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ED 330 582 SE 052 092 TITLE The State of Mathematics Achievement in West Virginia: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Acievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Mathematics Instruction; Mat,lematics 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; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP); *West Virginia ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the eth grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In West Virginia, 2,600 students in 101 public schools were assessed. This report describes the mathematics proficiency of West Virginia eighth-graders, compares their overall performance to students in the Southeast 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 mith scale, West Virginia students had an average proficiency of 256 compared to 261 nationwide. Many fewer students (West Virginia-7%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJ(/CRW) 0. NATIONAL CENTER FOR EDUCATION STATISTICS 11111. The STATE of at e Mies vement in WEST VIRGINIA The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD COPY AVAILABLE U S DEPARTMENT OF EDUCATION Oftwo (4 E oucattontat Research ancl Irnpro.,ement EDUC TIONAC RESOURCES INFORMATION CENTE R (ERIC) Ns document has been reproduced as rpcelyeld from rho Dotson or orgarh:eon ortgriiitaV ,t : Molt), (figrIges nave been made to mtypve reprodvct,on Quaid), Ftotnts of vtew or OPM,Onf stmted.n th.s docu ipm Co rroi necosseroy represent ottrcrai OE RI Pos,ton or porcv 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 2 What is The Nation's Report Card? THE NATION'S REPORT CARD. the National Assessment of Educational Progress (NAEP), is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1%9, assessments have been conducted periodically in reading, mathematics. science, writing, history/geography. and other fields, By making objective information on student performance available to polieymakers 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 academie 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 organizations. NAEP reports directly to the Commissioner, who is also responsible for providing continuing reviews, including validation studies and solicitation of public comment. on NAEP's conduct and usefulness. In 1988. Congress created the National Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The board is responsible for selecting the subject areas to be assessed, which may incLide adding to those specified by Congress; identifying appropriate achievement goals for each age and grade, developing assessment objectives, developing test specifications; designing the assessment methodology; developing guidelines and standards for data analysis and for reporting and disseminating results; developing standards and procedures for interstate, regional, and national comparisons; improving the form and use of the National Assessment; and ensuring that all items selected for use in tht 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-Warmn 13.0.C.ES. Saratoga Springs, New York Franck Alexander Associate Superintendent California Department of Education Sacramento. California David P. Battini High School History Teacher Cairo-Durham High School Cairo, New York Parrks C. Battle Teacher Horace Mann Elementary School Miami. Florida Mary R. Blanton Attorney Cromwell. Porter, Blanton & Blanton Salisbury, North Carolina Boyd W. Boehlje Attorney Gaass. Klyn. & I3oehlje Pella, Iowa Linda R. Bryant Teacher Greenway Middle School Teacher Center Pittsburgh, Pennsylvania Honorable Mkhael N. Castle Governor of Delaware Carve! State Office Building Wilmington, Delaware Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hartford, Connecticut Chester E. Finn, Jr. Professor of Education and Public Policy Vanderbilt University Washington, D.C. Miclusel S. Glode Wyoming State Board of Education Saratoga, Wyoming Christine Johason Principal Abraham Lincoln High School Denver. Colorado John Lindky Principal South Colby Elementary Sehool Port Orchard. Washington Cirl J. Moser Director of Schools The Lutheran Church Missouri Synod International Center St. Louis. Missouri Mark D. Musick President Southern Regional Education Board Atlanta, Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith, Arkansas Matthew W. Prophet, Jr. Superintendent Portland Oregon School District Portland. 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 Topures Attorney Law Offices of Frank Rogoricnski Coronado, California Herbert J. Wa lberg Professor of Education University of Illinois Chicago, Illinois Assistant Secretary for Educational Research and Improvement (Ex-Officio) U.S. Department of Education Washington. ^ Roy Truby Executive DiNctor. NACal Washington, D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STME of 111 hematles Achievement In WEST VIRGINIA The Trial State Assessment at Grade Eight Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education 4 U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Mann° Acting Assistant Secretary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEF Thal State Assessment's individual State reports are available directly from the participating States. Fa ordering infuriation, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Congress, Catalog Card Number: 91-61478 ISBN: 0.88685-14-9 The work upon which this publication is based wu perforated for the National Caner for Education Statistics, Office of Educational Research and Improvement, by Educational Testing Service. Educational Mating Service is an equal opportunityfrflinnative action employer. Educational Testing Service, ETS, and 0 am registered uadernarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION 7 Overview of the 1990 Trial State Anessment 8 This Report 9 Guidelines for Analysis 12 Profile of West Virginia 14 Eighth.Grade School and Student Characteristics 14 Schools and Students Assessed 1 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in West Virginia 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 PART TWO Finding a Context for Understanding Students/ Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics/ 39 Cunicuhim Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Delivered" 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are 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 West Virginia 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 history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments .hat NAEP has conducted since its inception. As a result of the legislation, the 1990 NAFP progxam included a Trial State Assessment Progyam in eighth-grade mathematics. National assesmnents in mathematics, reading. writing, and science were conducted simultaneously in 1990 at grades four, eight, and t welve . 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 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 urfiformly. The results of the monitoring indicated a high degiee of quality and uniformity across sessions. LJ THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia In West Virginia, 101 public schools participated in e assessment. The weighted school participation rate was 100 percent, which means that ll of the eighth-grade students in this sample of schools were representative of 100 percent f the eighth-grade public-school students in West Virginia. 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 10 percent had an Individualized Education Plan (IEP). 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 seivices 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 represcited 0 percent and 6 percent of the population, respectively. In total, 2,600 eighth-grade West Virginia public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligibk eighth-grade public-school student population in West Virginia. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from West Virginia on the NAEP mathematics scale is 256. This proficiency is lower 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, 3(X), and 350 -- on the NAEP scale. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia In West Virginia, 98 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 West Virginia (7 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; MeaJurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in West Virginia performed lower than students in the nation in Numbers and Operations, Geometry, Data Analysis, Statistics, and Probability, and Algebra and Functions. Students in West Virginia performed comparably to students in the nation in Measurement. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the West Virginia eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In West Virginia: White students had higher average mathematics proficiency than did Black or Hispanic students. Further, about the same percentage of White students as Black students and a greater percentage of White than Hispanic students attained level 300. The results by type of community indicate that the average mathematics performance of the West Virginia students attending schools in areas classified as "other" was about the same as that of students attending schools in disadvantaged urban areas and extreme rural areas. In West Virginia, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 30 points higher than that of students whose parents did not graduate from high school. The results by gender show that there appears to be no difference in the average mathematics proficiency of eighth-grade males and temales attending public schools in West Virginia. In addition, there was no difference between the percentages of males and females in West Virginia who attained level 300. Compared to the national results, females in West Virginia performed lower than femals across the country; males in West Virginia performed lower thar males across the country. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 3 West Virginia 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 infonnation, 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 somc 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 West Virginia are as follows: About three-quarters of the students in West Virginia (72 percent) were in schools where mathematics was identified as a special priority. This is about the same percentage as that for the nation (63 percent). In West Virginia, 75 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 West Virginia were taking eighth-grade mathematics (63 percent) than were taking a course in pre-algebra or algebra (35 percent). Across the nation, 62 percent were taking eighth-gade 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 West Virginia spent 15 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Acrors the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 11 4 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia In West Virginia, 8 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 45 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 West Virginia, 28 percent of the students never used a calculator to work problems in class, while 47 percent almost always did. In West Virginia, 43 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About half of the students (54 percent) had teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in West Virginia 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. Relatively few of the eighth-grade public-school students in West Virginia (9 percent) watched one hour or less of television each day; 16 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. THE 1990 NAEP TRIAL STATE ASSESSMENT 5 West Virginia THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educanbnal 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 Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands 4 a THE 1990 NAEP TRIAL STATE ASSESSMENT 7 West Virginia This report describes the performance of the eighth-grade public-school students in West Virginia 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 West Virginia. Part One describes the mathematics performance of the eighth-grade public-school students in West Virginia, the Southeast region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in West Vir&ia, the Southeast region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authoriimg voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since itsinception: 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 puipose of determining whether such an assessment yields valid, reliable State representaae data. (Section 406 (0( 2)(C)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(i))) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree ofquality and uniformity across sessions. 14 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patterned ter 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 the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council of Chief State School Officers in mid-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,' the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that tune. 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 overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-grade public-school students in West Vir&ia, in the Southeast region, and for the nation. Results also are provided for groups of students defined by shared characteristics -- race/ethnicity, type of community, parents' education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for West Virginia are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nationally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAEP program was necessary because the voluntary nature of the Trial State Asses,sment Progam did not guarantee representative national or regional results, since not every state participated in the program. I National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 15 THE 1990 NAEP TRIAL STATE ASSESSMENT 9 West Virginia ....,===.11111Milli RACE/ETHNICITY Results are presented for students of different racial/ethnic groups b .sed on the students' self-identificatinn 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 =ported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for West Virginia. TYPE OF COMMUNITY Results are provided for four mutually exclusive community types -- advantaged urban, disadvantned urban, extreme rural, and other -- as defined below: Advantaged Urban: Students in this gxoup live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are in professional or managerial positions. Disadvantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are on welfare or are not regularly employed. Extreme Rural: Students in this group five outside metropoi. an statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those 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 firush high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. .4 10 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia 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 Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURE 1 I Regions of the Country . , NORTHEAST SOUTHEAST CENTRAL WEST Connacticut Alabama INlnos Alaska Dolmans Arkansas Indiana Arizona District of Columbia Florida Iowa California Maine Groorgia Kansas Colo:ado Maryland Kentucky bilchigan Hawaii Massachusetts Louisiana blInnssota Idaho New Hampshirn Mississippi Missouri Montana New Army North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohio Oklahoma Rhoda island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming 17 THE 1990 NAEP TRIAL STATE ASSESSMENT 11 West Vfrginia Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual 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 -- rather than the entire population of eighth graders in public schools in the state or territory the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essmtial 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 oetween the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistically significant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) -- regardless of whether the sample means or sample proportions appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the difference is not statistically significant), the means or proportions are described as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the apparent magnitude of the difference between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence ;nterval included zero, and thus no difference could be assumed between the groups. When three or more groups are beingcompared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in seater detail in the Procedural Appendix. 8 12 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that then is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentageF (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on ...he rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT 13 West Virginia Profile of West Virainia EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table I provides a profile of the demographic characteristics of the eighth-gmde public-school students in West Virginia, the Southeast 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 West Virginia Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS 1900 NAEP TRIAL. STATE ASSESSMENT West Vira Southeast Nation 1 DEMOGRAPHIC SUBGROUPS Race/Ethnicity White 90 ( 0.7) 83 ( 3.0) 70 ( 0.5) Black 3 ( 0.5) 32 ( 3.0) 18 ( 0.3) Hispanic 4 ( 0.4) 3 ( 0.8) 10 ( 0.4) Asian 1 ( 02) ( 0.4) 2 ( 0.5) American Indian 2 ( 0.3) ( 0.1) 2 ( 0.7) Type of Community Advantaged urban 0 ( 0.0) ( 0.0) 10 ( 3.3) Disadvantaged urban 11 ( 2.7) 2 ( 2.3) 10 ( 2.8) Extreme rural 19 ( 4.0) 9 ( 5.3) 10 ( 3.0) Other 70 ( 4.8) 89 ( 5.8) 70 ( 4.4) Parents' Education Did not finish high school 12 ( 0.9) 14 ( 2.1) 10 ( 0.8) Graduated high school 38 ( 1.3) 27 ( its) 25 ( 1.2) Some education after high school /7 ( 0.8) 18 ( 1.7) 17 ( 0.9) Graduated college 27 ( 1.5) 32 ( 3.3) 39 ( 1.9) Gender Nate 52 ( 1.1) 49 ( 2.8) 51 ( 1.1) Female 4$ ( 1.1) 51 ( 2.8) 49(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. The percentages for Race/Ethnicity may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia SCHOOLS AND STUDENTS ASSESSED Table 2 pmvides a profile suimnarizing participation data for West Virginia schools and students sampled for the 1990 Trial State Assessment. In West Virgi , a, 101 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in West Virginia. TABLE 2 I Profile of the Population Assessed in I Wthlt Virginia EIGHTH-GRAVE PUBLIC SCHOOL, PARTICIPATION Weighted school participation rate before substitution Weighted school participation rate after substitution Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating schools 100% 100% 107 101 101 er, THE 1990 NAEP TRIAL STATE ASSESSMENT EIGHTH-GRADE PUBLIC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students selected to participate in the assessment Number of students withdrawn from the assessment Percentage of students who were of Limited English Proficiency Percentage of students excluded from the assessment due to Limited English Proficiency Percentage of students who had an individualized Education Plan Percentage of students excluded from the assessment due to Individualized Education Plan status Number of students to be assessed Number of students assessed SS% 3,065 152 0% 0% 10% 6% 2,761 2,600 I S West Virginia 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 10 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individimlizrd Education Plan and (in either ca3e) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP ot had an IEP represented 0 percent and 6 percent of the population, respectively. LI, total, 2,600 eighth-grade West Virginia public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligible eighth-grade public-school student population in West Virginia. 22 16 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in West Virginia 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 peiformance in these content areas was summarized on the NAEP mathematics scale, which ranges from 0 to 500. This part of the report contains :wo chapters that describe the mathematics proficiency of eighth-grade public-school students in West Virginia. Chapter 1 compares the overall mathematics performance of the students in West Virginia to students in the Southeast region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 summarizes the students' overall mathematics performance for subpopulations defined by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. 