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DOCUMENT RESUME ED 330 550 SE 052 060 T:TLE The State of Mathematics Achievement in California: The Trial State Assessment at Grade Eight. TNSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational A.,essment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS *California; National Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAZE') ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the MAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In California, 2,424 students in 98 public schools were assessed. This report describes the mathematics proficiency of California eighth-graders, compares their overall performance to students in the West region of the United States and the nation (using data from the NAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, parents' educational level, and gender). To provide a context for the assessment data, participating students, their mathematics teachers, and principals completed questionnaires which focused on: instructional content (curriculum coverage, amount of homework); delivery of math instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, California students had an averagP proficiency of 256 compared to 261 nationwide. Many fewer students (California-11%; U.S.-I2%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE If A II: in CALIFORNIA The Trial State Assesuoment at Grade Eight Crri AvAILABLE U S DEPARTMENT OP EDUCATION OtI, e. vl I U., abona, Resra,, n av-,1 ,r,c,formen1 If IOATIONAL RE SOURCES INEORMATiON CE NTE R IF R,C) Tnok ejoi ument nas open repiodut ed as ,ectn.tncl Nom Mr ON,F.Of, fl, Or9an,z at,on Cii,Vriating .t M,nor ( hanges navy tvatat (71a OP tt ,,,(1,0.1. rftOroClui 1101 Liulilli, Pomts vw* or op,,,.als. tt,1% MIX 6.1 rnent ostiroy op,pyro,1 nffir OE PI, Do5.1411, or polo Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD, the National Assessment of Educational Progress tNAEP). is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 19b9. assessments have been conducted periodically in reading. mathematics. science, writing. history/geography, and other fields. By making objective information on student performance available to policymakers at the national, state, and local levels. NAEP is an integral part of our nation's evaluation of the condition and progress of edueation. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics. the U.S. Department of Education. The Commissioner of Education Statistics is responsible. by law, for carrying out the NAEP project through competitive awards to qualified organizations. NAEP reports directly to the Commissioner, who is also responsible fin providing continuing reviews, including validation studies and solicitation of public eonunent. on NAEP's conduct and usefulness. In 198N. Congress created the National Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The board is responsible for selecting the subject areas to be assessed, which may include adding to those specified by Congress; identifying appropriaic aehievement goals for each age and grade; developing assessment objectives; developing test specifications; designing the assessment methodology: developing guidelines and standards for data analysis and for reporting and disseminating results: developing standards and procedures for interstate, regional, and national comparisons; improving the form and use of the National Assessment; and ensuring that all items selected for use in the National Assessment are free from racial, cultural, gender, or regional bias. The National Assessment Governing Etoerd Richard A. Boyd, Chairman Executive Director Martha Holden Jennings Foundation Cleveland. Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga AVarren Saratoga Springs. New York Francie Alexander Associate Superintendent California Department of Education Sarramento. California David P. Battini Hif,h School History Teacher Cairo-Durham High School Cairo. New York Parris C. Battle Teacher Horace Mann Elementary School Miami. Florida Mary R. Blanton Attorney Cromwell. Porter. Blanton & Blanton Salisbury, North Carolina Boyd W. BoehLie Attorney Gauss. Klyn. & Hoch lje Pella. Iowa Linda R. Bryant Teacher Greenway Middle School Teacher Center Pittsburgh. Pennsylvania Honorable Michael N. Castle Governor of Delaware Carvel State Office Building Wilmington. Delaware Honorable Naomi K. Cohen State of' Connecticut House of Representatives Legislative Office Building Hartford, Connecticut Chester E. Finn. Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.C. Michael S. Clode Wyoming State Board of Education Sarator. Wyoming Christine Johmson Principal Abraham Lincoln Iligh School Denver. Colorado John '.indley Pnncipal Soinh Colby Elementary School Port Orchard. Washington Carl 3. Moser Director of Schools The Lutheran Church Missoun Synod International Center St I mins. Missoun 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 Conunissioner of Education State Department of Education Denver. Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington. DC. Honorable Richard W. Riley Attorney Nelson. Mullins. Riley and Scarborough Columbia, South Carolina Thomas Topazes Attorney Lass Offices of Frank kogoiwnski Coronado. California Herbert J. Walberg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and Improvement (Ex-)fficio, U S. Department of Education Washington. D.C. Roy Tru:iy Executive Director, NAGB Washington. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS ,....... The STME of Mathematics Achievement in CALIFORNIA The Trial State Assessment at Grade Eight Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. anon Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Congreu Catalog Card Number: 91-61478 ISBN: 048685-14-9 The work upon which this publication is based was performed for the National Caner for EducationStatistics, Office of Educational Research and Improvement, by Educational Mining Service. Educational 'Mating Service is an equal oppommity/affirmative action employer. Ecivicemiorsal Tesiins Service, ETS, and are mginered trademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY 1 INTRODI1CTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of California 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematks Are Eighth-Grade Students in California Public Schools? 17 Chapter 1. Students' Mathematics Performance 1S Levels of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race/ 'Ethnicity 24 Type of Community 27 Parents Eduealion Level 29 Gender 31 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 0 Ill PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics" 39 Cuniculum 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 Da> 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 7 IV THE 1990 NAEP TRIAL STATE ASSESSMENT California THE NATION'S REPORT CARO EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included - tb; the first time in the project's history -- a provision authorizing voluntary state-by-f tale assessments on a trial basis, in addition to continuing its primary mission, the nation;4 assessments that NAEP has conducted since its inception. 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 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 pei ionnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT 1 California In California, 98 public schools participated in the assessment. The weighted school participation rate was 94 percent, which means that all of the eighth-grade students in this sample of schools were representative of 94 percent of the eighth-grade public-school students in California. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 9 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 7 percent had an Individualized Education Plan (1EP). 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 Engaish Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 5 percent and 4 percent of the population, respectively. In total, 2,424 eighth-grade California public-school students were assessed. The weighted student participation rate was 93 percent. This means that the sample of students who took part in the assessment was representative of 93 percent of the eligible eighth-grade public-school student population in California. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from California on the NAEP mathematics scale is 256. This proficiency is lower than that of students across thc nation (261). Average proficiency on the NAFP scale provides a global view of eighth waders' mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students' proficiency in geater detail, NAIT used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAIT scale. 2 'ME 1990 NAEP TRIAL SIMI ASSESSMENT wMa....1111Mmr. California In California, 95 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 California (11 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in California performed lower than students in the nation in Numbers and Operations and Data Analysis, Statistics, and Probability. Students in California performed comparably to students in th nation in Measurement, Geometry, and Algebra and Functions. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the California eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In California: White students had higher average mathematics proficiency than did Black or Hispanic students and about the same mathematics proficiency as did Asian students. Further, a greater percentage of White students than Black or Hispanic students and about the same percentage of White as Asian students attained level 300. The results by type of community indicate that the average mathematics performance of the California students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban area:, or areas classified as "other". In California, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 32 points higher than that of students whose parents did not graduate from high school. The results by gender show that there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in California. In addition, there was no difference between the percentages of males and females in California who attained level 300. Compared to the national results, females in California performed lower than females across the country; males in California performed lower than males across the country. THE 1990 NAEP TRIAL STATE ASSESSMENT 3 Cahfornia A Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational contexi for understanding information about student achievement. Some of the salient results for the public-school students in California are as follows: More than half of the students in California (69 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 California, 91 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 California were taking eighth-grade mathematics (59 percent) than were taking a course in pre-algebra or algebra (36 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 California spent 30 minutes doing mathematics homework each day; according to the students, most of them spent 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. Students whose teachers placed heavy instructional emphasis on Algebra and Fuactions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT California In California, 14 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 34 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 pement and 31 percent, respectively. In California, 19 percent of the students never used a calculator to work problems in class, while 46 percent almost always did. ln California, 36 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (76 percent) had teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by teachers who well certified at the highest level available in their states. Students in California who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of these materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. Some of the eighth-grade public-school students in California (16 percent) watched one hour or less of television each day; 11 percent watched six hours or more. Average mathematics proficiency was higher for students who spent one hour or less watching television than for students who watched television six hours or more each day. THE 1990 NAEP TRIAL STATE ASSESSMENT 5 California THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAFP) 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 , THE 1990 NAEP TRIAL STATE ASSESSMENT 7 California This report describes th performance of the eighth-grade public-school students in California 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 California. Part One describes the mathematics performance of the eighth-grade public-school students in California, the West region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in California, the West region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its int-eption: The National Assessment shall develop a trial mathematics assessment swvey instrument for the eighth grade and shall conduct a demonstration of the butrumnt in 1990 in States which wish to participate, with the putpose of determining whether such an assessment yields valid, reliable State representative data. (Section 406 (1)(2)(0(1) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(0)) As a result of the legislation, the 1990 N AEP program included a Trial State Assessment Program in eighth-gade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to rtpresent 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 of quality and uniformity across sessions. 