Percentage and Proficiency riarcontago and Proficiency State ( 0.9) 33 ( 0.9) 37 ( 1.0) 272 ( 1.5) 276 ( 1.4) 273 ( 1.4) Nation 28 ( 1.8) 31 ( '1.2) 41 ( 2.2) 258 ( 2.6) 269 ( 1.5) 25a ( 1.6) PARENTS' EDUCATION NS non-graduate State 37 ( 4.2) 18 ( 3.8) 44 ( 4.4) WIN ( 257 ( 4.0) Nation 27 ( 42) 26 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) HS graduate State 29 ( 2.2) 29 ( 1.9) 42 ( 1.9) 282 ( 2.1) 285 ( 1.9) 280( 2.0) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Sono college State 31 ( 2.9) 34 ( 2.3) 38 ( 3.5) 278 ( 2.3) 274 ( 1.8) 278 ( 2.8) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.8) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) College graduate State 30 ( 1.4) 30 ( 1.5) 34 ( 1.6) 279 ( 1.3) 284 ( 2.1) 286 ( 1.8) Nation 30 ( 2.5) 32 1 2.0) 38 ( 2.6) 289 ( 3.0) 278 ( 2.0) 275 ( 2.0) OENDER Male State 33 ( 1.4) 32 ( 1.8) 35 ( 1.8) 272 ( 1.8) 277 ( 1.7) 272 ( 1.9) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 21) 258 ( 2.9) 271 ( 260 ( 1.8) Female State 27 ( 1.2) 34 ( 1.4) 40 ( 1.5) 272 ( 1.9) 274 ( 1.8) 275 ( 1.7) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.8) 257 ( 3.0) 268 ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population or 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). 126 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 New Hampshire TABLE A14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAV TRIAL STATE ASSESSMENT Almost Evory Day Savant Times a Weak About Onea a Weak or Len TOTAL Proildow Porowdowe wd Prolidency Ikorambilo and Prolicianoy State 72 ( 1.4) 15 ( 13 ( 276 ( 268(1.7) 267 1.5 Nation 74 ( 1.9 14 ( 12 13 267 ( 1.2 252 ( 1.7) 242 4.5) MENEM Mite State 72 ( 1.5) 15 ( 0.8) 13 ( 1.4) 277 ( 1.1) 269 ( 1.7) 267 ( 1.5) Nation 76 ( 2.5) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 2.2) 252 ( 5.1)1 Hispanic State 58 ( 5.9) «Al 18 ( 5.0) ( *to) 23 ( 6.4) Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) TYPE OF COMMUNITY Advardagad ultan State 81 ( 3.9) 284 ( 3.2) 8 ( 1.2) ( «on 11 ( 3.8) 4m..) Nation 73(11.1) 266 ( 4.6)1 13 ( 1.7) 14 (10.4) *gm, ( Extrema rural State 84 ( 3.2) 279 ( 4.8)1 9 ( 4.1) ***) 7 ( 3.0) ***) Nation 68 (11.3) 15 ( 3.6) 17 ( 8.2) 263 ( 4.2)1 Other State 71 ( 1.5) 16 ( 03) 13 ( 1.4) 276 ( 4.0) 269 ( 1.8) 268 ( 1,5) Nation 75 ( 2.2) 14( 1.0) 10 ( 1.9) 267 ( 1.6) 252 ( 2.6) 239 ( 4.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with otution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A 14 I Students' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL STATE ASSESSMENT Mmost Every Day Several Times a Week . About Once a Wm* or Lass TOTAL Parositaga and Prsidoncy Pertortdaga and Prvedsita PereengelP ald linolkiency State 72 ( 14) 15 ( 0.7) 13 ( 1.3) 278 ( 1.0) 288 ( 1.7) 287 ( 1.5) Nation 74 ( 1.9) 14 ( 0.3) 12 ( 1.8) 287 ( 1.2) 252 ( 1.7) 242 ( 4.5) PARENTS' EDUCATION NS non-graduata State 62 ( 256 ( 3.9) 2.9) 15 ( 3.2) .411 23 ( 014 ( 4.5) *Pi Nation 64 ( 245 ( 3.4) 2.3) 18 ( 2.0) ( *el 18 ( 3.1) NS graduate State 71 ( 2.2) 15 ( 1.5) 13 ( 1.9) 263 ( 1.5) 259 ( 3.5) 259 ( 2.7) Nation 71 ( 3.6) 16 ( 1.8) 13 ( 2.8) 255 ( 1.5) 249 ( 3.2) 239 ( 3.4)1 S. coNage State 77 ( 277 ( 2.3) 1.9) 13 ( .44 ( 1,5) 10 ( 1.5) ,44) Nation 60 ( 270 ( 2.0) 1.9) 11 ( *** ( 12) 041 9 (( 1.7) *41 Collage graduate State 72 ( 1.7) 16 ( 1.1) 12 ( 1.5) 286 ( 1.1) 276 ( 2.4) 274 ( 2.4) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 260 ( 2.8) 257 ( 8.4)1 GENDER Mal* State 71 ( 2.0) 15 ( 1.2) 14 ( 2.1) 270 ( 1.1) 267 ( 2.2) 264 ( 2.4) Nation 72 ( 2.4) 18 ( 12) 12 ( 2.1) 258 ( 1.6) 252 ( 2.5) 242 ( 6.1) Female State 73 ( 1.6) 15 ( 1.1) 12 ( 12) 276 ( 1,5) 268 ( 25) 270 ( 2.0) Nation 78 ( Le) 13 ( 1.0) 11 ( 1.0) 265 ( 1.3) 250 ( 25) 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. 