23 THE 1990 NAEP TRIAL STATE ASSESSMENT 17 West Virginia CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-gade public-school students from West Virginia on the NAEP mathematics scale is 256. This roficiency is lower than that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency 0 200 NAEP Mathematics Scale 225 250 275 300 500 #10. Average Proficiency Wind Virginia all ( 0.9) 1-14 Soutwast ( N4 Nation 210 ( 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is maim 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 staustically significant difference between the populations. Differences reported are statistically different ai about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populatio-s of interest. 2 4 18 THE 1990 NAEP TRIAL STA E ASSESSMENT West Virginia 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 ley Is of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most'students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are given in Figure 3. It is important to note that the 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 West Virginia, 98 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 West Virginia (7 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). CONTENT AREA PERFORMANCE As previously indicated, the questions comprising the Trial State Assessment covered five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Figure 5 provides the West Virginia, Southeast reizon, and national results for each content area. Students in West Virginia performed lower than students in the nation in Numbers and Operations, Geometry, Data Analysis, Statistics, and Probability, and Algebra and Functions. Students in West Virginia performed comparably to students in the nation in Measurement. r 4. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 West Virginia FIGURE 3 f 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 niultiplication and division problems. These students can identify solutions to one-step word problems and select the greatest four-digit number in a list. In measurement, these students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of cOins. In geometry, these students can recognize simple figures. in data analysis, they are able to read simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numencal sentences and extend simple pattern sequences. LEVEL 250 Simple Multiplicative Reasoning and Two-Step Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to other clementary two-step word problems. In these basic problem-solving situations, they can identify missing or extraneous information and have some knowledge of when to use computational estimation. They have a rudimentary understanding of Such concepts as whole number place value, "even," "factor," and "multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information trom 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. 6 20 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia FIGURE 3 I Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasoning and Problem Solving involving Fractions, Decimals, Portents, 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 tractions, and recognize the equivalence between common tractions and decimals, including pictorial representations. They can interpret the meaning of percents :ass than and greater than 100 and apply the concepts of percentages to solve simple problems. The Se students demonstrate some evidence of using mathematical notation to interpret expressions, including those with exponents and negative integers. In measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relatIonshipS to Solve rOutine problems involving similar triangleS and SCale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequeoncy 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 aid 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 knowtedge 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 lolve problems. They can find the circumferences of circles and the surface areas of solid figur. 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 solve problems, Such as determining the slope of a line. In data analysis, these students can compute means from frequency tables and determine the probability of a simple event. In algebra, they can identify an equation describing a linear relation provided in a table and solve literal equations and a system of two linear equations. They are developing an understanding of linear functions and their graphs,as well as functional notation, including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. fl THE 1990 NAEP TRIAL STATE ASSESSMENT 21 West Virginia FIGURE 4 I Levels of Eighth-Grade Public-School i Mathematics Proficiency LEVEL 350 State Region Nation LEVEL NO State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation 22 0 20 40 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 I-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 0 ( 0.0) 0 ( 0.0). 0 ( 0.2) ( 0.8) 8 ( 1.8) 12 ( 1.2) 56 ( 1.4) 52 ( 3.2) 64 ( 1.6) OS ( 0.4) 94 ( 2.2) 97 ( 0.7) West Virginia FIGURE 5 I Eighth-Grade Public-School Mathematics I Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation Iptikkoi .4, -...,<N X144 SC, .71 siCi,.>. . . . . < ,7 0 200 225 250 275 300 Average Proficiency 2410 ( 0.9) 259 ( 2.9) 266 ( 1.4) 252 ( 1,3) 246 ( 3.8) 258 ( 1.7) 254 ( 0.9) 249 ( 2.6) 259 ( 1.4) 256 ( 1.2) 250 ( 3.3) 262 ( 1.8) 254 ( 1.0) 254 ( 2.7) 260 ( 1.3) 500 Mathematics Subseal. 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 )-1-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT 23 West Virginia 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, Black, and Hispanic students from West Virginia are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black or Hispanic students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that about the same percentage of White students as Rack students and a greater percentage of White than Hispanic students attained level 300. 30 24 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia FIGURE 6 I Average Eighth-Grade Public-School Mathematics Proficiency by Race/Ethnicity NAEP Mathematics Scat. 200 225 250 275 300 SOO Average Profidency West Virghtla White Black Hispanic Southeast White *A) an ( 4.1) 231, ( 3.3) S ( 3.0) Black 333 ( 4.111) Hispanic ( Nation White 1.5) 1-1/04 Black 2.1) Hispanic 243 241) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 31. THE 1990 NAEP TRIAL STATE ASSESSMENT 25 West Virginia DIE NATION'S REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARD I Mathematics Proficiency by Race/Ethnicity LEVEL. 300 ems White Black Hispanic Region White Block Hispanic Nation White Black Hispanic LEVEL 250 State White Black Hispanic Region White Black Hispanic Nation White Black Hispanic LEVEL 200 State White Black Hispanic Region White Black Hisparfic Nation White Black Hispanic t7..--0Pfum,11 ( 0.8) 2 ( 3.3) ( 1.0) 11 ( 2.7) 2 ( 1.6) mix 16 ( 1.5) 2 ( 1.3) 3 ( 1.1) 30 ( 1.4) 24 ( 5.7) 26 ( 5.7) 05 ( 3.6) 27 ( 5.1) aguk 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) . 10.10.1.1000M410.11 11, 0.140.01.11.0 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 intemst is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by I-4-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 3 r) 26 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in areas classified as "other", disadvantaged urban areas, and extreme rural areas (These are the "type of community" groups in West Virginia with student samples large enough to be reliably reported.) The results indicate that the average methematics performance of the West Virginia students attending schools in areas classified as "other" was about the same as that of students attending schools in disadvantagedurban areas and extreme rural areas. FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community NAEP ilaffomnades Seale 0 200 225 250 275 300 500 111 WIRT Average Proficiency West Virginia Disadvantaged urban Extreme rural Other Southeast Disadvantaged urban Extrema rural Ø MalifY Other 2111, Nation Disadvantaged urban Extreme rural Other &SY (1401 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 0-1-1). 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). 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 West Virginia FIGURE 9 LEVEL 300 Slat. Di Sadv. urban Ext. rural Other Re Sion Dlsadv. urban Ext. rural Other Nation Disadv. urban Ext. rural Other LEVEL 250 State Dlsadv. urban Ext. rural Other RSlon Disadv. urban Ext. rurai Other nation Dlsadv. urban Exl. rural Other LEVEL 200 State Disadv. urban Ext, rural Other Rgion Dlsadv. urban Ext. rural Other Nation Disadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community 0 20 40 60 80 Parcaotaga at or Ahoy* Pronchmey Lewis The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-14). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 1. Interpret with caution - the nature of the sample does not ar,OVV accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). Percentage 5 ( 1.3)1 5 ( 0.9)1 ( 0.9) out ***) 4 ( 4.2)! 9 ( 1.9) ( 2.1)1 ( 2.3)1 12 ( 1.2) 82 ( 4.7)1 58 ( 2.2)1 ( 1.9) mom 44 (17.4)1 53 ( 3.9) 411 ( 5 .0)1 56 ( 0.2)t 64 ( 2.3) 99 ( 0.7)1 96 ( 1.0)1 9111 ( 0.5) 20 (13.5)1 94 ( 2.2) 95 ( 1.5)1 97 ( 2.8)1 97 ( 1.0) 100 34 28 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (sec Figures 10 and 11). In West Virginia, the average mathematics proficiency of eighth-grade public-school studesits having at least one parent who graduated from college was approximately 30 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, a smaller percentage of students in West Vir Onia (27 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 higb school was 12 percent for West Virginia and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School Mathematics Proficiency by Parents' Education Most Virginia HS non-graduate HS graduate Some collage College graduate SOUthallit HS non-graduate HS graduate Some college College graduate Nation HS non-graduate HS graduate Some college College graduate 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 1-1-0). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 3 5 THE 1990 NAEP TRIAL STATE ASSESSMENT 29 West Virginia THE NATT REPORT 111.; FIGURE I I I Levels of Eighth-Grade Public-School CMW Mathematics Proficiency by Parents' Education LEVEL 300 State HS non-grad. HS graduate Some college College grad, Region HS non-grad. HS graduate SOme college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation 1-45 non-grad. 1-4S graduate Some college College grad. LEVEL 200 State 1-49 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. 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors arc presented in parentheses. With about 95 percent certainty, the value for each population of interest is within 1- 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 14.4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented Us this figure because so few students attained that level. 1 ( 0.7) 2 ( 0.8) 11 ( 2,0) 16 ( 1.5) 1 ( 0.0) 3 ( 1.7) ( 2.3) 19 ( 3.8) 1 ( 0.9) ( 1.5) 12 ( 1.4) 21 ( 1.9) 33 ( 2.9) 50 ( 1/) 00 ( 2.9) 75 ( 2.1) 211 ( 6.9) 45 ( 5.4) 61 ( 6.3) 72 ( 3.5) 37 ( 4.6) 59 ( 2.7) 71 ( 2.6) 78 ( 2.0) 95 ( 1.7) fie ( 0.6) 100 ( 0.4) 99 ( 0.4) 93 ( 3.5) 93 ( 2.4) 97 ( 2.5) 97 ( 2.6) ( 1.9) 97 ( 0.8) 99 ( 0.7) 99 ( 0.7) 100 36 30 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia GENDER As shown in Figure 12, there appears to In no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in West Virginia Compared to the national results, females in West Virginia performed lower than females across the country; males in West Virginia performed lower than males across the country. FIGURE 12 I Average Eightb-Grade Public-School i Mathematics Proficiency by Gender NAEP Mathematics Seale 200 225 250 275 300 500 Average Proficiency P40,011 1-104 144 West Virginia Male Female 1,4 ( 1-0) Southeast male Female 313 ( 2.5) Nation Male 1.11) Female 1.3) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency fr r each population of interest is within 1. 2 standard errors of the estimated mean (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 populauons. As shown in Figure 13, there was no difference between the percentages of males and females in West Virginia who attained level 200. The percentage of females in West Virginia who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in West Virginia who attained level 200 was similar to the percentage of males in the na:ion who attained level 200. 3" THE 1990 NAEP TRIAL STATE ASSESSMENT 31 West Virginia FIGURE 13 I Levels of Eighth-Grade Public-School I Mathematics Proficiency by Gender LEVEL 300 State Male Female Raglan Male Female Nation Male Female LEVEL 250 Sista Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female INO4 1-4141 1--00,04 114BINIMMI 1-0404 1-11001 Percentage 57 ( 2.1) 56 ( 1.8) 50 ( 3.8) 54 ( 3.8) 64 ( 2.0) 84 ( 1.8) 90 ( 0.5) 044 90 ( 0.6) 1-4001 93 ( 3.0) P411 97 ( 0.9) t+.4 97 ( 0.8) 0 20 40 so 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 11-14). 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. 3S 32 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia In addition, there was no difference between the percentages of males and females in West Virginia who attained level 300. The percentage of females in West Virginia who attained level 300 was smaller than the percentage of females in the nation who attained level 300. Also, the percentage of males in West Virginia who attained level 300 was smaller than 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. :3 9 THE 1990 NAEP TRIAL STATE ASSESSMENT 33 West Virginia TABLE 3 I Eighth-Grade Public-School Mathematics Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1010 NAEP TRIAL STATE ASSESSMENT Numbers and Operation Measurement OeonselTY Data RIWY1111' Statistics, Pod Probability Algebra and Functions TOTAL PraidowN Prackincy State 280 ( 02) 262 ( 1.3) 264 ( 0.0) 2 Region 259 ( 22) 248 ( 32) 240 ( 22) 265:1 Nation 206 ( 12) ( 1.7) 25e ( 14) 282 1.8 RACE/ETHNICITY White State 251 ( as) 254 ( 1-2) 256 ( 0.9) ( 1.1) Region 268 ( 3.0) 265 ( 4.2) 259 ( 3.5) 283 ( SA) Nation 273 ( 1.6) 267 ( 2.0) 207 ( 12) 272 ( 12) Slack State 241 ( 52) 230 ( 5.1) 331 ( 4.2) 24 ( 504) Region 242 ( 3.1) 222 ( 5.8) 226 ( 42) 21a ( 65) Nation 244 ( 3.1) 227 ( 3.6) 234 ( 28) 231 ( 3.8) Hispanic State Region 237 ( 13) ( *en 228 ( 5.4) 4.24, 233 ( 3.8) 227 ( 5.1) Nation 248 ( 2.7) 238 ( 3.4) 243 ( 3.2) 239 ( 3.4) TYPE OF COMMUNITY Disadvantaged urban State Region 263 ( 2.1)1 h1-0 252 ( 3.1)4 257 ( 2.9)1 Mt* 258 ( 2.5)1 ( *41 Nation 255 ( 3.1)1 242 ( 4.9)1 248 ( 17)1 247 ( 4.6)1 Extreme rural State 280 ( 1-3)4 254 ( 1.6)1 252 ( 1.3)4 254 ( 1.0)1 Region 254 ( 9.8)! 241 (17.1)1 244 (18.4)t 245 (13.7)1 Nation 258 ( 4.3)1 254 ( 4.2)1 253 ( 4,5)1 257 ( 5.0)1 Other State 259 ( 1.2) 252 ( 1.6) 254 ( 1.2) 258 ( 1.6) Region 259 ( 3.3) 248 ( 4.0) 249 ( 2.7) 251 ( 3.8) Nation 266 ( 1.9) 257 ( 2.4) 269 ( 1.7) 281 ( 2,2) Pialklincy 1.1 260 1.3 259 1.0) 264 ( 34) 208 ( 1.4) 230 ( 4.2) 235 ( 4.5) 237 ( 23) 228 I 3.3) *On 243 ( 3.1) 255 ( 2.4)1 247 ( 3.2)1 253 1.0); 251 (14.7)1 256 ( 4.8)1 253 ( 1.3) 255 ( 3.0) 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 t 2 standard errors of the estimate for the sample. Interpret with caution - thr 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 0 34 THL 1990 NAEP TRIAL STATE ASSESSMENT West 4- itia TABLE 3 I Eighth-Grade Public-School Mathematics (wntinued) i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT NumbilLtd OPraw,u Measurement Geometry Data Mys* Statisticsal, and Probability TOTAL Madam Piviiciency Proficiency Prolidency Proficient:1r State 260 ( 0.9) 252 ( 1.3) 254 ( 0.9) 256 ( 1.2) 254 ( 1.0) Region 269 ( 2.9) 246 ( 3.8) 249 ( 2.6) 260 ( 254 ( 2.7) Nation 266 ( 1.4) 258 ( 1.7) 260 ( 1,4) 262 ( 1 280 ( 1.3) PARENTS' EDUCATION HS nen-graduat State 247 ( 2.0) 235 ( 22) 239 ( 2.0) 237 ( 2.5) 238 ( 2.0) Region 243 ( 4.5) 227 ( 6.1) 237 ( 4.1) 234 ( 4.7) 240 ( 3.5) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) 240 ( 3.1) 242 ( 3.0) HS graduate State 254 ( 1.3) 24$ ( 1.4) 249 ( 1.0) 250 ( 1.2) 248 ( 1.3) Region 252 ( 4.7) 235 ( 5.3) 242 ( 13) 242 ( 5.4) 247 ( 4.5) Nation 259 ( 1,8) 2411 ( 2.1) 252 ( 1.6) 253 ( 22) 253 ( 2.0) Some college State 267 ( 1.9) 258 ( 2.4) 281 ( 1.8) 265 ( 2.1) 261 ( 1.9) Region 265 ( 3.5) 257 ( 6.3) 253 ( 4.2) 260 ( 3.9) 280( 5.7) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 263 ( 2.2) College graduate State 274 ( 1.5) 268 ( 2.2) 267 ( 1.6) 272 ( 1.8) 269 ( 1.6) Region 275 ( 3.9) 264 ( 4.8) 263 ( 3.6) 267 ( 4.6) 270 ( 4.11 Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.8) 276 ( 2.2) 273 ( 4.7) GENDER Male State 261 ( 1.3) 255 ( 1.7) 255 ( 1.4) 256 ( 1.6) 253 ( 1.6) Region 257 ( 3.6) 249 ( 4.4) 249 ( 3.2) 249 ( 3.9) 253 ( 3.2) Nation 266 ( 2.0) 262 ( 2.3) 260 ( 1.7) 262 ( 2.1) 260 ( 1.6) Female State 259 ( 1.1) 249 ( 1.4) 253 ( 1.1) 255 ( 1.3) 254 ( 1.2) Region 261 ( 2.9) 243 ( 4.0) 248 ( 2.4) 251 ( 3.7) 255 ( 2.6) Nation 266 ( 1.4) 253 ( 1.6) 258 ( 1.5) 261 ( 1.6) 260 ( 1.4) 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 t 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 35 West Virginia THE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valusK " and of itself, but it becomes more useful for improving instruction and settini it4.y when supplemented with contextual information about schools, teachers, and Audents. 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, instructioi, 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 ..'he factors that appear to be related to eighth-fgade public-school students' proficiency in the subject, and provide an educational context for understanding information on student achievement. It is im?ortant to note that the NAEP data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. flowever, 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 pTactices, teacher qualifications, and conditions beyond school that facilitate learning and ihstniction fundammtal aspects of the educational process in the country. THE I990.NAEP TRIAL STATE ASSESSMENT 4 2 37 West Vitginia 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 indirated new and more successful ways of teaching and learning, incorporating more hands-on tivities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by Sooks or worksheets. Also, it is widely recognized that home environment has an mi--amous impact on future academic achievement. Yet, as shown in Chapters 3 and 7, large proportions of students report having spent much more time each day watching television than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 4 38 THE 1990 NAEP TRIAL STATE PSSESSMENT West Virginia 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 policyrnakers 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.3 This chapter focuses on curricular and instructional content issues in West Virginia public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: About three-quarters of the eigIith-grade students in West Virginia (72 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curtis McKnight, e al., The Underachieving Curricubim- 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). 4 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 West Virginia In West Virginia, 75 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Many of the students in West Vh.ginia (88 percent) were taught mathematics by teachers who teach only one subject. More than half (60 percent) of the students in West Virginia were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was equally prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in I West Virginia Eighth-Grade Public Schools PERCENTAGE OF STUDENTS IWO NAEP TRIAL STATE ASSESSMENT West Virginia Saaut 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 pubhc-school students who are offered a course in algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who teach only mathematics Percentage of eighth-grade students in public schools who are assigned to a mathematics class by their ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics instruction per week Percentage Percentage Iswentage 72 ( 4.7) 70 (10.6) 63 ( 5.9) 75 ( 4.7) 60 (10.9) 78 ( 4.6) 88 ( 3.1) 77 (10.6) 91 ( 3.3) 60 ( 4.0) 58 ( 8.0) 83 ( 4.0) 30 ( 3.3) 51 (11.1) 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 7! 