8 THE 1990 NAEP TRIAL. STATE ASSESSMENT California The Trial State Assessment was based on a set of mathematics objectives newly developed for the program ,..nd patterned after the consensus process described in Public Law 98-511, Stztion 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 time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An 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 California, in the West region, and for the nation. Results also are provided for groups of students defmed 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 California 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 renal and national results from the 1990 national NAEP program was necessary because the voluntary nature of the Trial State Assessment Program did not guaramee representative national or regional results, since not every state participated in the program. National Council of Teachers of Mathematics, Curriculum and Evaluaaon Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT * 9 California RACE/ETHNICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Procedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for California. TYPE OF COMMUNITY Results are provided for four mutually exclusive community types -- advantaged urban, disadvantaged urban, extreme rural, and other -- as defined below: Advantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportic n 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 live outsidr; metropolitan statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or gyaduated college. The response indicating the higher level of education was selected for reporting. 10 THE 1990 NAEP TRIAL STATE ASSESSMENT California 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 :n 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 Vir&ia 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 regioa. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURE 1 I Regions of the Country NORTHEAST SOUTHEAST CENTRAL. WEST Connecticut Alabama Illinois Alaska Delaware Arkansar Indiana Arizona District of Columbia Florida Iowa California Maine Georgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana New Jersey North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohio Oklahoma Rhode island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming THE 1990 NAEP TRI ILL STATE ASSESSMENT 11 Cahfornia Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristici 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 -- ratherthan 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 errorof the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistica4 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, thc confidence interval included zero, and thus no difference could be assumed between the groups. When three or more groups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendix. 12 THE 1990 NAEP TRIAL STATE ASSESSMENT California It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are repotted 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 calculate4 to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT 13 California Profile of California EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in California, the West 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 California Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS 1960 NAEP TRIAL STATE ASSESSMENT California West Nation DEMOGRAPHIC SUBGROUPS RacelEthnicity Percentage Percentage Percentage White 45 ( 1.8) 63 ( 1.9) 70 1 0.5) Black 7 ( 0.8) 7 ( 2.0) 16 ( 0.3) Hispanic 35 ( 1.4) 21 ( 1.5) 10 0.4) Asian 12 ( 1.1) 4 ( 1.3) 2 ( 0.5) American Indian 2 ( 0.4) 4 ( 2.3) 2 ( 0.7) Type of Commonty Advantaged urban 16 ( 4.5) 14 ( 8.5) 10 ( 3.3) Disadvantaged urban 18 ( 4.5) 19 ( 7.5) 10 2.8) Extreme rural 0 ( C.()) 10 ( 3.8) 10 ( 3,0) Other 65 ( 5.9) 58 (10,1) 70 ( 4.4) Parents' Education Did not finish high school 11 ( 0.7) 10 ( 1.3) 10 ( 0.8) Graduated high school 17 ( 0.9) 19 ( 2.5) 25 ( 1.2) Some education atter high school 18 ( 0.7) 16 ( 1.2) 17 ( 0.9) Graduated Conege 38 ( 1.6) 42 ( 4.0) 39 ( 1.9) Gender Male 51 ( 0.9) 56 ( 2.1) 51 ( 1.1) Female 49 ( 0.9) 45 ( 2.1) 49 ( 1.1) 'The standard errors of the esumated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure 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 t-ue . Parents' Education, for which some students responded "I don't know." Throughout this report, percentage, less than 0.5 percent are reported as 0 percvnt. 14 THE 1990 NAEP TRIAL STATE ASSESSMENT California SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for California schools and students sampled for the 1990 Trial State Assessment. In California, 98 public schools participated in the assessment. The weighted school participation rate was 94 percent, which means that all of the eighth-grade students in this sample of schools were representative of 94 percent of the eighth-grade public-school students in California. TABLE 2 I Profile of the Population Assessed in California EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before Substitution Weighted school participation rate after substitution Number of schools originally sampled Number of schools not ehgible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating schools 94% 94% 100 2 0 0 98 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 ot students assessed 93% 2,990 135 9% 5% 7% 4% 2,019 2,424 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Cabfornia In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 9 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 7 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 5 percent and 4 percent of the population, respectively. In total, 2,424 eighth-grade California public-school students were assessed. The weighted student participation rate was 93 percent. This means that the sample of students who took part in the assessment was representative of 93 percent of the eligible eighth-grade public-school student population in California. r: 2 16 THE 1990 NAEP TRIAL STATE ASSESSMENT Cahfornia THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in California Public Schools? The 1990 Thal State Asses&ment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAEP mathematics scale, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficiency of eighth-grade public-school students in California. Chapter 1 compares the overall mathematics performance of the students in California to students in the West region and the nation. It also presents the students' average proficiency separateb 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. r ) THE 1990 NAEP TRIAL STATE ASSESSMENT 17 California CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency ofeighth-grade public-school students from California on the NAEP mathematics scale is 256. This proficiency is lower than that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School Mathematics Proficiency /MEP Mathematics Scale 200 225 250 275 300 SOO TIN WOW CMCI Average Proflciency PM California 256 ( 1.3) 1-...1 West 261 ( 2.6) Ifis Nation 261 ( 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 1- 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Differences reported arc statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. IS THE 1990 NAEP TRIAL STATE ASSESSMENT California LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are given in Figure 3. It is important to note that the definitions of these levels are based solely on student performance on the 1990 mathematics a:,sessment. 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 California, 95 percent of the eighth graders, compared to 97 p.ftreent 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 California (11 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 California, West region, and national results for each content area. Students in California performed lower than students in the nation in Numbers and Operations and Data Analysis, Statistics, and Probability. Students in California performed comparably tc students in the nation in Measurement, Geometry, and Algebra and Functions. A- THE 1990 NAEP TRIAL STATE ASSESSMENT 19 California FIGURE 3 I Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-step word problems and select the greatest four-digit number in a list. In :1,`: :surement, these students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numerical sentemes and extend simple pattern sequences. LEVEL 250 1 Simple Multiplicative Reasoning and Two-Step Problem Solving 1 Students at this level have extended their underStanding of quantitative reasoning with whole numbers trom additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to other elementary two-step word problems. In these basic problem-solving situations, they can identify missing or extraneous information and have some knowledge of when to use computational estimation. They have a rudimentary understanding of such concepts as whole number place value, "even," "factor," and "multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an Initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and probability, in algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expre$sions. 20 THE 1990 NAEP TRIAL STATE ASSESSMENT California FIGURE 3 i Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasoning and Problem Solving involving Fractions, Decimals, Percents, Elementary Geometric Propertiu, and Simple Algebraic Manipulations Students at this level are able to represont, interpret, and perfOrm simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify frections, and recognize the equivalence between common fractions and decimals, including pictorial representations. They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expressions, including those with exponents and negative integers. In measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open Iinea: sentences and inequalities by substitution, and checking and graphing an interval representing a compound inequality when it is described in words. They can determine and apply a rule for simple functional relations and extend a numerical pattern. LEVEL 350 Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to include some propertieS of exponents. They can recognize scientific notation on a calculator and make the transition between scientific notation and decimal Pntation. In measurement, they can apply the, knowledge of area and perimeter of rectangles a "angles to solve problems. They can find the circumferences of circles and the surface areas ot solid figures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirect measurement. These students also can apply their knowledge of the properties of geometric figures to 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 21 California FIGURE 4 1 Levels of Eighth-Grade Public-School l Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Regiun Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation 0 20 40 60 80 Perc.ntagi ( 0.1) 0 ( 0.4) 0 ( 0.2) ( 1.0) 12 ( 2.4) 12 ( 1.2) 56 ( 1.6) 03 ( 2.8) 64 ( 1.6) p+.1 95 ( 0.9) 1.1.4 97 ( 1.0) 1 1.04 97 ( 0.7) 100 Percentage at or Above Proficiency Levels Hy 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 percvntage (95 percent confidence interval, denoted by 0-4-0). If the confidence intervals for the populations do not overlap, there is P statistically significant difference between the populations. 22 THE 1990 NAEP TRIAL STATE ASSFSSMENT California ME MOWS REPORT CARD FIGURE 5 I Eighth-Grade Public-School Mathematics 1 Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation .. .--A ALGEBRA AND FUNCTIONS p-emi 1. P.41111 1-001 1 10.4mi00,104 1-4,11.14 l GEOMETRY P.-..4041141 DATA ANALYSIS, STATISTICS, AND PROBABILITY 1-----loio.44 1-1^11 1P-104 10-10,1 /1.. MUMS AND OPERATIONS repit 1,-01 141 MEASUREMENT 0 200 225 250 275 300 Average Proficioncy 259 ( 1.2) 264 ( 2.6) 265 ( 1.4) 252 ( 1.5) 258 ( 3.0) 259 ( 1.7) 255 ( 1.3) 260 ( 2.6) 259 ( 1.4) 254 ( 1.7) 262 ( 3.6) 262 ( 1.8) 256 ( 1.3) 259 ( 2.4) 260 ( 1,3) SOO Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 1- 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. gr% THE 1990 NAEP TRIAL STATE ASSESSMENT 23 California 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 woups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Black, Hispanic, and Asian students from California are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black or Hispanic students and about the same mathematics proficiency as did Asian students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a &eater percentage of White students than Black or Hispanic students and about the same percentage of White as Asian students attained level 300. 24 THE 1990 NAEP TRIAL STATE ASSESSMENT California FIGURE 6 1 Average Eighth-Grade Public-Scbool Mathematics Proficiency by Race/Ethnicity NAEP Mathematics Seale 0 200 225 250 275 300 SOO Average Prolichincy FM 1P-141 PIM 1.404 11011..4.011 -10.1 PM P.4.1 1.-44 California WI lie 271 ( 1.4) Black =3 2.2) Hispanic 222 14) Asian 111 .4 22) Mat White 2.14 ( 3.2) Black 241 ( top. Hispanic 244 ( 2:7) Asian mos ( 4P11 Nation White ( 14) Black 231 ( 2.1) Hispanic 243 ( 2.0) Asian 210 ( 5.8)1 The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within -± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1.-4-1). 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). THE 1990 NAEP TRIAL STATE ASSESSMENT 25 California FIGURE 7 Levels of Eighth-Grade Public-School i Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Black Hispanic Asian Raglan White Black Hispanic Asian Nation White Black Hispanic Asian LEVEL 250 State White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Aslan LEVEL 200 State Wtlite Black Hispanic Asian Region White Black Hispanic Asiln Nation White Black Hpanic Asian 1 1...1 11.11.1101111104 11./primmeril 1,..441N 1.#mswisrassoigNINP Ipmiww.0111111.01111 1-94 p4 111111.1111 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent celainty, the alue for each populat:un of interest is within 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 14-4). if the confidence intervals for the populations do no: overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 26 THE 1990 NAEP TRIAL STATE ASSESSMENT Percentage 16 ( 1.6) 1 ( 1.1) 2 ( 0.5) 2A ( 3.4) 16 ( 3.2) ( 5.0)1 3 ( 1.6)) 15 ( 1.5) 2 ( 1.3) 3 ( 1.1) 31 ( 6.2)1 75 ( 1.7) 27 ( 3.7) 31 ( 2.4) 73 ( 3.4) 74 ( 3.3) 44 (12.9)1 41 ( 5.4) x** ..) 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) BO ( 5.6)1 100 0.3) 97 4.1) 90 1.9) BO 0.9) 29 0,8) 95 3.01' 93 1 2.0) mt. ..) 