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). 126 THE 1990 NAM' TRIAL STATE ASSESSMENT 123 New Hampshire TABLE A15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAER TRIAL STATE ASSESSMENT At Lust Swami Times a Weak _ About Once a We* Leas Than Malady TOTAL and Priliciancy Mrs Odom Ilveromeds. dad lorsadeacy State 43 ( 271 ( 1.3) 0.9) 27 ( 272 ( 0.9) 1.6) 30 ( 279 1.0) 1.9) Nation 38 ( 2.4) 25 ( 14) 37 ( 24) 263 ( 2.2) 261 ( 1.4) 272 ( RACE/ETHNICITY White State 43 ( 1.4) 27 ( 0.0) 29 ( 1.1) 272 ( 0.9) 272 ( 1.6) 280 ( 2.0) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 262 ( 2.5) 269 ( 1.5) 277 ( 2.0) Hispanic State 41 ( 6.9) 23 5.9) 31 ( 5.8) IN. on Mit ( 141 Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 238 ( 3.9) 247 ( 3.3) 248 ( 3.3) TYPE OF CoMMUNITY Advantaged urban State 29 ( 44. 4.5) ( *el 54 ( 298 ( 2.5) 5,6) Nation 50 ( 9.0) 19 ( 4.9) 31 ( 9.3) 271 ( 3.3)1 *re 290 ( 5.3)1 Extreme rural State 41 ( 5.4) *4* ( +el 30 ( 5.9) 29 ( 5.2) Nation 42 (10.1) 30 ( 4.4) 28 ( 7.5) 249 ( 4.0)1 256 ( 3.4)1 207 ( 7.3)1 Other State 44 ( 1.5) 28 ( 1.0) 26 ( 12) 271 ( 1.0) 273 ( 1.5) 260 ( 1.9) Nation 36 ( 2.9) 26 ( 1.2) 96 ( 29) 252 ( 3.0) 261 ( 2.1) 272 ( 1A) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). .4_i_tI(' 124 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A15 1 Students' Reports on the Frequency of (confirmed) 1 Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL At Load Several Tknes STATE ASSESSMENT a Week 'Wald Once a Week Lass Than Weekly TOTAL Perooniagoe and Pre Wow Porconlaffe and Proficiency Percentage and Pulliciency State 43 1.3) 27 ( 0.9) 30 ( 1.0) 271 272 ( 12) 279 ( 1.9) Nation 38 2.4) 25 ( 1.2) 37 ( 2.5) 253 ( 22) 261 ( 1.4) 272 ( 1.9) PARENTS' EDUCATION ItS non-graduate State 38 ( 4.3) 28 (( 3.8) 34 ( 3.9) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) NS graduate State 42 ( 3.3) 29 ( 2.1) 29 ( 2.4) 282 ( 1.8) 259 ( 2.4) 285 ( 2.8) Nation 40 ( 3.2) 29 ( 2.2) 32 ( 3.6) 247 ( 2.7) 258 ( 2.5) 262 ( 2.2) Some college State 42 ( 3.0) 27 ( 22) 31 ( 2.0) 273 ( 1.9) 277 ( 32) 279 ( 2.9) Nation 34 ( 3.4) 26 ( 22) 40 ( 259 ( 2.3) 289 ( 2.8) 271 ( 2.8) College graduat State 45 ( 1.8) 26 ( 1.5) 28 ( 1.4) 278 ( 1.4) 282 ( 1.9) 292 ( 2.3) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 273 ( 2.5) 285 ( 2.3) GENDER Male State 43 ( 1.8) 28 ( 1.4) 29 ( 1.6) 272 ( 1.4) 270 ( 1.3) 278 ( 2.4) Nation 30 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 283 ( 2.3) 274 ( 2.4) Female State 44 ( 1.8) 26 ( 1.4) 30 ( 1.7) 270 ( 1.4) 274 ( 2.7) 280 ( 2.3) Nation 37 ( 25) 25 ( 15) 38 ( 2.6) 253 ( 2.1) 259 ( 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 is insufficient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 New Hampshire TABLE Al8 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT , Ow a Caiculator Teacher Exp laku Calculator Usa Yes No Yes No TOTAL Paraerdage and Preiciency Percentage and Proficiency Percentage and Madam Percentage and Proficiency State 90 ( 0.3) ( 0.3) 51 1.2) 49 ( 1.2) 274 ( 0.9) 272 ( 1.1) 276 ( 12) Nation 97 ( 0.4) 3 i 0.4) 49 ( 2.3) 51 ( 2.3) 283 ( 1.3) 234 ( 3.8) 258 ( 1.7) 266 ( 1.5) RAcvETHNICITY White State 99 ( 0.3) 50 ( 1.3) 50 ( 1.3) 274 ( 0.9) ( "4/ 273 ( 1.1) 276 ( 1.3) Nation 98 ( 0.3) 2 ( 0.3) 40 ( 2.6) 54 ( 2.6) 270 ( 1.5) Mit ( IMP) 266 ( 1.8) 273 ( 1.8) Hispanic State 99 ( 254 ( 0.9) 3.9) I ( 0.9) 64 ( 7.0) ( .41 36 ( 7.0) Nation 92 ( 12) 8 ( 12) 63 ( 4.3) 37 ( 4.3) 245 ( 2.7) ( 243 ( 3.4) 245 ( 2.9) TYPE OF COMMUNITY Advantaged trban State 99 ( 1.2) 1 ( 1.2) 59 ( 1.9) 41 ( 1.9) 281 ( 3.4) 273 ( 3.2) 290 ( 4.9) Nation 99 ( 1.0) 1 ( 1.0) 45 (12.2) 55 (12.2) 281 ( 31)1 276 ( 2.5)1 285 ( 84)1 Extrema nral State 98 ( 278 ( 1.6) 4.5)1 2 ( 1.6) 44..) 