2 standard errors of the estimate for the sample. ao THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in West Virginia are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in West Virginia were taking eighth-grade mathematics (63 percent) than were taking a course in pre-algebra or algebra (35 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 West Virginia who were enrolled in pre-algebra or algebra courses exhibited higher avexage 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-pade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 41900 MEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation a- 1 Percentage and Profickncy Percentage and Proficiency Percentage and Proficiency What kind of mathematics class are you taking this year? Eighth-grade mathematics 63 ( 2.0) 64 ( 3.7) 62 ( 2.1) 244 ( 1.2) 241 ( 3.4) 251 ( 1.4) Pre-itigebra 19 ( 1.8) 23 ( 4.4) 19 ( 1.9) 267 ( 1.3) 269 ( 4.6)1 272 ( 2.4) Algebra 17 ( 1.2) 11 ( 2.2) 16 ( 1.2) 291 ( 1.8) 296 ( 4.8)1 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because 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. 4 6 THE 1990 NAM) TRIAL STATE ASSESSMENT 41 West Virginia Further, from Table AS in the Data Appendix:4 About the same percentage of females (37 percent) and males (33 percent) in West Virginia were enrolled in pre-algebra or algebra courses. In West Virginia, 36 percent of White students, 23 percent of Black students, and 24 percent of Hispanic students were enrolled in pm-algebra or algebra courses. Similarly, 34 percent of students attending schools in areas classified as "other", 36 percent in schools in disadvantaged urban areas, and 40 percent in schools in extreme rural areas were enrolled in pm-algebra or algebra courses. MATHEMAI1CS 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 West Virginia spent 15 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 West Virginia, 5 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 West Virginia and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. 6 For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations race/ethnicity, type of community, parents' education level, and gender. 47 42 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia The results by race/ethnicity show that 3 percent of White students, 1 percent of Black students, and 2 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 5 percent of White students, 5 percent of Black students, and 6 percent of Hispanic students spent no time doing mathematics homework. In addition, 1 percent of students attending schools in areas classified as "other", 3 percent in schools in disadvantaged urban areas, and 7 percent in schools in extreme rural areas spent an hour or more on mathematics homework daily. In comparison, 5 percent of students attending schools in areas classified as "other", 5 percent in schools in disadvantaged urban areas, and 7 percent in schools in extreme rural areas 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 west VWginia Southeast Nation About how much time do students spend on mathematics homework each day? Percentage and Proficiency 5 ( 1.9) 252 4.6)1 48 ( 3.3) 251 ( 1.3) 35 ( 32) 281 ( 2.3) 9 ( 1.8) 268 ( 5.3)I 3 ( 1.0) .41 Percentage and Proficiency 1 ( 1.0) *4. 44 ( 7.5) 248 ( 5.1)I 44 ( 7.6) 260 ( 5.4)I 8 ( 2.7) ( G") Percentage and Proficiency 1 ( 0.3) *4.) 43 ( 4.2) 256 ( 2.3) 43 ( 4.3) 286 ( 2.8) 10 ( 1.9) 272 ( 5.7)1 4 ( 0.9) 275 ( 5.1)I 16 minutes 30 minutes 45 mkades An hour or more 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 er Lire 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). S THE 1990 NAEP TRIAL STATE ASSESSMENT 43 West Virginia 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 WOO MEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation About how much time do you usually spend each day on mathematics homework? Nom 15 minutes 30 misaites 45 minu4s An hoir or more Paraentage Patio Imlay 15 ( 1.4) 256 ( 1.6) 90 ( 1.1) 2515 ( 1.1) 20 ( 1.0) 256 ( 1.5) 15 ( 0.6) 254 ( 1.4) 14 ( 0.9) 255 ( 2.4) Percentip PerisMage e nd and Prollaimy ProMaletsy 11 ( 1.9) 237 ( 5.4) 25 ( 1.6) 253 ( 3.3) 33 ( 2.5) 258 ( 3.0) 17 ( 2.2) 26i ( 23) 14 ( 1.4) 247 ( 4.6) 9 ( 0.8) 251 ( 2.6) 31 ( 2.0) 284 ( 1.9) 32 ( 1.2) 263 ( 1a) 16 ( 1.0) 263 ( 1.9) 12 ( i.t) 258 ( 2.1) The standard errors of the estimated statistics appear in parentheaes. 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. And, according to the students (Table 7 and Table A7 in the Data Appendix): In West Virginia, some of the students (15 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, II percent of the students in West Virginia 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 11 percent of White students, 9 percent of Black students, and 12 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 15 percent of White students, 14 percent of Black students, and 22 percent of Hispanic students spent no time doing mathematics homework. 44 THE 1990 NAB? TRIAL STATE ASSESSMENT West Virginia In addition, 10 percent of students attending schools in areas classified as "other", 17 percent in schools in disadvantaged urban areas, and 11 percent in schools in extreme rural areas spent an hour or more on mathematics homework daily. In onmparison, 16 percent of students attending schools in areas classified as "other", 12 percent in schools in disadvantaged urban areas, and 11 permit in schools in extremc rural areas spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometty, and measurement.' Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic; measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. $ National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 5 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 45 West Virginia 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 emphagis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whme teachers placed little or no emphasis on Algebra and Functions. Students whose te..nhers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed Vale or no emphasis on the same areas. 46 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1190 NAEP TRIAL STATE ASSESSMENT 1 West Virginia Southeast Nation Paraentage ana Pn Adonay Paraantais and Prelidoncy Parcae.. ana Praddangli Teacher "emphasis" categories by content areas Numbers and Operations Heavy emphasis 48 ( 50 ( 7.3) 49 ( 3.8) 255 ( 1.6) 256 ( 3.1)1 200 ( 1.6) Little or no emphasis 13 ( 1.6) 15 ( 4.8) 15 ( 2.1) 281 ( 3.6) 262 ( 7.7)i 287 ( 3.4) IlAaasuromeot Heavy emphasis 13 ( 2.4) 13 ( 6.8) 17 ( 3.0) 241 ( 3.6)1 242 ( 7.6)1 250 ( 5.9) Little or no emphasis 41 ( 3.7) 22 ( 6.1) 33 ( 4.0) 262 ( 2.7) 259 (10.7)1 272 ( 4.0) Gaomatry Heavy emphasis 14 ( 16) 22 ( 7.0) 28 ( 3.8) 252 ( 2.5) 253 ( 7.5)1 260 ( 3.2) Little or no emphasis ( 3.9) 22 C 8.8) 21 ( 3.3) 256 ( 2.2) 253 ( 8.7)1 284 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 8 ( 2.0) 19 5.9) 14 ( 2.2) 259 ( 3.7); 274 ( 5.8)1 269 ( 4.3) Little or no emphasis 6.5 ( 3.6) 54 (10.4) 53 ( 4.4) 256 ( 1,8) 248 ( 5.4)1 281 ( 2.9) Algebra and Functions Heavy emphasis 41 ( 2.6) 42 ( 6.0) 46 ( 3.6) 275 ( 1.7) 277 ( 5,6) 275 ( 2.5) Little or no emphasis 27 ( 3.6) 21 ( 8.1) 20 ( 3.0) 235 ( 2.0) 238 ( 6.7)1 243 ( 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 ertimate for ale 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. r:e") t. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 West Virginia 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 cuniculum coverage, mathematics homework, and instructional emphasis has revealed the following: About three-quarters of the eighth-grade students in West Virginia (72 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In West Virginia, 75 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 West Virginia were taking eighth-grade mathematics (63 percent) than were taking a course in pre-algebra or algebra (35 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 West Virginia spent 15 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 West Virginia, some of the students (15 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 11 percent of the students in West Virginia 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 heav y instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 5 3 48 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia CHAPTER 4 MIRO II 111111-11111112111 111111111111111111 RI miumr411 essous. 'A 11111511111111111111111 RM %1111111,111111 "V11111111101111'4811111 11111111. NUM r.. MI 111111111ORIIIMII A111111111111111111111111111 How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning or for those who come from different cultural backgrounds is an important aspect of teaching.* An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide infomiation 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. e' National Council of Teachers of Mathematics, Professional Standards for the Teaching of Alathematics (Reston, VA: National Council of Teachers of Mathematics, 1991), THE 1990 NAEP TRIAL STATE ASSESSMENT 49 West Virginia From Table 9 and Table A9 in the Data Appendix: In West Virginia, 8 percent of the eighth-gcade students had mathematics teachers who reported getting all of the resources they needed, while 45 percent of the students woe 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 West Virginia, 7 percent of students attending schools in areas classified as "other", 23 percent in schools in disadvantaged urban areas, and 1 percent in schools in extreme rural areas had mathematics teachers who got all the resources they needed. By comparison, in West Virginia, 50 percent of stuoents attending schools in areas classified as "other", 25 percent in schools in disadvantaged urban areas, and 37 percent in schools in extreme rural areas were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had higher mathematics achievement levels than those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation Percentage Percentage Percentage of the following statements is true about how well supplied you are by your rWhich school system with the instructional and and and materials and other resources you need to teach your class? Proficiency Proficiency Proficiency I get ail the resources 1 med. S ( 1.9) tS 4.0) 13 ( 2.4) 265 ( 3,5)i 258 (122)1 265 ( 4.2) I get most of the resources I need. 47 ( 4.5) 71 ( 9.5) 58 ( 4.0) 257 ( 1,5) 255 ( 3.3)1 265 ( 2.0) I get some or none of the resources I need. 45 ( 4.3) 21 ( 9.7) 31 ( 42) 253 ( 1.4) 257 ( 13.0)1 261 ( 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 entsre population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia 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 inforniation on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: Less than half of the students in West Virginia (39 percent) worked mathematics problems in small groups at least once a week; some never worked mathematics problems in small poups (20 percent). The largest percentage of the students (68 perwnt) used objects like rulers, counting blocks, or geometric shapes less than once a week; somc never used such objects (12 percent). In West VirOnia, 85 percent of the students were assigned problems from a mathematics textbook almost every day; 0 percent worked textbook problems about once a week or less. About one-quarter of the students (29 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (32 percent). Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Curriculum, gghty-second Yearbook of the National Society for the Study of Education (Chicago. IL: University of Chicago Press, 1983). 56 THE 1990 NAEP TRIAL STATE ASSESSMENT 51 West Virginia TABLE 10 I Teachers' Reports on Patterns of Mathematics I Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1990 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation , Percentage and Poroonloge and Percontaeo and About how often do students work problems In small groups? Proficiency Pfolidincy Proficiency At least once a week 39 ( 3.5) 44 ( 82) 50 ( 4.4) 258 ( 2.0) 255 ( 4.7)1 280 ( 2.2) Less than once a week 41 ( 3.5) 4$ ( 8.3) 43 ( 4.1) 257 ( 1.3) 258 ( 3.9)1 264 ( 2.3) Never 20 ( 2.5) ( 4.1) 8 ( 2.0) 253 ( 2.7) 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 Prot Iciency Proficiency At least once a week 19 ( 3.6) 19 { 82) 22 ( 3.7) 254 ( 2.3) 243 ( 4.3)1 254 ( 3.2) Less than once a week 68 ( 4.1) 65 (10.3) 69 ( 3.9) 254 ( 1.0) 257 ( 3.8)1 263 ( 1.9) Never 12 ( 2.3) 270 ( 44) *** ( ****) 9 ( 2.6) 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). 52 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE 11 I Teachers' Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1880 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation About how often do students do problems Porcentags end Percents. Peralnik9, 1 and and from textbooks? Proficiency Prilloienw Piciiciancy Almost every day 85 ( 2.8) 75 ( 7.8) 62 ( 3.4) 257 ( 1.0) 259 ( 3.1) 267 ( 1.8) Several timos a week 15 ( 2.6) 22 ( 7.8) 31 ( 3.1) 257 ( 2.5) 248 ( 5.2)1 254 ( 2A) MOW once a week or lass 0 ( 0.2) ( "4) 3 ( 2.8) ( ,fre.) 7 ( 1.8) 280 ( 5.1)1 About how often do students do problems on worksheets? Percentage and Percentage and Percentage and Proacioncy Proadenoy ProNdency At least several times a week 29 ( 3.2) 30 ( 8.6) 34 ( 3.8) 253 ( 2.0) 251 ( 3.4)1 256 ( 2.3) About ono. a week 39 ( 3.4) 44 ( 9.1) 33 ( 3.4) 255 ( 1.8) 256 ( 3.7)1 260 ( 23) Less than weeidy 32 ( 3.4) 27 ( 8.6) 32 ( 3.8) 262 ( 2.1) 263 ( 6.0)1 274 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within I 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). The next section presents the students' responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. rt: THE 1990 NAEP TRIAL STATE ASSESSMENT 53 West Virginia COLLABORATING IN SMALL GROUPS ln West Virginia, 56 percent of the students reported never working mathematics problems in small groups (see Table 12); 19 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 1 Students' Reports oti the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation PanNintap and Pralciency Parianta. and ProOlatenca Povindaga and OPmedanay How often do you work in small groups In your mathematics class? I At feast once a week 19 ( 1.9) 2$ ( 3.9) 2$ ( 2.5) 254 ( 11) 251 ( 4.8) 25$ ( 2.7) Less than once a week 25 ( t4) 2$ ( 2.2) 2$ ( 1.4) 2$7 ( 1.2) 250 ( 3.9) 267 ( 2.0) Never 56 ( 2.3) 49 ( 4.8) 44 ( 2.9) 256 ( 1.1) 252 ( 2.4) 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. Examining the subpopulations (Table A 12 in the Data Appendix): In West Virginia, 17 percent of students attending schools in areas classified as "other", 34 percent in schools in disadvantaged urban areas, and 17 percent in schools in extreme rural areas u orked in small groups at least once a week. Further, 19 percent of White students, 19 percent of Black students, and 28 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 (18 percent and 20 percent, respectively). 54 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: About half of the students in West Virginia (45 percent) never used mathematical objects; 24 percent used these objects at least once a week. Mathematical objects were used at least once a week by 25 percent of students attending schools in areas classified as "other", 21 percent in schools in disadvantaged urban areas, and 21 percent in schools in extreme rural areas. Males were as likely as females to use mathematical objects in their mathematics classes at least once a week (25 percent and 23 percent, respectively). In addition, 23 percent of White students, 19 percent of Black students, and 36 percent of Hispanic students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency At least once a week 24 ( 1.8) 23 ( 3.4) 28 ( 1.8) 249 ( 1.8) 242 ( 3.6) 258 ( 2.6) Less than once a week 31 ( 1.4) 29 ( 2.5) 31 ( 1.2) 260 ( 1.1) 281 ( 3.5) 289 ( 1.5) Never 45 ( 2.3) 48 ( 4.5) 41 ( 2.2) 257 ( 1.2) 254 ( 3,0) 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 popu!ation is within 2 standard errors of the estimate for the sample. G 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 55 West Virginia MATERULS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in West Virginia 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): Many of the students in West Virginia (84 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 84 percent of students attending schools in areas classified as "other", 81 percent in schools in disadvantaged urban areas, and 86 percent in schools in extreme rural areas. TABLE 14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation - How often do you do mathematics problems from textbooks in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Almost every day 84 ( 1.2) 78 ( 2.4) 74 ( 1.9) 258 ( 1.0) 257 ( 2.6) 267 ( 1.2) Several times a week 12 ( 1.0) 14 ( 1.9) 14 ( 0.8) 247 ( 1.9) 246 ( 4.4) 252 ( 1.7) About once a week or less 4 ( 03) 8 ( 2.7) 12 ( 1.8) 232 ( 2.6) 222 ( 5.3)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 NAH2 TRIAL STATE ASSESSMENT West Virginia And, for the frequency of worksheet usage (Table 15 and Table Al5 in the Data Appendix): About one-quarter of the students in West Virginia (26 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 areas classified as "other", 32 percent in schools in disadvantaged urban areas, and 14 percent in schools in extreme rural areas. TABLE 15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF 3TUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 19110 NAEP TRIAL. STATE ASSESSMENT West Virginia Southeast Nation How often do you do mathematics problems on worksheets in your mathematics class? Pementage and Proficiency Percentage and Profidency Percentage anti Proficiency At least several times a week 26 ( 2.4) 38 ( 4.3) 38 ( 2.4) 249 ( 1.5) 24$ ( 4.3) 253 ( 2.2) About once a week 30 ( 1.5) 32 ( 1.5) 25 ( 1.2) 25$ ( 1.4) 254 ( 2.8) 261 ( 1.4) Less than witeidy 43 ( 2.4) 29 ( 3.9) 37 ( 2.5) 260 ( 1.3) 263 ( 3.3) 272 ( 1.9) The standard errors of the estimated statistics appear it., 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. 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 West Virginia TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation Patterns of classroom instruction Percentage of students sotto woe* mathematics problem in small groups At least once a week Less than once a week Never Percentage of students who use *acts like rulers, coating blocks, or geometric solids At least once a week Less than once a week Never [ 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 use a mathematics worksheet At least several times a week About once a week Less than weekly Percentage Percentage Perownege Sunnite Teadwas inimangs Teachers Inahints Taschers 19 ( 1.9) 39 ( 3.5) 26 ( 3,9) 44 ( 11.2) 211 ( 2.5) 50 ( 4.4) 25 ( 1.4) 41 ( 3.5) 26 ( 2.2) 4$ ( 11.3) 28 ( 1.4) 43 ( 4.1) 58 ( 2.3) 20 ( 2.5) 49 ( 4.6) 7 ( 4.1) 44 ( 2.9) $ ( 2.0) 24 ( 1.8) 19 ( 3.8) 23 ( 3.4) 19 ( 8.2) 2$ ( 1.8) 22 ( 3.7) 31 ( 1.4) 88 ( 4.1) 29 ( 23) 85 (10.3) 31 ( 12) 89 ( 3.9) 45 ( 2,3) 12 ( 2.3) 48 ( 43) 10 ( 8.1) 41 ( 2.2) 9 ( 2.8) Percentage Percentage Percentage Studied:a Teactws Students Teachers Students Teachers $4 ( 1.2) 85 ( 2.6) 78 ( 2.4) 75 ( 7.8) 74 ( 1.9) 62 ( 3.4) 12 ( 1.0) 15 ( 2.6) 14 I 1.9) 22 ( 7.8) 14 ( 0.8) 31 ( 3.1) 4 ( 0.5) 0 ( 0.2) 8 ( 2.7) 3 ( 2.8) 12 ( 1.8) 7 ( 8) 26 ( 2.4) 29 ( 3.2) 38 ( 4.3) 30 ( 6.6) 38 ( 2.4) 34 ( 3.8) 30 ( 1.5) 39 ( 3.4) 32 ( 1.5) 44 ( 9.1) 25 ( 12) 33 ( 3.4) 43 ( 2.4) 32 ( 3.4) 29 ( 3.9) 27 ( 8.6) 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 r 2 standard errors of the estimate for the sample. 63 58 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia 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 inathematic 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: Lgss than half of the students in West Virginia (39 percent) worked mathematics problems in small groups at least once a week; some never worked in small groups (20 percent). The largest percentage of the students (68 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and some never used such objects (12 percent). In West Virginia, 85 percent of the students were assigned problems from a mathematics textbook almost every day; 0 percent worked textbook problems about once a week or less. About one-quarter of the students (29 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weeldy (32 percent). And, according to the students: In West Virginia, 56 percent of the students never worked mathematics problems in small groups; 19 percent of the students worked mathematics problems in small groups at least once a week. About half of the students in West Virginia (45 percent) never used mathematical objects; 24 percent used these objects at least once a week. Many of the students in West Virginia (84 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. About one-quarter of the students in West Virginia (26 percent) used worksheets at least several times a week, compared to 38 percent in the nation. THE 1990 NAEP TRIAL STATE ASSESSMENT 59 West Virginia CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to performcalculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks. The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or pennitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. 