99 1 0.4) 99 3.1) 23 I 1.6) 97 I 2.5)1 1 Calffornia TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, disadvantaged urban areas, and areas dawdled as "other". (These are the "type of community" groups in California with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the California students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas or areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community NAEP Mathematics Scale 200 225 250 275 300 500 Average Proficiency California Advantaged urbar. Disadvantaged urban Other West fet Advantaged urba-t 278 ( 3.5)f 242 ( 4.1)! 258 ( 1.8) 282 ( 3.1)! 1-41141 1+4 Disadvantaged urbbn 288 ( SA), 0110014011 Other 260 3.8) P-4-1 Nation Advantaged urban 281 ( 3.8)1 Disadvantaged urt)an 740 ( 3.5)1 l-4001 Poi Other 281 ( 1.8) The standard errot s are presented in parentheses. With about 95 peraint cvrtatnt}, the average mathematic:: proficiency for each population of interest is within t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by H-4). If the confidence intervals for the populations do not overlap, thore 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 27 California FIGURE 9 LEVEL 300 Stahl Adv. urban Dtsadv. urban Other Region Adv. urban Disadv. urban Other Nation Ma. urban D4sadv. urban Other LEVEL 250 State Adv. urban Dmadv. urban Other Re 91an Mv. urban Disadv. urban Other Nation Mv. urban Dtsadv. urban Other LEVEL 200 State Adv. urban Disadv. urban Other Region Adv. urban Disadv. urban Other Nation Adv. urban Disadv. urban Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community /41.00101 .4 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors or the estimated percentage (95 percent confidence interval, denoted by 1.4-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 100 28 THE 1990 NAEP TRIAL STATE ASSESSMENT Percentage 25 ( 3.9)1 4 ( 1.6)1 9 ( 1.2) 31 ( 31)1 ( 3.5)1 10 ( 1.8) 2$ ( 4.8)1 7 ( 2.1)1 12 ( 1.2) 90 ( 3.$)1 37 ( 8.5p 93 ( 2.4) 83 ( 3.3)' 57 ( 8.0)i 82 ( 5.0) 83 ( 4.6)1 49 ( 5.0)1 64 ( 2.3) 100 ( 0.4)1 ( 2.7)1 913 ( 0.9) 100 ( 0.0) 96 ( 2.0)1 96 ( 1.7) 100 ( 0.0) 95 ( 1.5p 97 ( 1.0) California PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In California, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 32 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, about the same percentage of students in California (38 percent) and in the nation (39 percent) had at lmtst one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 11 percent for California and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School Mathematics Proficiency by Parents' Education NAEP Mathematics Scale 200 225 250 275 300 500 WE WORT Average Proficiency 14111 14I California HS non-graduate HS graduate Some college College graduate 220 ( 215 ( 2113 ( 271 2.1) 1.5) 1.9) 1.7) West HS non-graduate 240 ( 4.4) Plool HS graduate 250 ( 2.2) 1-4,1 Some college 21111 ( &O) 11.4"I College graduate 203 ( 2.6) Nation P41 HS non-graduate 243 ( 2.0) HS graduate 254 ( 1$) 141 Some college SN 1.7) 141 College graduate 274 ( 1.6) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence interval, denoted by P.44). 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 29 California 1E NATION'S REPORT FIGURE I I I Levels of Eighth-Grade Public-School CARD i 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. RIP9ion HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 Stat 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. 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by t-1-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 30 THE 1990 NAB!' TRIAL STATE ASSESSMENT 2 ( 1.3) 2 ( 0.8) 11 ( 1.7) 20 ( 2.0) 2 ( 2.3) 2 ( 1.3) 15 ( 2.8) 21 ( 3.5) ( 0.9) 3 ( 14) 12 ( 1.4) 21 ( 18) 33 ( 3.7) 45 ( 2.9) 57 ( 3.3) 74 ( 2.0) 44 ( 6.8) 51 ( 4.4) 78 ( 4.1) ( 3.6) 37 ( 4.6) 86 ( 2.7) 71 ( 2.6) 7111 ( 2.0) ( 2.4) 93 ( 1.9) 98 ( 0.8) 98 ( 0.7) 99 ( 3.2) 97 ( 1.6) 99 ( 0.7) 99 ( 0.7) 96 ( 1.9) 97 ( 0.8) 99 ( 0.7) 99 ( 0.7) California GENDER As shown in Figure 12, there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in California. Compared to the national results, females in California performed lower than females across the country; males in California performed lower than males across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender NAEP Mathematics Scale 0 200 225 250 275 300 500 Average Proficiency IRPOR1 CAN ==LI California psi Male 1.0) mos Female ( 1.2) West Male 2112 ( 3.5) P4m1 Female ( 2.0) Nation psi Male 202 ( 1.8) Female 31110 ( 1.3) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in California who attained level 200. The percentage of females in California who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in California who attained level 200 was similar to the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASSESSMENT 31 California FIGURE 13 I Levels of Eighth-Grade Public-School Mathematics Proficiency by Gender LEVEL 300 THE PINION'S REPORT CARD State Male r--eng Female 144 Region Male 1---40mi Female Nation male Female Ipat LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female ..4*004 twwwgle.1.111.1101 Percentage 12 ( 1.4) 9 ( 1.0) 13 ( 3.1) 11 ( 2.2) 14 ( 1.7) 10 ( 1.3) 57 ( 1.9) 55 ( 1.9) es ( 4.1) 61 ( 3.2) 84 ( 2.0) 64 ( 1.8) pemi 96 1.3) P1.1 94 1 1.0) -1-4 97 1.21 1-44 96 1.0) 4.4 97 1 0.9) 97 0.8, 0 20 40 60 60 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so tew students attained that level. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT atWootia In addition, there was no differret40 101V,^tAi1 priZeltages Of males and females in California who attained level WI, Vt PievettAge f ktnales in California who attained level 300 was similar to the perlilkO ç ilk&lks anion who attained level 300. Also, the percentage of males iltiVAildriVO v.4110 atUd level 300 was similar to the percentage of males in the natio04 'A. 0 t4jji Ievel 3r,113. CONTENT AREA PERFORIWO Table 3 provides a summary of VPIellt Eti Ntforitarice by race/ethnicity, type of community, parents' educationl kAtel, Nriok. THE 1990 NAV TRIAL STATE ASW\401/41 33 California TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Numbers and Optwations Measurement Geometry _ Data Analysis ' Statistics, and Probability Algebra and Relators TOTAL Proficiency Proficiency Proficiency Proficiency Proficiency State 259 ( 1.2) 252 ( 15) 255 ( 1.3) 264 ( 1.7) 256 ( 1.3) Region 264 ( 2.6) 258 ( 3.0) 260 ( 2.6) 292 ( 3.6) 259 ( 2.4) Nation 266 ( 1A) 258 ( 1.7) 259 ( 1.4) 262 ( 1.8) 260(1.3) RACE/ETHNICITY White State 273 ( 1.5) 269 ( 1.7) 267 ( 1.7) 274 ( 1.9) 270 ( 1.5) Region 271 ( 3.2) 267 ( 3.9) 267 ( 3.0) 272 ( 4.4) 267 ( 2.8) Nation 273 ( 1.6) 267 ( 2.0) 26; ( 15) 272 ( 1.8) 268 ( 1 4) Black State 237 ( 3.4) 219 ( 4.6) 235 ( 3,0) 231 ( 3.9) 236 ( 3.5) Region 250 ( 6.8)1 240 (10.7)1 249 ( 5.7)1 244 ( 8.7)1 248 ( 7.4)1 Nation 244 ( 3.1) 227 ( 3.6) 234 ( 2.8) 231 ( 3.8) 237 ( 2.7) Hispanic State 241 ( 1.6) 232 ( 1.9) 239 ( 1.8) 230 ( 2.1) 238 ( 1$) Region 248 ( 3.5) 239 ( 42) 245 ( 4.4) 240 ( 4,7) 243 ( 4.0) Nation 248 ( 2.7) 238 ( 3.4) 243 ( 3.2) 239 ( 3.4) 243 ( 3.1) Asian State 275 ( 2.8) 265 ( 3.8) 271 ( 2.7) 274 ( 2.8) Region ( *01 ( ( Nation 285 ( 5.9)1 27$ ( 8.3)1 275 ( 5.9)1 282 ( 8.9)1 278 ( 6.7)1 TYPE OF COMMUNITY Advantaged urban State 279 ( 4.0)1 275 ( 3.6)1 276 ( 3.6)1 280 4.2)1 277 ( 3.3)1 Region 284 ( 3.6); 283 ( 2.7)1 279 ( 8.9)1 288 ( 4.1)1 279 ( 2.9)1 Nation 283 ( 3.2)1 281 ( 3.2)1 277 ( 5.2)1 285 ( 4.8)1 277 ( 4.8)1 Disadvantaged urban State 246 ( 4.4)1 237 ( 4.4)1 243 ( 4.1)1 236 ( 5.8)1 242 ( 3.6)1 Region 260 ( 5.4)1 250 ( 8.9)1 256 ( 45)1 255 ( 8.311 254 ( 4.6)1 Nation 255 ( 3.1)1 242 ( 4.9)1 248 ( 3.7)1 247 ( 4.6)1 247 ( 3.2)1 Other State 259 ( 1.8) 252 ( 2.1) 255 ( 1.8) 254 ( 2.3) 256 ( 1.8) Region 262 ( 3.5) 255 ( 4.2) 258 ( 3.4) 259 ( 4.2) 258 ( 3.5) Nation 268 ( 1.9) 257 ( 2.4) 259 ( 1.7) 281 ( 2.2) 261 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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 b2 students). 34 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE 3 I Eighth-Grade Public-School Mathematics (matinued) I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Numbers and OPerations *Retirement Geometry Data Ana 111212' Statistics, and Probability Algebra and Functions TOTAL Proficiency Proficiency Proclaim', Praia ism Proficiency State 259 ( 12) 252 ( 1.5) 255 ( 254 ( 1.7) 256 ( 1.3) Region 264 ( 2.6) 258 ( 3.0) 200 ( ' 262 ( 3.6) 250 ( 2.4) Nation 266 ( 1.4) 258 ( 1.7) 259 ( 252 ( 1.8) 260 ( 1.3) PARENTS EDUCATION HS non-graduate State 243 ( 2.3) 234 ( 2.9) 242 ( 2.5) 233 ( 3.3) 240 ( 2.7) Region 24$ ( 4.2) 242 ( 6.2) 246 ( 4.9) 246 ( 6.2) 245 ( 5.1) Nation 247 ( 2.4) 237 ( 3.8) 242 ( 2.2) 240 ( 3.1) 242 ( 3.0) NS graduate State 248 ( 1.9) 238 ( 2.4) 244 ( 1.6) 243 ( 2.5) 247 ( 1.7) Region 254 ( 2.5) 245 ( 3.0) 251 ( 3.6) 249 ( 3.2) 250 ( 2.4) Nation 259 ( 1.8) 248 ( 2.1) 252 ( 1.8) 253 ( 22) 253 ( 2.0) Some college State 267 ( 2.1) 261 ( 2.3) 259 ( 2.4) 262 ( 2.9) 264 ( 2.0) Region 272 ( 2.7) 268 ( 5.3) 264 ( 3.9) 271 ( 4.9) 264 ( 32) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 263 ( 22) College graduate State 274 ( 1.8) 268 ( 1.9) 27D ( 1.7) 273 ( 2.1) 269 ( 2.1) Region 275 ( 2.7) 271 ( 3.0) 271 ( 2.3) 276 ( 4.3) 272 ( 2.8) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 276 ( 2.2) 273 ( 1.7) GENDER Male State 260 ( 1.6) 256 ( 1.8) 258 ( 1.7) 257 ( 2.2) 256 ( 1.7) Region 264 ( 3.8) 263 ( 3.5) 281 ( 3.4) 264 ( 4.1) 260 ( 3.3) Nation 266 ( 2.0) 262 ( 2.3) 260 ( 1.7) 262 ( 2.1) 260 ( 1.6) Female State 259 ( 1.3) 247 ( 1.6) 253 ( 1.5) 252 ( 1.7) 256 ( 1.5) Region 263 ( 2.5) 252 ( 2.9) 259 ( 2.9) 280 ( 4.0) 259 ( 2.8) Nation 266 ( 1.4) 253 ( 1.6) 258 ( 1.5) 281 ( 1.9) 260 ( 1.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within i 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Cahfornia THE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics pro' is valuable in and of itself, but it becomes more useful for improving instruc:. -lid setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information on student achievment. It is important to note that the NAEP data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. THE 1990 NAEP TRIAL STATE ESSMENT 37 California Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, aS described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that horne environment has an enormous 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. A, 38 THE 1990 NAEP TEAL STATE ASSESSMENT California CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics progyams.' This chapter focuses on curricular and instructional content issues in California 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: More than half of the eighth-grade students in California (69 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. Curtis McKnight, et al., Thr inderachieving Cur-1,-u1um As.cessing US Srhool Mathematics from an International Perspective, A National Keport on the Second International Mathematics Study (Champaign. 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). A THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Cahfornia In California, 91 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Many of the students in California (85 percvnt) were taught mathematics by teachers who teach only one subject. About three-quarters (72 percent) of the students in California 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 California Eighth-Grade Public Schools PERCENTAGE OF STUDENTS _ MO KAEP TRIAL STATE ASSESSMENT California West Nation Percentage of eighth-grade Students in public schools that identified mathematics es receiving special emphasis in school-wide goals and objectives, instruction, in-service training, etc. Percentage of eighth-grade public-school stuOentS 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 Percardage 69 ( 4.4) 61 ( 8.6) 83 ( 5.9) 91 ( 1.6) 82 ( 4.7) 78 ( 4.6) 85 ( 3.6) 98 ( 1.6) SI ( 3.3) 72 ( 3.4) 64 ( 8.3) 63 ( 4.0) 38 ( 3.6) 25 ( 5.9) 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 t 2 standard errors of the estimate for the sample. 40 THE 1990 NAEP TRIAL STATE ASSESSMENT California CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in California are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in California were taking eighth-grade mathematics (59 percent) than were taking a course in pre-algebra or algebra (36 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 California who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. Tliis result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 19SO MEP TRIAL STATE ASSESSMENT California West Nation What kind of mathematics class are you taking this year? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Eighth-grade mathematics 59 ( 1.9) 63 ( 2.7) 62 ( 2,1) 242 ( 1.1) 252 ( 2.4) 251 ( 1.4) Pre-algebra 21 ( 1.4) 15 ( 2.7) 19 ( 1.9) 272 ( 2.2) 266 ( 3.6) 272 ( 2.4) Algebra 16 ( 1.0) 17 ( 1,8) 15 ( 1.2) 293 ( 2,0) 299 ( 4.5) 296 ( 2.4) ,mR011 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percvnt certainty that, for each population of interest, the value for the entire population is within -i- 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ^-1 `:- 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 41 California Further, from Table A5 in the Data Appendix:* About the same percentage of females (38 percent) and males (35 percent) in Ca,lifornia were enrolled in pre-algebra or algebra courses. In California, 43 percent of White students, 27 percent of Black students, 23 percent of Hispanic students, and 55 percent of Asian students were enrolled in pre-algebra or algebra courses. Similarly, 47 percent of students attending schools in advantaged urban areas, 31 percent in schools in disadvantaged urban areas, and 37 percent in schools in areas classified as "other" were enrolled in pre-algebra or algebra courses. MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in California spent 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the laigest 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 California, 2 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 6 percent of the students in California and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. ` For every table in the body of the report that includes estimates of average proficiency,the Data Appendix provides a corresponding table presenting the results for the four subpopulauons race 'ethnicity, type of community, parents' education level, and gender. NI 42 THE 1990 NAEP TRIAL STATE ASSESSMENT California The results by race/ethnicity show that 6 percent of White students, 5 percent of Black students, 4 percent of Hispanic students, and 14 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 2 percent of White students, 2 percent of Black students, 2 percent of Hispanic students, and 1 percent of Asian students spent no time doing mathematics homework. In addition, 8 percent of students attending schools in advantaged urban areas, 3 percent in schools in disadvantaged urban areas, and 6 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 0 percent of students attending schools in advantaged urban areas, 1 percent in schools in disadvantaged urban areas, and 2 pescent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT California Wail Nation Percentage and Proficiency 2 ( 0 ) 11.1111 ( INN ) Percentage and Proficiency ^11.4 *** ) Pfreentail* and , Proficiency About how much time do students spend 1 on mathematics homework each day? None 16 minutes 30 ( 3.1) 42 ( 6.7) 43 ( 42) 247 ( 2.0) 258 ( 4.2) 256 ( 2.3) 30 minutes 52 ( 2.9) 43 ( 6.2) 43 ( 4.3) 257 ( 2.0) 264 ( 4.7) 266 ( 2.8) 46 minutes 10 ( 1.2) 9 ( 2.3) 10 ( 12) 273 ( 52) 270 ( 6.5)1 272 ( 5.7)1 An hour or more 6 ( 0.0) 5 ( 1.9) 4 ( 0.0) 260 ( 5.7) 11-** ) 278 ( 5.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 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). u THE 1990 NAEP TRIAL STATE ASSESSMENT 43 California TABLE 7 1 Students' Reports on the Amount of Time They i Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL STATE ASSESSMENT California West 1 Nation _ About how much time do you usually spend each day on mathematics homework? partentaga and Pralichancy Percentage and Praiklaney Parcentaga and Praildency None ( 0.8) 12 ( 1.7) 9 ( 0.8) 247 ( 2.8) 254 ( 4.2) 251 ( 2.8) 16 minutes 29( 1.1) 31 ( 4.5) 31 ( 2.0) 254 ( 1.5) 263 ( 3.8) 284 ( 1.9) 30 minutes 35 ( 1.0) 28 ( 1.7) 32 ( 1.2) 280 ( 1.6) 261 ( 2.9) 2R3 ( 1.9) 45 minutes 16 ( 0.7) 15 ( 1.6) 16 ( 1.0) 258 ( 2.0) 267 ( 42) 286 ( 1.9) An hour or more 13 ( 0.9) 14 ( 1.7) 12 ( 1.1) 255 ( 3.0) 261 ( 4.5) 25$ ( 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 t 2 standard errors of the estimate for the sample. And, according to the students (Table 7 and Table A7 in the Data Appendix): In California, relatively few of the students (7 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 13 percent of the students in California 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 10 percent of White students, 17 percent of Black students, 12 percent of Hispanic students, and 23 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 8 percent of White students, 4 percent of Black students, 9 percent of Hispanic students, and 4 percent of Asian students spent no time doing mathematics homework. 4 44 THE 1990 NAEP TRIAL STATE ASSESSMENT California In addition, 11 percent of students attending schools in advantaged urban areas, 13 percent in schools in disadvantaged urban areas, and 12 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 5 percent of students attending schools in advantaged urban areas, 6 percent in schools in disadvantaged urban areas, and 8 percent in schools in areas classified as "other" spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement.5 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 gaphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. 5 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, V A: National Council of reachers of Mathematics, 1989). , t THE 1990 NAEP TRIAL STATE ASSESSMENT 45 California The responses of the assessed students' teachers to the topic emphasis questions for each content area were combined to create a new variable. For each question in a particular content area, a value of 3 was given to "heavy emphasis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 46 THE 1990 NAEP TRIAL STATE ASSESSMENT Cahfornia TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT California West Nation R wastage end Proficiency Percentage and Proldency Percentage and Prdiciency Teacher "emphasis" categories by content areas Numbers and Operations Heavy emphasis 40 ( 3.1) 42 ( 7.4) 49 ( 3.8) 251 ( 1.7) 257 ( 3.8) 280 ( 1.8) Little or no emphasis 22 ( 22) 13 ( 2.1) 15 ( 2.1) 282 ( 3.5) 291 ( 8.6) 287 ( 3.4) Measurement Heavy emphasis 21 ( 2.5) 11 ( 2.8) 17 ( 3.0) 248 ( 2.7) 251 ( 7.7)1 250 ( 5.6) Little or no emphasis 25 ( 2.7) 38 ( 5.3) 33 ( 4.0) 288 ( 3.3) 275 ( 8.3) 272 4.0) Geometry Heavy emphasis 25 ( 31) 24 ( 8.3) 28 ( 3.8) 259 ( 2.7) 260 ( 2.8)1 260 ( 32) Little or no emphasis 22 ( 2.5) 16 ( 4.5) 21 ( 3.3) 258 ( 2.8) 277 (11.4)1 284 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 17 ( 2.7) 14 ( 3.7) 14 ( 22) 263 ( 5.0) 264 (10.6)' 269 ( 4.3) Little or no emphasis 48 ( 3.1) 54 ( 6.3) 53 ( 4.4) 251 ( 2.8) 202 4.9) 261 ( 2.9) Algebra and Functions Heavy emphasis 46 ( 2.4) 43 ( 5.6) 46 ( 3.6) 273 ( 2.4) 277 ( 52) 275 ( 2.5) Little or no emphasis 19 ( 1.9) 23 ( 5.1) ( 3.0) 236 ( 2.3) 243 ( 4.2)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 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 California SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: More than half of the eighth-grade students in California (69 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In California, 91 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 California were taking eighth-grade mathematics (59 percent) than were taking a course in pre-algebra or algebra (36 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 ofeighth-grade students in public schools in California spent 30 minutes doing mathematics homework each day; according to the students, most of them spent 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 California, relatively few of the students (7 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 13 percent of the students in California and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 48 THE 1990 NAEP TRIAL STATE ASSESSMENT California CHAPTER 4 ynxx 1111111111111111111111111111111 imiamissem arnimour 111-11 11111M1111mtima IINOMi III IIIIIIII N.751111111111111/11 1ONS VMS. .11111111IF,11111111 ill11111111111111111Ell 111111111111111111111111 How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning or for those who come from different cultural backgrounds is an important aspect of teaching.' An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. 6 \ at lona] Council of 1 eacoers of Mathematics. Professional Standards for the Teaching of Mathematics (Reston. VA: anonal Council of Teachers of Mathematics, 1991). THE 1990 Is; AEP TRIAL STATE ASSESSMEN1 49 California From Table 9 and Table A9 in the Data Appendix: In California, 14 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 34 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 California, 10 percent of students attending schools in advantaged urban areas, 9 percent in schools in disadvantaged urban areas, and 17 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in California, 29 percent of students attending schools in advantaged urban areas, 31 percent in schools in disadvantaged urban areas, and 33 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had mathematics achievement levels similar to 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 1990 NAEP TRIAL STATE ASSESSMENT California I Wes! Nation Which of the following statements is true ; about how well supplied you are by your ! school system with the instructional I materials and other resources you need 1 to teach your class? I gat all the resources I need. I got most of the moures I need. I get som t. or none of the resources I need. Pe/ventage and Proficiency Percentage Percentage and and Prondency Pro &Wig 14 ( 2.1) 15 ( 52) 13 ( 2.4) 253 ( 3.4) 261 ( 5.9)1 265 ( 4.2) 53 ( 3.7) 62 ( 3.8) 56 ( 4.0) 260 ( 2.1) 266 ( 4.1) 265 ( 2.0) 34 ( 3.6) 23 ( 6.1) 31 ( 4.2) 253 ( 2.4) 257 ( 3.7)1 261 ( 2.9) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that. for each population of interest, the value for the entire population is within ± 2 standard 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 California PA1TERNS Di CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practi..e and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: More than half of the students in California (59 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics problems in small groups (9 percent). The largest percentage of the students (58 percent) used objects like nilers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (7 percent). In California, 64 percent of the students were assigned problems from a mathematics textbook almost every day; 9 percent worked textbook problems about once a week or less. I.ess than half of the students (35 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (34 percent). 7 Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Curriculum. Eighty-second Yearbook of the National Society for the Sndy of Education (Chicago. IL: University of Chicago Press, 1983). THE 1990 NAEP TRIAL STATE ASSESSMENT 51 California TABLE 10 I Teachers' Reports on Patterns of Mathematics' Instruction PERCENTAGE oF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT California West Ration 11, Percentage and Proficiency Percentage and Proficiency Percentage and Proacifncy About how often do Students work problems in small groups? At least once a week 59 ( 3.1) 57 ( 8.9) 50 ( 4.4) 259 ( 2.0) 282 ( 4.2)i 260 ( 2.2) Less than once a week 22 ( 2.9) 39 ( 7.6) 43 ( 4.1) 254 ( 2.8) 266 ( 4.5) 264 ( 2.3) Never 9 ( 1.8) 3 ( 2.2) 8 ( 2.0) 250 ( 6.3)1 277 ( 5.4)( About how often do students use objects Percentage Percentage Percentage like rulers, counting blocks, or geometric and and and solids? Proficiency Proficiency Proficiency At least once a week 35 ( 3.8) 34 ( 82) 22 ( 3.7) 252 ( 2.5) 256 ( 4.9)i 254 ( 32) Less than once a week 58 ( 3.7) 57 ( 6.4) 69 ( 3.9) 257 ( 1.9) 265 ( 4.0) 263 ( 1.9) Never 7 ( 1.2) 9 ( 2.6) 269 ( 72) 282 ( 5.9)1 The standard errors of the esumated staustics 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. ! 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). $2 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE II I Teachers' Reports on Materials for I Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT California Nation Percente9e and Proficiency Penentage and Proficiency Percentage and Prone:fancy About how often do students do problems from textbooks? Almost ovary day 84 ( 3.2) 55 ( 6.0) 62 ( 3,4) 259 ( 1.9) 270 ( 3.3) 267 ( 1.8) Several dews a week 27 ( 2.8) 38 ( 5.1) 31 ( 3.1) 254 ( 24) 258 ( 5.2) 254 ( 2.9) About once a mob or less 9 ( 2.1) 250 ( 5.4)I 9 ( 4.9) ( 41 7 ( 1.8) 280 ( 5.1)4 About how often do students do problems on worksheets? Pmentage and Percentage and PercenLap and Proficiency Proficiency Proficiency At lead several times a week 35 ( 3.1) 25 ( 52) 34 ( 3.8) 253 ( 2.8) 258 ( 4.3)! 258 ( 2.3) About once a week 31 ( 2.9) 34 ( 4.6) 33 ( 3.4) 2$8 ( 3.0) 258 ( 4.1) 280 ( 2.3) Loss than weekly 34 ( 2.9) 41 ( 5.6) 32 ( 3.6) 280 ( 2.9) 274 ( 4.2) 274 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the yalue for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). The next section presents the stuients' responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT 53 California COLLABORATING LN SMALL GROUPS In California, 40 percent of the students reported never working mathematics problems in small groups (see Table 12); 35 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 1 Students' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY r 1990 NAEP TRIAL STATE ASSESSMENT California West Nation - How often do you work in small groups in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Prondenc7 At least once a week 35 ( 2.0) 35 ( 4.8) 28 ( 2.5) 256 ( 2.0) 258 ( 4.2) 25$ ( 2.7) Less than once a week 25 ( 1.2) 29 ( 2.8) 2$ ( 1.4) 260 ( 1.8) 271 ( 3.1) 267 ( 2.0) Never 40 ( 2.0) 36 ( 4.6) 44 ( 2.9) 254 ( 1.7) 258 2.0) 281 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said wnh 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. Examining the subpopulations (Table Al2 in the Data Appendix): In California, 33 percent of students attending schools in advantaged urban areas, 39 percent in schools in disadvantaged urban areas, and 38 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 35 percent of White students, 35 percent of Black students, 35 percent of Hispanic students, and 32 percent of Asian students worked mathematics problems in small groups at least once a week. Females were as rtkely as males to work mathematics problems in small groups at least once a week (36 percent and 34 percent, respectively). 