4.1 Nation 96 ( 1.3) 4 ( 1.3) 42 ( 6.7) 58 ( 8.7) 257 ( 3.9)1 ( 251 ( 4.8)1 261 ( 4.4)1 Other State 99 ( 0.3) 1 ( 0.3) 49 ( 1.4) 51 ( 1.4) 274 ( 0.9) 272 ( 1.0) 276 ( 1.3) Nation 97 ( 0.5) 3 ( 0.5) 50 ( 2.7) 50 ( 2.7) 263 ( 1.7) P33 ( 5.4) 258 ( 2.1) 206 ( 2.0) 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 t 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). 126 131 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A18 Students' Reports on Whether They Own a (ccultinued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Om a Calculator Teacher Eagi tains Calculator Use Yes No Yes No TOTAL State Nation PARENTS EDUCATION HS nan-gracksata State Nation HS graduate State Nation Sam collage State Nation **ago gradual* State t4ation pENDER M. State Nation Female State Nation Ilardentap and Pcsidanclf 99 0.3) 274 0.9) 97 OA) 263 1.3) 07 ( 1.3) 255 ( 2.5) 92 ( 1.6) 243 ( 2.0) 97 ( 0.9) 262 ( 1.2) 97 ( 0.6) 255 ( 1.5) 99 ( 0.4) 276 ( 1.5) 96 ( 0.9) 268 ( 1.8) 100 ( 0.2) 284 ( 1.0) 99 ( 0.2) 275 ( 1.6) 99 ( 0.3) 274 ( 1.0) 97 ( 0.5) 264 ( 1.7) 96 ( 0.4) 274 ( 1.3) 97 ( 0.5) 262 ( 1.3) Parcantaga and Pnieclancy ( 0.3) ( Para IMP and Prollelanay 51 ( 12) 272 ( 1.1) Pantardaga and Pre Wong/ 49 ( 276 ( 1.2 3 ( 0.4) 49 ( 2.3) 51 ( 2.3 234 ( 3.6) 256 ( 1.7) 260 ( 1.5) 3 ( 1.3) 45 ( 5.4) SS ( 5.4) 252 ( 2.3) 257 ( 4.0) ( 1.6) 53 ( 4.6) 47 ( 4.6) INFO ( *el 242 ( 2.9) 243 ( 2.5) 3 ( 0.9) ...) 51 ( 261 ( 1.9) 1.7) 49 ( 262 ( 1.9) 1.6) 3 ( OAS) 54 ( 3.0) 48 ( 0.0) 252 ( 1.9) 258 ( 2.0) 1 ( 0.4) se* ( *en 53 ( 274 ( 2.5) 1.9) 47 ( 278 ( 2.5) 2.1) 4 ( 0.9) qpipe) 48 ( 265 ( 3.2) 2.4) 52 ( 268 ( 3.2) 22) 0 ( 0.2) 50 ( 1.9) 50 ( 1.9) 282 ( 12) 286 ( 1.4) ( 02) 40 ( 2.6) 54 ( 2.6) 268 ( 2.2) 280 ( 1.9) sish ( 0.3) 51 ( 272 ( 1.9) 1.3) 49 ( 275 ( 1.9) 1.8) 3 ( 0.5) 51 ( 2.6) 49 ( 2.6) 25$ ( 2.1) 269 ( 2.1) 2 ( 0.4) 51 ( 1.8) 49 ( 1.8) ( 272 ( 1.4) 276 ( 1.7) 3 ( 0.5) 47 ( 2.5) 53 ( 24) ( ***1 258 ( 1.7) 253 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 3 A. THE 1990 NAEP TRIAL STATE ASSESSMENT 127 New Hampshire TABLE A19 1 Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 IMP TRIAL STATE ASSESSMENT 11"rng Png"Ins In Class Doing Problems at Ham Taking Quizzes or Tests Almost I Always P ;ter Almost Always Never Almost Always Never TOTAL Percentage and Proficiency Perceitage and Proficiency Percentage and Preficiency Parcontege Portents. and and Prelicieney Proficiency Percentage and Prolidency State 32 ( 1-3) 30 ( 1.1) 27 ( 1.0) 22 ( 17 ( 47 ( 1.3) 266 ( 1.2) 281 ( 1.4) 270 ( 1.3)."` 276 ( 1/ 265 ( 1.9 281 ( 1.3) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9 27 ( 1.4 30 ( 2.0) 254 ( 1.5) 272 ( 1A) 261 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) RACE/ETMNICITY Mite State 31 ( 1.3) 31 ( 1.2) 27 ( 1.0) 22 ( 1.0) 17 ( 1.1) 47 ( 1.4) 267 ( 1.3) 262 ( 1.4) 270 ( 1.4) 277 ( 1.0) 286 ( 2.0) 281 ( 1.4) Nation 48 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 25 ( 1.6) 32 ( 2.3) 262 ( 1.7) 278 ( 1.3) 270 ( 1.7) 269 ( 2.3) 263 ( 2.6) 279 ( 12) Hispanic State 30 ( 6.9) 24 ( ( 5.7) *01 24 ( 6.6) 21 ( Mt* ( 5.8) 21 ( 6.4) 441 38 ( IMIMI 5.8) 4.41 Nation 51 ( 2.9) 16 ( 3.5) 20 ( 3.2) 21 ( 2.1) 28 ( 2.7) 22 ( 3.9) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1) 237 ( 3.2) 256 ( 4.2) TYPE OF COMMUNITY Advantaged urban State 26 ( ( 3.9) 37 ( 292 ( 6.0) 3.9)1 17 ( 3.5) 29 ( *iv ( 0.2) 17 ( 4.8) .4s) 56 ( 289 ( 5.5) 4.5) Nation 51 ( 270 ( 5.4) 4.7)1 23 (10.7) ( 1 32 ( 274 ( 6.1) 4.9)! 15 ( 2.4) ***) 31 ( 31) 281 ( 7.ey 28 ( 28$ ( 9.8) 4.2)1 Extreme rural State 28(11.5) .** 28 ( 3.3) 13 ( 2.9) 10 ( 7.9) 49 ( ( 4.2) *IP ) Nation 46 ( 246 ( 7.4) 4.3)1 29 ( 268 ( 8.5) 8.1)! 