5 National Assessment of Educational Progress, Mathemaric3 Obj (lives 1990 Assessment (Prmceton, NJ: Educational Testing Service, 1958). National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 6 5 60 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia Table 17 provides a profile of West Virginia eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 20 percent of the students in West Virginia had teachers who allowed calculators to be used for tests. About the same percentage of students in West Vuginia and in the nation had teachers who pemitted unrestricted use of calculators (11 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of West Virginia Policies on Calculator Use PERCENTAGE OF STUDENTS MO NAEP TRIAL STATE ASSESSMENT West Virginia Souttisast Nation Percentage of eighth-grade students in public schools whose teachers permit the unrestricted use of caculators 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 access to caladatore owned by the school Percentage Percentage peresnatie If ( 2.0) 6 ( 3.1) 18 ( 3.4) 20 ( 2.9) 15 ( 8.1) 33 ( 4.5) 45 ( 4.4) 58 (11.8) se ( 4.6) The standard errors of the estimated siatisti4S 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. 66 THE 1990 NAEP TRIAL. STATE ASSESSMENT 61 West Virginia THE AVAILABILITY OF CALCULATORS In West Virginia, most students or their families (98 percent) owned calculators (Table 18); however, fewer students (42 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In West Virginia, 42 percent of White students, 44 percent of Black students, and 46 percent of Hispanic students had teachers who explained how to use them. Females were as likely as males to have the WC of calculators explained to them (41 percent and 44 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 MOO NAEP TRIAL STATE ASSESSMENT West Vkg NU Southeast Nation Parcantap and Prcacioncy 06 ( 0.3) 256 ( 0.9) 2 ( 0.3) 242 ( 3.9) Percentage and Proadancy Parcantaw and Preaciany 08 ( 1.2) 254 ( 2.4) 4 ( 1.2) *a* ( Paroantage and Preaching Percentage OW Wee ChstcY 97 ( OA) 263 ( 13). 3 ( 0.4) 234 ( 3.8) Parcentage and Proaderia Do you or your family own a calculator? Yes N Does your mathematics teacher explain how to use a calculator for mathematics problems? Yos 42 ( 1.9) 48 ( 5.9) 49 ( 2.3) 252 ( 1.4) 250 ( 3.9) 258 ( 1.7) No 58 ( 1.9) 54 ( 5.9) ( 2.3) 259 ( tO) 256 ( 2.5) 268 ( 4.5) aww.m 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). 6" 62 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia ME 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 we-- asked how frequently (never, sometimes, almost always) they used caleulalors 'orking problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In West Virginia, 28 percent of the students never used a calculator to work problems in class, while 47 percent almost always did. Some of the students (19 percent) never used a calculator to work problems at home, compared to 24 percent who almost always used one. Less than half of the students (36 percent) never used a calculator to take quizzes or tests, while 22 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation _ Percentage and Pro Salem Percents& and Proficiency Percentage and Madam How often do you use a calculator for the following tasks? Working problams in class Almost always 47 ( 1.1) 46 ( 3.0) 48 ( 1.5) 249 ( 1.1) 243 ( 2.8) 254 ( 1.5) Never 28 ( 1.6) 26 ( 4.0) 23 ( 1.9) 266 ( 1.3) 266 ( 3.1) 272 1 1.4) Doing problems at home Almost always 24 ( 12) 29 ( 3.1) 30 ( 1. 253 ( 1.3) 252 ( 3.6) 261 ( Never 19 ( 0.9) ( 1.8) 19 ( 0.9) 262 ( 1.8) 258 ( 4.4) 263 ( 1.8) Taking quizzes or tuts Almost always 22 ( 1.1) 31 ( 2.1) 27 ( 1.4) 250 ( 1.9) 240 ( 3.8) 253 ( 2.4) Never 36 ( 1.4) 35 ( 3.1) 30 ( 2.0) 267 ( 12) 270 ( 3.1) 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. Cs THE 1990 NAEP TRIAL STATE ASSESSMENT 63 West Virginia WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know whem 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 instnictions and practice on how to use a calculator prior to the assessment. During the assessment, students wereallowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that requited 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 di 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 neimer. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who dki not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students ..ho used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 6" 64 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in West Virginia were in the High group than were in the Other group. A smaller percentage of males than females were in the High group. In addition, 44 percent of White students, 40 percent of Black students, and 34 percent of Hispanic students were in the High soup. TABLE 20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1900 NAEP TRIAL STATE ASSESSMENT West Virginia 1 Southeast Nation "Calculator-use- group Nigh Percentage and Proddency 44 ( 1.1) 263 ( 1.3) 56 ( 1.1) 249 ( 1,0) Percentage Percentage and and Preficiancy Proficiency 42 ( 2.4) 244 ( 2.9) 58 ( 2.4) 247 ( 2.6) 42 ( 1.3) 272 ( 1.6) ( 1.3) 255 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 2990 NAEP TRIAL STATE ASSESSMENT 65 West Virginia SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instructional time to teaching students how to perform routine calculations by hand. Using calculators to replace this time-consuming process would create more instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 20 percent of the students in West Virginia had teachers who allowed calculators to be used for tests. About the same percentage of students in West Virginia and in the nation had teachers who permitted unrestricted use of calculators (11 percent and 18 percent, respectively). In West Virginia, most students or their families (98 percent) owned calculators; however, fewer students (42 percent) had teachers who explained the use of calculators to them. In West Virginia, 28 percent of the students never used a calculator to work problems in class, while 47 percent almost always did. Some of the students (19 percent) never vsed a calculator to work problems at home, compared to 24 percent who almost always used one. Less than half of the students (36 percent) never used a calculator to take quizzes or tests, while 22 percent almost always did. 71 66 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has became an issue of increasing importance to federal, state, and local governments. As part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.9 Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In West Virginia, 43 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About half of the students (54 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. Almost all of the students (95 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). 72 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 West Virginia TABLE 21 I Profile of Eighth-Grade Public-School 1 Mathematics Teachers PERCENTAGE OF STUDENTS 111110 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation - Percentage of students whine mathematics teachers reported having the blowing degrees ParaNdase PonnedalP Powidego Bachelor's degree ST ( 58 ( 50 ( 4.21 Master's or specialist's degree 43 ( 3.5 39 ( 11.4 42 ( 4.2) Doctorate or professional degree ( 0.0 3 ( 5.1 2 ( 1.4) Percentage of students vitae. mathematics Nathan have the Mewing typos of teaching certificates that are receptized by West Virgbia No regular certification 15 ( 2.5) 5 ( 2.3) 4 1-2) Regular certification but less than the highest available 31 ( 3.4) 53 (104) 29 ( 4.3) Highest certification available (permanent or long-term) 54 ( 3.7) 42 (10.7) 88 ( 4.3) Percentage of students %Owe mathematics teachers home the blowing types of teachbg certilcates that are recognized by West Virginia Mathematics (middle school or secondary) 95 ( 1.5) 84 ( 5.1) 84 ( 22) Education (elementary or middle school) 2 ( 0.8) 14 ( 4.8) 12 ( 2.8) Other 3 ( 1.2) 2 ( 1.5) 4 ( 14) The standard errors of the estimated stAtistiCS appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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 West Virginia Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In West Virginia, 46 parent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 parent of the students across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in West Virginia (11 percent) wtre taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and Graduate Fields of Study PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation What was your undergraduate major? Percentage Potenisse percentage Mathematics 40 ( 4.2) 44 ( CO) 43 ( 3.9) Education 42 ( 3.9) 43 ( 9.0) SS ( 3.6) Other 12 ( 3.6) 14 ( OS) 22 ( 3.3) What was your graduate major? Pmentege Percentage Percentage Mathematics 11 ( 2.5) 15 ( 5,4) 22 ( 3.4) Edwation 43 ( 4.$) 43 ( 9.6) 3$ ( 3.5) Other or no graduate level study 40 ( 4,$) 41 ( 6.1) 40 ( 8.4) 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. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT 69 West Virginia Teachers' responses to questions concerning their in-service tzaining for the year up to the Trial State Assessment (Table 23) show that: In West Virginia, 22 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. About one-quarter of the students in West Virginia (21 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 CF STUDENTS 1980 NAEP TRIAL STATE ASSESSMENT During the last year, how much time total have you spent on in-service education in mathematics or the teaching of mathematics? None Ono to 15 hours 111 hours or more Percentage Pordottogs Perestitago 21 ( 3.5) 11 ( 6.0) 11 ( 2.1) 57 ( 3.a) 46 (12.0) 51 ( 4.1) 22 ( 32) 43(10.1) 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. 0.1 70 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement." Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. Them 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' edumtional backgrounds and experience reveals that: In West Virginia, 43 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About half of the students (54 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students %ere taught by mathematics teachers who were certified at the highest level available in their states. In West Vuginia, 46 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 West Virginia (11 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. 1° Archie E. Lapointe, Nancy A. Mead, and Gary W. Philhps, A World of Differences An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). " Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematks Achievement. NA Ers 1990 Assessment of the Nation and the Mal Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). 76 THE 1990 NAEP TRIAL STATE ASSESSMENT 71 West Vitrinia In West Virginia, 22 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. About one-quarter of the students in West Virginia (21 percent) had mathematics teachers who spent no time on in-se:vice education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. 72 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia CHAPTER 7 The Conditions Beyond School that Facilitate Mathematics Learning and Teaching Because students spend much more time out of school each day than they do in school, it is reasonable to expect that out-of-school factors greatly influence students' attitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, encouragement, and participation in student learning experiences are powerful influenc;es. 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. 78 THE 1990 NAEP TRIAL STATE ASSESSMENT 73 West Virginia 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 schobling. Students participating in the Trial State Assessment were asked about the availability of newspapers, magaimes, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports on Types of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , IWO MEP TRIAL STATE ASSESSMENT Mut Virginia $oultwasi Nation Does your family have, or receive on a regular basis, any of the following items: more than 25 books, an encyclopedia, newspapers, magazines? Zero to two typos Throe typos Four typos Pernwlealle and Invilkieney awl Pralidanay Por****** owl friffakosy 20 ( 1.0) 29 ( 2.3) 21 ( 1.0) 243 ( 1.5) 23S ( 34) 244 ( 2.0) 32 ( 1.1) 29 ( 2.4) 30 ( CO) 256 ( 12) 24$ ( 4.4) 238 ( 47 ( 1.3) 49 ( 2.7) 4$ ( 12) 291 ( 1.2) 209 ( 23) 272 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estiMate for the sample. The data for West Virginia reveal that: Students in West Virginia 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 West Virginia About the same percentage of Black and Hispanic students had all four types of these reading materials in their homes as did White students. About the same pertentage of students attending schools in areas classified as "other" as in disadvantaged urban areas and extreme rural areas had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is genesally seen as detracting from time spent on educational pursuits. Students participating in the Trial State ssessment were asked to report on the amount of television they watched each day (Table 23). TABLE 23 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT West Virginia Southeast Nation How Much television do you usually watch each day? Percentage and Preaclency Pementage and Preedency Percentage aid Proficiency One hour or less 9 ( 0.6) 12 ( 1.3) 12 ( 0.8) 263 ( 2.5) 262 ( 6.2) 269 ( 22) Two hours 20 ( 0.9) 19 ( 2.1) 21 ( 0.9) 263 ( 1.6) 25$ ( 42) 28$ ( 1.8) Three hours 25 ( 0.7) 22 ( 1.9) 22 ( 0.8) 256 ( 1.5) 258 ( 3.3) 285 ( 1.7) Fotr to Nye hours 30 ( 0.8) 28 ( 1.6) 28 ( 1.1) 254 ( 1.0) 251 ( 3.6) 200 ( 1.7) Six hours or more 16 ( 0.7) 18 ( 1.4) 16 ( 1.0) 243 ( 1.6) 236 ( 2.8) 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. s THE 1990 NAEP TRIAL STATE ASSESSMENT 7 5 West Virginia From Table 25 and Table A25 in the Data Appendix: In West Virginia, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Relatively few of the eighth-grade public-school students in West Virginia (9 percent) watched one hour or less of television each day; 16 percent watched six hours or more. About the same percentage of males and females tended to watch six or more hours of television daily. However, a somewhat smaller percentage of males than females watched one hour or less per day. In addition, 15 percent of White students, 33 percent of Black students, and 27 percent of Hispanic students watched six hours or more of television each day. In comparison, 9 pescent of White students, 5 percent of Black 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 West Virginia, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in West Virginia (40 percent) did not miss any school days in the month prior to the assessment, while 25 percent missed three days or more. In addition, 24 percent of White students, 28 percent of Black students, and 36 percent of Hispanic students missed three or more days of school. 76 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia Similarly, 26 percent of students attending schools in areas classified as "other", 24 percent in schools in disadvantaged urban areas, and 22 percent in schools in extreme rural areas missed three or more days of school. TABLE 26 I Students' Reports on the Number of Days of school Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAP TRIAL STATE A. :! *... NiENT West Virginia Southeast Nation How many days of school did you miss last month? Percentege and Proedency Percantage and Predation Pereatage and Madam None 40 ( 1.2) 48 ( 1.6) 45 ( 1.1) 200 ( 1,2) 253 ( 3.4) 265 ( 1.6) One or two days 35 ( 0.9) 32 ( 1.7) 32 ( 011) 258 ( 1.0) 280 ( 2.8) 200 ( 1.5) Thm days or more 25 ( 1.0) 22 ( 1.5) 23 ( 1.1) 2413 ( 1.6) 242 ( 3.7) 250 ( 1.0) 4111,. IIROMM=Mft, 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. 82 THE 1990 NAEP TRIAL STATE ASSESSMENT 77 West Virginia STUDENTS' 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.12 Students were asked if they agreed or disagreed with five statements designed to elicit their perceptions of mathematics. These included statements about: Personal experience with mathematics, including students' enjoyment of mathematics and level of confidence in their mathematics abilities: I like mathematics; I am good in mathematics. Value of mathematics, inelding students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for solving everyday problems. A student "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly agree" were given a value of 1 (indicating very positive att:tudes about the subjrct), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception index according to whether they tended to strongly agree with 'LIN statements (an index of 1), tmded to agree with the statements (an index of 2), or teuded to be undecided, to disagree, or to strongly disagree with the statements (an index of 3). Table 27 provides the data for the students' attitudes toward mathematics as defmed by their perception index. The following results were observed for West Virginia: ...verage mathematics proficiency was highest for students who were in the "sttougly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. About one-quarter of the students (28 percent) were in the "strongly agree category (perception index of 1). This compares to 27 percent across the nation. About one-quarter of the students in West Virginia (22 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). ia National Council of Teachers of Mathematics, Curricutian and Evahiation Standards for School Mathematics Reston, VA: National Council of Teachers of Mathematics, 1989). a 78 THE 1990 NAEP TRIAL STATE ASSESSMENT West Vbginia TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MOD NAEP TRIAL STATE ASSESSMENT I Wait Virgki la Sou Itteast Nation _ Student "perception Index" groups Strongly agree ("perception index" of 1) Alm ("perception index" of 2) Undecided, disagree, strongly disagree ("perception Index" of 3) 25 ( 1.2) 206 ( 1.2) 50 ( 1.0) 255 ( 4.0) 22 ( OA) 245 ( 14) $O ( 2.7) 255 ( s.7) 45 ( 2.1) S51 ( SA) 25 ( SO) 244 ( 2.7) 27 (1.3) 271 1.9), 40( lb) 222 ( 4.7) 24 ( 1.2) 2$1 ( 14) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. The data related to out-of-school factors show that: Students in West Virginia 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 materials showed higher mathematics proficiency than did students who had zero to wo types. 8 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 79 West Virginia Relatively few of the eighth-grade public-school students in West Virginia (9 percent) watched one hour or less of television each day; 16 percent watched six hours or more. Averaw mathematics proficiency was lowest for students who spent six hours or more watching television each day. Less than half of the students in West Virginia (40 percent) did not miss any school days in the month ptior to the assessment, while 25 peroent 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 (28 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was higjicst for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" categorY. 80 THE 1990 NAEP TRIAL STATE ASSESSMENT i West Virginia THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon which the assessment was based, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Educational 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 incomplete block (13IB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The first step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT 81 West Virginia The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- thm first consisting of general backgrourJ questions and the second consisting of mathematics background questions -- and thaw blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnait -A and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required appxoximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every other block in one booklet. Seven assessment booklets were used in the Thal State Assessment Program. The booklets weTe spbukd or interleaved in a systematic sequence so that each booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as described in the introduction to this 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 Al). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Fig= A2). Data Analysis and Scales Om 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 on which performancv 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 over.411 performance in the assessment. National Assessment of Educational Progress, Mathematics Objectives: 1990 Assessment (PrincetPhi, NJ: Educational Testing Service, 1988). 82 87 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia FIGURE Al I Content Areas Assessed INumbers and Operations DE MONS !EMT lie=in GARD1M" This content area focuses on students' understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-world situations, as well Ls 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 . :auded. 1 Measurement This content area focuses on students' ability to describe real-world objects using numbers. Students are asked to Identify attributes, select appropriate units, apply measurement concepts, and communicate measurement-related ideas to others. Questions era included that require an ability to read Instruments using metric, customary, or nonstandard units, with emphasis on precision and accuracy. Questions requiring estimation, measurements, end applications of measurements of length, time, money, temperature, mass/weight, area, volume, Cape City, and angleS aro also included In this content area. 11.111.1. 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. Fate Analysis, 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 inter pret data are n3cessary skills in the contemporary world. Questions emphasize appropriate methods for gathering data, tha visual exploration of data, and the development and evaluation of arguments based on data analysis. Algebra and Functions This content area is brosd 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 %clay 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. ss THE 1990 NAEP TRIAL STATE ASSESSMENT 83 V West Virginia FIGURE A2 I Mathematical Abilities The fallowing three categories of mathematical abilities ans not to be construed as hierarchical. For example, problem solving involves interactions between conciotual knowledge and procedural skills, but what is considered complex problem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. [Conceptual Understanding =414. Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts; can use and interrelate models, diagrams, and varied representations of concepts; can Identify and apply principles; know and can apply facts and definitions; can compare, contrast, and integrate related concepts and principles; can recognize, interpret, and apply the signs, symbols, and terms used to represent concepts; and can interpret the assumptions and relations 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. Problem Solving In problem Solving, students are required to use their reasoning and analytic abilities when they encounter new situations. Problem solving includes the ability to recognize and formulate problems; determine the sufficiency and consistency of data; use strategies, data, models, and relevant mathematics; generate, extend, and modify procedures; use reasoning (i.e., spatial, inductive, deductive, statistical, and proportional); end Judge the reasonableness end correctness of solutions. S (3 84 THE 1990 NAB? TRIAL STA'rc ASSESSMENT West Virginia A scale ranging from 0 to 500 was created to report performance for each content area. Each content-area 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 pedonnance along a scale. Traditionally, pesformance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In conttast, the NAEP scale anchoring is accomplished by descaing what students at selected levels know and can do. Thk. scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defmed, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define performanc it each of the four levels on the scale, NAEP analyzed sets of mathematics items from the 1990 assessment that discriminated well between adjacent levels. The criteria for selecting these "benchmark" items were as follows: To degf,....e performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To define performance at each of the higher levels on the scale, items were chosen that were: a) answered correctly by at least 65 percent of students whose proficiency was at or near that level; and b) answered incorrectly by a majority (at least 50 percent) of the students performing at or near the next lower level. The percentage of students at a level who answered the item correctly hLd 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 West Virginia Once these emrirically selected sets of questions had been identified, mathematics educators analyzed the questrms and used their expert judgment to characterize the knowledge, skills, raid understandings of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.2 Questionnaires for Teachers and Schools AS part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and the ,:se of various instructional approaches. Because of the nature of thc sampling for tho Trial State Assessment, the responses to the mathematics teacher questionnaire du not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia FIGURE A3 I Example Items for Mathematics Proficienq Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 (2) II %ea Oat hob scr 0 T. twit WI ape teme De eme ma Am Daum bait el lea as shwa Am. Kik Iamb lem MD lie had et liale dom. AY& ME will Mee Iho Mos ha ix At 0 The Ise via the 14111 TM lea Me tie palm& 0 The Ms wish the tubber bah UN siert at EXAMPLE 2 saes at mar MOM AT MRAWAT IMMO She Dm The Doe Dm Orate Mit Uri=Orpleh a. How am Imes of mow woe pitied N Theaeityf CD SS 60 70 0 SO CD SO 0 I deal Wm. Grade 4 Neal Pemontage Correct: 73% Percentage Correct for Anchor Levels: 251 85 91 100 Grade 4 Overall Percentage Correct 834 Percentage COITSICi for Amtax Levels: il20 nig 222 75 91 100 Grade 8 Overall Percentage Wrest 89% Percentage Correct for Moho( Levels: 222 222 222 222 78 87 98 100 9 2 West Virginia FIGURE A3 I Example Items for Mathematics Proficiency. Levels (continued) ILovol 250: Simple MuMplkadvo Reasoning and Two-Stop Problem Solving 1 EXAMPLE 1 7. What is the value of a + when n 3 I Answer. EXAMPLE 2 The saWe 41eve abors do mobs 61 Raw of kis ask,. Op As ads below, Nab s doh mob eassorms dis dsw tbe Laid ma pon al she Aids sr. wile die wow bak rim Mid yam UM LINI Ic Ns Is esiniss? 0 Ws ON. EXAMPLE 3 6. Whom is podded limbo& lam balm IAA kw Was Modal. She hes 24 both. IN0 orgest ustlace blip kw Hai we bow way how as w1 sooli 024-4..0 024+41..0 0 24 + 0 0 24 10 4,8.0 CDS4e41 lusaw. Grade Mond Porowt000 Pomo*. Cared XS Mil 2o se Grad, Moral Pomontogo Porooftee Comet 222 21 se Commit 76% for Mahar Lavoie: NG 2:11 98 Correct 73% for Moho, Lovett al 92 92 Clads °moll Poroontogo Porooritogo correct ZS Mil 37 71 Correct 77% for Anchor Lev** NG 5114 96 100 ME 1990 NAEPISIAL STA111 ASSESSMENT West yirgutia FIGURE A3 1 Example Items for Mathematics Proficiency Levels (continued) EXAMPLE i /4. IL 11 limb ei elm Memos Mom die mak al Illomme Mr ahem aim& «at dm Um it o co CID V 4 EXAMPLE 2 lo lib* slid was tbet s flees is babe* a Its 9 feel bele***eleemei 1/7 **We mad b lobes *MP glbe r-!** loge *out km* Mos b. wail be reeneemied b7 s mile seise Immo, bass WO o § o I 0 7 0 li PiIimlow be seieelmer as ihis imemint 0 I'm 0 Noe BEST COPY AVAILABLE COO 8 04oroll Pommies Comm OM Peroontio Come fat Ando' Lovely ain 0312 32Q AM 33 48 Tt 90 Grade 12 Orwell Poroontles Comet itrib POKOINVO(10 Correct for liPcbar WOE 2Q2 XiQ ZS 3D2 40 79 96 Grads 1 04040 poro~ Correct 6916 Pellelittig. COM* for McItor Levels SI 2E2 211 MO 17 48 88 80 94 89 West Virginia FIGURE A3 f Example Items for Mathematics Proficiency Levels (=timed) Level 350: Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability EXAMPLE 1 allow*** MT rola datiallanaimi Named da-fiaaras. a 6 0 I 5 5 a U. llotia taiiI. haw away aft ea be la *a tri OD 101 43 IVO IV 300 011201 EXAMPLE 2 17. bylaw bra yea lard yam same to sassalaa IL Mow Grade Dane Pimentos Correct 34% Percentage Correct for Mcbor 29A ES BM 22Q 13 19 $3 88 Grade 12 Overaii Percentage Conict: 49% Percentage Correct for Anchor Levet*: 2122 2211 202 220 22 48 90 Grade 8 Overall Percentage Correct: 15% Percentage COIT1K4 for Anchor Lewis: 222 2§2 222 1 4 28 74 Grade 12 Overall Percentage Correct: 27% Percentage Correct for Anchor Levels; 002 022 2Mt 222 3 22 74 r 90 ME 1990 NAEP TRIAL STATE ASSESSMENT West Virginia 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 individuah 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 instxuction received by representative samples of eigjith-grade students in public schools. Although this approach may provide a different perspective from that which w3uld be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAErs 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) arc. estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the petformance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAEP) arc subject to a certain degee of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like almost au estimates based on assessment measures, NAEP's total group and subgroup proficiency estimates are subject to a second source of uncertainty, in addition to sampling error. As previously noted, each student who participated in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, ,nit equally appropriate, set of the assessment questions -- or the entire set of questions - somewhat different estimates of total gioup and subgroup proficiency might have beP-. obtained. Thus, a second source of uncertainty arises because :sach student was administered a subset of the total pool of questions. THE 1990 NAEP TRIAL STATE ASSESSMENT 96 91 West Virginia In addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a background question in a certain way or the proportion of students in certain racial/ethnic gioups) reflect only simpling 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 unce7'ainty associated with all samples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population 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 interval for the corresponding population quantity. This means that with appmximately 95 percent certainty, the average performance of the entire population of interest (e.E., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures forobtaining accurate confidence intervals are quite complicated. " 92 THE 1990 NAEP TRIAL STATE ASSESSMENT . West Virginia 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, zilch 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 urual4) 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 might be interested in answering the question: Do students who reported spending 45 minutes or moi e doing mathematics homework each day exhibk higher average mathematics proficiency than students who reported spending IS minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is higher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means diff,er, 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 statement 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. AF dismssed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associatdd with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the 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. S THE 1990 NAEP TRIAL STATE ASSESSMENT 93 West Virginia As an example, suppose that one were interested in determining whethes 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 errors for females and males were as follows: Grou p Average Proficiency Standard Error Female , _ 259 , 2.0 Male 255 ,,...._ , 2.1 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 Nri.02 + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean diftrence 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., WM 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.3 Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to maw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence val included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a statistically signifcant difference in the population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. 3 The procedure described above (especially the estimation of the standard error of the difference) is, in a strict sense, only appropriate when the statistics being compared come from independent samples. For certain comparisons in the report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used. C I/ 94 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significance is being performed. Howevex, 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 attributat le 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 proctdure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence interval; in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the 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 'I". In such cases, the standard errors -- and any confidence intervals or significance tests involving these standard errors -- should be interpreted ca.utiously. Further details concerning procedures for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defmed by race/ethnicity and type of school community, as well as `py gender and parents' education level. NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) ani four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not 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. 10 0 THE 1990 NA& TRIAL STATE ASSESSMENT 95 West Virginia The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or territory, divided by the standard devLtion of the proficiencj in the total population. If the true difference between subgroup 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. Fuxther detailb 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 rules used to select them are shown below. Percentage Description of Text in Report p = 0 None 0 < p S 10 Relatively few 10 < p S 20 Some 20 < p S 30 About one-quarter 30 < p S 44 Less than half 44 < p s 55 About half 55 < p s 69 More than half 69 < p S 79 About three-quarters 79 < p S 89 Many 89 < p < 100 Almost all p = 100 All 96 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia THE NATION'S REPORT CARD DATA APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains corresponding data for each level of the four reporting subpopulations race/ethnicity, type of community, parents' education level, and gender. 1 0 2 n112. 1990 NAEP TRIAL STATE ASSESSMENT 97 West Virginia TABLE A5 I Students' Reports on the Mathematics Class 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL EigMh-grade STATE ASSESSMENT Mathematics Pr* 4191lwa AMINN.M111, TOTAL Parcentaga and Pal blowy Pententaga an* Prat:kw Perandage and ProlIcianca State 26344 "1.21 19 ( 11) 297 ( 15) 12) 291 15) Nation 82 2.1 19 ( 1.9) 15 12) 251 ( 14) 272 ( 2.4) 296 ( 2.4) RACE/ETHNICITY White State 82 ( 1.9) 19 ( 1.9) 17 ( 12) 24$ ( 1.2) 268 ( 1.3) 292 ( 1.8) Nation 59 ( 25) 21 ( 2.4) 17 ( 1.5) 250 ( tel 277 ( 2.2) 300 ( 2.3) Mack State 73 ( 5.6) 13 ( 4.2) 10 ( 4.2) Nation 72 ( 4.7) 16 ( 3.0) 9 ( 2-2) 232 ( 3.4) 246 ( 8.4) Hispanic State 72 ( OA) 227 ( 3.7) 10 ( 4.8) 4,04, f 8 ( 3.1) ( 441 Nation 75 ( 4.4) 13 ( 32) 8 ( 1.5) 240 ( 2.4) MIN (11111 TYPE OF COMMUNITY Oludvantagad urban State 64t 6.9) 249 ( 4.3)1 20 ( 73) ( «pi 16 ( 3.4) ***) Nation 65 ( 6.0) 240 ( 4.0)1 18 ( 4.1) *el 14 ( 3.3) 287 ( 4.2)1 Wren* rural State 59 ( 4.6) 24 ( 5.0) 16 ( 4.1) 243 ( 2.4)1 266 ( 2.2)1 263 ( 5.4)1 Nation 74 ( 4.5) 249 ( C.1)1 14 ( 5.0) .40) 7 ( 2.2) Other State 64 ( 2.3) 17 ( 1.9) /7 ( 1.3) 243 ( 1.2) 267 ( 1.6) 294 ( 1.9) Nation 51 ( 2.2) 20 ( 2.1) 1$ ( 1.4) 251 ( 2.0) 272 ( 2.6) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate 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. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1±3 98 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE AS I Students' Reports on the Mathematics Class (cmtinued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL Eighth-grade STATE ASSESSMENT Pialhematice Pre-algebra Algebra TOTAL Psnisatip Prslidsess, lisressises and Proliclany Paressises Pnlidstosy State 16 ( ( 1.2 28? ( 01 ( 1.8 Nation 82 2.1) 19 ( 1.9 IS ( 121 251 14) 2?2 298 ( 24 PARENTS' EDUCATION nemgroduate State $5 ( 2.2) 10 ( 1.9) 3 ( Nation 298 ( 7? 1.5) 33) 13 i ;.*Ali .b ( 3 ( 1.1 graduate 241 ( 2.1) State ( 24) 20 ( 11 1.4) 242 ( 1.2) 283 ( 1.5 281 23 Nation ( 2.8) 8 1.1 249 ( 1.9) 268 ( 31) 277 ( 521 Some college State 58 ( 2.9) 21 ( 3.0) 20 ( 2.8) 250 ( 1.7) 270 ( 2.1) 217 ( 21 Nation 80 ( 3.1) 21 ( 2.9) 15 ( 11 257 ( 2.1) 27$ ( 2.8) 295 ( 32 College graduate State 48 ( 2.9) 22 ( 2.5) 30 ( 1.8) 252 ( 1.9) 272 ( 2.3) 298 ( 1.7) Nation 53 ( 2.7) 21 ( 2.3) 24 ( 1.7) 2511 ( 1.5) 27$ ( 2.8) 303 ( 2.3) GENDER Maki State 85 ( 2.1) is ( 20) 18 ( 1.8) 245 ( 1.3) ( 1.9) 295 ( 2.1) NatiOn 83 ( 2.1) 18 ( 1.5) 15 ( 1.2) 252 ( 1.8) 275 ( 2.9) 299 ( 2.5) Renate State 82 ( 242 ( 2.4) 14) 20 ( 1.9) 26Sf 1.5) 1? ( 288 ( 1.5) 2.3) Nation 81 ( 2.8) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 289 ( 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 ,sie entire population is within * 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 West Virginia TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Nona 15 Miona los 30 Minutes 45 Minutes An Hour or Moro TOTAL Pervenine and Widow 5 ( 1.9) 252 ( 4.6)1 1 ( 0.3) 5 ( 2.0) 254 ( 4,2$ ( 0.3) 04. ..**) 5 ( 2.6) ..**) ( 0.7) *44) 8 ( 3.6) ( DA) *** ( 4") $ ( 4.7) 4.44 441 0 ( 0.0) .44(44* ) 7 ( 5.4) .444 4444j 0 ( 44. 4.4.4) 5 ( 2.2) ( .") 1 ( 0.4) ( "11 Parandase and Paillaioncy ( Si) 251 ( 1.3) 43 ( 4.2) 250 ( 2.3) 48 ( 3.3) 252 ( 1.3) 3$ ( 4.5) 260 ( 2.2) SI ( 8.5) rt. ( 55 t 7.8) 232( 3.1) 49 ( 6.9) 46 ( 7.8) 245 ( 3.0)1 5$ (13.5) 256 ( 3.0)1 41 (12.6) 236 ( 2.1p 252 ( 3.2)1 68 (142) 253 ( 54)1 45 ( 4.0) 249 ( 1.7) 37 ( .1.3) 256( 3.1) Perandap and Prelialeany 35 ( 32) 261 ( 43 ( 200 ( 35 ( 3.2) 262 ( 2.2) 45 ( 5.1) 270 C 2-7) 3? ( 9.0) 40 ( 6.7) 248 ( 5.3) 96 ( 8.1) ***) 34 ( 6.8) 251 ( 4.2)1 33 (13.2) 262 ( 5.9)1 36 ( 9.4) 253 ( 9.1:91 24 ( 6.3) 25$ ( 4.1)1 14 (10.9) 444,4 ( eel 3$ ( 3.8) 261 ( 2.6) 49 ( 5.1) 265 ( 245) Pannonian. and Preadengt 9 ( 18) 200 ( 6.3p 10( 1.9) 272 ( 5.7$ 10 ( 1.9) 268 ( 5.5)1 11 ( 2.4) 277 ( 73)1 6 ( 3.5) **Or ( ***) 3 ( 1.2) 44* ( 444.) 7 ( 3.3) 44* 4,41 13 ( 2.9) 4.4.4 ( 441 ( 1.3) 12 ( 5.9) 4.4 44-4) (44) 11 ( 22) 270 ( 6.0)1 10 ( 2.4) 276 ( 8.6)1 Parandega and Praciewri 3 ( 1.0) .40 ( 4 0.9) 278 ( 5.1p 3 ( 1.4) 44*144*) 4 ( 0.9) 279 ( 5.8)1 1 ( 1.4) ..**) 2 ( 0.8) 44,4 4,44) 2 ( 1.7) Mble Gt) ( 3 ( 3.3) 4.4 ( 10 ( 82) 4PN ) 7 ( 4.2) 444, ( 441 10 ( 7.3) 4.4 ( 4.41 1 ( 0.6) 444 ( 4-4,1 4 ( 1.11 282 (11.6p State Nation RACE/ETRNICITY State Nation Slack State Nation NIspanIc State Nation TYPE OF COMMUNITY Olsadvantagod urban State Nation Extreme rural State Nation What 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 t 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE A6 (continued) Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT None 15 Mimeos 31:1 Minutes 45 Minutes An Nour or Mors TOTAL Perceniefe and Proficiency ( 1.9) 252 ( 4.6)1 ( 0.3) *el 3 ( 1.3) ern 1 ( 0.6) 0-«* ( 6 ( 2.7) ( "4) ( 0.5) 011. ( fen 5 ( 2.1) 1 ( 0.9) ( 0 ( 0.3) *** *** ( 1 ( 0.3) *** ( "") 5 ( 2.2) 4.4. 1 ( 0.4) *** (44*) Pereennige and Proliciency 48 ( 3.3) 251 ( 1.3) 43 ( 4.2) 256 ( 2.3) 53 ( 5.1) 240 ( 2.1) 49 ( 6.3) 240 ( 2.8) 51 ( 3.8; 248 ( 1.5) 249 ( 3.1) 48 ( 4.0) 2S9 ( 2.4) 44 ( 5.4) 265 ( 2.6) 40 ( 3.1) 2e1 ( 2.1) 40 ( 4.7) 265 ( 2.5) 4$ ( 3.4) 251 ( 1.4) 44 ( 4.4) 257 ( 29) 46 ( 3.8) 250 ( 1.7) 41 ( 4.4) 255 ( 2.3) Perceniege and Proildency 35 ( 3.2) 261 ( 2.3) 43 ( 4.3) 200 ( 22) 32 ( 5.0) 240 ( 3.1) 40 ( 6.1) 248 ( 3.7) 33 ( 3.7) 253 ( 2.2) 44 ( 5.3) 258 ( 2.7) 37 ( 4.0) 268 ( 3.1) 43 ( 6.8) 270 ( 3.8) 39 ( 3.3) 276 ( 2.7) 44 ( 4.1) 277 ( 3.0) 36 3.3) 282 ( 2.9) 43 ( 4.3) 268 ( 2.9) 34 ( 3.5) 259 ( 2.4) 43 ( 4.7) 284 ( 2.8) Percentage and Prolidency 9 ( 1.8) 268 ( 5.3)1 10 ( 1.9) 272 ( 5.7)1 10 ( 3.9) .44 ( 4141 0 ( 1.7) 4") ( 1.7) 258 ( 42)1 9 ( 3.1) 10 ( 2.1) *44(14*) 7 2.1) 1144 **-a) 13 ( 2.4) 282 ( 5.4) 11 ( 2.3) 287 ( 6.1)1 ( 1.9) 206 ( 5.4)1 9 ( 1.9) 273 ( 7.3)1 10 ( 2.0) 267 ( 6.1)1 ( 2.0) 272 ( 5.7)1 Pereentage and Proiklency 3 1 1.0) .44.) 