54 THE 1990 NAEP TRIAL STATE ASSESSMENT California USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A13 in the Data Appendix summarize these data: Izss than half of the students in California (40 percent) never used mathematical objects; 32 percent used these objects at least once a week. Mathematical objects were used at least once a week by 29 percent of students attending schools in advantaged urban areas, 35 percent in schools in disadvantaged urban areas, and 35 percent in schools in areas classified as "other". Males were as likely as females to use mathematical objects in their mathematics classes at least once a week (34 percent and 31 percent, respectively). In addition, 30 percent of White students, 33 percent of Black students, 34 percent of Hispanic students, and 35 percent of Asian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHFMATICS PROFICIENCY 1990 NAP TRIAL STATE ASSESSMENT California West Nation How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Percentage wid Profidency Percentage and Proficiency Percentage and Proficiency At least once a week 32 ( 2.0) 36 ( 3.5) 28 ( 1.8) 253 ( 1.9) 260 ( 4.0) 258 ( 2.8) Less than one* a week 28 ( 1.3) 28 ( 1.8) 31 ( 1.2) 264 ( 1.9) 269 ( 2.7) 269 ( 1.5) Never 40 ( 1.9) 38 ( 3.3) 41 ( 2.2) 254 ( 1.4) 256 ( 2.8) 259 ( 1.8) The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 55 California MATERIALS FOR MATHEMATICS LNSTRUCTION The percentages of eighth-grade public-school students in California who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table Al4 in the Data Appendix): More than half of the students in California (69 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 73 percent of students attending schools in advantaged urban areas, 65 percent in schools in disadvantaged ufoan areas, and 67 percent in schools in areas classified as "other". TABLE 14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1900 NAEP TRIAL STATE ASSESSMENT California West Nation 1 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 69 ( 2.0) 71 ( 3.5) 74 ( 1.9) 262 ( 1.3) 267 ( 2.4) 267 ( 1.2) Several times a week 17 ( 1.1) 15 ( 1.5) la ( 0.8) 247 ( 2.5) 251 ( 2.4) 252 ( 1.7) About once a week or less 14 ( 1.5) 14 (.3.1) 12 ( 1.8) 240 ( 2.8) 242 (11.2)1 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, tor 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. 56 THE 1990 NAEP TRIAL STATE ASSESSMENT California And, for the frequency of worksheet usage (Table 15 and Table A 15 in the Data Appendix): Less than half of the students in California (44 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 36 percent of students attending schools in advantaged urban areas, 55 percent in schools in disadvantaged urban areas, and 42 percent in schools in areas classified as "other". TABLE 15 I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT California West Nation Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency 7-How often do you do mathematics I Problems on worksheets in your I mathematics class? Al least several times a week 44 ( 2.4) 35 ( 4.0) 38 ( 2.4) 249 ( 1.9) 250 ( 4.2) 253 ( 22) About once a week 24 ( 1.2) 23 ( 2,6) 25 ( 12) 257 ( 1.8) 262 ( 2.1) 261 ( 1.4) Less than weeidy 33 ( 41 ( 37 ( 2.5) 266 ( 2.0) 270 ( 3,4) 272 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said wit' -,out 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard en urs 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 California TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT California West Nation _ Patterns of Classroom instruction Percentage of students veto work mathematics problems In 101411 groups At least once a week Less than ortce a Week Never Percentige of students who use objects like rulers, counting blocks, or geometric solids At least once a week Less than once a week Never Materials for mathematics 1 instruction Percentage of students *to use a mathematics textbook Almost every day Several times a week About once a week or less Percentage of students vMo use a mathematics worksheet At least several times a week About once a week Less than weekly Percentage Percentage Percentage Students Teachers Students Teachers Students Teechers 35 ( 2.0) 59 ( 3.1) 35 ( 4.8) 57 ( 8.9) 28 ( 2.5) 50 ( 4.4) 25 ( 1.2) 32 ( 2.9) 29 ( 2.8) 39 ( 7.6) 28 ( 1.4) 43 ( 4.1) 40 ( 2.0) 9 ( 1.8) 36 ( 4.8) 3 ( 2.2) 44 ( 2.9) 8 ( 2.0) 32 ( 2.0) 35 ( 3.8) 36 ( 3.5) 34 ( 82) 28 ( 1.8) 22 ( 3.7) 28 ( 1.3) 58 ( 3.7) 28 ( 1.8) 57 ( 8.4) 31 ( 1.2) 89 ( 3.9) 40 ( 1.9) 7 ( 1.2) 36 ( 3.3) 8 ( 3.0) 41 ( 2.2) 9 ( 2.8) Percentage Percentage Percentage Students Teacher's Students Teachers Students Teachers 69 ( 2.0) 84 ( 3.2) 71 ( 3.5) 55 ( 8.0) 74 ( 1.9) 62 ( 3.4) 17 ( 1.1) 27 ( 2.8) 15 ( 1.5) 36 ( 5.1) 14 1 0.8) 31 ( 3.1) 14 ( 1.5) 9 ( 2.1) 14 ( 3.1) 9 ( 4.9) 12 ( 1.8) 7 ( 1.8) 44 ( 2.4) 35 ( 3.1) 35 ( 4.0) 25 ( 5.2) 38 ( 2.4) 34 ( 3.8) 24 ( 1.2) 31 ( 2.9) 23 ( 2.6) 34 ( 4.6) 25 ( 1.2) 33 ( 3.4) 33 ( 2.3) 34 ( 2.9) 41 ( 4.1) 41 ( 5.9) 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 2 standard errors of the estimate for the sample. 58 THE 1990 NAEP TRIAL STATE ASSESSMENT Cahfornia SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery practices and resources. It appears that mathematics textbooks and worksheets continue to play a major role in mathematics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachers: More than half of the students in California (59 percent) workeil mathematics problems in small groups at least once a week; relatively few never worked in small groups (9 percent). The largest percentage of the students (58 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (7 percent). In California, 64 percent of the students were assigned problems from a mathematics textbook almost every day; 9 percent worked textbook problems about once a week or less. Less than half of the students (35 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (34 percent). And, according to the students: In California, 40 percent of the students never worked mathematics problems in small groups; 35 percent of the students worked mathematics problems in small groups at least once a week. Less than half of the students in California (40 percent) never used mathematical objects; 32 percent used these objects at least once a week. More than half of the students in California (69 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. Less than half of the students in California (44 percent) used worksheets at least several times a week, compared to 38 peicent in the nation. THE 1990 NAEP TRIAL STATE ASSESSMENT 59 California CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to tree them from time-consuming computations and to permit them to focus on more challenging tasks.' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. s National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). C5 60 THE 1990 NAEP TRIAL STATE ASSESSMENT California Table 17 provides a profile of California eighth-gxade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 50 percent of the studwats in California had teachers who allowed calculators to be used for tests. A greater percentage of students in California than in the nation had teachers who permitted unrestricted use of calculators (31 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of California Policies on i Calculator Use PERCENTAGE OF STIMENTS , 1990 NAEP TRIAL STATE ASSESSMENT California West Nation _._ Percentage of eighth-grade Students in public schools whose teachers permit the unrntricted use of calculators Percentage of eighth-grade students in public schools whose teachers permit the use of calculators for tests Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned by the school Percentage Percentage Percentage 31 ( 3.0) 20 ( 4.9) 18 ( 3.4) 50 ( 3.9) 48(8.8) 33 ( 4.5) 83 ( 2.9) 72 ( 7.4) 56 ( 4.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Cabfornia THE AVAILABILITY OF CALCULATORS In California, most students or their families (97 percent) owned calculators (Table 18); however, fewer students (58 percent) had teachers who explained the use of calculators to them. From Table A 18 in the Data Appendix: In California, 58 percent of White students, 61 percent of Black students, 61 percent of Hispanic students, and 50 percent of Asian students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (58 percent and 58 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1900 NAEP TRIAL STATE ASSESSMENT Cilifornia West Nation - Do yOu or your family own a calculator, Yes No Does your mathematics teacher explain how to use a calculator for mathematics problems? Percentage and Proficiency 97 ( 0.4) 257 ( 1.2) 3 ( 0.4) 232 ( 3.8) Percantaspe and Proficiency Percentage and Proficiency 96 ( 0.6) 263 ( 2.6) 4 ( 0.6) se. ( Percentage and Proficiency Percentage and Proficiency 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( 3.8) Peiventage and Proficiency Yes 58 ( 1.8) 59 ( 3.4) 49 ( 2.3) 254 ( 1.3) 280 ( 2.7) 258 ( 1.7) No 42 ( 1.8) 41 ( 3.4) 51 ( 2.3) 281 ( 1.7) 265 ( 3.0) 266 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percvnt certainty that, for each population of interest, the value for the enure population is within t 2 standard errors of the estimate for the sample *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 THE 1990 NAEP TRIAL STATE ASSFSSMENT California THE USE OF CALCULATORS As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment. .41idents were asked how frequently (never, sometimes, almost always) they used ulators for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In California, 19 percent of the students never used a calculator to work problems in class, while 46 percent almost always did. Some of the students (16 percent) never used a calculator to work problems at home, compared to 33 percent who almost always used one. About one-quarter of the students (30 percent) never used a calculator to take quizzes or tests, while 23 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 MO MEP TRIAL STATE ASSESSMENT California West Nation , Percentage and Proficiency Percentage and Proficiency Percentage and Prof Haney How often do you use a calculator for the 1 following tasks? L-- Working problems In class Almost always 46 ( 1.6) 53 ( 2.1) 48 ( 1.5) 250 ( 1.7) 255 ( 2.6) 254 ( 1.5) Never 19 ( 1.6) 14 ( 2.4) 23 ( 1.9) 264 ( 2.1) 266 ( 3.0) 272 ( 1.4) Doing problems at home Almost always 33 ( 1.5) 29 ( 1,7) 30 ( 1.3) 257 ( 1.7) 263 ( 3.3, 261 ( 1.8) Never 16 ( 1.1) 19 ( 1.6) 19 ( 0.9) 259 ( 2.3) 258 ( 3.7) 263 ( 1.8) Taking quizzes or tests Almost always 23 ( 1.5) 25 ( 1.6) 27 ( 1.4) 253 ( 2.9) 259 ( 3.9) 253 ( 2.4) Never 30 ( 1.7) 22 1 3.0) ( 2.0) 266 ( 1.4) 270 ( 13) 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 63 California WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not te use a calculator for each item in the calculator sections, and they were asked to inOicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items werc defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. Ilowever, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the character: ,ics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT California The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in California 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, 47 percent of White students, 38 percent of Black students, 38 percent of Hispanic students, and 50 percent of Asian students were in the High group. TABLE 20 J Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT California West I Nation 1 "Caiculator-use" group Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency High 43 ( 1.1) 38 ( 2.6) 42 ( 1.3) 265 ( 1.7) 273 ( 2.7) 272 ( 1.6) Other 57 ( 1.1) 62 ( 2.6) 58 ( 1.3) 248 ( 1.3) 253 ( 2.8) 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 enure population is within A 2 standard errors of the estimate for the sample. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 California 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 instructionl 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, 50 percent of the students in California had teachers who allowed calculators to be used for tests. A greater percentage of students in California than in the nation had teachers who permitted unrestricted use of calculators (31 percent and 18 percent, respectively). In California, most students or their families (97 percent) owned calculators; however, fewer students (58 percent) had teachers who explained the use of calculators to them. In California, 19 percent of the students never used a calculator to work problems in class, while 46 percent almost always did. Some of the students (16 percent) never used a calculator to work problems at home, compared to 33 percent who almost always used one. About one-quarter of the students (30 percent) never used a calculator to take quizzes or tests, while 23 percent almost always did. 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Cabfornia CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has become an issue of increasing importance to federal, state, and local government .Ns part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.° Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In California, 36 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 time-quarters of the students (76 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. About three-quarters of the students (72 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. National Council of Teachers of Mathematics, Professional Standardc fOr rhe 7'eaching of Matherniitio (Reston, V A: \ational Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 67 California TABLE 21 1 Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT California West I Nation 11, Percentage of students whose mathematics teachers reported having the following degrees Percentage Percentage Percentage Bachelor's degree 84 ( 3.3) SS ( 2) 56 ( 42) Master's or specialist's degree 35 ( 3.2) 32 ( 52) 42 ( 42) Doctorate or professional degree I ( 0.6) ( 0.0) 2 ( 1.4) Percentage of students whose mathematics teachers have the following types of teaching certificates that are recognized by California No regular certification 11 ( 2.0) ( 2.4) 4 ( 1.2) Regular certification but less than the highest available 13 ( 2.3) 20 ( 3.3) 29 ( 4.3) Highest certification available (permanent or long-term) 76 ( 2.5) 74 ( 3.3) 66 ( 4.3) Percentage of students Mean mathematics teachers have the Mowing types of teaching certificatn that are recognized by California Mathematics (middle school or secondary) 72 ( 3.4) 88 ( 3.0) 84 ( 2.2) Education (elementary or middle school) 24 ( 3.3) 9 ( 2.8) 12 ( 2.6) Other 4 ( 0.8) 2 ( 1.3) 4 ( 1.5) AV 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 undergaduate and graduate majors and their in-service training. a t) 68 THE 1990 NAEP TRIAL STATE ASSESSMENT California Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In California, 22 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 California (12 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and I Graduate Fields of Study PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT California West Nation 41. What was your undergraduate major? _ _ Percentage Percentage Percentage Mathematics 22 ( 2.0) 31 ( 5.9) 43 ( 3.9) Education 27 ( 2.7) 34 ( 8.6) 35 ( 3.8) Other 51 ( 2.6) 35 ( 8.6) 22 ( 3.3) What was your graduate major, Percentage Percentage Percentage L Mathematics 12 ( 2.2) 19 ( 4.7) 22 ( 34) Education 49 ( 3.1) 36 ( 4.5) 38 ( 3.5) Other or no graduate level study 39 ( 3.0) 45 ( 5.4) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard ei rors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 69 California Teachers' responses to questions concerning their in-service training for the year up to the Thal State Assessment (Table 23) show that: In California, 43 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Relatively few of the students in California (10 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS 1900 MEP TRIAL STATE ASSESSMENT California West Nation"-1 During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? None One to 16 hours 16 hours or more Percentage Porcentage Poraiwitage 10 ( 1.9) 11 ( 3.0) 11 ( 2.1) 47 ( 2.9) 45 ( 7.0) 51 ( 4.1) 43 ( 2.9) 44 ( 0.9) 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 .1 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT California 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.1° 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 wiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In California, 36 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (76 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In California, 22 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 vtith the same major. Some of the eighth-grade public-school students in California (12 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. '° Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Differences An International Assessment of Mathematks 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 Mathematics Achievement NAEP's 1990 Assessment of the Nation and the Plul Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991), THE 1990 NAEP TRIAL STATE ASSESSMENT 71 California In California, 43 percent of the eighth-grade public-school students had teachers who spent at least 1E1 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Relatively few of the students in California (10 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. 72 THE 1990 NAEP TRIAL STME ASSESSMENT Cahfornia CHAPTER 7 The Conditions Beyond School that Facilitate Mathematics Learning and Teaching Because students spend much more time out of school each day than they do in school, it is reasonable to expect that out-of-school factors greatly influence students' attitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, encouragement, and participation in student learning experiences are powerful influences. Together, teachers and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment and mathematics proficiency, students participating in the Trial State Assessment were askul a series of questions about themselves, their parents or guardians, and home factors related to education. h.! THE 1990 NAEP TRIAL STATE ASSESSMENT 73 California AmouNr OF READING MATERIALS IN ME HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students participating in the Trial State Assessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports on Types of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MO NAEP TRIAL STATE ASSESSMENT California West Nation - - , _ - ^ Does your family have, or receive on a regular basis, any of the following items: more than 25 books, an encyclopectia, newspapers, magazines? Zero to two types Three types Four types Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency 32 ( 1.2) 24 ( 1.6) 21 ( 1.0) 242 ( 1,4) 245 ( 4.1) 244 ( 2.0) 31 ( 1.0) 31 ( 1.4) 30 ( 1.0) 256 ( 1.6) 258 ( 2.4) 258 ( 1.7) 37 ( 1.4) 45 ( 1.9) 48 ( 1,3) 269 ( 1.6) 273 ( 3.2) 272 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. The data for CAlifornia reveal that: Students in California who had all four of these types of materials in thy 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 California A smaller percentage of Black, Hispanic, and Asian students had all four types of these reading materials it their homes than did White students. A greater percentage of students attending schools in advantaged urban areas than in disadvantaged urban areas or areas classified as "other" had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in thr "rtial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT California West Nation 1 How much television do you usually , I watch each day? Percentage and Proficiency Percentage and Proficiency Pen:engage and Proficiency One hour or less 16 ( 0.9) 14 ( 1.8) 12 ( 0.8) 266 ( 2.1) 269 ( 3.6) 209 ( 2.2) Two hours 24 ( 0.9) 20 ( 1.8) 21 ( 0.9) 259 ( 1.7) 266 ( 3.6) 283 ( 1.8) Three hours 23 ( 1.0) 20 ( 1.2) 22 ( 0.8) 257 ( IS) 262 ( 3.2) 265 ( 1.7) Four to five hours 26 ( 1.0) 29 ( 1.7) 28 ( 1.1) 251 ( 1.5) 263 ( 2.9) 260 ( 1.7) Six hours or more 11 ( 0.7) 16 ( 2.0) 16 ( 1.0) 244 ( 2,7) 246 ( 2.6) 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 uf the esilMAiC for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 75 California From Table 2$ and Table A25 in the Data Appendix: In California, average mathematics proficiency was higher for students who spent one hour or less watching television than for students who watched television six hours or more each day. Some of the eighth-grade public-school students in California (16 percent) watched one hour or less of television each day; 11 percent watched six hours or more. About the same percentage of males and females tended to watch six or more hours of television daily. However, a smaller percentage of males than females watched one hour or less per day. In addition, 8 percent of White students, 28 percent of Black students, 12 percent of Hispanic students, and I I percent of Asian students watched six hours or more of television each day. In comparison, 19 percent of White students, 8 percent of Black students, 14 percent of Hispanic students, and 20 percent of Asian students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in tir Data Appendix: In California, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in California (39 percent) did not miss any school days in the month prior to the assessment, while 28 percent missed three days or more. In ,..ddition, 27 percent of White students, 26 percent of Black students, 35 percent of Hispanic students, and 15 percent of Asian students missed three or more days of school. 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Cabfornia Similarly, 22 percent of students attending schools in advantaged urban areas, 31 percent in schools in disadvantaged urban areas, and 28 percent in schools in areas classified as "other" missed three or more days of school. TABLE 26 I Students' Reports on the Number of Days of 1 School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP T"'m.. STATE ASSESSMENT California Wiwi Nation How many days of school did you miss last month? Percentage and Pronciency Percentage and Proficiency Petvestage and Proficiency None 39 ( 0.9) 43 ( 2.7) 45 ( 1.1) 283 ( 1.8) 288 ( 3.5) 255 ( 1.8) One or two days 33 ( 1.1) 30 ( 1.4) 32 ( 0.9) 259 ( 1.6) 26$ ( 3.0) 266 ( 1.5) Throe days or more 28 ( 1.3) 27 ( 1.8) 23 ( 1.1) 246 ( 1.6) 250 ( 3.1) 250 ( 1,9) The standard errors of the estimated stausucs appear in parentheses. It can be said with about 95 percent certainty that, for each population of mterest, the value for the entire population is within 1. 2 standard errors of the estimate for the sample. ME 1990 NAEP TRIAL STATE ASSESSMENT 77 California 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.1 2 Students were asked if they agreed or disagreed with five statements designed to elicit their perceptions of mathematics. These included statements about: Personal experience with mathematics, including students' enjoyment of mathematics and level of confidence in their mathematics abilities: I like mathematics; I am good M mathematics. Value of matLematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for solving everyday 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 I (indicating vet)/ positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disageee" were given a value of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception inde r. according to whether they tended to stronfily agree with the statements (an index of 1), tended to agree with the statements (an inuex of 2), or tended to be undecided, to disagree, or to strongly diragree with the statements (an index of 3) Table 27 provides the data for the students' attitudes toward mathematics as defined by their perception index. The following results were observed for California: Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. About one.quarter of the students (25 percent) were in the "strongly agee" category (perception index of I). This compares to 27 percent across the nation. About one-quarter of the students in California (23 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). 12 National Council of Teachers of MathematIcs, Curriathim and Evaluation Standards for School Mathematic's (Reston, VA: National Council of Teachers of Mathematics, 1989). 75 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT California West I Nation I Student "perception Index" groups Percentage and Proficiency Percentage and Proficiency Percentage and Proaciency Strongly agee 25 ( 1.1) 27 ( 1.9) 27 ( 1.3) ("perception index" of 1) 268 ( 1.7) 273 ( 3.9) 271 ( 1.9) Agree 51 ( 0.8) 48 ( 15) 49 ( 1.0) ("perception index" of 2) 257 ( 1,4) 262 ( 2.4) 262 ( 1.7) Undecided, disagree, strongly disagree 23 ( 0.9) 25 ( 2.1) 24 ( 1.2) ("perception index" of 3) 244 ( 2.0) 249 ( 2.9) 251 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. 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 California 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 two types THE 1990 NAEP TRIAL STATE ASSESSMENT 79 California Some of the eighth-grade public-school students in California (16 percent) watched one hour or less of television each day; 11 percent watched six hours or more. Average mathematics proficiency was higher for students who spent one hour or less watching television than for students who watched television six hours or more each day. Less than half of the students in California (39 percent) did not miss any school days in the month prior to the assessment, while 28 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. About one-quarter of the students (25 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. 80 THE 1990 NAEP TRIAL STATE ASSESSMENT California 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 cornmittees, 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 (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics iteh-ls 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 81 California The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment requited approximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets were spiraled or interleaved in a systematic sequence so that each booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as described in the introduction to this report.' The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure A 1). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on students' performance on the set of mathematics items they received. IRT provides a common scale on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This common scale males it possible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. 'National Assessment of Educational Progress, Mathematics Ohjectiv9s 1990 Asr.sspnent (Princeton, NJ: Educational Tesung Service, 1988). r 82 THE 1990 NAEP TRIAL STATE ASSESSMENT California FIGURE Al I Content Areas Assessed Numbers and Operations This content area focuses on students' understanding of numbers (whole numbers, fractions, decimals, Mtegers) and their application to real-world situations, as well as computational and estimation situations. Understanding numerical relatiOnShipS as expressed in ratios, proportions, and percents Is emphasized. Students' abilities in estimation, mental Computation, use of calculators. generalization of numerical patterns, and verification of results are also included. Measurement This content area focuses on students' ability to describe real-world objects using numbers. Students are asked to identify attributes, select appropriate units, apply measurement concepts, and communicate measurement-related ideas to others. QueStions are included that require an ability to read instruments using metric, customary, or nonstandard units, with emphasis on precision and accuracy. Questions requiring estimation, measurements, and applications of measurements of length, time, money, temperature, massfweight, area, volume, capacity, and angles are also included in this content area. Geometry This content area focuses on students' knowledge of geometric figures and relationships and on their skills in working with this knowledge. These skiHs 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 relatiormhips. Data 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 interpret data are necessary skills in the contemporary world. Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysis. [Algebra and Functions This content area is broad in scope, covenng algebraic and functional concepts in more informal. exploratory ways fo- the eighth-grade Trial State Assessment. Proficiency in this concept area requires both manipulative facility and conceptual understanding: it involves the ability to use algebra as a means of representation and algebraic processing as a problem-solving tool. Functions are viewed not only in ierms of algebraic formulas, but also in terms of verbal descnptions, tables of values, and graphs. THE 1990 NAEP TRIAL STATE ASSESSMENT 83 California FIGURE A2 I Mathematical Abilities The following three categories of mathematical abilities are not to be construed as hierarchical. For example, problem solving involves interactions between conceptual knowledge and prOcedural skills, but what is considered complex problem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. Conceptual Understanding Students demonstrate conceptual understanding in mathematics when they provide evidence that 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; con 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): and judge the reasonableness and correctness of solutions. 84 THE 1990 NA rP TRIAL STATE ASSESSMENT California 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 defming performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. ln contrast, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define .,,-.Irfonnance at 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 ;allows: To define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To define performance at each of the higher levels on the scale, items were chosen that were: a) answered correctly by at least 65 percent of students whose proficiency was at or near that level; and b) answered incorrectly by a majority (at least 50 percent) of the students performing at or near the next lower level. The percentage of students at a level who answered the item correctly had to be at least 30 points higher than the percentage of students at the next lower level who answered it correctly. THE 1990 NAEP TRIAL STATE ASSESSMENT 85 California Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandinp of students perfotming at each level. Each of the four pmficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.' Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six 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 liven to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and the use of various instructional approaches. Because of the nature of the sampling for the Trial State Assessment, the responses to the mathematics teacher questionnaire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. r 86 THE 1990 NAEP TRIAL STATE ASSESSMENT California FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 Imam lei 0 Coif 0 Liam Sas T. Linda bad dine Ism buss an OW male sise end three dificivnt bads of balk as shawls above U she fins each box with the bed et bans shows' winch boa will bar all/ rwisa beLls to el CD Tht boa with the minis halls CD The bee with the ma bens CD The boa witha rubber belle You Cgiet tea EXAMPLE 2 00 80 70 AO to oo to BOXES OF MAT PICKED AT FARAWAY FARMS 1.1 Nis 111 1%1 Dim Of The Met Lam% Chypehisa W MINNOW flW IMNIMINIWO 9. How issay boitcs ad obtain was picked oa Thuridayl CD 55 CID 60 CD 70 CID SO CD 90 CD I don't know. Fo Grade 4 Overall Percentage Correct: 73% Percentage Correct for Anchor Levels: Etc &52 65 91 too Grade 4 Overall Percer:w.: Correct: 80% Percentage Correct for Anchor Levels: g2I2 NI2 a3.5Q 91 100 Grade 8 Overall Percentage Correct: 89% Percentage Correct for Anchor Levels: 4/c2 2Z2 AQQ 2§Q 87 96 100 THE 1990 NAEP TRIAL STATE ASSESSMENT 87 California FIGURE M I Example Items for Mathematics Proficiency Levels (continued) ILevel 250: Simple Multiplicative Reasoning and Two-Step Problem Solving EXAMPLE 1 7. What Ls the value of n + 5 when n i 3 Answer. EXAMPLE 2 Grade 8 Overall Percentage Percentage Correct Correct 78% for Anchor Levels: 222 ZOO 202 122 29 89 95 98 The table stove shows below, snake a cycle pen ol the slick sugh 146,01 MICR SURVEY USULTS Grade 8 Overall Percentage Percentage Correct ag 2E2 ol kw color. On dr circle 21 68 dote in the Wale Labs: each Wee. Correct 73% for Anchor Levels: ACQ 222 92 92 Cake at liale liarcesoas SIM Sews 17 73 'huh 107 she results of savoy pooh to Woman the mai she COMP bait Dad you use A. caladium en this ;gestic& 0 yes 0 No EXAMPLE 3 G. Kathleen is paciang buebills into boxes. Each boa hohls 6 baseballs She has 24 balls. Which number sentence will help hes rind out how many boxes she will need; CO 24 6 - ati 24+6.8 0 CD 24 +6 0 01) 24 a 6 CID I don i know, . Grads 8 Overall Percentage Percentage Correct glif2 37 71 51 o Correct: 77% for Anchor Levels: 2% 95 100 THE 1990 NAEP TRIAL STATE ASSESSMENT California FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 300: Reasoning and Problem Solving involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE 1 141. Which ot the folkarisq shows !be result at 414pW4 the stove man& over the lane fi t EXAMPLE 2 W 15r petal man that class Is builLies, a tat 15 hut bus a mamma bY a uak ses4s1 3 long. 14 tbe use acals a and, bans 35 ins MO would be repusersal by s scale ateds1 bow imsay cubes bight MI yea the calculate! ea this quastus! Yu 0 No Grads 6 Overall Percentage Correct: 60% Percentage Correct for Anchor Levels: 221 a4C1 33 49 77 90 Grade 12 Overall Percentage CcIrrect: 75% Percentage Correct for Ancho? Levels: g129 gE2 Kg 01.411.0 46 79 95 Grad. 8 Overall Percentage Percentage Correct Zi4 17 46 Correct 59% for Anchor Levels: 12Q AN se 99 ME 1990 NAEP TRIAL STATE ASSESSMENT S9 California FIGURE A3 1 Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability EXAMPLE 1 al' %Waco* i547 rein us tho foilouoAg miens ot dot-hitures 6 * . I 2 ) 4 16. liteteh:ss / Auerr of dot Noon ts continual. bow cosny dots will bc tn the EXAMPLE 2 7. ttplain bow you found yous Answer to question 16 Atmests Grade 8 Overall Percentage Correct: 34% Percentage Correct for Anctlor Levels: i2Q 215l2 NO Ng 13 19 53 as Grade 12 Overall Percentage Correct: 49% Percentage Correct for Anchor UMW aQ4 44 224 IN 22 48 90 Grade 8 Overall Percentage Correct: 15% Percentage Correct for inchor Levels: a,12 11/Q 1 4 28 74 Grade 12 Overall Percentage Correct: 27% Percentage Correct for Anchor Levels: g412 ar2Q 1§Q 3 22 74 90 TI1E 1990 NAEP TRIAL STATE ASSESSMENT California SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAME An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEP's goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually' all statistics that are based on samples (including those in NAFP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. like ahnost all estimates based on assessment measures, NAFP's total group and subgoup proficiency estimates are subject to a second so tree of uncertainty, in addition to sampling error. As previously noted, each student who participated in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropriate, set of the assessment questions -- or the entire set of questions -- somewhat different estimates of total group and subpoup proficiency might have been obtained. Thus, a second source of uncertainty arises because each student was administered a subset of the total pool of questions. t) 'HIE 1990 NAEP TRIAL STATE ASSESSMEN1 93 California 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 magiitude 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 groups) reflect only sampling error. NAEP uses a methodology called the jackknife procedure to estimate these standard errors. Drawing Inferences from the Results One of the goals of the Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the partifmlar sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples to make inferences about the population. The use of confidence 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 approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency ofthe students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confiderwe interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals arc quite complicated 92 THE 1990 NAEP TRIAL STATE ASSESSMENT California Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defmed 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 more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is higher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in peiformance between the two groups in the population because of the uncertainty associated with the estimated avrrage 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. As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the 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 sigmficant (different) at the .05 level. e-) THE 1990 NAEP TRIAL STATE ASSESSMENT 93 California As an example, suppose that one were interested in determining whether the average mathematics proficiency of eighth-grade females is highor than that of eighth grade males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard effors 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 fenaales and males is four points (259 - 255). The standard error of this difference is = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.8 and + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-gado females and males in public schools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used tf draw 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 anfidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a statistically significant difference in the population because of the magnitude of the standard errors. Cf.mversely, a difference that appears to be large may not be statistically significant. 3 'I'he procedure described above (especially the estimation of the standard error of the difference) is, "*. a strict sense, only appropriate when the statistics being compared come from independent samples. For certam comparisons in the report, the groups were not independent. In those cases, a different (and more appropnate) estimate of the standard error of the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMENT Cabfornia The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significance is being performed. However, in each chapter of this report, many different goups are being compared (i.e., multiple sets of confidence intervals are being analyzed). When one considers sets of confidence intavals, statistical theory indicates that the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. If one wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP arc statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol "!". In such cases, the standard errors -- and any confidence intervals or significance tests involving these standard errors -- should be interpreted cautiously. Further details concerning procedures for identifying such standard 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 defined by race/ethnicity and type of school communi4r, as well as by gender and parents' education level. NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander. and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these goups was not sufficiently high to permit accurate estimation of proficiency and/or background variable rf.!sults. 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 95 California 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 6ghth-grade public-scbool population in the state or territory, divided by the standard deviation of the proficiency in the total population. If the true difference between subgroup and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical report. Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "Idmost 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 Repiart p = 0 None 0 < p _C. 10 Relatively few 10 < p _5 20 Some 20 < p 5_ 30 About one-quarter 30 < p 5.' 44 Less than half 44 < p 5_ 55 About half 55 < p _5 69 More than half 69 < p 5 79 About three-quarters 79 < p 5. 89 Many 89 < p < 100 Almost all p = 100 All 4 r- A' ILl 96 THE 1990 NAEP TRIAL STATE ASSESSMENT Cakfornia 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 earl level of the four reporting subpopulations race/ethnicifv, type of community, pments' education level, and gender. THE 1990 NAEP TRIAL STATE ASSESSMENT 97 California TABLE A5 I Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Eighth-wade Mathematics -_ Pre-algebra Algebra TOTAL Percentege and Proildency 59 ( 1.9) 242 ( 1.1) 6:2 ( 2.1) 251 ( 1.4) 51 ( 2.4) 256 ( 1.3) 59 ( 2.5) 259 ( 1.6) 71 ( 4.8) 227 ( 3.5) 72 ( 4.7) 232 ( 3.4) 73 ( 2.5) 230 ( 1.4) 75 ( 4.4) 240 ( 2.4) 42 ( 4.0) 251 ( 2.7) 32 6.5) ( SIN ; 47 ( 4.6) 261 ( 3.3)1 55 ( 9.4) 269 ( 2.5)1 67 ( 5.3) 232 ( 3.2)1 65 ( 6.0) 240 ( 4.0)3 60 ( 2.5) 242 ( 1,5) 61 ( 2.2) 251 ( 2.0) Percentage and Proadattelf 21 ( 1.4) 272 ( 2.2) 19 ( 1.9) 272 ( 2.4) 26 ( 1.7) 280 ( 1.7) 21 ( 2.4) 277 ( 22) 19 ( 2.9) 16 ( 3.0) 246 ( 6.4) 14 ( 1.9) 256 ( 4.5) 13 ( 3.9) 24 ( 3.0) 275 ( 3.7) es") 24 ( 3.9) 287 ( 4.0)1 22 ( 7.9) *4* ( *I ) 19 ( 4.7) 262 ( 9.5)1 18 ( 4.1) 21 ( 1.8) 270 ( 2$) 20 ( 2.1) 272 ( 2.8) Percentage and Prenciency 18 ( 1.0) 293 ( 2.0) 15 ( 1.2) 296 ( 2.4) 18 ( 1.4) 304 ( 1.8) 17 ( 1.5) 300 ( 2.3) 04* ( 9 ( 22) .1,11 10 ( 1.3) 268 ( 4.1) 6 ( 1.5) *44 ) 30 ( 3.4) 299 ( 2.7) 41 ( 7.4) ( ..**) 22 ( 2.8) 310 ( 2.7)1 21 ( 4.4) 4.. ) 41** *IN 14 ( 3.3) 287 ( 4.2)1 15 ( 1.4) 291 ( 2.9) 16 ( 1.4) 294 ( 2.7) State Nation RACE/ETHNICITY White State Nation Made State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Other State Nation dimsr AP' The standard errors of the estimated statistiCs appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 98 o- I THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE AS Students' Reports on the Mathematics Class (mntinued) 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY hit90 NAEP TRIAL. STATE ASSESSMENT Eighthgrade Mathematics I Pri-algebra TpTAL. Percantage and Proficiency Percentage and Pmficiesta Percentage 'madam State 59 ( 1.9) 21 ( 1.4) 18 ( 1.0) 242 ( 1.1) 272 ( 22) 293 2.0) Nation 82 ( 2.1) 19 ( 1.9) 1$ 1.2) 251 ( 1.4) 272 ( 2.4) 298 2.4) PARENTS EDUCATION 1111 non-graduate State 79 ( 234 ( 3.3) 2.3) 10 ( 2.1) 9 ( 22) .441 Nation 77 ( 241 ( 3.7) 2.1) 13 ( 3.4) ( «pi 3 ( 1.1) sel HS graduate State ( 239 ( 2.7) 1.6) 13 (.1.9) ( von 9 ( 1.9) ..**) Nation 70 ( 2.6) 18 ( 2.4) ( 1.1) 249 ( 1.9) 206 ( 3.5) 277 ( 5 2) Some colktga State 55 ( 2.7) 26 ( 2.6) 18 ( 2.3) 251 ( 2.0) 273 ( 3.1) 298 ( 3.1) Nation 60 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 276 ( 2.8) 295 ( 3.2) College graduate State 46 ( 2.4) 26 ( .9) 23 ( 15) 251 ( 1.7) 280 ( 22) 302 ( 22) Nation 53 ( 2.7? 