20 ( itit 2.5) 14-1 23 ( 203 ( 3.9) 4.4)l 24 ( elpit 8.8) 37 ( 270 ( 8.3) 4.0)1 Other State 32 ( 1.4) 30 ( 12) 29 ( 12) 20 ( 1.1 18 ( 1.2) 45 ( 1$) 267 ( 1.2) 281 ( 1.4) 270 ( 1.4) 278 ( 1.5) 267 ( 2.1) 281 ( 1.2) Nation 48 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1.8) 29 ( 2.1) 254 ( 2.1) 272 ( 11)) 283 ( 2.3) 263 ( 2.8) 253 ( 2.7) 275 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimer 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). 128 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A 19 I Students' Reports on the Use of a Calculator (continued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1560 NAEP TRIAL STATE ASSESSMENT Working Problems in Class Doing Problems at Mons , Taking Quizzes or Tests Almost Always Never Almost Always Never Almost Always Never TOTAL Percentese and Prolicieney 32 ( 1.2 48 1.5 254 13) 34 ( 3.8) am* ( «in State Nation PARENTS' EDUCATION Its nongraduate State Nation 54 ( 3.3) 240 ( 2.3) NS graduat State 35 ( 2.5) 255 ( 1.7) Nation 52 ( 2.5) 249 ( 1.4) Some college State 29 ( 23) 272 ( 2.9) Nation 48 ( 23) 258 ( 2.1) Coney* graduate State 30 ( 1.4) 278 ( 1.9) Nation 45 ( 1.9) 285 ( 1.7) ORDER "tale State 32 ( 1.7) 265 ( 1.5) Nation 50 ( 1.7) 255 ( 1.9) Female State 31 ( 13) 267 ( 1.8) Nation 48 ( 2.0) 25,2 ( 1.7) Percenta. Poroentege Paraentege Percentese Perowtese and end and end Prolidany Prefideney Preficiency Preficiency Prolicience 30 1.0) 22 1.0 1.1) 47 1.3 281 1.4 270 276 1.7 285 201 1.3 23 1.9 30 1.3 19 0.9 27 1.4 30 2.0 272 1.4) 261 ( 1.8 263 1.8 253( 2.4 274 1.3 32 ( 3.1) 22 ( 3.21 23 ( 4.5) 151 .3;1) 43 4.1) *ye ( 441 cit ( ,,... ipe ) 200 191 3.8) 26 ( 3.1) 22 2.8) 32 ( 3.15) 24 5.2 1 244 ( 3.8) 244 4.2) 237 ( 2,3) 251 43 26 ( 2.0) 27 ( 2.3) 22 ( 2.0) 17 ( 2.3) 43 ( 23 271 ( 2.1) 259 ( 13) 207 ( 3.1) 253 ( 3.3) 271 ( 2.3 20 ( 2,4) 29 ( 1.9) 18 ( 1,5) 28 ( 1.11) 27 ( 2.2 285 ( 2.7) 250 ( 2.4) 256 ( 2.4) 246 ( 24) 266 ( 2.0 31 ( 33) 26 ( 23) 25 ( 23) 21 ( 2.2) 45 ( 5.3) 281 ( 2.3) 273 ( 2.1) 277 ( 2.9) 270 ( 4.2) 280 1.9) 26( 2.8) 28 ( 2.0) 20 ( 1.9) 28 ( 2.4) 35 2.5) 272 ( 2.5) 287 ( 3.0) 26$ 1 3.2) 255 ( 3.6) 275 2.0) 31 ( 1.5) 28 ( 1,5) 20 ( 1.2) 16 ( 1.3) 49 ( 1.4) 290 ( 1.0) 278 ( 1.9) 285 ( 2.2) 275 ( 2.8) 269 ( 1.3) 25 ( 2.4) 33 ( 2.0) 16 ( 1.4) 26 ( 1.8) 33 ( 2.7) 284 ( 1.8) 274 ( 2.2) 278 ( 23) 288 ( 2.8) 235 ( 2.0) 30 ( 1.5) 20 ( 1.3) 23 ( 1.5) 18 ( 1.3) 46 ( 2.0) 281 ( 2.2) 271 ( 13) 273 ( 2.8) 268 2.7) 281 ( 1.8) 20 ( 2.0) 29 ( 1.6) 19 ( 1.3) 27 1,5) 26 ( 2.1) 275 ( 2.2) 264 ( 23) 263 ( 2.5) 256 3.0) 277 ( 1.9) 31 ( 1.7) 26 ( 1.7) 20 ( 1.4) 19 ( 1.7) 47 ( 1.7) 281 ( 1.6) 288 ( 1.5) 280 ( 1.9) 263 ( 23) 281 ( 1.6) 2e ( 2.1) 32 ( 1.6) 1$ ( 1.2) 27 ( 1.8) 33 ( 2.1) 259 ( 1.6) 250 ( 1.7) 263 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because thr "Sometimes" category is not included. *** Sample size is insufficient to permit a rebable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 New Hampshire TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL "Calculator-Use "Calculator-Use STATE ASSESSMENT Nigh Group Other Group _ TOTAL Percentage and Prelinientv Pareentsga and *cadency State 48 ( 1.5) 52 ( 1.5) 279 ( 1.3) 268 ( 12) Nation 42 ( 1.3) 38 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACE/ETHNICITY %bite State 46 ( 1.6) 51 ( 1.8) 2$0 ( 1.4) 267 ( 1.3) Nation 44 1.4) 58 ( 1.4) 277 ( 1.7) 263 ( 1.7) Hispanic State 49 (10.1) 51 (10.1) 411 Ration 36 ( 4.2) 64 ( 42) 254 ( 4.6) 238 ( 3.0) TYPE OF COMMUNITY Advantaged urban State 48 ( 5.4) 52 ( 54) 292 ( 3.4) 269 ( 5.4) Nation 50 ( 3.8) 50 ( 3.8) 288 ( 4.9)1 275 ( 4.4)! Extreme rural State 53 ( 2.7) ( Nation 39 ( 5.6) 61 ( 5.6) 269 ( 4.4)1 248 ( 4.3)1 Other State 50 ( 1.6) 50 ( 1.6) 279 ( 1.4) 268 ( 1.4) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample, ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A20 I Students' Knowledge of Using Calculators (continued) 1 PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Nigh "CalculatorUse" Group Other "Calculator-Use" Grow TOTAL Percentage and Pro Money Percentage and aredleieney State 48 1.5) 62 ( 1.5) 279 ( 1.3) 2ee ( 1.2) Nation 42 ( 1.3) 56 ( 1.3) 272 ( 1.8) 255 ( 1.5) PARENTS' EDUCATION IIS nongradisate State 50 ( 62) 50 ( ( 6.2) 641 Nation 34 ( 3.3) 66 ( 3.3) 24$ ( 4.4) 242 ( 2.4) HS graduate State 43 ( 3.0) 57 ( 3.0) 26$ ( 2.4) 255 ( 2.3) Nation 40 ( 2.2) 60 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some college State 48 ( 3.9) 52 ( 3.9) 279 ( 2.2) 270 ( 2.4) Nation 48 ( 2.2) 52 ( 2.2) 277 ( 2.6) 258 ( 2.5) College graduate State 53 ( 2.2) 47 ( 22) 289 ( 1.8) 277 ( 1.8) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER WI* State 49 ( 2.0) 51 ( 2.0) 279 ( 1.6) 267 ( 1.6) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 46 ( 2.3) 52 ( 2.3) 280 ( 1.8) 265 ( 2.1) Nation 45 ( 1.8) 55 ( 1.8) 269 ( 1.7) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 New kr- aoshire TABLE A24 I Students' Reports on Types of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Foie Tyres , TOTAL Palmtop and trolidency Pannone Pircentage and and Prillekency Illnikkony State 12 ( OA) 27 ( 1.3) 81. ( 1.3) 261 ( 271 ( 14) 27? ( 1.2) Nation 21 ( 1.0) 30 ( 1.0) .4. ( 1.3) 244 ( 2.0) 258 ( 1.7) ( 1.5) #111_411CITY Wine State 11 ( 0.7) 27 ( 1.2) M2 ( 1.3) 262 ( 2.2) 272 ( 1.5) 278 ( 1.2) Nation 18 ( 1.1) 29 56 ( 1.5) 251 ( 2.2) 268 ( 1.5) 276 ( 1.7) Hispanic State 22 ( 83) 24 ( 6.9) 54 ( 7.3) *44 ( "a ("a) Nation 44 ( 3.0) 90 ( 2.4) 28 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) TYPE OF COMMUNITY Advantaged urban State 15 ( 2.4) Impo, 32 ( 274 ( 4.5) 3.4) 53 ( 290 ( 8.5) 4.6) Nation 13 ( 3.8) «Hi ( 81 ( 281 ( 4,9) 3.6)1 Extreme mid State 11 ( 4.6) 444 ( 19 ( fret ( 8.2) IN* ) 70 ( 280 ( 9.8) 5.5) Nation 17 ( 4.9) 33 ( 3.2) 50 ( 5.1) 253 ( 4.3)1 283 ( 5.8)1 Other State 11 ( 0.8) 27 ( 1.2) 02 ( 1.4) 283 ( 2.2) 271 ( 1.5) 277 ( 1.0) Nation 22 1.6) 90 ( 1,3) 48 ( 1.6) 244 ( 2.6) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 3 7 132 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A24 I Students' Repods on Types of Reading (continued) i Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1900 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Four Types TOTAL Perosetage and Proachincy Perserdsle and Praaciancy Parchltaas and Preachingly State 12 ( 0,5) 27 ( 1.3) 61 ( 1.3) 261 ( 2.1) 271 ( 1.4) 277 ( 1.2) Nation 21 ( 1.0) 30 ( 1.0) 4$ ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) PARENTS Roue-avow NS non-graduate State 35 ( 4.9) 36 ( 4.7) 254 ( 3.0) ( Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 248 ( 3.3) KS graduate State 18 ( 1.8) 31 ( 2.1) 53 ( 1.7) 256 ( 3.1) 280 ( 2.1) 265 ( 1.8) Nation 20(2.2) 33 ( 1.9) 40 ( 1.7) .248 ( 2.2) 253 ( 2.7) 280 ( 2.1) Sem college State 11 ( 1.8) 30 ( 3.0) 59 ( 2.9) 277 ( 2.4) 277 ( 2.1) Nation 17 ( 1.5) 32 ( 1 7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduate State ( 1.1) 22 ( 1.3) 71 ( 1.5) 268 ( 3.8) 282 ( 2.2) 285 ( 1.3) Nation 10 ( 0.8) 28 ( 1.8) 62 ( 2.0) 254 ( 2.8) 280 ( 1.8) OENOER Mate State 13 ( 1.4) 27 ( 1.9) 60 ( 1.7) 280 ( 2.7) 271 ( 1.8) 277 ( 1.3) Nation 21 ( 1.5) 31 ( 1.5) ( 1.4) 244 ( 23) 259 ( 2.1) 273 ( 2.0) Female State 11 ( 0.9) 28 ( 1.6) 03 ( 1.9) 262 ( 2.9) 270 ( 2.2) 278 ( 1.5) Nation 22 ( 1.2) 29 ( 1.4) 49 ( 1.9) 244 ( 2.2) 258 ( 1.9) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with 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). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 133 New Hampshire TABLE A25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One Hour or Loss - Two Hours Three Hours - Fotr to Five Hours Sbi Hours or More - TOTAL State 'talon RACEIETHWITY WAD Stata Nation Hispanic State Nation Tyn OF COMMUNITY Advantaged urban State Nation Extrema rural State Nation Mar State Nation Ponsniage ihomminpik Mom by Pere$919. and oil sad and Priedamm Widow ilineals9W Pffilkkorm Pfradisiy 17 ( 20 ( 1.1 7 0.71 232 99 271 ( 1.7 21: I 1.61 111 12 01 21 ( 0.91 22 0.3 23 1.1 18 1.0i 239 2.2 21911 ( 1.8 235 1.7 MOO 1.7 240 (1.7) 1$ ( 0.9) 27 ( 1.1) 25 ( 0.0 24 ( 0.9) 3 O. 233 ( 2.1) 279 ( 1.8) 274 ( 1.0 208 ( 1.1) 254 13 ( 1.0) 23 ( 1,2) 24 ( 1.1 27 ( 1.4) 12 1.2 273 ( 2.5) 275 ( 2,2) 272 ( 1.9 ) 207 ( 1.7) al 14 i 2.4)n eirt ( *** Zi !It 24 ( 7.1) i e 8 ( 4.4) 31 ( 7.3) 17 1 ) 5.0) 20 ( 251 19 ( 2.1) 31 3.1) 171 17) 245 ( 3.2 242 ( 5.8) 247 2.5) 238 ( 3.41) 24 ( ( 18 ( 44. ( 59) 4.1 1.4) 27 ( 204 25 *4m 2.2) OA) 4.3) *41 24 44. 21 .00 17 (( 5.2) .41 22 ( 3.7) OK* ( 31 es. 14 ( 4, 3.3) ***) 19 ( 2.0) 14* ( 23 44. 17 ( 0.9) 28 ( 13) 24 262 ( 1.9) 279 ( 1.0) 274 12 ( 1.0) 21 ( 1.0) 23 203 ( 2.8) 209 ( 2.3) 05 19 2.3) *hp 41.10) 30 (4.3) *In 28 26 258 25 20$ 27 250 7 2.8) «in 3.8) 0.7) 3$ ) 1.4) 2.5) ( 11) ( 11191. ( 2.7) 19 ( 3.6)1 ( ( 1.1) 7 ( ( 1.2) 254 ( ( 1.2) 17 ( ( 22) 240 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). 3'1 134 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A25 I Students' Reports on the Amount of Time Spent (ccsntinued) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ - MO NAEP TRIAL. One Hour or Ttwee Few to Flee SIN Hours or STATE ASSESSMENT Leas Two Hours Hours Hours Yore - TOTAL Peniannina and Prakinaqr 171 232 12 2113 0.9) ( 14) ( 03) ( 21) State Nation mum, %mato* KS nan-graduat. State 18 ( 3.4) ire* Nation 12 ( 2.2) 44.1 HS graduate State 10 ( 1.6) 262 ( 4.4) Nation ( 1.0) 249 ( 4.7) 8onte coMege State 14 ( 1.7) 283 ( 32) Nation 10 ( 1.4) College gracksate State 23 ( 1.4) 291 ( 2.5) Nation 17 ( 1.3) 282 ( 2.6) GENDER Male State 15 ( 1.1) 281 ( 2.7) Nation 11 ( 0.9) 289( 3.3) Fumble State 20 ( 1.6) 283 ( 2.6) Nation 14 ( 1.1) 269 ( 2.8) Panioniaga Panadase Parawdap Paramiago and and aid and Ihndidency Pregidenay Praidency Pridiciany 21 1.1) 276 21 0.9 208 14 20 ( 2.9) ***) 20 ( 3.1) ( 22 ( 1.8) 268 ( 2.5) 17 ( 1.4) 257 ( 2.8) 29 ( 2.5) 278 ( 2.5) 25 ( 2.4) 276 ( 2.7) 29 ( 1.9) 286 ( 1.9) 22 ( 1.6) 280 ( 2.5) 25 ( 1.6) 278 ( 1.9) 22 ( 1.2) 267 ( 2.6) 28 ( 1.7) 278 ( 2.5) 20 ( 1.3) 269 ( 2.2) 24 ( 0.8 "1.21 7 ( 0,7) 274 ( 1.81 28825 255 ( 3.0) 22 ( 0.8 28 1.1 16 ( 1,0) 285 ( 1.7) 280 ( 1.7) 245 ( 1,7) 22 ( 4.4) 26 ( 3.7) 16 ( ipe* 3.2) 21 ( 111141 2.8) eel 28 244 ( 2.9) ( 3.2) 20 ( 2.4) 11 28 ( 23) 32 ( 2.6) 10 ( 1.3) 285 ( 2.7) 256 ( 2.5) 261 ( 3.0) 23 ( 2.0) 32 ( 2.3) 19 ( 1.6) 259 ( 32) 253 ( 2.5) 248 ( 3.0) 25 ( 274 ( 2.1) 3.6) 24 275 ( 2.0) ( 1.9) 8 ( «pa ( 1.7) 23 ( 2.6) 28 ( 22) 14 ( 15) 269 ( 3.5) 267 ( 2.5) 242 ( 3.4) 24 ( 1.3) 20 ( 1.7) 4 ( 0.7) 281 ( 2.0) 277 ( 1.5) 23 ( 1.1) 26 ( 1.5) 12 ( 1.1) 277 ( 2.2) 270 ( 2.4) 256 ( 3.2) 24 ( 1.0) 27 ( 1.4) 9 ( 1.0) 274 ( 1.7) 270 ( 15) 266 ( 3.9) 22 ( 1.0) 28 ( 1.3) 17 ( 1,5) 267 ( 2.2) 282 ( 2.1) 248 ( 2,5) 25 ( 1.5) 22 ( 12) 6 ( 0.9) 274 ( 2.1) 266 ( 1.9) 262 ( 3,5) 23 ( 1.4) 28 ( 1.6) 16 ( 12) 264 ( 1.8) 258 ( 1.9) 241 ( 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). 