4 ( 0.9) 27$ ( 5.1;1 2 ( 1.8) *a* ( 4 ( 1.3) ( «pi) 3 ( 1.0) 2 ( 0.7) 4 ( 12) 5 ( 4.3) 4.44, 2 ( 09) 5 ( 1.3) 279 ( 7.7)1 3 1.3) 4 ( 0.9) 4.44 ( 41 State Nation PARENTS EDUCATION S non-graduate State Nation NS graduate State Nation Santo college State Nation College graduate State Nation GENDER Male State Nation Female State Natrc The standard errors of the eslimated statistics appear in yarentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for The ertire 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 (fwer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSW4NT 101 West Virginia TABLE Al I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AHD AVERAGE MATHEMATCS PROFICIENCY 100 NAEP TRIAL STATE ASSESSMENT Now 15 Mktutis 30 Minutes 45 Minutes An Now or More you'd. State Nation geggimarciTv Whit* State Nation Madc State Nation litspank State Nation TYPE OF COMMUNITY Disadvantaged urban State Nation Extreme nraI State Nation Other State Nation twaroodip mod frellolona 12 ( 1.7) 12 ( 3.7) 11 ( 2.9) 4'N ( 8 ( 2.3) 16 ( 1.3) 257 ( 2.2) 9 ( 1.0) 250 ( 33) twoodege farassiiip Paresedw sose and and Prallaisaqf Proickom Pilikkocy 15 $O ( 1.1) 20 15 ( 0.5 258 254$ ( 1.1) 258 1.5 264 ( 1/1 0 OA 31 (2.0) 32 '12 ) 10 ( 1.0} 251 (21) 264 ( 1.9) 2113 1 203 ( 11) 15 ( 1.1) 31 ( 1.1) 29 ( 1.0) 15 0.9) 2e0 ( 2.0) 25$ ( 1.0) 251 ( 1.8) 254 10 ( CO) 33 ( 2.4) 32 ( 1.3) 15 02 25$ ( 3.4) 210 ( 1.9) 270 ( 2.1) 277 ( 22 14 i 3A) 2$ ( 5.9) 32 ( 4.0) 17 ( 3.9) «Iw on t in ( fi) 44,* ( en. 7 ( 1.5) 26 i 2.5) 33 ( 2.7) 15 ( 2.3) " ( ') 241 ( 33) 237 ( 35) 240 ( 3.8) 22 ( 43) 25 ( 4.4) 24 ( 4.9) 18 ( 3.7) 12 ( 13) 27 ( 3.0) 30 ( 21) 1? ( 2.1) ' ( ") 24$ ( 33) .145 ( 3.4) 241 ( 4.3) 27 ( 3.8) 263 ( 3.8)1 24 ( 3.3) 253 ( 4.9)1 32 ( 2.7) 256 ( 2.0)1 36 ( 4.6) 200 ( 3.5)1 310 ( 1.2) 256 ( 1.4) 30 ( 1.8) 283 ( 2.3) 26 ( 261 ( 3.9 31 ( 3.0 247 ( 4.7)1 32 ( 1.6) 252 ( 2.8)1 31 ( 2.9) 25S ( 5.1)1 2$ ( 12) 256 ( 1A) 32 ( 1.3) 264 ( 23) 1$ 2.3) 20 ( 12) 250 ( 46)1 14 ( 23) 258 ( 3.0)1 18 ( 3.8) 14 ( 0.9) 253 ( 12) 15 ( 1.1) 287 ( 2.1) lievablep mad PrOdowir 11 256 24 12 1.1 25$ 3.1 2; 1 4 121 11 ( 1.3 2811 ( 33) 9 ( 4*. I( ow 1$ ( 1 232 ( 3.7 12 ( 3.0) "" ( ***) 17 ( 4.8) 14 ( 2.2) 44 ( .4 41 11 ( 1.3) (( 2.7) NIP411) 10 01) 255 ( 3.1) 13 ( 1.1) 258 ( 3.6) The standard errors of the estimated statistics appear M parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean pr oficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 - 1 102 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia 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 Wes 15 Minutia 30 Minutes 48 Minutes An Hour or Moro TOTAL State Nation PARENTS' EDUCATION Pommy tive Proildency 15 ( 1.1) 25$ ( 1.6) ( 0.8) 251 ( 2.8) 19 ( 2.8) .44 ( 17 ( 3.0) ral 15 ( 1.4) 253 ( 2.0) 10 ( 1.7) 248 ( 4.2) 14 ( 1.7) ( .41 9 ( 1,2) 13 ( 1.7) 274 ( 3.4) 7 ( 0.9) 265 ( 3.8) 19 ( 1.5) 259 ( 2.2) 11 ( 1.1) 255 ( 3.9) 11 ( 1.2) 255 ( 2.8) 7' ( OA) 248 ( 4.1) Pareadage sive Pcsillaisiscy 90 ( 2$6 ( 1.1 SI ( 2.0 264 ( 1.0) 34 ( 2.7) 241 ( 3.1) 26 ( 3.3) 240 ( 4.0) 28 ( 1.4) 251 ( 1.5) 33 ( 2.2) 259 ( 3.2) 34 ( 2.5) 264 ( 2.4) 30 ( 2.7) 266 ( 3.0) 31 ( 1.8) 270 ( 1.9) 31 ( 3.4) 275 ( 2.0) 31 ( 1.5) 257 ( 1$) 34 ( 2.4) 264 ( 2.8) 29 ( 1.7) 258 ( 1.7) 2$ ( 2.0) 263 ( 1.5) Perosniago and Psseldency 29 ( 1.0) 256 ( 1.5) 32 ( 1.2) 263 ( 1.9) 25 ( 2.4) 241 ( 2$) 34 ( 4.4) 248 ( 2.6) 31 ( IA) 249 ( 1.8) 31 ( 1,9) 254 ( 2.4) 30 ( 2.1) 262 ( 2.8) 36 ( 2.1) 266 ( 2.6) 27 ( 1.9) 272 ( 2.4) 31 ( 2.0) 275 ( 2.5) 27 ( 1.4) 257 ( 2.2) 29 ( 1.3) 208 ( 2.4) 31 ( 1.4) 255 ( 11) 35 ( 1.7) 260 ( 2.0) Perositso ane Madams 15 0.8) 254 1.4) 18 1.0) 286 ( 1.9) 15 ( 22) 11t4-1 12 ( 25) ( *el 15 ( 1.2) 24$ ( 2.4) 16 ( 1.4) 25$ ( 2.8) 14 ( 1.9) IP41* 14 ( 1.8) 274 ( 3.5) 16 ( 1.4) 267 ( 2.7) 18 ( 1.2) 278 ( 3.2) 14 ( 1.1) 254 ( 2$) 15 ( 1.2) 265 ( 3.0) IS ( 1.2) 253 ( 2.2) 17 ( 1.0) 287 ( 2.4) Parassisiis Pralcismy 11 ( 0.9) 255 ( 2.4) 12 ( 1.1) 26$ ( 3.1) ( 1.4) *Mt ( **I 10 ( 2.2) .44 ) 11 ( 1.3) 252 ( 2.7) 11 ( 1.5) 244 ( 3.4) ( 1.6) ( 1.5) ***) 14 ( 1$) 2e7 ( 5.0) 14 ( 1.9) 271 ( 2.8) O ( 0.9) 258 ( 3.7) 11 ( 1.4) 258 ( 4.1) 13 ( 1.3) 254 ( 2.9) 13 ( 1.3) 258 ( 3.3) HI nan-gradnate State Nation R$ graduate State Nation Sarno cads,' State Nation CONItg graduate State Nation GENDER MM. State Nation Fano Is State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each populafion of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 0 THE 1990 NAEP TWAL STATE ASSESSMENT 103 West Virginia TABLE AO I Teaches' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT limbers and Operations Maasursintant Ottantaby Heavy Emphasis Little or No Emphasis - Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No 1 Emphasis TOTAL State Nation Mina State Nation Back State Nation Hispanic State Nation TYPE OF COMMUNITY uhtadvantagad tirban State Nation Extreme rural State Notion Other State Nation poulataip .11224.204%) P4204204r 30.320222.2 semi aid sod Miaow 21040:44022 01121214002 Pe202,107/1. 1.24/14.2!*10,303100.2 : 264$ Si 31 241 9 15 2.1 17 283 1.8 2.7 ( 3.4 250 44 ( 13 ( 14) 13 ( 2.4 41 ( SA) 14 ( 4.0) 267 2.2) 222 ( 31) 2$2 OA 277 4.3) 2115 $1 03 1.5 283 ( 3.7) 243 34 204 2.0) 46 3.7 10 ( 24) 14 34 30 (4.7) 27 4A 22 201} epee *in 45 ( 9.3) 8 ( 3.0) .t.1 is se to 54 7.9) 11 ( 33) 2$ ( 7.4) 23( 5.7) 23 24 71 243 ( 43) "1' ( eft) 226 ( 2.2)4 231 ( Li)1 242 SA 233 4.7 Imp* ( *.t.) fit5 5.41 23( ( Si ( 8.4) 9 ( 3.5) 13 ( 4.13) 47 ( 0.7) ( 2.2) ..2;(( "44.1) $4 ( 54) 27 OA IS (5.5) 248 ( 4.8) .41 ".1 255(44)4 ( 55 ( 9.5) 0 ( 2.9) 0 ( 0.0) 41 (14.4) 0 f 0.0) 30 (134) NO ( 4.0 I *** ( "") "" ( ***) 252 ( 54)4 ) 255 ( 0.7)4 48 (12.0 9 ( 4.0) 32 (103) 21 ( 9.5) 33 (113) 13 ( 7.3) 25$ ( 9.3)1 ' ( "") 23$ ( 0.4)1 "." ( ) 240 3.2)1 "' I "hi $2 ( al) 2 ( 24) 24 ( 7.2) 44 ( 2.4) 0.3 30 ( 9.3) 250 ( 23)4 m ( 44.) 242 ( 45)4 250 ( 3.2)1 252 34 253 ( 3.9)/ 53 (12.4) 0 ( 3.0) 0 ( 4.9) 32 111./ 9 0.1 10 i 7.9) 257 ( 7.1)4 ip.,* ( .....) ( .4,41 285 If ..... ( ..4, .4.. «1 43 ( 4.2) IS ( 2.1) 12 ( 2.7) 40 ( 4.3) 15 ( 3.2) 30 ( 4.0) 253 ( 1.9) 280 ( 4.3) 241 ( 44)1 284 ( 3.2) 252 ( 2.8)4 258 ( 2.7) 52 ( 4.1) 18 ( 2.7) 18 ( 10) 34 ( 5.3) 28 ( 44) 24 ( 4.3) 200 ( 2.3) 288 ( 3.8) 253 ( 7.1)1 270 ( 4.8) ND ( 19) 245 ( 5.7) 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. The percentages may not total WO percent because the "Moderate emphasis" category is not included. I Interpret with mution - 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). IC 104 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE A8 I Teachers' Reports on the Emphasis Given to (ccmtinued) I Specific Matkmatics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Manners and Heavy Emphasis J Little or No Emphasis Heavy 1 Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation PARENTS' EDUCATION le non-graduate State Nation RS graduate State Nation Some wipe State Nation College graduate State Nation GENDER Mai* State Nation Female State Nation Per04801. Povio1114. Pcomiese Pamionage Parcods. Parawasee smi ad ail amd end aid Mildew* Madam" Freedom Madam Pre Wow Profligacy 44 3.7 13( 1.6 255 1.0 211 3.11 40 33 15 2.1 22) 1.8 287 14 SS ( 54) 7 ( 24) 247 2.3) MI* ( 60 6.9) 7 ( 2.3) 251 ( 34) ( *ft') ( 42) 40 ( 1.8) 252 ( 1.7) 200 ( 5.0) 55 ( 41) 11 ( 2.6) 259 ( 2.9) *** ( 40 ( 4.7) 16 ( 3.1) 261 ( 2.6) *** ( 4") 47 ( 4.4) 17 ( 3.3) 285 ( 2.6) 284 ( 4.1)1 42 ( 3.6) 19 ( 2.4) 264 ( 3.0) 293 ( 3.5) ( 4.1) 19 ( 2.4) 200 ( 2.8) 298 ( 3.4) 47 ( 4.0) 256 ( 1.9) 48 ( 4.1) 261 ( 2.5) 48 ( 3.7) 264 ( 1.7) 51 ( 3.9) 260 ( 2.0) 12 ( 1.8) 281 ( 4.8) 14 ( 2.1) 287 ( 4.4) 14( 11) 282 ( 3.7) 15 ( 2.4) 266 ( 3.3) 13( 2.4) 41 ( 3,7 14( 2.0 241 ( 3.8 17 ( 3.0 262 33 2. 4.0 252 ( 26 ( 2.5 3.8 250 ( 5.8 272 4.0 260 ( 3.2 ) 15 ft* ( 3.9) 33 ( 243 ( 5.0) 5.0) 16 ( *** ( 40) 44) 22 5.3) ***) 25 ( 5.3) ( *el 32 ( *** ( 6.3) ***) 14 ( 3.0) 38 ( 42) 15 ( 3.3) 230 ( 4.4)1 254 ( 3.1) 249 ( 2.9)1 17 ( 3.9) 27 ( 5.0) 27 ( 4.5) 251 ( 6.1)1 253 ( 4.7)I 255 ( 4.2) 13 ( 2.8) 43 ( 4.7) 13 ( 2.8) ( *IN') 268 ( 5.0) *** ( "") 12 ( 2.7) 32 ( 5.5) 27 ( 5.0) "4' ( *44) 279 ( 4.5) 262 ( 4.8)1 10 ( 2.1) 48 ( 3.8) 13 ( 2.1) 256 ( 5.0)1 277 ( 3.0) 262 ( 3.8) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3.81 13 ( 2.5) 40 ( 3.7) 14 ( 2.7) 245 ( 4.3)1 266 ( 3.3) 253 ( 3.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 258 ( 6.7) 276 ( 4.8) 263 ( 3.8) 12 ( 2.5) 41 ( 4.1) 14 ( 2,8) 238 ( 4.2)1 258 ( 3.0) 251 ( 3.3)1 17 ( 32) 35 ( 4.3) 27 ( 3.9) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 37 3.2 250 2.2 21 3.3 264 ( 5.4) 31 ( 5.0) :Ai 3.5) 201 6.7) 4.** 4mk.) 34 ( 4.4) 249 ( 2.5) 24 ( 5.1) 248 ( 4.8$ 40 ( 4.8) 281 ( 4.2) 23 ( 4.1) 270 ( 4.7) 40 ( 3.9) 269 ( 2.7) 21 ( 2.0) 280 ( 64) 38 ( 4.1) 256 ( 2.4) 20 ( 3.3) 206 ( 6.8) 35 ( 3.9) 256 ( 2.8) 23 ( 3.5) 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 fcr the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may mit 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). ito THE 3990 NAEP TRIAL STATE ASSESSMENT 105 West Virginia TABLE AS I Teachers' Reports on the Emphasis Given To (Pantinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Mgebra and Functions Heavy Emphasis Little or No Emphasis Heavy EAphasis Little or No Emphasis TOTAL Percentage and Proficiency Percentage and Profidency Percentage and Proficiency Percentage and Pinlidency State ( 2.0) 55 ( 3.6) 41 ( 2.6) 27 ( 3.6) 259 ( 3.7)1 256 ( 1.8) 275 ( 1.7) 235 ( 2.0) Nation ( 2.2) 53 ( 4.4) 415 3.6) 20 ( 3.0) 209 ( 4.3) 261 ( 2.9) 275 ( 243 ( 3.0) RACEIETHNICITy WNW State 9 ( 2.1) 65 ( 3.7) 42 ( 2.7) 26 ( 3.6) 200 ( 3.5)1 258 ( 1.7) 276 ( 1.7) 237 ( 22) Nation 14 ( 2.4) 53 ( 5.0) 48 ( 4.2) 18 ( 2.8) 276 ( 4.1) 271 ( 3.1) 201 ( 3.0) 251 ( 13) Black State 3 ( 444 ( 1.9) 441 71 444 ( 5.8) ( 444) ( 444) 26 ( .44 ( 7.3) 441 Nation 14 ( 44 ( 3.4) 444) 53 225 ( 8.2) ( 4.3) 39 253 ( 7.1) ( 6.3) 27 ( 226 ( 6.9) 2.2)1 Hispanic State 9 ( 444 ( 4.2) 4441 57 04- ( 7.3) .44,) 35 st44. ( 6.1) ) 41 ( 444 ( 6.6) 444) Nation von OF COMMUNITY 45 ( 444 4.1) 441 66 246 ( 6.3) ( 4.4) 48 257 ( 5.9) ( 4.0)1 18 ( **4 ( 4.2) "4) Disadvantaged urban State 444 ( 441 03 281 (10.2) ( 4.9)r 46 270 (10.4) ( 5.8)1 10 ( 6.3) Nation 19 ( 444 9.4) 34 236 (11.4) ( 8.2)! 53 254. (11.8) ( 6.3)1 20 ( 444 ( 0.4) 444) F3dreene neat State 16 ( 6.3) 47 (10.1) 36 ( 6.7) 34 ( 8.2) 250 ( 4.3)1 250 ( 3.7)t 274 ( 3.6)1 238 ( 5.2)1 Nation 5 ( 444 ( 5.4) *44) 65 254 (10.9) ( 0.7)1 33 44.4 ( 8.1) ***) 42 (18.0) 241 ( 5.9)1 Other State 8 ( 2.2) 70 ( 3.3) 42 ( 3.1) 27 ( 4.2) 264 ( 5.1)1 257 ( 2.2) 276 ( 2.2) 235 ( 2.3) Nation 15 ( 2.9) 53 ( 52) 47 ( 4.3) 17 ( 3.3) 267 ( 4.7) 260 ( 3.4) 278 ( 2.8) 245 ( 4.4)1 The standard errors of the estimated statistics appear in parentheses. ft can be said with about 95 percent certainty that, for each population of irnerest, the value for the entire population is within ± 2 staivitrd 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). 1 106 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE AS I Teacheis' Reports on the Emphasis Given To (Mitin Ued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ______----------- IKO NAEP TRIAL STATE ASSESSMENT - Data Analysis, Statistics, and Probability Algabra and Fon:dons Heavy Emphasis Little or No Emphasis Heavy Emphasis I' Little or No Emphasis TOTAL ParadmININ and Percentage NW Pralidancy Pramtap Pronalway State 2.0) 85 ( SA) 41 2.6) 250 *7)1 2$6 ( 1.8) 275 1.7) Nation 14 2.2) 53 ( 4.4) 46 3A) 200( 43) 261 ( 2.0) 275 ( 2S) PARENTS EDUCATION noniraduats State 7 ( 2.8) 63 ( 5.1) 20 ( 4.5) 230 ( 3.3) 250 ( 4.0) Nation 0( 3.0) 53 ( 7.7) 2$ ( 5.2) 240 ( 8.2) ( NS graduals State II ( 3.0) 82 ( 4.2) 35 ( 29) 255 ( 39 ), 249 ( *1.7) 2fid ( 22) Nation 17 ( 3.7) 54 ( $A) 44 ( 4.8) 261 ( GA)I 247 ( 2.9) 265 ( 3,5) Soma college State ( 19) *** ( ***) 67 ( 3.9) 266 ( 3.1) 40 ( 3.1) 279 ( 3.5) Nation 13 ( 2.5) **4. 57 ( 51) 270 ( 3.7) 445 ( 4.8) 278 ( 3 n) Collage graduate State 7 ( 1.4) 88 ( 3.8) 274 ( 2.3) 58 ( 3.0, 284 ( 1.9) Nation 1$ ( 2.4) 53 ( 4.4) 50 ( 3A) 282 ( 4.5) 275 ( 3.8) 288 ( 3.0) GENDER M. State 9 ( 2.0) 88 ( 3.7) 39 ( 29) 282 ( 4.2)1 256( 2.1) 278 ( 2.0) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 275 ( 5.8) 260 ( SS) 276 ( 3.2) Female State ( 2.4) 63 ( 3.7) 44 ( 2.8) 258 ( 4.8)1 257 ( 2.0) 273 ( 2.1) Nation 18 ( 2.4) 53 ( 4.5) 48 ( 3.8) 203 ( 4.4) 262 ( 2.8) 274 ( 2.7) .Panaentais and Preeoldncy Zi2A 20 ( 3.0 243 ( 3.0 35 ( 59) 230 ( 3.0) 29 ( 0.9) ent. 30 ( 43) 24 ( 2.9) 23 ( 39) 239 ( 3.4) 25 ( 3.41) 242 ( 3.5) IT ( 3.1) 4PROr ( eon 17 ( 3.2) 243 ( 33) 1$ ( 2.4) 249 ( 4.0) 28 ( 3.7) 238 ( 2.6) 22 ( 3.6) 243 ( 3.0) 26 ( 3.8) 234 ( 2.8) 18 ( 29) 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 errois 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). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT 107 West Virginia TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1191110 NAEP TRW I Oet AN the Sesames 1 I Get Most of the 1 Oat Some or None of STATE ASSESSMENT Need Resources I Need the Swum= I Need I TOTAL State Nation RAVETHNICITY White State Nation Mack State Nation Hispanic State Nation TYPE OF COMMUNITY Disadvantaged urban State Nation &drone mai State Nation Other State Nation ( 47 f 4 288 ( 3.4 250 ( 11 11 ( 23 50 I 4.8 278 ( 270 ( 2.3) ( 4.1) 42 (9.3) ...) 1t5 4.2) 52 ( 8.6) 241 ( 5.311 242 ( 2.4) 8 ( 2.4) ..,) 58 ( 84),1 ( 23 ( 7.8) 44 ( 4.9) 248 ( 7211 250 ( 2.0) 23 (12.4) 52 (12.0) 257 ( 4.$)1 10 0.e) *01 40 251 (13.1) ( 5.4)1 ( 0.4) ***) 02 256 ( 05) ( 1.9)1 2 ( 2.0) 54 (10.4) 4.0 1111, 200 ( ta)4 7 ( 2.0) 42 ( 5.3) 207 ( 4.6)1 2$7 ( 2.0) 11 ( 2.9) 5$ ( 5.4) 265 ( 3.9)4 204 ( 2.1) 4S I SO (4.0) 207 f 33) IL.:1 ( 7.2) 230 ( 4.9) 37 ( 0.2)) 34 ( 7.7) 244 ( 3.0)4 25 259 4.0)1 50 14.5) 253 ( 55)1 37 ( 0.9) 255 ( 4.1)1 43 (10.3) 257 ( 5.0)1 50 ( 5.0) 253 ( 1.6) 31 ( 5.6) 203 ( 4.2) The standard errors of the estimated tunnies 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). 113 108 THE 1990 NAEP TRIAL STATE ASSESSMENT West rwg inia TABLE A9 I Teachers' Reports on the Availability of (continued) I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 4900 NAEP TRIAL I Get Ali the RIISOUress 1 I Get Most of the I Get Some or None of STATE ASSESSMENT Need Resources I Need the Resources I Need . .. TOTAL pannedalli and Pradialsnay ( 1.9) 205 ( 9.5)1 13 ( 2.4) 26$ ( 4.2) Padventage and Pralkiancy 47 ( 4.5) 257 ( 1,5) 58 ( 4.0) 25S ( 2.0) Paraananas and Pralialleacy 45 ( 2$3 ( 1.4 31 ( 4.2 261 ( 2.9) State Nation PARENTS EDUCATION 14S non-graduate State $ ( 1.9) 47 ( 5.9) 48 ( 5.8) 242 ( 2.2) 239 ( 22) Nation 8 ( 2.8) 64 ( 5.7) 3$ ( as) ( 244 ( 2.7) 243 ( MS graduate State 7 ( 2.1) 47.( 5.0) 4$ ( 4.0) 252 ( 3.6)1 250 ( 1.3) 249 ( 1.6) Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.9) 253 ( 4.8)1 256 ( 1.9) 25e ( 2.8) Some colfege State 8 ( 2.5) 4$ ( 5.3) 4$ ( 5.0) Mr* ( 265 ( 2.8) 200 ( 2.0) Nation 13 ( 3.3) 62 ( 4.3) 25 ( 4.1) IP** ( Iran 269 ( 2.5) 267 ( 3.8) Canoga graduate State 10 ( 2.5) 49 ( 4.7) 41 ( 4.5) 281 ( 4.1)1 271 ( 2.2) 268 ( 2.1) Nation 15 ( 2.9) $6 ( 4.9) 30 ( 6.1) 278 ( 5.4)1 276 ( 2.2) 273 ( 3.7) GENDER Male State ( 2.0) 46 ( 4.3) 45 ( 4.3) 265 ( 4.3)i 258 ( 1.0) 254 ( 2.0) Nation 13 ( 2.6) 67 ( 4.0) 30 ( 4.0) 264 ( 5.0)I 265 ( 2.6) 264 ( 3.3) Amato State ( 2.0) 48 ( 5.0) 45 ( 4.7) 265 ( 3.9)1 255 ( 1.6) 253 ( 1.6) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 288 ( 3.9) 264 ( 2.0) 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). 1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 West Virginia TABLE Al Oa I Teachers' Reports on the Frequency of Small i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week _ Less Than Once a Week Neve r TOTAL Penintage and Prollalianty Percentage and Pro Wang Pimentos* and Predidency State 39(34) 41 ( 3.5) 20 ( 2.5) 250 ( 2.0) 257 ( 1.3) 253 ( 2.7) Nation 50 ( 4.4) 43 ( 4.1) ( 2.0) 200 ( 2.2) 264 ( 2.3) 277 ( 5.4)I RACE/ETHNICITY *Ult. State 39 ( 3.5) 42 ( 3.5) 19 ( 2.5) 200 ( 2.0) 258 ( 1.3) 256 ( 2.4) Nation 49 ( 4.8) 43 ( 4.5) 8 ( 2.3) 265 ( 2.7) 271 ( 2.2) 285 ( 4.9)1 Black State 27 ( 8.7) 39 ( 7.4) ipe.1 34 ( .44 ( 9.1) .*) Nation 47 ( 0.1) 45 ( 7.0) 9 ( 4.1) 240 ( 3.4) 238 ( 4.0) *** ( HIspanic State 42 ( 7.2) 38 ( 6.3) 20 ( 5.8) Nation 84 ( 248 ( 7.2) 2.5) 32 247 ( 8.9) 8.3)! 4 ( *** ( 1.4) **) TYPE OF COMMUNITY Disadvantaged urban State 58 (11.4) 34 (12.7) 8 ( 4.1) 256 ( 5.3)1 264 ( 3.6)1 Nation 70 (11.7) 21 ( 9.0) 9 ( $.5) 248 ( 4.8)1 249 ( 8.7)1 ( *GO ) Extreme rural State 55 ( 8.3) 37 ( 7.9) ( 3.8) 258 ( 2.2)1 253 ( 3-5)! Nation 35 (14.6) 58 (17.1) 9 ( 98) 255 ( 5.5)1 258 ( 5.9)1 Other State 31 ( 3.6) 44 ( 4.3) 25 ( 3.6) 259 ( 2.9) 257 ( 1.6) 253 ( 3.0) Nation 50 ( 4.4) 44 ( 4.5) 6 ( 1.8) 260 ( 2.4) 264 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 115 110 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE AlOa I Teachers' Reports on the Frequency of Small (cmitinued) i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STAT SMENT E ASSES , At Lust Once a Week Lass Than Once a Weak New TOTAL Percentage and Picidancy Paruntalre and Pralkdanw Poseanfasa and Pultelanny State 39 ( 15) 41 ( 34) 20 ( 24) 25S ( 2.0) 267 ( 1.3) 253 ( 2.7) Nation 50 ( 44) 43 ( 4.1) ( 2.0) 200 ( 2.2) 204 ( 2.3) 277 ( 5.4)1 PARENTS' EDUCATIOR RS neniraduata State 30 ( 4.4) 44 ( 4.7) 20 ( 4.7) 241 ( 3.2) 244 ( 2.7) Nation 60 ( 244 ( 6.4) 12) 39 ( 244 ( 64) 3.2)1 1 ( +.4 ( 1.4) .41 NS graduate State 39 ( 42) 40 ( 3.7) 21 ( 3.0) 252 ( 2.0) 252 ( 1.5) 246 ( 2.6) Nation 49 ( 252 ( 4.8) 2.8) 45 ( 257 ( 5.1) 22) 6 (( 2.5) .41 Sem =New State 40 ( 4.4) 41 ( 4,3) 19 ( 32) 265 ( 3.0) 203 ( 1.8) 201 ( 3.6)f Nation 51 ( 5.2) 42 ( 5.1) college graduate 266 ( 3.4) 268 ( 32) ^1111 ( fit/ State 39 ( 3.7) 43 ( 4.4) 19 ( 3.4) 275 ( 2.5) 268 ( 2.1) 268 ( 3.7)1 Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 27$ ( 3.0) 288 ( 4.9)1 GENDER Mats State 40 ( 3.8) 40 ( 3.7) 20 ( 2.8) 259 ( 2.4) 258 ( 1.7) 253 ( 3.2) Nation 50 ( 44) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 265 ( 3.1) 27$ ( 5.3)1 Female State 37 ( 3.5) 43 ( 3.5) 20 ( 2.4) 257 ( 2.2) 250 ( 1.9) 252 ( 2.9) Nation SO ( 4.7) 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.0)f The standard errors of the eeimated statistics appear in parentheses. It can be said with about 9$ percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). IIG THE 1990 NAEP TRIAL STATE ASSESSMENT 111 West Virginia TABLE AlOb I Teachers' Reports on the Use of Mathematical 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT At Lust Once a Week Loss Thorn Once a Week Never TOTAL Percentage and Pro 'Money Percentage and Prolicdency Percentage and Proficiency State 19 ( 3.8) 88 ( 4.1) 12 ( 2.3) 254 ( 2.3) 254 ( tO) 270 ( 4.5) Nation 22 ( 3-7) CO ( 3.9) 0 ( 2.8) 254 ( 3.2) 283 ( 1.9) 282 ( 5.9)1 RACE/ETNgICITY White State 19 ( 3.6) 88 ( 4.1) 13 ( 2.3) 254 ( 2.1)1 258 ( 1.1) 273 ( 4.0) Nation 17 ( 4.0) 72 ( 4.2) 10 ( 2.7) 261 ( 1.8)! 289 ( 2.1) 285 ( 8.2)1 Slack State 8 ( 3.5) 4«.) 75 «H. ( 5.9) ( 17 ( 7.5) Nation 22 ( 5.9) 70 ( 6.3) 8 ( 3.9) 233 ( 5.9)1 241 ( 2.9) Hispanic State 83 ( SD) 6 ( 2.9) HI* ( ) 230 ( 3.9) Nation 39 247 ( 7.5) ( 3.8) 55 245 ( 7.3) ( 3.8)1 ( 2.6) «.) TYPE OF COMMUNITY Disadvantaged urban State 24 (12.9) 08 (12.3) 8 ( 4.6) 254 ( 6.1)1 257 ( 3.4)1 Nation 39 (11.4) 59 (12.1) 2 ( 1.8) 247 ( 7.5)1 253 ( 7.0)1 Extreme rural State 31 ( 9.6) 55 ( 9.7) 11 ( 5.4) 257 ( 3.2)1 253 ( 2.6)1 ( Nation 27 (14.9) 85 (14.61 8 ( 3.9) 262 ( 2.8)1 Other State 16 ( 3.8) 71 ( 4.9) 13 ( 2.8) 252 ( 3.4)1 254 ( 1.2) 269 ( 5.6)1 Nation 19 ( 4.3) 72 ( 5.0) 9 ( 3.3) 253 ( 3.9)1 263 ( 2.2) 281 ( 7 .1)! The standard errors of the estirnated 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). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE AIM I Teachers' Reports on the Use of Mathematical (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Rreticiency Percentage and Prollickktey Percentage and Proficiency State 19 ( 3.6) 66 ( 4.1) 12 ( 2.3) 254 ( 2.3) 254 ( 1.0) 270 ( 4.5) Nation 22 ( 3.7) 69 ( 3.9) ( 2.6) 254 ( 3.2) 263 ( 1.9) 262 ( 5.9)1 PARENTS EDUCATION HS non-graduate State 18 ( ( 4.0) .44) 73 ( 240 ( 4.7) 1.9) 9 ( IMF* ( 3.5) 41.111 Nation 25 ( ees. 5.6) e**) 66 ( 243 ( 7.2) 2.2) 9 ( 6.5) co44.) HS graduate State 23 ( 4.4) 67 ( 4.4) 10 ( 2.3) 250 ( 2.3)1 249 ( 1.3) 261 ( 4.1)1 Nation 23 ( 248 ( 4.8) 4.0)i 70 ( 25$ ( 5.3) 2.2) 7 ( 2.8) lite) Some college State 17 ( 3.4) 69 ( 5.3) 14 ( 3.5) 257 ( 3.2)1 281 ( 1.7) 1144 ( 11111 Nation 18 ( 4.0) 73 ( 4.3) 261 ( 4.4)1 269 ( 2.3) College graduate State 17 ( 3.7) 67 ( 4.8) 16 ( 3.0) 288 ( 32)1 288 ( 1.7) 283 ( 4.0)1 Nation 20 ( 19) 69 ( 3.7) 11 ( 2.5) 266 ( 3.5)1 274 ( 2.2) 297 ( 42)i GENDER Male State 19 ( 3.3) 68 ( 3.9) 13 ( 2.5) 56 ( 2.5) 255 ( 1.2) 273 ( 4.8)I Nation 22 ( 4.1) 09 ( 4.1) 8 ( 2.0) 255 ( 41) 285 ( 2.1) 287 ( 7.2)t Female State 20 ( 4.1) 69 ( 4.5) it ( 2.4) 252 ( 2.7)1 254 ( 1.4) 267 ( 4.9)1 Nation 21 ( 3.6) 69 ( 4.2) 10 ( 3.3) 254 ( 3.3) 282 ( 1.9) 278 ( 6.0)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *4'. Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 113 West Virginia TABLE Alla I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Weakor] Less TOTAL State Nation RA0E/aNNICITY INfitte State Nation Mack State Nation Itispank State Nation TYPE Of COMMUNITY Disadvantaged urban State Nation Extreme rural State Nation Other State Nation 12411.401 267 1.1 ant Prolielaray. Is( ( 3.1) 254 (to) 2110 linesii!mv let 1.11 8.1 114 ( 2.8) 25$ ( 1.0) 64(SJ 272 ( 1.9) 63 ( 4.5) see) 56 ( 76 244 ( 4.0) ( 4,4) 233 ( 17) Of ( 6.8) 251 ( 11) 74 (13.3) 257 ( 1.6)1 SS (10.7) 252 ( 4.7)1 95 ( 2.2) 256 ( 1.5)1 50 (10.6) 268 ( 4.0)1 83( 2.9) 257 ( 1.4) 63 ( 3.2) 267 ( 2.3) 18 ( 2.9) 25$ ( 23)1 28 ( 32) 204 ( 14) 17 ( 4.5) *6* ( ow* 41 ( 7.9) 233 ( 11 ( 4.3) 444 32 ( 240 ( 4.31 25 (13.3) 1/**) 31 (11.1) 243 ( 8.0)I 4 ( 22) ilt4n* ( 40 (10.0) 247 ( 74)1 ( 3.0) 25$ ( 2.3)1 31 ( 34) 255 ( 3.1) 0.2) elk/ **I 2.$ ) 284 ( 0 0.0) vim 2 ( 14) ( ( 1.0) ( 2.3) *** ( ***) 1 ( 01) ***) 4 ( 2.2) ( ( 0.4) ( et* ) 10 ( 7.3) fool 0 ( 02) ( 6 ( 1.9) 257 ( 5.8)1 11 ,111., The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certamty that, for each population of interest, the value for the entire population is within ± 2 standard errors of tne 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 Wcst Virginia TABLE Al la I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT Aknost Evan/ Day Saw* Timm a Weak About Once a Weak or Lass TOTAL Parantapt and Preedgacy per0111Maal and Prellolency Percentage end Prolldency State $5 ( 2.6) 15 ( 2.6) 0 ( 0.2) 257 ( 1.0) 257 ( 2.5) ( Nation 62 ( 3.4) $1 ( 3.1) ( 1.8) 267 ( 1.6) 264 ( 2.6) 260 ( 5.1)1 PARENTS' EDUCATION NS non-graduate State $4 ( 240 ( 3.9) 1.9) 15 ( Hht 3.9) **I 1 ( 0.7) «v.) Nation 67 ( 5.5) 27 ( 52) 6 ( 2.1) 245 ( 3.2) 00* ( NS graduate State $5 ( 2.7) 15 ( 2.7) ( 0.2) 251 ( 1.0) 250 ( 2.8) ( ***) Nation 61 ( 4.4) 34 ( 3.7) 257 ( 2.5) 250 ( 2.9) *** ( Soma college State 84 ( 2.9) 18 ( 2.9) ( 0.0) 264 ( 2.0) ( Nation 63 ( 4.2) 28 ( 17) ( 1.9) 272 ( 2.7) 258 ( 5.2) ( "") Cottage graduate State 85 ( 32) 14 ( 32) 0 ( 0.3) 271 ( 1.6) 270 ( 2.7)1 ( ***) Nation 61 ( 261 ( 4.0) 2.2) 31 ( 265 ( 3.9) 3-1) 8 ( *** ( 3.1) ***) GENDER M. State 84 ( 2.8) 18 ( 2.9) ( 0.3) 25$ ( 1.4) 257 ( 3.6) Nation 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 289 ( 2.1) 256 ( 3.8) 261 ( 6.7)1 Female State 86 ( 2.7) 14 ( 2.7) 255 ( 1.2) 257 ( 2.4)1 Nation 85 ( 3.6) 28 ( 3.3) 266 ( 1.8) 253 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I 2 0 THE 3990 NAEP TRIAL STATE ASSESSMENT 115 West Virginia TABLE Al ib I Teachers' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week About Once a Week Lass than Wieldy TOTAL. Peroontege Proficiency Percentage and Proficiency Perconiari end Proficiency State 29 ( 3.2) 30 ( 3.4) 32 ( 3.4) 253 ( 2.0) 255 ( 1.6) 262 ( 2.1) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 258 ( 2.3) 260 ( 2.3) 274 ( 2.7) RACE/ETHNICITY VA* State 29 ( 3.2) 39 ( 3.5) 32 ( 3.4) 254 ( 2.0) 257 ( 1.5) 264 ( 2.0) Nation 32 ( 4.1) 33 ( 3.5) 3$ ( 3.8) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Slack State 18 ( ( 5.3) 53 ( 8.3) *el 29 ( 7.1) Nation 45 ( 7.5) 31 ( 7.8) 23 ( 6.3) 232 ( 3.1)1 243 ( 2.3)1 248 ( 7.0)1 Hispanic State 40 ( 8.8) 34 ( 7.1) 11114 ( ) Nation 41 ( 7.7) 28 ( 5.3) 33 ( 7.5) 242 ( 32)1 244 ( 5.1)1 257 ( 2.3)1 TYPE OF COMMUNITY Ofeadvanteged urban State 17 ( 5.7) 51 (13.4) 32 (14.0) 260 ( 3.8)1 258 ( 3.9)1 Nation 50 (13.9) 22 (112) 28 (10.7) 237 2.4)1 258 ( 8.3)1 263 ( )1 Extreme rural State 23 ( $.0) 40 ( 9.0) 38 (10.3) 254 ( 3.5)1 254 ( 32)1 200 ( 2.6)1 Nation 27 (14.3) 49 (12.7) 24 (101) 258 ( 8.7)I 4.4P *4+ ) Other State 32 ( 4.0) 37 ( 3.7) 31 ( 3.9) 253 ( 2.4) 254 ( 22) 262 ( 3.0) Nation 30 ( 4.4) 35 ( 4.3) 36 ( 4.2) 258 ( 3.3) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 r' 316 THE 3990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE Al lb I Teachers' Reports on the Frequency of (wntinued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MOO 14AEP TRIAL At Least Several Tknes STATE ASSESSMENT a Week About Once a Week Less than Weeidyj t TOTAL Percentage and Pnplidency Percentage and Proficiency Peroentage and Proficiency State 29 ( 32) 30 ( 3.4) 32 ( 3.4) 253 ( 2.0) 255 ( 1.6) 282 ( 2.1) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 258 ( 2.3) 280 ( 2.3) 274 ( 2.7) PARENTS EDUCATION NS nen-graduate State 30 ( 5.5) 38 ( 5.7) 31 ( 5.3) 239 ( 2.7) 240 ( 2.8) 243 ( 3.7) Nation 35 f 84) 239 ( 3.5) 29 ( 8.3) 14.1 38 ( 250 ( 8.9) 4.531 IIS graduate State 28 ( 3.9) 41 ( 4.1) 31 ( 3.8) 248 ( 1.8) 250 ( 2.0) 25$ ( 1.3) Nation 35 ( 250 ( 5.3) 3.8) 3$ ( 250 ( 4.5) 2.7) 30 ( 263 ( 4.8) 3.4) Same college State 30 ( 3.2) 44 ( 3.8) 30 ( 3.3) 262 ( 3.8) 258 ( 2.4) 272 ( 3.2) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 280 ( 2.6) 286 ( 42) 278 ( 2.6) Wieser graduate State 29 ( 3.1) 36 ( 3.7) 34 ( 3.8) 267 ( 2.3) 269 ( 22) 275 ( 3.0) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 284 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Male State 29 ( 3.4) 38 ( 3$) 33 ( 3.6'1 253 ( 2.6) 256 ( 1.9) 283 ( 2.2) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3$) 257 ( 3.2) 281 ( 2.8) 275 ( 3.2) Renate State 28 ( 3.2) 40 ( 3.7) 32 ( 16) 253 ( 2.1) 254 ( 2.0) 280 ( 2.5) Nation 34 ( 4.1) 32 ( 31) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT 117 West Virginia TABLE Al2 I Students' Reports on the Frequency of Small I Group Work PERCOITAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1890 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Peroseisge Proliciancy $14woodage and Pirslidency perosoldid and Predialancy State 19 ( 1.9) 25 ( 58 (2.3) 254 ( 1.8) 257 ( 1.2 258 V) Nation 28 ( 45) 28 ( IA 44 2M 258 ( 2.7) 267 ( 2.0) 261 (1.13) RACE/ETHNIC TY White State 19 ( 1.9) 25 ( 1.5) 56 ( 22) 256 ( 1.7) 252 ( 1.0) 25b ( 13) Nation 27 ( 2.9) 29 ( 13) 44 ( 3.5) 268 ( 3.1) 272 ( 1.9) 270 ( 1.7) Sink State 19 ( 4.3) 044 ( 441 21 ( 4.3) 44, .4.4) 50 ( 5.8) .41 Nation 23 ( 3.0) 24 ( 3.6) 48 ( 4.7) 234 ( 3.0) 245 ( 4.6) 234 ( 3.1) Hispanic State 28 ( 5.1) 32 ( 4.4) 41 ( 4.7) ( ( Nation 37 ( 5.2) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) TYPE OF COMMUNITY Disadvantaged urban State 34 ( 8.8) 24 ( 6.1) 42 (10.5) 255 ( 3.5)1 281 I 33)1 258 ( 2.5$ Nation 31 ( 5.7) 20 ( 2.8) 49 ( 6.3) 245 ( 4.0)! 267 ( 8.4)1 245 ( 3.7p Extreme rural State 17 ( 4.6) 32 ( 3.9) 51 ( 6.1) 254 ( 3.81' 258 ( 22)1 255 ( 1.7)1 Nation 34 (10,8) 27 ( 3.8) 39 (11.8) 249 ( 5.2)1 264 ( 3.5)1 256 ( 6.2$ Other State 17 ( 1.9) 24 ( 1.5) 59 ( 2.4) 253 ( 2.7) 256 ( 1.6) 256 ( 1.3) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 264 ( 2.1) 262 ( 22) The stmdard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 118 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE Al2 I Students' Reports on the Frequency of Small (cmtinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT At Least Once a week Loss Than Once a Week Never 141=11,* TOTAL Ponsidags an. Prolkaacy State 19 ( 1,9) 254 1.4) Nation 2$ 2.5) 25$ 2.7) PARENTS' EDUCATION KS non-graduate State 19 ( 2.4) ( dhlh11) Nation 29 ( 4.5) 242 ( 3.4) Id graduate State 18 ( 2.2) 248 ( 2.4) Nation 28 ( 3.0) 251 ( 3.7) Sam college State 23 ( 2.9) 260 ( 2.9) Nation 27 ( 3.9) 265 ( 3.6) College graduate State 18 ( 22) 269 ( 3.4) Nation 2$ ( 3.0) 270 ( 2.7) GENDER Male State 20 ( 2.0) 255 ( 2.4) Nation 31 ( 2.9) 259 ( 3.3) F4111110 State 18 ( 1.9) 252 ( 2.1) Nation 26 ( 2.4) 25? ( 2.8) Parawarea and frallcianay Pecamisay ad Pnediary 25 50 2.3 257 12 250 1.1 2014 44 267 ( 2.0) 291 21 ( 2.6) 236 ( 3.3) 24429 3.1 28 2.0) 253 1.5) 28 1.8) 261 2.6) 25 ( 2.1) 263 ( 2.7) 27 ( 2.4) 268 ( 3.3) 26 ( 2.0) 271 ( 2.3) 28 ( 1.9) 273 ( 2.8) 24 ( 1.7) 257 ( 1.9) 28 ( 1.7) 26$ ( 2.8) 26 ( 1.7) 25? ( 1.7) 27 ( 1.8) 266 ( 1.7) 00 ( 3.2) 242 ( 2.1) 42 ( 4.5) 242 ( 2.7) 56 ( 2.6) 250 ( 1.0) 43 ( 3.4) 252 ( 1.7) 52 ( 3.3) 265 ( 2.3) 48 ( 3.4) 266 ( 2.1) 56 ( 2.8) 270 ( 1.7) ( 3.6) 27$ ( 2.2) 56 ( 2.4) 257 ( 1.5) 41 ( 2.9) 262 ( 1.8) S5 ( 2.5) 255 ( 1,1) 47 ( 3.2) 260 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the valui for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 West Virginia -111111 TABLE A13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRIAL. STATE ASSESSMENT At Least Ones a Week Lass Than Once Week Never _ TOTAL Parawdzie and Pro Adana Pargentaga and Pralkiency Pereartli and Prallakoncy State 24 ( 1.8) 31 ( 14) 45 ( 23) 24a ( 1.8) 200 ( 1.1) 257 ( 1.2) Nation 28 ( 1.8) 31 ( 12) 41 ( 2.2) 265 ( 28) 209 ( 1.5) 259 ( 1.6) RACE/ETHNICITY WM. State 23 ( 1.5) 31 ( 1.4) 48 ( 23) 251 ( 1.7) 261 ( 1.2) 259 ( 1.1) Nation 27 ( 1.9) 33 ( 1.6) 40 ( 2.5) 206 ( 2.6) 275 ( 1.6) 208 ( 1.8) Black State 19 ( 52) ( 36 ( 044 ( 53) ***) 48 ( 6.7) Nation 27 ( 3.3) 27 ( 3.2) 418 ( 4.5) 234 ( 3.7) 248 ( 4.5) 232 ( 2.8) Hispanic State 36 HI* ( 4.8) ( 25 ( ( 3.6) 041 Nation 38 ( 42) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) TYPE OF COMMUNITY Disadvantaged urban State 21 ( 3.5) 28 ( 4.1) 51 ( 5.0) 248 ( 4.2)1 26 ( 3.0)1 257 f 2.9)1 Nation 35 ( 6.6) 19 ( 2.1) 46 k 6.4) 249 ( 5.3)1 256 ( 5.7)1 246 ( 4.8)1 Extreme rural State 21 ( 4.6) 34 ( 3.8) 48 ( 5 8) 253 ( 3.9)1 257 ( 1.7)1 25$ ( 2.0)1 Nation 21 ( 3.1) .41 37 ( 262 ( 4.7) 4.7)1 43 ( 251 ( 5.0) 5.2)1 Other State 25 ( 2.1) 31 ( 1.6) 44 ( 2.6) 249 ( 1.9) 259 ( 1.5) 257 ( 1.5) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 258 ( 2.9) 270 ( 1.8) 260 ( 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 1-7 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1. 1,7:. 5 120 THE 1990 NAEP TRIA:. STATE ASSESSMENT West Virginia TABLE A13 I Students' Reports on the Use of Mathematics (continued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Lust Once a Week Less Than Ones a Week Never TOTAL Parcentag and Prat:fancy Percentage and Pralldency Parcantaga and Proildancy State 24 ( 31 ( 1.4) 45 ( 2.3) 24a ( 1.8) 260 ( 1.1) 257 ( 1.2) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.6) 269 ( 1.5) 259 ( 1.6) PARENTS' EDUCATION noniracluate State 22 ( 2.6) 29 ( 3.0) 50 ( 3.5) 238 ( 4.2) 246 ( 2.5) 239 ( 2.1) Nation 27 ( 4.2) 28 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) NS graduate State 24 ( 2.4) 33( 1.8) 43 ( 3.1) 244 ( 1.9) 255 ( 1.3) 250 ( 1.5) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some college State 22 ( 2.4) 31 ( 2.5) 47 ( 3.2) 253 ( 2.8) 266 ( 2.2) 266 ( 2.6) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.6) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) College graduate State 25 ( 2.7) 29 ( 2.1) 45 ( 2.6) 264 ( 2.5) 272 ( 2.1) 272 ( 1.7) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.6) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Mate State 25 ( 1.8) 31 ( 1.5) 44 ( 2.4) 249 ( 2.5) 261 ( 1.5) 258 ( 1.6) Nation 32 ( 2.0) 30 ( 1,5) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 23 ( 2.4) 30 ( 1.5) 47 ( 2.7) 250 ( 2.1) 25$ ( 1.5) 255 ( 1.4) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 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 of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 126 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 West Virginia TABLE A14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 !MEP TRIAL STATE ASSESSMENT Almost Every Day Several Tino s a Week t Abou Once a Week or Lass TOTAL flanionesse Pre&lam penostage 1141WCINdip and Prefickney State 1114 12) 1.0) 4 ( 2511 1.0) 247 1.9) 232 2.6 Nation 74 IA) 14 0.8) 12 ( 1.8 267 ( 1.2) 252 1.7) 242 ( 4.5) RACEIETHNICITY WM* State 135 ( 1.3) 11 ( 1.0) 4 ( 0.5) 240 ( 0.9) 249 ( 2.0) 232 ( 32) Nation 76 ( 2.5) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 2.2) 252 ( 5.1)1 Mack State 80 ( 5.8) 232 ( 4.3) 17 ( 5.5) ( eel 3 ( 1.9) 1141 Nation 71 ( 2.8) 15 ( 1.7) 44 ( 3.2) 240 ( 2.9) 232 ( 3.1) 223 ( 6.1)t Hispanic State 79 ( 3-7) 234 ( 3.9) 13 ( 3.0) 614 ***) ( 2.6) Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) TYPE OF COMMUNITY Disadvanialied urban State $1 ( 42) 259 ( 2.0)1 16 ( 3.5)1 3 ( 1.1) 4,4,) Nation ( 2.8) 15 ( 2.5) iS ( 22) 253 ( 3.7)1 243 ( 4.4)i 235 ( 8.5)1 Wren* rural State 86 ( 1.9) 5 ( 1.0) 258 ( 1.1)1 *44 ( **I *) II41* 441 Nation 66 (11.3) 263 ( 4.2)1 15 ( 3.8) 11.41, *el 17 ( 8.2) 4 ) Other State 84 ( 1.5) 12 ( 1.1) 4 ( 0.8) 258 ( 1.3) 245 ( 2.1) 233 ( 2.9) Nation 75 ( 2.2) 14 ( 1.0) 10 ( 11) 267 ( 1.5) 252 ( 2.6) 239 ( 4.3)! The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). le' s 122 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE A14 I Students' Reports on the Frequency of (continued) I Mathematics Textbook Use PERCENTAGE OF STMENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL. STATE ASSESSMENT Almost Every Day Several Tktms a Week About Once a Via* or Less TOTAL and Pralicioncy Parasalage Proficiency Paresodage and Prolickstcy State 84 ( 1.2) 12 ( 1.0) 4 ( 0.5) 258 ( 1.0) 247 ( 1.9) 232 ( 25) Nation 74 ( 1.9) 14 ( 0.6) 12 ( 1.6) 267 ( 1.2) 2$2 ( 1.7) 242 ( 45) PARENTS EDUCATION 1115 non-graduate State 77 ( 243 ( 3.3) 1.7) 18 ( 3.1) 4r**) 5 ( 1.3) .4e) Nation 64 ( 245 ( 3.4) 2.3) 18 ( 2.0) lb (( 3.4) KS graduate State 82 ( 1.6) 13 ( 1.1) S ( 0.8) 252 ( 0.9) 245 ( 2.3) itErf ( ) Nation 71 ( 3.6) 16 ( 1.8) 13 ( 2.6) 258 ( 1.6) 249 ( 3.2) 239 ( 3.4)1 Same collies State 68 ( 26$ ( 1.6) 1.6) ( 1.5) *s4) 4 ( 1.1) Nation 80 ( 270 ( 2.0) 1.6) ***) **age graduate State 90 ( 1.5) 8 ( 1.3) 2 ( 0.8) 272 ( 1.5) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 200 ( 2.6) 257 ( 6.4)1 GENDER M. State 83 ( 1.4) 12 ( 1.2) 5 ( 0.7) 259 ( 1.3) 248 ( 2.9) 232 ( 3.6) Nation 72 ( 2.4) 18 ( 1.2) 12 ( 2.1) 268 ( 1.6) 252 ( 2.5) 242 ( 6.1) Female State 85 ( 1.6) 11 ( 1.2) 257 ( 1.1) 24$ ( 22) Nation 76 ( 1.8) 13 ( 1.0) 11 ( 1.6) 265 ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 123 West Virginia TABLE A15 I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week a About Once a WW1: LOU Than Muddy TOTAL Peroentaps and Anita fancy Perandase and Prallafancy Parowdega and Prieldenay State 26(2.4) 30 ( 1.5) 43 ( 2A) 249 ( 1.5) 255 ( 14) 2e0 ( 1.3) Nation 38 ( 2.4) 25 ( 1.2) 37 ( 15) 253 ( 2.2) 261 ( 1.4) 272 ( 1.9) RACE/ETHNICITY White State 26 ( 2.5) 90 ( 1.4) 251 ( 1.4) 257 ( 1.3) 262 ( 1.2) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 262 ( 2..5) 26941.5) 277 ( 2.0) Black State 33 ( 5.8) 25 ( 4.9) *44 1.61 Nation 48 ( 3.8) 32 ( 2.7) 20 ( 3.1) 232 ( 4.3) 241 ( 2.9) 241 ( 4.4) Hispanic State 24 ( 5.4) 33 ( 52) IN4* 43 4 5.4) *ea Nation 44 ( 41) 25 ( 3.4) 32 ( 43) 238 ( 3.9) 247 ( 3.3) 248 ( 3.3) TYPE OF COMMUNITY Disadvantaged urlaan State 32 ( 6.1) 36 ( 4.7) 32 ( 4.1) 253 ( 5.0)1 258 ( 4.1)1 263 ( 2.6)1 Nation 37 ( 5.8) 23 ( 3.6) 41 ( 6.7) 240 ( 4.8)1 253 ( 4.1)1 255 ( 4.2)1 Extreme rural State 14 ( 3.1) 2$ ( 3.5) 58 ( 5.7) 245 ( 4.1)1 253 ( 2.1)1 280 ( 1.6)1 Nation 42 (10.1) 30 ( 4.4) 28 ( 7.5) 249 ( 4.0)1 256 ( 3.4)1 267 ( 7.3)? Other State 29 ( 2.9) 30 ( 1.8) 41 ( 2.9) 249 ( 1.6) 25$ ( 1.8) 280 ( 1.8) Nation 36 ( 2.9) 26 ( 1/) 38 ( 2.9) 252 3.0) 201 ( 2.4) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE A15 I Students' Reports on the Frequency of (continued) 1 Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week About Once a Week ., LASS Than %Wady TOTAL POMO. and Prolicioney Percentage and Pinckney Percentage and Proficiency State 20 ( 2.4) 30 ( 1.5) 43 ( 2.4) 243 ( 1.5) 255 ( 1.4) 260 ( 1.3) Nation 35 ( 2.4) 25 ( 42) 37 ( 2.5) 253 ( 2.2) 261 ( 1.4) 272 ( 1.9) PARENTS EDUCATION KS non-graduate State 33 ( 4.4) 27 ( 2.3) 40 ( 42) 236 ( 2.7) 240 ( 3.2) 245 ( 2.4) Nation 41 ( 4.5) 30 ( 22) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) HS graduate State 26 ( 3.0) 31 ( 2.0) 43 ( 3.1) 245 ( 1.8) 249 ( 1.7) 255 ( 1.4) Nation 40 ( 3.2) 29 ( 2.2) 32 ( 3.6) 247 ( 2.7) 256 ( 2.5) 262 ( 22) Some coHege State 22 ( 2.5) 32 ( 2.0) 48 ( 2.8) 256 ( 2.4) 264 ( 3.0) 207 ( 2.1) Nation 34 ( 3.4) 26 ( 2.2) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) College gracksate State 25 ( 2.5) 30 ( 22) 44 ( 2.9) 263 ( 2.2) 270 ( 2.4) 274 ( 2,2) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 273 ( 2.5) 285 ( 2.3) GENDER Male State 26 ( 2.2) 31 ( 1.7) 42 ( 2.7) 250 ( 2.2) 256 ( 1.8) 261 ( 1.7) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 263 ( 2.3) 274 ( 2.4) Female State 26 ( 2.9) 29 ( 1.8) 45 ( 2.5) 249 ( 1.4) 254 ( 2.0) 259 ( 1.5) Nation 37 ( 2.5) 25 ( 1.5) 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 pol.ulation is within ± 2 standard errors of the estimate for the sample. 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 West Virginia TABLE A18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 PIMP TRIAL STATE ASSESSMENT Own a Calculator Teacher Expains Calculator Use r Yes No Yes No TOTAL State Nation RACEIETHNICITY Percantage aad Pro *am* 08 ( 0.3) 258(0.9) 97 ( OA) *31 13) 90 ( 03) 258 ( 0.6) 103 ( 0.3) 270 ( 1.5) 98 ( 1.8) 233 ( 4.2) 93 ( 1.5) 237 ( 2.8) 94 ( 1.7) 233 ( 3.5) 92 ( 12) 245 ( 2.7) 98 ( 1.1) 259 ( 2.2)1 94 ( 1.2) 250 ( 3.5)1 97 ( 0.6) 256 ( 1.0)1 96 ( 1.3) 257 ( 3.9)1 98 ( 0.4) 2$6 ( 1.2) 97 ( 0.5) 283 ( 1.7) Parcantaga and Pradency 2 ( 03) 242 ( 3.9) 3 ( 04) 2$4 ( 3.8) 2 ( 0.3) 2 ( 0.3) 1144 *el 2 ( 1.8) 44. tr0-1 7 ( 1.5) ( *** ( ***) 8 ( 12) Irk* 14-1 2 ( 1.1) ( 8 ( 12) *** ( ***) 3 ( 0.8) ( ***) 4 ( 1.3) ( *441 2 ( 0.4) *** ( ***) 3 ( 0.5) 233 ( 5.4) Perasntaga and PsAlciancy 42 ( 1.9) 252 ( 1A) 49 ( 2.3) 25$ ( 1.7) 42 ( 1.9) 254 ( 1.3) 48 ( 2.8) 268 ( 1.8) 44 ( 5.7) ***) 53 ( 4.9) 235 ( 3.8) 48 ( 4.8) 83 ( 4.3) 243 ( 3.4) 48 ( 8.4) 255 ( 2.9)1 53 ( 7.5) 247 ( 4.1)1 43 ( 8.0) 255 ( 2.0)1 42 ( 8.7) 251 ( 4.8)1 42 ( 2.1) 251 ( 1.7) 50 ( 2.7) 25$ ( 2.1) Paramtaga and Proadency 58 ( 1.9) 25ti ( 1.0) St ( 2.3) 203 ( 1.5) 58 ( 1.9) 281 ( 1.0) 54 ( 2.0) 273 ( 1.8) 58 ( 5.7) 47 ( 4.9) 239 ( 2.7) 54 ( 4.8) v1 37 ( 4.3) 24$ ( 2.9) 54 ( 6.4) 260 ( 3.2)1 47 ( 7.,5) 251 ( 3.6)1 57 ( 8.0) 256 ( 1.8)1 58 ( 8.7) 281 ( 4.4)1 58 ( 2.1) 259 ( 1.2) 50 ( 2.7) 286 ( 2.0) VA*. State Nation Slack State Nation Hispanic State Nation TYPE OF COMMUNITY Ofsatbran lard urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated Statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability uf this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 126 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE Al8 Students' Reports on Whether They Own a (continued) Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 NAEP TRIAL STATE ASSESSMENT Ow a calculator Teacher Exp Mks Calculator Use Yes No Yes No 1MUMMI.MINNIMIMMINIMIIMMMIOPENININIIIMPINIMMEMPOIM...=011 TOTAL State Nation PARENTS' EDUCATION Vareambia atel *Whoa 96 ( 03) 293011 0.41:41 263 ( 13i 96 ( 1.3) 241 ( 1.8) 92 ( 1.8) 243 ( 2.0) 98 ( 0.5) 250 ( 0.8) 97 ( 0.8) 255 ( 1.5) 95 ( 0.6) 264 ( 1.5) 96 ( 0.9) 288 ( 1.8) 99 ( 0.4) 271 ( 1.3) 99 ( 0.2) 275 ( 1.8) 06 ( 0.5) 257 ( 1.3) 81(0.5) 284 ( 1.7) 96 ( 0.5) 255 ( 1.0) 97 ( 0.5) 262 ( 1.3) Penontige and Mildew 2 ( 0.3 242 ( 39 3( 0.41 234 ( 4 ( 1.3) 8 ( 1.8) ( "41 2 ( 0.5) 44..) 3 ( 0.8) *** ( 2 ( OA) 4 ( 0.9) ( e") ( 0.4) .44) ( 0.2) ( 2 0.5) 441 3 ( 0.5) 44. 3 ( 0.5).) Panuntaga and Pre Mem 42 ( 252 ( 1.4 49 j 2.31 258 1.7) 42 ( 3.4) 239 ( 2.5) 53 ( 4.6) 242 ( 2.9) 45 ( 22) 247 ( 1.4) 54 ( 3.0) 252 ( 1.9) 40 ( 2.9) 257 ( 2.4) 48 ( 3.2) 265 ( 2.4) 40 ( 2.8) 207 ( 2.1) 48 ( 2.6) 268 ( 22) 44 ( 2.3) 253 ( 2.0) 51 ( 2.6) 258 ( 2.1) 41 ( 2.0) 251 ( 1.5) 47 ( 2.5) 258 ( 1.7) Parcentaga and Proficiency 58 ( 25a ( 1.0 51 ( 2.3 2ee (14) 58 ( 3.4) 242 ( 2.2) 47 ( 4.6) 243 ( 2.5) 55 ( 2.2) 253 ( 1.1) 415 ( 3.0) 258 ( 2.0) 80 ( 2.9) 287 ( 1.8) 52 ( 32) 288 ( 22) 80 ( 2.8) 272 ( 1.6) 54 ( 2.6) 280 ( 1.9) 56 ( 2.3) 259 ( 1.4) 49 ( 2.6) 2es ( 2.1) 58 ( 2.0) 258 ( 1.2) 53 ( 2.5) 263 ( 1.6) NS naci-grackaate State Nation HS graduate State Nation Sem college State Nation College graduate State Nation GENDER Male State Nation State Nation IIrm The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 West Virginia TABLE A19 I Students' Reports on the Use of a Calculator 1 for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 NAEP TRIAL. STATE ASSESSMENT Problems in Class Doing Problems at Keno Taking Quizzes or Tests Almost Always Never Almost Always Never Almost Always , Never TOTAL. Per0 Mtn* and Pra Wang NrONItir, and Proficiency PINOWItip and Proficiency PereMap and Prodciency Percentage and Proficiency Percentage and Proficiency State 47 ( 1.1) 2$ ( 1.0) 24 ( 1.2) 19( 0.9) 22 ( 1.1) 36 ( 1.4) 249( 1.1) OS ( 1.3) 253 ( 1.3) 252 ( 1.11) 250( 1.9) 267 ( 1.2) Nation 4$ ( 1.5) 23 ( 1.9) 30 ( 1.3) 19( 0.9) 27 ( 1.4) 30 ( 2.0) 254( 1S) 272 ( 1.4) 261 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) RACE/ETHNICITY white State 40 ( 1.2) 29 ( 1.7) 24 ( 1.3) 18 ( 1.0) 22 ( 1.1) 37 ( 1.5) 250 ( 1.1) 207 ( 1.3) 255 ( 1.3) 264 ( 1.6) 251 ( 1.8) 268 ( 1.2) 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) 209 ( 2.3) 263 ( 2.8) 279 ( 1.2) Mack State 5$ ( 44, ( 0.3) es. ( 441 19 ( so, ( 8,0) 22 ( eee 5.7) 441 14 ( eee ( 4.9) 23 (( 5.9) 441 Nation ( $.2) 20 ( 3.0) 31 ( 2.9) 18 ( 1.9) 38 ( 3.3) 24 ( 3.1) 232 ( 2.4) 249 ( 4.0) 233 ( 3.3) 248 ( 5.5) 230 ( 3.6) 251 ( 4.1) Hispanic State 51 ( 5.5) 22 ( 4.1) 444 tee) 24 ( 3.3) 441 21 ( 4.5) 1144 *el 44, 1441 4.4e Iran ( ( ( ( ( ( Nation 51 ( 2.9) 16 ( 3.5) 26 ( 3.2) 29 ( 2.1) 26 ( 2.7) 22 ( 3.1) 239( 2.8) 252 ( 3.3)I 238 ( 4.6) 244 ( 3.1) 237 ( 3.2) 256 ( 4.2) TYPE OF COMMUNITY Disadvantaged urban State 52 ( 4.7) 26 ( 5.2) , 25 ( 3.8) 19 ( 3.2) 34 ( 5.5) 36 ( 4.2) 250 ( 2.9)1 271 ( 3.7)1 251 ( 3.1)1 254 ( 3.8)t 269 ( 4.0)1 Nation 52 ( 3.1) 22 ( 4.5) 30 ( 3.3) 24 ( 2.3) 27 ( 2.9) 27 ( 4.8) 241 ( 3.8)1 259 ( 5.4)1 246 ( 5.2)1 254 ( 4.6)1 240 ( 4.9)1 263 ( 5.0)1 Extreme rural State 4$ ( 2.3) 25 ( 2.5) 27 ( 2.8) 17 ( 2.0) 24 ( 2.4) 28 ( 2.8) 250 ( 1.8)1 262 ( 2.7)1 253 ( 2.3)1 255 ( 3.4)1 251 ( 4.0)1 263 ( 2.3)1 Nation 48 ( 246 ( 7.4) 4.3)1 29 ( 268 ( 6.5) 6.1)1 20 ( 2.5) 444 ( eee) 23 ( 263 ( 3.9) 4.4)1 24 ( .44 ( 0.0) 144) 37 ( 270 ( 8.3) 4.0)1 Other State 48 ( 1.3) 30 ( 2.0) 23 ( 1.3) 19 ( 1.1) 21 ( 1.1) 38 ( 1.7) 248 ( 1.3) 267 ( 1.7) 253 ( 1.7) 263 ( 2.2) 249 ( 2.5) 288 ( 1.5) Nation 48 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1.8) 29 ( 2.1) 2$4 ( 2.1) 272 ( 1.8) 283 ( 2.3) 263 ( 2.8) 253 ( 27) 275 ( 1.0) 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, Ihe value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). It) t 128 THE 1990 NAEP TRIAL STATE ASSESSMENT West Vitginia TABLE A19 I Students' Reports on the Use of a Calculator (continued) i for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE-MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT . Wwiting Plea 1.1111 in am Doing Probietns at Nom Taking Quizzes or Tests Almost Always _ Never Almost . Always ' Newer Ainnst Always Never . TOTAL Percentase and pcalkieney 47 1.1) 249 48 1.5 2$4. ( 1.5 Percantege end Madam 2e ( 1.5) XV ( 1.3) 23 ( 1.9) 272 ( 1.4) State Nation PARENTS' EDUCATION HS non-graduate State 50 ( 31) 23 ( 2.0) 238 ( 1.9) 252 ( 3.2) Nation 54 ( 3.3) 19 ( 3.8) 240 ( 2.3) "11 ( "") NS graduat State 51 ( 1.9) 25 ( 2.0) 246 ( 1.3) 280 ( 1.7) Nation 52 ( 2.5) 20 ( 2.4) 249 ( 1.4) 255 ( 2.7) Some college State 42 ( 2.3) 35 ( le) 257 ( 2.3) 271 ( 2.1) Nation 46 ( 2.8) 26 ( 2.8) 2511 ( 2.1) 272 ( 2.5) Collage graduate State 39 ( 1.7) 34 ( 2.5) 251 ( 2.2) 27$ ( 1.0) Nation 45 ( 1.9) 25 ( 2.4) 285 ( 1.7) 284 ( 1.8) GENDER Maio State 49 ( 1.4) 25 ( 1.6) 250 ( 1.5) 288 ( 2.1) Nation 50 ( 1.7) 20 ( 2.0) 255 ( 1.0) 275 ( 2.2) Female State 44 ( 1.5) 32 ( 2.3) 248 ( 1.4) 265 ( 1.7) Nation 45 ( 2.0) 26 ( 2.1) 252 ( 1.7) 289 ( 1.8) Iserceniade Porcenta Se Palate. fteelelie and and and and !cadency Ileadency Pradener 24 1.2 19 0.9) n 1.1 38 ( 253 1.3 262 250 1.9 257 i 1.2 X) 1.3 19 0.9 27 1.4 30 ( 2.0 261 1,8 263 1.8 253 24 274 ( 1.3) 23 ( 2.8) 20 ( 2.8) 22 ( 2.8 ) 28 ( 2.8 235 ( 3.3) 248 3.0) 235 ( 3.1 255 ( 2.9 26 ( 3.1) 22 2.0) 32 ( SS 24 ( 342 244 ( 3.$1 244 4.2) 237 ( 2.3 251 ( 43 28 ( 1.5) 18 ( 1.2) 24 ( 1.7) 32 1.8 240 ( 1.41) 255 ( 2.2) 246 ( 2.2) 259 15 29 ( 1.9) 18 ( 1$) 26 ( 1.11) 27 2.2 250 ( 2.4) 258 ( 2.4) 248 ( 24) XS ( 2.0) 24 ( 1.9) 20 ( 2.2) 21 ( 2.1) 44 ( 2.8) 259 ( 3.6) 270 ( 3.8) 200 ( 3.5) 273 ( 2.1) 28 ( 2.0) 20 ( 1.9) 26 ( 2.4) 95 ( ZS) 267 ( 3.0) 258 ( 3.2) 255 ( 3.8) 275 ( 2.0) 24 ( 1.7) 20 ( 1.5) 21 ( 1.6) 43 ( 2.4) 265 ( 2.8) 277 ( 2.5) 251 ( 3.1) 279 ( 1.8) 33 ( 2.0) 18 ( 14) 28 ( 1.8) 31 ( 2.7) 274 ( 2.2) 278 ( 2.8) 268 ( 2.5) 285 ( 2.0) 22 ( 1.4) 258 ( 2.2) 29 ( 1.5) 264 ( 2.8) 25 ( 1.5) 250 ( 1.9) 32 ( 1.8) 250 ( 1.7) 19 ( 1.2) 282 ( 2,5) 19 ( 13) 283 ( 2,5) 18 ( 1.4) 262 ( 2.2) 18 ( 1.2) 283 ( 2.1) 22 ( 1.4) 250 ( 2.4) 27 ( 1,5) 255 ( 3.0) 23 ( 1.5) 250 ( 2.5) 27 ( 1.8) 251 ( 2.4) 31 ( 14) 270 ( 1.9) 26( 2.1) 217 ( 1.0) 41 ( 1.8) 265 ( 1.4) 33 ( 2.1) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certctinty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 West Virginia TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - WOO NAEP TRIAL "Caksdater-Use" 'Calculator-Use" STATE ASSESSMENT NO Onto Other Grow TOTAL Parcentase and Pride Nagy Parastais gni Pralidency State 44 ( 1.1) Se ( 1.1) 263 ( 1.3) 2461 ( 1.0) Nation 42 ( 1.3) 55 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACE/ET1NICITY WMte State 44 ( 12) 36 ( 12) 264 ( 1.3) 251 ( 1.1) Netion 44 ( 1.4) 58 ( 1.4) 277 ( 1.7) 263 ( LT) Slack State 40 ( 5.5) 44* 1111 00 ( 5.5) ( Nation 37 ( 3.4) 63 ( 3.4) 243 ( 3.9) 231 ( 3.0) Hispank State 34 ( 5.5) *al 68 ( 5.5) 44) Nation 38 ( 42) 84 ( 42) 234 ( 4.6) 238 ( 3.0) TYPE OF COMMUNITY Disadvantaged urban State 46 ( 33) 54 ( 3.3) 264 ( 3.7)1 253 ( 2.7)1 Nation 38 ( 4.2) 82 ( 4.2) 262 ( 5.6)1 244 ( 3.9)1 Extrema rural State 47 ( 3.0) 53 ( :s.0) 263 ( 2.7)1 247 ( 2.1)1 Nation 39 ; 5.6) 61 ( 5.6) 269 ( 4.4)1 248 ( 4.3)! Other State 42 ( 1.3) 58 ( 13) 203 ( 1.6) 249 ( 1.2) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) The stand.rd 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 ASSESSMLNT West Vitginia TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAEP TRIAL "Calculator-Use" "Calculator-Use" STATE ASSESSMENT High Group Other Grow - TOTAL Ihramtige and prolldency Percentage and Proficiency State 44 ( 1.1) SS ( 1.1) 263 ( 1.3) 249 ( 1.0) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) PARENTS EDUCATION " non-grftduato State 40 ( 3.2) 60 ( 3.2) 247 ( 2.8) 235 ( 2.1) Nation 34 ( 3.3) 66 ( 3.3) 24$ ( 4.4) 242 ( 2.4) HS graduate State 38 ( 1.7) 62 ( 1.7) 256 ( 1.4) 245 ( 1.2) Nation 40 ( 2.2) 60 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some collage State 52 ( 2.9) 48 ( 2.9) 2es ( 2.7) 257 ( 2.2) Nation 4$ ( 2.2) 52 ( 2.2) 277 ( 2.6) 258 ( 2$) College graduate State 48 ( 1.9) 52 ( 1.9) 277 ( 2.1) 262 ( 2.1) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER Mate State 40 ( 1.5) 80 ( 1$) 266 ( 2.1) 249 ( 1.5) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 47 ( 2.0) 53 ( 2.0) 261 ( 1.4) 248 ( 1.8) Nation 45 ( 1.8) 55 ( 1.8) 2611 ( 1.7) 254 ( 1.3) wo. 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. 13C THE 1990 NAEP TRIAL STATE ASSESSMENT 131 West Virg:t TABLE A24 I Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MD NAEP TRIAL STATE ASSESSMENT . Zero to Two Types _ Three Types Four Types TOTAL Peroerdegs and Proficiency Noonday, and Prelidency Panlefflage and Prodding/ State 20 ( 1.0) 22 ( 1.1) 47 i 243 ( 1.5) 256 ( 1.2) 281 ( Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) RAIMETHNICITY White State 20 ( 1.0) 33 ( 1.1) 48 ( 1.4) 245 ( 1.5) 257 ( 1.3) 263 ( 1.1) Nation 18( 1.1) 29 ( 1.3) 56 ( 1.5) 251 ( 2.2) 258 ( 1.5) 276 ( 1.7) Mack State 33 ( gimp 5.8) **) 29 ( *4* ( 4.4) 38 ( 444 ( 4.5) Nation 31 ( 1.9) 38 ( 22) 33 ( 2.4) 232 ( 3.2) 233 ( 3.9) 245 ( 3.3) Hispanic State 26 ( 4.3) 33 ( 4.3) 42 ( 4.8) *4* ( 441 ( Nation 44 ( 3.0) 30 ( 2.4) 28 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) (YPE OF COMMUNITY Disadvantaged urban State 20 ( 1.8) 35 ( 255 ( 2.3) 2.8)1 45 ( 206 ( 2.1) 2.2)1 Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.8) 243 ( 2.9)1 247 ( 3.7)1 257 ( 4.9)1 Extreme rural State 21 ( 1.4) 33 ( 1.9) 47 ( 1.7) 243 ( 3.7)1 256 ( 1.8)1 200 ( 1.7)1 Nation 17 ( 44, 4.9) ***) 33 ( 253 ( 3.2) 4.3)1 50 ( 283 ( 5.1) 5.8)1 Other State 20 ( 1.3) 32 ( 1.4) 48 ( 1.7) 243 ( 1.7) 255 ( 1.8) 261 ( 1.6) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 1.5) 244 ( 2.6) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimate stativics appear in parentheses. It can be said with about 95 percent certainty that, for each population oi .nterest, 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 determinatk r.f the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). ,r) 7 132 THE 2990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE A24 I Students' Reports on Types of Reading (continued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10$0 NAER TRIAL STATE ASSESSMENT Zero to ft* Types Three Types FOUr Types TOTAL Pennntage and Pre*: fancy Percentage and Preectancy Percentage and Pretkiency State 20 ( 1.0) $2 ( 1.1) 47 ( 1.3) 243 ( 1.5) 2$G ( 1.2) 261 ( 1.2) Nation 21 ( 1.0) 30 ( 1.0) 43 ( 1.3) 244 ( 2.0) 25$ ( 1.7) 272 ( 1.5) PARENTS' EDUCATION NS non-graduate State 38 ( 2.7) 38 ( 3.0) 20 ( 25) 236 ( 2.6) 243 ( 2.5) 244 ( 3.1) Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 248 ( 3.3) NS graduate State 24 ( 1.8) 33 ( 1.7) 43 ( 2.0) 243 ( 2.1) 251 ( 1.5) 253 ( 1.5) Nation 26 ( 22) 33 ( 1.9) 40 ( 1.7) 246 ( 2.2) 253 ( 2.7) 280 ( 2.1) Some college State 14 ( 1.8) 33 ( 2.0) 53 ( 2.7) 249 ( 3.4) 264 ( 2.7) 266 ( 2.0) Nation 17 ( 1.5) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduate State 8 ( 12) ,.*) 29 ( 269 ( 2.3 63 ( 272 ( 2.3) 1.6) Nation ( 0.8) 28 ( 62 ( 2.0) 254 ( 2.8) 269 ( 24) 280 ( 1.8) GENDER Male State 20 ( 1.4) 34 ( 1.5) 47 ( 1.7) 243 ( 2.2) 257 ( 1.8) 262 ( 1.8) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 21) 273 ( 2.0) Female State 21 ( 1.3) 31 ( 1.4) 48 ( 1.6) 242 ( 1.7) 254 ( 1.5) 261 ( 1.3) Nation 22 ( 1.2) 29 ( 1.4) 49 ( 1.9) 244 ( 2.2) 256 ( 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). 138 THE 2990 NAEP TRIAL STATE ASSESSMENT 133 West Virginia TABLE A25 I Students' Reports on the Amount of Thne Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY r1990 NAEP TRIAL STATE ASSESSMENT One Hour or Lass Two Hours Three Hours Four to Five Howe tlix Heirs or More TOTAL f RACE/ETHNICITY Percentner and Prollioncy ( 0.9) 283 ( 2.5) 12 ( 0.8) 259 ( 2.2) ( 0.8) 284 ( 2.8) 13 ( 1.0) 275 ( 2.5) ( 2.2) ( 8 0.8) 440 ( *HI 8 ( 2.7) IMP* ( hal 14 ( 2.4) IMP* ( 11 ( 2.0) ( .44) ( 1.2) *4. ) ( 1.3) 14 ( 3.3) 9 ( 0.7) 282 ( 3.1) 12 ( 1.0) 288 ( 2.6) Pecoontage Pentantap and and Poneichncy Prnadiney 20 ( 0.8) 25 ( 0,1) 203 ( 1.8) 21 ( 0.9) 22 0.8 2001( 1.8) 205 1.7 21 ( 0.0 25 ( 0.8) 205 ( 1.6) 259 ( 1.4) 23 ( 1.2 24 ( 1.1) 275 ( 2.2 272 ( 1.9) 9 ( 3.2 19 ( 4.0) «H. ( ..**) 13 ( 1.7) 17 ( 2.1) 239 ( 7.0) 239 ( 5.0) 20 ( 3.7) 19 ( 3.5) *fir ( 11 0,61 20 ( 2.5) 19 ( 2.1) 245 ( 32) 242 ( 5.6) 10 ( 2.3) 22 ( LS) 263 ( 32)1 17 ( 3.1) 19 ( 2.1) 250 ( 4.0)1 255 ( 5.0)1 21 ( 1.9) 23 ( 1.6) 250 ( 3.0)1 258 ( 2.7)1 10 ( 2.6) 23 ( 2.0) 21 ( 1.1) 25 ( 01) 285 ( 1.8) 257 ( 21 ( 1.0) 23 ( 1.2) 289 ( 2.3) 2155 ( 2.1) Ilerantsin and Preficlancy 30 ( 0.0) 254 ( 1.0) 28 ( 1.1) 200 ( 13) 30 ( 0.9) 255 1.1) 2? 1.4) 28? 13) 34 ( 3.8) ismks 32 ( 1.8) 239 ( 4.0) 27 ( 4.0) 31 ( 3.1) 247 ( 3.5) 29 ( 1.7) 257 ( 3.6)1 34 ( 2.4) 251 ( 4.7)1 31 ( 22) 255 ( 2.2)1 28 ( 2.7) 256 ( 3.6)1 30 ( 1.0) 253 ( 1.4) 27 ( 12) 259 ( 2.2) Parandago and Proadancy 243 1 18 1.0 245 tT is ( 245 ( 12 ( 1.2 253 ( 33 ( 5.8) vim) 32 ( 2.2) 233 ( 25) 27 ( 4.7) 17 ( 1.7) 236 ( 39) 16 ( 2.3) *44 *al 20 ( $2) 238 ( 4.5)1 17 ( 1.3) 243 ( 28)1 19 ( 32) 15 ( 0.9) 241 ( 1.9) 17 ( 1.4) 248 ( 2.5) Wets State Nation Slack State Nation Hispanic State Nation TYPE OF COMMUNITY Disadvantaged urban State Nation Extreme rum! State Nation Other State Nation . The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean preficiency. " Sample size is insufricient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE A25 I Students' Reports on the Amount of Time Spent (continued) I Ws telling Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 MEP TRIAL STATE ASSESSMENT , _ O ne Hoar or Lass TWo HOUR Three NOM Fear to Five Hairs _ Six HOUR Or More TOTAL lisramitaga ant Praildency Parondape Ihr411441am elannalay and Prellakmay and Prallalancy Peramniaga and Madam State 4( 0.0) 20 04) 25 0.7) 90 ( 04) le ( 01) 203 ( 2.5 20 258 14) 254 ( 243 ( 1.6) Nation 12 ( 21 22 0.4) 28 ( 1.1 le ( 1.0) 204 ( 2.2 288 1.8 ( 1.7) 200 ( 1.7 245 ( 4.7) PARENTS' EDUCATIOD MS noryjniduate State 8 (( 1.4) 18 ( .. 2.1)*) 20 ( 4.,ko 2.5) *41 30 ( 243 ( 2.6) 24) 24 ( 233 ( 2.5) 3.3) Nation 12 ( de* ( 2.2) 20 ( imm 3.1) 21 ( 4414t ( 2.8) fin 28 ( 244 ( 24) 3.2) 20 ( .0.0* 2.4) 44.1 HS graduate State 9 ( 1.0) 18 ( 1.4) 25 ( 1A) 32 ( 1.8) 17 ( 1.3) 253 ( 2.9) 257 ( 2.0) 263 ( 2.1) 247 ( 1.7) 242 ( 2.0) Nation 8 ( 4.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 19 ( 1.6) 249 ( 4.7) 257 ( 2.8) 249 ( 3.2) 253 ( 2.5) 243 ( 3.0) Some college State 18 ( 2.0) 27 ( 2.2) 34 ( 1.9) 11 ( 1.4) ( 271 ( 3.9) 265 ( 3.4) 259 ( 2.1) Mkt ( *Pi Nation 10 ( 1.4) 25 ( 2.4) 23 ( 2.6) 28 ( 2.2) 14 ( 1.5) 275 ( 2.7) 269 ( 3.5) 267 ( 2.5) 242 ( 3.4) College graduate State 11 ( 1.3) 26 ( 1.7) 26 ( 14) 26 ( 1.9) 12 ( 1.3) 280 ( 3.6) 276 ( 2.3) 271 ( 2.0) 268 ( 2.2) 251 ( 3.3) Nation 17 ( 1,3) 22 ( 1.6) 23 ( 1.1) 2S ( 1.5) 12 ( 1.1) 282 ( 2.6) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255( 3.2) GENDER Maki State 8 ( 0.7) 20 ( 1.1) 24 ( 1.4) 32 ( 1.2) 16 ( 1.0) 263 ( 3.2) 266 ( 2$) 251 ( 2.3) 256 ( 1$) 244 ( 1.8) Nation 11 ( 0.9) 22 ( 1.2) 22 ( '1.0) 25 ( 1.3) 17 ( 1.5) 269 ( 3.3) 267 ( 2.6) 267 ( 2.2) 262 ( 2.1) 248 ( 2$) Female State 10 ( 1.0) 21 ( 1.2) 25 ( 0.9) 28 ( 1.3) 15 ( 1.1) 262 ( 2.8) 261 ( 1.9) 259 ( 2.0) 251 ( 1.4) 241 ( 2.1) Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 1.6) 15 ( 1.2) 269 ( 2.8) 209 ( 2.2) 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 West Virginia TABLE A26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT NW la Om or Two Days , Mrs* Da Its or More TOTAL %rootage and Prancioncy Percentage and Proadency Parcaidage and Prafidancy State 40 ( 1.2) 35 ( 0.9) 25 ( 1.0) 260 ( 12) 258 ( 1.0) 246 ( 1.6) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 285 ( 1.8) 208 ( 1.5) 250 ( 1.9) RACE/ETHNICITY White State 41 ( 1.2) 35 ( 1.0) 24 ( 1.1) 261 ( 1.1) 259 ( 1.0) 249 ( 1.7) Nation 43 ( 12) 34 ( 1.2) 23 ( 1,2) 273 ( 1.8) 272 ( 1.7) 258 ( 2.1) Slack State 47 ( ( 6.2) 25 ( 4.9) ***) 28 ( 5.3) Nation 56 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 2$ ( 4.8) 36 ( 4.4) 11.4 ( *44 ) - ) Nation 41 ( 3.3) 32 ( 2 2) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) TYPE CIF COMMUNITY Disadvantaged unaan State 39 ( 3.1) 37 ( 2.5) 24 ( 2.8) 262 ( 1.9)i 257 ( 2.8)1 253 ( 5.3)" Nation 42 ( 3.7) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 256 ( 42)! 218 ( 6.3)1 Extreme neat State 37 ( 3.2) 41 ( 1.8) 22 ( 2.5) 259 ( 2.2)1 257 ( 1$)1 246 ( 2.8)1 Nation 43 ( 257 ( 4.4) 4.1)1 32 ( 284 ( 42) 5.8)1 25 ( 3.9) ** Other State 42 ( 1.4) 33 ( 1.1) 26 ( 1.3) 260 ( 1$) 258 ( 1.3) 246 ( 2.0) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 285 ( 2.2) 286 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate F.Izterrnination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). Fi 136 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE A26 I Students' Reports on the Number of Days of (continued) i School Mined PERCENTAGE OF STJDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL None One or Two Days Three Days or Mors STATE ASSESSMENT TOTAL Parcentaile and Prelidency Perconfeas and Meadow Percentege and Proficiency State 40 ( 1.2) 35 ( 0.0) 25 ( 1.0) 260 ( 1.2) 250 ( 1.0) 240 ( 1.6) Nation 45 ( ass ( 4.1) 1.8) 32 ( 203 ( 0.9) *1.5) 23 ( 250 ( 1.1) 1.9) PARENTS EDUCATION NS non-graduat State 29 ( 2.0) 35 ( 2.9) 36 ( 2.7) 247 ( 3.0) 241 ( 2.4) 235 ( 2.1) Nation 36 ( 3.2) 26 ( 3.1) 38 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) FIS graduate State 41 ( 2.0) 33 ( 1.4) 25 ( 1.8) 252 ( 1.6) 253 ( 1.3) 243 ( 1.9) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.6) 249 ( 2.4) Some toiler State 44 ( 2.4) 38 ( 2.5) 20 ( 2.1) 269 ( 2.6) 261 ( 2.3) 255 ( 3.3) Nation 40 ( 1.8) 37 ( 1.6) 23 ( 1.6) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) College graduate State 44 ( 1.9) 37 ( 2.0) 20 ( 2.0) 272 ( 1.9) 271 ( 1.9) 263 ( 3.6) Nation 51 ( 1.6) 33 ( 1.2) 10 ( 1.3) 25 ( 2.1) 277 ( 1.7) 265 ( 3.1) GENDER Male State 41 ( 1.0) 34 ( 1.2) 25 ( 1.3) 200 ( 1.9) 258 ( 1.4) 248 ( 2.3) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 1.4) 266 ( 2.0) NT ( 2.1) 250 ( 2.6) Female State 40 ( 1.5) 35 ( 1.3) 25 ( 1.4) 200 ( 1.6) 257 ( 1.5) 244 1 1.7) Nation 43 ( 1A) 32 ( 1.1) 25 ( 1.3) 264 ( 2.3) 266 ( 1.7) 250 ( 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. 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 West Virginia TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , MO NAEP TRIAL STATE ASSESSMENT Wm* *Om AMPS Undecided, DIsagrea, 1 $im* Magee 1 TOTAL State Nation RACE/ETHNICITY Mita State Nation Mack State Nation MI:panic State Nation TYPE OF COMMUNITY Disadvantaged urban State Nation Wrenn nral State Nation Other State Nation 29 ( 12 IS( 12 27 ( 131 271( 1.9 24 ( 1.3) 246 ( 12) 2. ( 1.9) 279 ( 2.0) 22 ( 4.9) di* ( 32 ( 2.5) 247 ( 4.1) 29 ( 4.9) OMR ( «in 24 ( 2.5) 257 ( 5.5) 27 ( 2.8) 288 ( 44)1 26 ( 2.9) 280 ( 5.6)! 26 ( 3.3) 263 ( 2.8)1 34 ( 2.8) 270 ( 3.9)1 29 ( 15) 207 ( 15) 27 ( 14) 271 ( 2.4) and Prollaism 50 ( 1.0) 1.0 262 1.7 51 ( 11) 257 ( tO) 4S ( 1.3) old Pralickacv 22 ( 0,S 245 ( 1.4} 24 ( 251 ( 1.8) 22 ( 1.0) 247 ( 1.5) 26(1.5) 272 ( t8) 55 ( 5.2) Mk* ( 114.1 257 ( 2.0) 23 ( 6.5) 00. ( Mr* 52 ( 23) ie ( 1.91 233 ( 3.3) 227 ( 4.2 411 (( 4-9) 23 (( 4.1) 48 ( 2.6) 28 ( 2.1) 244 ( 2.2) 238 ( 3.8) 50 ( 2.8) 23 ( 2.1) 250 ( 2.7)1 245 ( 2.9)1 48 ( 2.9) 24 ( 3.2) 242 ( 4.8)1 240 ( 4.5)1 51 ( 2.8) 23 ( 2.1) 256 ( 1.2)1 248 ( 3.7)1 49 ( 2.2) 17 ( 14) 252 ( 4.1)1 411111/ ( 49 ( 1.2) 22 ( 1.1) 254 ( 1.3) 244 ( 1.7) 48 ( 1.2) 25 ( 1.4) 263 ( 2.2) 250 ( 1.2) 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. '1** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 ti 138 THE 1990 NAEP TRIAL STATE ASSESSMENT West Virginia TABLE A27 Students' Perceptions of Mathematics (continued) PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT A. &Toni Illf fire Avon Undecided, Disagree, Spingly Disarm" TOTAL Percentage and Proficiency Percent". and Prellatency State 26 ( 1.2) 50 ( 10) 208 ( 1.2) 255 ( tO) Nation 27 ( 1.3) 49 ( 1.0) 271 ( 1.9) 202 ( 1.7) PARENTS' EDUCATKIN KS non-graduate State 23 ( 3.0) 51 ( 2.8) 249 ( 3.8) 242 ( 1.8) Nation 20 ( .10%. 2.0) 11111 50 ( 243 ( 3.3) 2.8) NS graduate State 28 ( 1.8) 53 ( 1.5) 259 ( 1.7) 250 ( 1.3) Nation 27 ( 2.1) 47 ( 2.3) 202 ( 2.7) 255 ( 2.3) Sante college State 30 ( 2.7) 47 ( 2.1) 277 ( 3.2) 259 ( 1.9) Nation 28 ( 2.5) 47 ( 2.4) 274 ( 3.1) 207 ( 1.9) College graduat State 33 ( 1.7) ( 1.8) 270 ( 2.0) 270 ( 2.0) Nation 30 ( 2.3) 51 ( 1.8) 280 ( 2.4) 274 ( 22) GENDER Mal State 2$ ( 1.3) 51 ( 1.3) 267 ( 1.9) 258 ( 1.0) Nation 29 ( 1.5) 48 ( 12) 273 ( 2.3) 203 ( 2.0) Female State 28 ( 1.7) 49 ( 14) 208 ( 1.5) 254 ( 1.3) Nation 28 ( 1.7) 50 ( 1.7) 209 ( 2.1) 202 ( 12) PliaNdele and Prellidenay 22 ( 0.8) 245 ( 1A) 24 ( 1.2) 251 ( VI) 2. ( 2.8) 230 ( 3.1) 90 ( 3.8) 23$ ( 4.3) 21 1.3) 241 ( 14) 26 ( 2.0) 246 ( 2.4) 23 ( 2.4) 252 ( 2.4) 25 ( 1.8) 258 ( 3.2) 19 ( 1.4) 261 ( 2.5) 19 ( 1.8) 280 ( 2.5) 21 ( 1.1) 248 ( 2.1) 24 ( 1.4) 251 ( 2.4) 23 ( 1.0) 244 ( 1.7) 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. *** Sample size is thsuffictent to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Stathtics (NCES), Educational Testing Service (Ers), Westat, and National Computer Systems (NCS). The peograir benefitted from the contributions of hundreds of individuals at the state and local levels Governors, Chief State School Officers, State and District Teat Directors, State Coordinators, and &strict administrators who tirelessly provided their wisdom, experience, and hard work. Finally, and most importantly, NAEP is grateful to the students and school staff who partidpated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (CCSSO) for its considerable contautions to the program, especially its managesnent of the National Assessment Plannb3g Project. That project resulted in the mathematics framework and objectives for the asseument and recommendations about reporting the results of the program. In particular, we note the significant contributions of Ramsay Selden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering. Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through DiCES, in the Office of Educational Research and Improvement of the US. Department of Educatkm. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, 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 Foam. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people -- from school districts, colleges and universities, and State Education Agencies worked tireleuly to help Ers staff develop the assessment and a framework for interpreting the results. Under the NAEP contract to EIS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mazzeo, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koala, state service& Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distaution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lyn') Zaback. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analysts. They Wel' e assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Korner wrote the text for the report. Kent Ashworth was responsible for coordinating the cover design and final printing of this report. Special thanks are also due to many individuals for their invaluable assistance in reviewing the reports, especially the editors who improved the text and the analysts who checked the data. I c;