140 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 New Hampshire TABLE A26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None One or Two Days Three Days or More TOTAL Percentage and PrallotancY Percentage and Proidancy Porventage and Proficiency State 39 ( 1.2) 30 ( 1.3) 22 ( 12) 279 ( 0.9) 276 ( 1.2) 261 ( 1.6) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 200 ( 1.5) 250 ( 1.9) RACE/ETHNICITY White State 39 ( 12) 39 ( 1A) 22 ( 12) 279 ( 0.9) 277 ( 1.3) 261 ( 1.7) Nation 43 ( 12) 34 ( 1.2) 23 ( 12) 273 ( 1.8) 272 ( 1.7) 256 ( 2.1) Hispanic State 29 ( oak* 7.5) .44) 35 ( 6.6) eon Nation 41 ( 3.3) 32 ( 2.2) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) TvpE OF COMMUNOY Advantaged urban State 28 ( 289 ( 4.2) 5.5) 42 ( 284 ( 4.3) 3.3) 30 ( 6.8) 4+1 Nation 47 ( 2.3) 38 ( 2.6) 15 ( 3.7) 264 ( 4.4)1 279 ( 4$)1 ( Extrwne rural State 39 ( 7.3) 37 (10.0) 24 ( 4.6) .41 Nation 43 ( 4.4) 32 ( 42) 25 ( 32) 257 ( 4.1)1 264 ( 5.8)1 Other State 39 ( 1.3) 39 ( 1.4) 21 ( 1.0) 279 ( 1.0) 275 ( 12) 262 ( 1.6) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2,2) 266 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature or the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 141 136 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A26 I Students' Reports on the Number of DayS of (continued) I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 191110 MEP TRIAL STATE ASSESSMENT None One or TwooasJ Three Din% or Mom] Peroonlaga and Poundage and pardt10111 and TOTAL Prodding PliNolancy Podding State 2S ( 1.2) 39 ( 1.3) 22 ( 1.2) 279 ( 0.0) 276 ( 1.2) 261 ( 1.6) Nation 45( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 208 ( 1.5) 250 ( 1.9) PARENTS' EDUCATION NS non-graduate State 30 ( 4.2) ste ( wan 30 ( 4.4) ( 33 ( 044 4.9) Nation 36 ( 3.2) 26 ( 3.4) 38 ( 3.5) graduate 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) State 30 ( 2.1) 41 ( 22) 24 ( 1.9) 200 ( 1.5) 2e4 ( 18) 251 ( 2.6) Nation 43 ( 2.1) 31 ( 1.0) 27 ( 1.9) 255 ( 2.0) 257 ( 2.6) 249 ( 2.4) Some co/lege State 38 ( 3.7) 39 ( 32) 23 ( 2.6) 280 ( 2.7) 276 ( 1.9) 200 ( 2.5) Nation 40 ( 1.8) 37 ( 1.6) 23 ( 1.6) 270 ( 3.0) 271 ( 2,5) 253 ( 3.1) College graduate State 42 ( 1.9) 39 ( 1.7) 19 ( 1.4) 287 ( 12) 266 ( 1.6) 270 ( 2.5) Nation 51 ( 1.0) 33 ( 1.2) 16 ( 1.3) 275 ( 2.1) 277 ( 1.7) 285 ( 3.1) GENDER Male State 41 ( 1.5) 39 ( 1.7) 21 ( 1.3) 279 ( 1.4) 275 ( 1.6) 259 ( 22) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 1,4) 208 ( 2.0) 267 ( 2.1) 250 ( 2.6) Female State 37 ( 1.6) 39 ( 1.5) 24 ( 1.7) 278 ( 1.5) 277 ( 1.7) 263 ( 2.6) Nation 43 ( 1A) 32 ( 1.1) 25 ( 1.3) 264 ( 2.3) 266 ( 1.7) 250 ( 1.8) 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 New Hampshire TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Shull* Agrws *PH r Undecided, Disagree, Strongly Disagree , TOTAL Parasnasgs and Preiciana. Pononsin and Pralladony Periods.* and PreSdincy State 1.3) 52 ( 1.4) 1.2) 283 13) 273 .90) 280 1.5) Nation 27 1.3) 49 1.0) 24 1,2) gmplerr. 271 1.9) 262 1.7) 251 1.8) Mite State 28 ( 1.4) 83 ( 14) 19 ( 1.2) 234 ( 1.8) 274 ( 1.0) 281 ( 1.6) Nation 28 ( 1.6) 48 ( 1.3) 28 ( 1.5) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Hispanic State 45( 5.9) 30 ( 62) 25 ( 5.6) 4144, ( del Nation 24 ( 2.5) 43 ( 2.13) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 236 ( 3.8) TYPE OF COMMUNITY Advantaged urban State 20 294 ( 1.3) ( 5.7) 54 ( IA) 280 ( 4.4) 19 ( *44 3.8) 41.1 Nation 17 ( 3.2) 55 ( 2.4) 28 ( 4.2) 280 ( 4.1)1 14 ( 44 Extreme meal State 33 ( 3.4) 56 ( ipth. ( 4.2) ( 3.1) Nation 34 270 ( 2.8) ( 3.9)1 49 ( 252 ( 22) 4.1)1 17 ( 4". 1.4) Other State 29 ( 1.5) 52 ( 1.0) 20 ( 1.2) 283 ( 1.3) 274 ( 1.0) 261 ( 1.5) Nation 27 ( 1.4) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with &bout 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. 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), 138 THE 1990 NAEP TRIAL STATE ASSESSMENT New Hampshire TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1190 KAEP TRIAL STATE ASSESSMENT Sim* ACP* Agree Undecided, 0111111me, Stransty Disarm TOTAL State Nation PARENTS' EDUCATION Pam110411 and Pralk1114118 29 263 1 27 1.3 271 ( KS non-graduatia State 94 WA* 5.8) 414.1 Nation 20 ( ee 2.6) elh.) NS graduate State 22 ( 2.2) 272 ( 2.2) Nation 27 ( 2.1) 262 ( 2.7) Soon collage State 32 ( 2.6) 282 ( 2.8) Nation 2$ ( 2.5) 274 ( 3.1) Ciage graduate State 31 ( 1.9) 291 ( 1.4) Nam 90 ( 2.3) 280 ( 2.4) GENDER M. State 30 ( 1.7) 283 ( 1.6) Nation 28 ( 1.5) 273 ( 2.3) Eames State 26 ( 2.0) 283 ( 2.1) Nation 26 ( 1.7) 209 ( 2.1) INIMMIRM11 fleramtape Prallellow 62 ( ( 49 ( 1.0 282 ( 1.1 2,444018. ANO Proislowe 1 30 12 1 24 1.2 2211 1.6 48 ( 7.4) 20 ( 3.3) 253 3.8) 50 3.3) 30 1 3.61 243 2.M 224 ( 4.3 58 2.4) 22 2.1 262 1.5) 252 2.51 47 2.9) 20 2.0 255 2.3) 245 ( 2.4) 49 ( 3.13) 18 ( 2 275 ( 1.8) 287 31 47 ( 2.4) 25 1.11 267 ( 1.9) 258 3.2 52 ( 2.1) 18 ( 1.5) 284 ( 1 5) 288 ( 2.6) 51 ( 1.01 19 ( 1.8) 274 ( 2.2) 208 ( 2.5) 51 ( 1.8) 273 ( 1.3) 48 ( 12) 263 ( 2.0) 53 ( 2.3) 274 ( 1A) 50 ( 1.7) 282 ( 1.8) 19 ( 1.4) 1.8) 24 14) 251 2.4) 19 ( 1.6) 281 ( 2.4) 25 ( 1.9) 252 ( 1,9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 41" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 4 4 THE 19 90 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative efkirt anon staff from State Educed= Agencies, the National Center fix Education Statistics (NOES), Educatioaal Testing Savice Westat, and National Computer Systems (NCS). The pengram benefitted from the contributions of hundreds el individuals at the state mid local kvels Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and &Via administrators who tirelessly provided their wisdom, expetience, and hard work. Finally, and most impoctantly, NAEF is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of agef State School Officers (CCSSO) for its considerable coatributions to the program, especially its =augment of the National Assayment Planning Project. That project resuked hi the mathematics framework and objectiws for the assessment and recommendations about reporting the results of the proffam. In particular, wee note the sipificant cootributkins of Ramsay Selden, Director of the State Education Assessment Ceuta for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Commktees of the National Assessment Planning Project. The Trial State Assessment was funded through 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 Guy Phillips, Eugene Own, Stephen Gorman, 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 Matheniatics Scale Anchoring PAW& These people from school &Arleta, colleges and universities, and State Education Agencies worked tirelessly to help ETS staff develop the assessment and a framework for interpreting the results. Under the NAEF cootract to ETS, Archie Lapointe sand as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mame°, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffiez, state services. Sampimg 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, cristribution, and processing 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 Faris, David Freund, Bruce Kaplan, Edward KuTick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Fizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Kaffir.: wrote the text for the report Kent Ashworth was responsible for coordinating the cover design and final printing of this report Special thanks are also due to many individuals for their invaluable assistance in reviewing the reports, especially the editors who improved the teA and the analysts who checked the data. 1 4 5 GOVERNMRST PRINTING OFFICE : 1491 0 - 243-215 QL CRK