21 ( 2.3) 24 ( 1.7) 269 ( 1.5i 278 ( 2.8) 303 ( 2.3) GENDER Male State 61 ( 2.2) 19 ( 1.5) 18 ( 1.3) 244 ( 1.3) 275 ( 2.4) 294 ( 2.5) Nation 83 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 294 ( 25) Route State 58 ( 2.2) 22 ( 1.6) 18 ( 1.4) 240 ( 1.3) 269 ( 2.5) 292 ( 2.5) Nation 61 ( 2.6) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the va)ue 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 99 California TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Now 15 Mimeo 30 Minutes _ 45 Minutes An Hair or More TOTAL. Percentage and Proficiency 2 ( 0.5) ors* ( *el ( 0.3) 2 ( 0.7) 111191t ) ( 0.3) 2 ( 1.7) ( 0.7) ( 2 ( 0.7) 1 ( 0.8) ** ( ( 0.5) ( "") 0 ( 0.0) ( ***) 0 ( 0.0) 1 ( 0.9) e- 1 ( 0.8) ( "") 0 ( 0.0) ( 2 ( 0.8) *4. ( ***) ( 0.4) Percentage end Proficiency 30 ( 3.1) 247 ( 2.0) 43 ( 4.2) 256 ( 2.3) 29 ( 3.4) 260 ( 2.4) 39 ( 4.5) 266 ( 2.2) 30 ( 5.6) ( 55 ( 7.8) 232 ( 3.1) 34 ( 3.8) 233 ( 2.2) 46 ( 7.8) 245 ( 3.0)1 21 ( 3.8) 29 ( 7.8) **.) 31 ( 6.5) 260 ( 5.1)1 61 (11.3) 273 ( 3.1)1 37 ( 6.2) 241 ( 5.5)1 41 (12.6) 236 ( 2.1)I 36 ( 4.6) 247 ( 2.7) 37 ( 4.3) 256 ( 3.1) Pettentes* and Proficiency 52 ( 2.9) 257 ( 2.0) 43 ( 4.3) 265( 2.6) 55 k. 3.1) 271 ( 2.3) 4,i ( 5.1) 270 ( 2.7) 50 ( 8.8) 232 ( 4.7) 40 ( 6.7) 246 ( 5.3) 52 ( 3.8) 237 ( 22) 34 ( 6.8) 251 ( 4.2)1 47 ( 5.3) 269 ( 3.6) 37 ( 8.8) 53 ( 6.8) 282 ( 5.4)1 32 ( 8.6) Ilr** 53 ( 55) 241 ( 6.3)1 36 ( 9.4) 253 ( 9.0)1 48 ( 4.6) 256 f 2.2) 49 ( 5.1) 265 ( 2.5) Percentage and Proficiency 10 ( 12) 273 ( 5.2) 10 ( 1.9) 272 ( 5.7)1 8 ( 1.4) 294 ( 5.4) 11 ( 2.4) 277 ( 7.8)1 12 ( 4.4) ( .") 3( 1.2) 13 ( 2.9) ( "s) ( ***) 10 ( 5.4) ( ***) ea* *el 5 ( 3.4) t-e *AM ) 12 ( 5.9) ( 1.7) 274 ( 5.4) 10 ( 2.4) 276 ( 8.6)1 Percentage end Proficiency 0 I 0.9) 280 ( 5.7) 4 ( 0.9) 276 ( 5.1)1 6 ( 1.1) 4 ( 0.9) 279 ( 5.8)1 5 ( 2.5) .0110 *114 ) 2 ( 0.8) -** 441 4 ( 1.0) ( "gi 7 ( 2.1) *** ( ***) 14 ( 3.2) *** ( .44) 24 (102) *** ( e") 0 ( 0.0) *4. ( 3 ( 1.7) Rt. 10 , 6.2) 6 ( 1.5) 273 (11.5)1 4 ( 1.1) 282 (11.6)1 State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation Asian State Na;ion TYPE OF COMMUNITY Advantaged urban State Natron Disadvantaged urban State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). glf e- r- 100 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A6 (continued) 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 Nene 15 Minutes 30 Minutes 45 Minutes - An Hour or More TOTAL Parcerdage and Proficiency 2 ( 0.5) 1 ( 0.3) *** ( .") *** ( 1 ( 0.8) 3 ( 0.9) 0+0 ( 041 0.5) *** ) 2 ( 0.8) *** ( ***) ( 1 ( 0,4) *** ( Rh. 1 ( 0.4) Percentage and Proficiency 30 ( 3.1) 247 ( 2.0) 43 ( 4.2) 250 ( 2.3) 34 ( 5.1) 241 ( 3.9) 49 ( 6.3) 240 ( 2.8) 33 ( 4.4) 240 ( 22) 43 ( 52) 249 ( 3.1) 28 ( 3.1) 260 ( 3.7) 44 ( 5.4) 285 ( 2.6) 26 ( 3.2) 256 ( 2.9) 40 ( 4.7) 265 ( 24) 30 ( 3.3) 248 ( 2.1) 44 ( 4.4) 257 ( 2.9) 30 ( 3.3) 247 ( 2.5) 41 ( 4.4) 255 2.3) Percentage and Pendency 52 ( 2.9) 237 ( 2.0) 43 ( 43) 20S ( 2.6) 56 ( 4.7) 238 ( 2.8) 40 ( 6.1) 245 ( 3.7) 52 ( 4.4) 245 ( 2.4) 44 ( $.8) 258 ( 2.7) 55 ( 3.5) 263 ( 2.9) 43 ( 5.8) 270 ( 3.6) 52 ( 3,4) 271 ( 2.7) 44 ( 4.1) 277 ( 3.0) 53 ( 3.1) 280 ( 2.3) 43 ( 4.3) 288 ( 2.9) 51 ( 3.1) 253 ( 2.2) 43 ( 4.7) 264 ( 2.8) Percentap Proficient* 10 ( 12) 273 ( 5.2) 10 ( 1.9) 272 ( 5.7)1 7 ( 2.1) ( *el 8 ( 2.3) 111141. ( 3.1) Mr* ( ***) 7 ( 2.1) 13 ( 1.7) 201 ( 5.4) 11 ( 2.3) 287 ( 8.1)1 ( 1.4) 274 ( 6.7) 9 ( 1.9) 273 ( 7.3)i 10 ( 1.5) 271 ( 4.6) 11 ( 2.0) 272 ( 5.7)) Peetentage and Pendency 0 ( 0.9) 260 ( 5.7) 4 ( 0.9) 278 ( 5.1)1 2 ( 1.1) 4 ( 1.3) RIM 11** ) *** 7 ( 1.7) ( 4 ( 1.0) *** ".) 8 ( 1.4) 291 ( 5.5) .441 6 ( 1.1) 280 ( 6.2) 5 ( 1.3) 279 ( 6 ( 1.0) 280 ( 7.4) 4 ( 0.9) ( State Nation PARENTS' EDUCATION NS non-graduate State Nation graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statistics apislar in parentheses. It can be said with about 95 percent certainty that, for each population of interes:, ttr alue for the entire populatiqn is within ± 2 standard errors of the estimate for the sample. Interpret wittl 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 101 California TABLE A7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1040 NAEP TRIAL STATE ASSESSMENT Nene 16 Minutes 30 Minutes 46 Minutes An Now or More TOTAL Pereentaw and Prendancy 2477 "2.0i ( 0.0) 251 ( 2.0) ( 1.1) 263 ( 3.3) 10 ( 1.0) 258 ( 3M 4 ( 1.8) ( ***) 7 ( 1.5) ( 9 ( 1.3) 231 ( 3.1) 12 ( 1.8) ( 4 ( 12) ( «4) 4 ( 2.0) ( 0.1 5 ( 1.2) ( .41 8 ( 2.5) 40.4. 6 ( 0.5) *Ai.) 12 ( 3.7) 8 ( 1.1) 249 ( 3.8) 9 ( 1.0) 250 ( 3.8) Payouts.* and Profidency 29 ( 1.1) 254 ( 1.5) 31 ( 20) 264 ( 1.9) 31 ( 1.6) 267 ( 1.8) 33 ( 2.4) 270 ( 1.9) 29 ( 4.1) 20 ( 2.5) 241 ( 3.8) 28 ( 1.6) 235 ( 1.8) 27 ( 3.0) 246 ( 3.6) 24 ( 2.6) 270 ( 4.3) 22 ( 4.8) *** ***) 29 ( 3.7) 272 ( 4.9)1 41 (124/ 278 ( 3.0)1 31 ( 3.3) 244 ( 4.0)1 24 ( 3.3) 263 ( 4.9)1 30 ( 1.4) 264 ( 2.3) 30 ( 1.8) 263 ( 2.3) Percentage and Proficiency 35 ( 1.0) 200 ( 1.0) 32 ( 12) 203 ( 1.9) 37 ( 1.6) 274 ( 2.0) 32 ( 1,3) 270 ( 2.1) 31 ( 4.2) vim) 33 ( 2.7) 237 ( 3.5) 36 ( 1.7) 241 ( 22) 30 ( 2.8) 246 ( 3.4) 33 ( 3.0) 272 ( 4.1) 31 ( 5.6) r* 39 ( 2.4) 283 ( 3.4)1 31 ( 6.6) 230 ( 4.6)1 37 ( 2.5) 242 ( 5.3)1 31 ( 3.0) 247 ( 4.7)1 35 ( 1.2) 200 ( 2.5) 32 ( 1.3) 204 ( 2.3) Percentage and Proficiency 18 ( 0.7) 258 ( 2.0) 16 ( 1.0) 266 ( 1.9) 14 ( 0.9) 275 ( 2.3) 15 ( 0.9) 277 ( 22) 20 ( 3.5) 18 ( 2.3) 240 ( 3.8) 17 ( 1.3) 236 ( 2.5) 17 ( 2.1) 241 ( 4.3) 17 ( 2.1) ( 18 ( 3.9) ( ***) 16 ( 1.5) IWO 41 12 ( 3.3) t 4141 14 ( 2.2)vi 20 ( 1.9) 250 ( 4.8)1 15 ( 1.1) 255 ( 34) 15 ( 1.1) 267 ( 2.1) Percentage and Pro Went. 13 ( 0.9) 255 ( 3.0) 12 ( CI) 258 ( 3.1) 10 ( 1.2) 274 ( 3.3) 11 ( 1.3) 260 ( 3.3) 17 ( 3.2) ( *el 16 ( 14) 232 ( 3.7) 12 ( 1.2) 232 ( 3.7) 14 ( 1.7) eft ( ***) 23 ( 3.2) 271 ( 4.1) 25 i 6.2) ( } 11 ( 2.6) ( ".) 7 ( 3.4) ( 4") 13 ( 2.0) 14 ( 2.2) ,4,41 12 ( 1.2) 255 ( 3.2) 13 ( 1.1) 258 ( 3.6) State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged trban State Nation Disadvantaged urban State Nation Onier 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. 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 thal 62 students). 1 r- p-r. 1 102 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A7 1 Students' Reports 013 the Amount of Time They (emitinued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . 19110 NAEP TRIAL STATE ASSESSMENT _._ None 15 Minutes 30 Minutes 45 Minutes S. An Hour or More TOTAL Percentage and Proficiency Perceitage and Proficiency Percentage and Prolidency Percentage and Proficiency Percentage and Proficiency State ( 0.8) 29 ( 1.1) 35 ( 1.0) 18 ( 0.7) 13 ( 0.9) 247 ( 2.8) 254 ( t$) 260 ( 1.6) 258 ( 2.0) 255 ( 3.0) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 10 ( 1.0) 12 ( 1.1) 251 ( 2.8) 2.4 ( 1.9) 263 ( 1.9) 288 ( 1.9) 258 ( 3.1) PARENTS EDUCATION HS non-grackatte State 10 ( IMIIP 2.2) Mtn 29 ( 239 ( 3.0) 3.6) 39 ( 242 ( 2.6) 21) 11 ( 1.7) 12 ( ( 2,5) 444) Nation 17 ( 3.0) 26 ( 33) 34 ( 4.4) 12 ( 2.5) 10 ( 2.2) 248 ( 4.0) 246 ( 2.6) ( HS graduate State 9 ( 1.8) 30 ( 2.7) 36 ( 2.6) 16 ( 2.0) 10 ( 1.5) Vi 243 ( 2.9) 24$ ( 2.5) 245 ( 32) Nation 10 ( 1.7) 33 ( 2.2) 31 ( 1.9) 18 ( 1.4) 11 ( 1.5) 248 ( 4.2) 259 ( 32) 254 ( 2.4) 256 ( 2.8) 244 ( 3,4) Some college State 7 ( 1.2) 28 ( 2.3) 36 ( 2.3) 17 ( 1.8) 12 ( 1.5) Mr* ) 259 ( 2.9) 270 ( 21) 281 ( 4.0) **IF 1111 Nation 9 ( 12) 30 ( 2.7) 36 ( 2.1) 14 ( 1.8) 11(1.5) 266 ( 3.0) 268 ( 2.6) 274 ( 3.5) Coitege graduate State 8 ( 0.8) 30 ( 1.5) 35 ( 1.8) 17 ( 1.2) 13 ( 1.3) ( 288 ( 2.1) 278 ( 2.4) 274 ( 3.5) 269 ( 5.0) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 285 ( 3.6) 275 ( 2.0) 275 ( 2.6) 278 ( 3.2) 271 ( 2.8) GENDER Male State 9 ( 1.0) 31 ( 1,8) 3$ ( 1.6) 14 ( 1.1) 10 ( 0.9) 249 ( 31) 257 ( 1,9) 261 ( 2.2) 261 ( 3,1) 255 ( 4.2) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 284 ( 2.8) 266 ( 2.4) 265 ( 3.0) 258 ( 41) Female State 6 ( 0.9) 27 ( 1.4) 38 ( 1.4) 17 ( 1,0) 15 ( 1,4) 245 ( 3.6) 250 ( 1.7) 2$6 ( 1.7) 256 ( 2.4) 256 ( 3.7) Nation 7 ( 0.9) 26 ( 2.0) 35 ( 1.7) /7 ( 1.0) 13 ( 1.3) 248 ( 4.1) 263 ( 1.5) 280 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, lb: each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 103 California FABLE AS I Teachers' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TR/AL STATE ASSESSMENT - *unbars and Operations Ottemeby Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL PinsMage soW proftionw 40 ( 3.1) 261 ( 1.7) 49 ( 3.8) 260 ( 1.8) 39 ( 3.7) 264 ( 2.1) 46 ( 3.7) 267 ( 2.2) 44* ( 441 54 ( 7.9) 243 ( 4.3) 43 ( 3.5) 237 ( 2.7) 47 ( 8.7) 246 ( 4.6) 35 ( 4.8) 258 ( 3.4) 32 ( 9.8) es* 31 ( 7.7) 286 ( 4.9)1 28 (13.0) ..**) 33 ( 8.4) 241 ( 6.2)1 4.8 (12.1) 255 ( 8.3)1 45 ( 4.7) 248 ( 2.4) 52 ( 4.1) 260 ( 2.3) AmmaNp and ftWkism, 22 ( 22) 282 ( 3.5) 16 ( 2.1) 287 ( 3.4) 21 ( 2.4) 297 ( 3.8) 16 ( 2.4) 289 ( 3.5) 24 ( 4.1) 11 ( 3.3) te 16 ( 2.5) 257 ( 5.3) 11.414t 4HHt ) 37 ( 4.3) 293 ( 52) 77 ( 5.2) .44 ( 26 ( 5.9) 304 ( 5.1)1 16 ( 4.2) .441 22 ( 7.7) 273 (14.2)1 9 ( 4.0) elm) 19 ( 3.2) 278 ( 8.1)1 18 ( 2.7) 286 ( 3.8) limmedapp and Prokftemy 21 ( 2.5 248 ( 2.7 17 ( 3.0 250 ( 5.6) 22 ( 3.8) 200 ( 3.5) 14 ( 3.4) 259 ( 8.9)! 12 ( 3.8) 26 (7.4) 226 ( 2.8)1 22 ( 3.1) 230 ( 3.3) 23 ( 4.1) RA* ( *el 17 ( 3.0) 4111 23 ( 5.6) .44 ( 24 ( 7.6) 266 ( 8.3)1 9 ( 7.0) 26 ( 8.0) 239 ( 7.9)1 39 (10.3) 238 ( 8.4)1 4$ ( 3.9) 242 ( 4.1)1 16 ( 3.9) 253 ( 7.1)1 Nmunbelp Ammftip and god Proldomy 25 2.7 25 t1.1 33 4.0 28 3.8 272 ( 4.0) 260 ( 3.2) 25 ( 3.1) 29 ( 3.7) 206 ( 3.2) 208 ( 3.5) 36 ( 4.7) 27 ( 44) 277 ( 4.3) 286 ( 3.3) 22 5.7) 15 ( 5.2) 114. .) 23 ( 5.7) 33 ( 7.9) 238 ( 8.1)1 242 ( 5.8)1 23 ( 3.7) 24 ( 4.0) 242 ( 2.9) 242 ( 3.1 ) 34 ( 5.8) 27 ( 6.8). 25$ ( 4.4)! ( *el 36 ( 4.7) 23 ( 4.0) 280 ( 5.8) 44 ( 8.9) *41 27 ( 5.4) 28 ( 7.0) 293 ( 8.3)1 275 ( 8.6)1 40 ( 85) 38 ( 9.4' 287 ( 4.9)! 13 ( 5.2) 18 ( 6.4) elhO *Mt ) 21 ( 6.5) 33 (11.8) 11.) 248 ( 82)1 26 ( 4.1) 31 ( 4.0) 283 ( 4.0) 254 ( 2.5) 34 ( 5.3) 28 ( 4.8) 270 ( 4.8) ( 3.9) Mmerdage sod Prilkftmw 22 tri 21 3.3( 264 5.41 20 ( 3.0) 271 ( 3.8) 22 ( 3.4) 273 ( 5.8) 18 ( 4.5) 24 ( 7.3) 233 ( 4.7)1 23 ( 3.3) 235 ( 3.8) 16 ( 5.5) 444. ( ,1 28 ( 32) 273 ( 8.1) 14 ( 6.8) 18 ( 5.7) ( 444) 13 ( 3.2) 17 ( 4.7) .44 18 ( 7.8) ( «Del 20 ( 33) 255 ( 4.7) 24 ( 4.3) 265 ( 5.7) State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a renable estimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABI E AS Teachers' Reports on the Emphasis Given to (cmtinued) i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRULL STATE ASSESSMENT Numbers and Operations Measurement Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Little or No Emphasis Emphasis TOTAL Parcantago and Praticiancy Parentage and Proffelancy Percentage and Praftelancy Percantaas and Ihniciany Penantaa and Prolkthancy Persantap and Pranciancy State 40 ( 3.1) 22 ( 2.2) 21 ( 2.5) 25 ( 2.7) 25 ( 3.1) 22 ( 2.5) 251 ( 1.7) 282 ( 3.5) 248 ( 2.7) 268 ( 3.3) 269 ( 2.7) 256 ( 2.8) Nation 49 ( 3.8) 15 ( 2.1) 17 ( 3.0) 33 ( 4.0) 28 ( 3.8) 21 ( 3.3) 260 ( 1.8) 287 ( 3.4) 250 ( 59) 272 ( 4.0) 280 ( 3.2) 284 ( 5.4) PARENTS ED1JCAT10A NS non-graduate State 45 ( 242 ( 4.4) 4.4) 12 ( 3.3) 21 ( se* 3.7).) 23 ( es. ( 4.5) *** 414.111 Nation 60 ( 251 ( 6.9) 3.4) ( 2.3) *** ( elm) 25 ( 5.3) gm* ( 4.44) 32 ( 6.3) ) 20 ( grew ( 8.7) HS graduate State 43 ( 4.2) 18 ( 3.3) 22 ( 3.3) 25 ( 38) 22 ( 4.8) 23 ( 3.3) 243 ( 3,0) 260 ( 4.4) 233 ( 8.0) 249 ( 5.2) 242 ( 3.941 240 ( 4.5) Nation 55 ( 259 ( 4.6) 2.9) 11 ( 2.8) ( v.) 17 ( 251 ( 3.9) 6.1)! 27 ( 253 ( 5.0) 4.7)f 27 ( 255 ( 4.5) 4.2) 24 ( 246 ( 5.1) 4.8)1 Some college State 38 ( 4.0) 24 ( 3.2) 22 ( 3.3) 24 ( 38) 29 ( 3.8) 17 ( 2.9) 259 ( 2.7) 284 ( 5.8) 252 ( 5.4) 275 ( 5.9) 261 ( 4.9) 203 ( 6.5) Nation 47 ( 4.4) 17 ( 3.3) 39 ( 5.5) 27 ( 5.0) 23 ( 4.1) 265 ( 2.8) 284 ( 4.1)1 270 ( 4.5) 262 ( 4.8)1 270 ( 4.7) College graduate State 98 ( 3.6) 27 ( 2.8) 19 ( 3.1) 27 ( 3.2) 27 ( 3.2) 22 ( 2.9) 281 ( 2.5) 297 ( 3.7) 259 ( 4.2) 287 ( 4.2) 271 ( 4.0) 273 ( 3.8) Nation 44 ( 4.1) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 289 ( 2,6) 298 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3,8) 280 ( SA) GENDER Male State 40 ( 3.4) 21 ( 2.3) 21 ( 2.5) 24 ( 2.7) 24 ( 3.1) 22 ( 2.8) 252 ( 2.1) 285 ( 4.2) 250 ( 3.9) 272 ( 4.4) 281 ( 3.3) 257 ( 3.3) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 281 ( 2.5) 287 ( 4.4) 258 ( 6,7) 275 ( 4.8)* 283 ( 3.8) 288 ( 8.8) Female State 40 ( 3.2) 22 ( 2.2) 21 ( 2.8) 26 ( 2.9) 26 ( 3.4) 22 ( 2.8) 249 ( 2.4) 279 ( 3.5) 241 ( 3.9) 283 ( 3.4) 256 ( 3.0) 255 ( 3.4) Nation 51 ( 3.9) 45 ( 2.4) 17 ( 32) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 260 ( 2.0) 286 ( 3.3) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 263 ( 5.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 105 California TABLE AS I Teachers' Reports on the Emphasis Given To (c°ntinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1000 RAEP TRIAL STATE ASSESSMENT Data Anatysis, Statistics, anC Probability Algebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage and Prolicioncy 17 ( 2.7) 263 ( 5.0) 14 ( 2.2) 269 ( 4.3) 20 ( 3.4) 279 ( 4.5) 14 ( 2.4) 278 ( 4.1) 10 ( 4.1) ***) 14 ( 3.4) IP ( 15 ( 2.8) 233 ( 8.5) 15 ( 4.1) ( 44) 17 ( 4.2) *111 34 ( 8.7) ...) 26 ( 6.7) 293 ( 8.3)1 11 ( 6.6) eV* ) 9 ( 4.3) ..) 19 ( 9.4) 4 ( 22 ( 4.2) 256 ( 5.7)1 15 ( 2.9) 267 ( 4.7) Peroentaga and Proficiency 46 ( 3.1) 251 ( 2.8) 53 ( (4) 261 ( 2.9) 45 ( 3.8) 272 ( 2.4) 53 ( 5.0) 271 ( 3.1) 58 ( 7.5) 225 ( 5.0) 53 ( 82) 225 ( 4.3) 51 ( 4.0) 227 ( 3.0) 56 ( 6.3) 246 ( 4.4) 49 ( 4.1) 265 ( 4.9) S5 ( 7.1) ...) 33 ( 7.1) 276 ( 6.5)1 85 (194) 284 ( 7.4)1 65 ( 8.0) 232 ( 6.8)1 34 (11.4) 236 ( 8.2)1 411 3.7) 254 ( 3.3) 53 ( 5.2) 260 ( 3.4) Percentage and Proffekoncy 46 ( 2.4) 273 ( 2.4) 46 ( 3.6) 275 ( 2.5) 52 ( 2.9) 284 ( 2.7) 48 ( 4.2) 281 ( 3.0) 31 ( 5.6) .44 ( .44) 39 ( 7.1) 253 ( 6.3) 35 ( 3.0) 249 ( 2.7) 46 ( 5.9) 257 ( 4.0)1 66 ( 3.7) 287 ( 3.7) 61 ( 8.1) .44) 57 ( 6.0) 289 ( 4.7)1 41 ( 8.9) 296 ( 7.9)1 47 ( 7.0) 257 ( 5.0p 53 (11.8) 254 ( 6.3)1 44 ( 4.0) 270 ( 4.0) 47 ( 4.3) 276 ( 2.8) Percentage and Proficiency 19 ( 1.9) 230 ( 2.3) 20 ( 3.0) 243 ( 3.0) 16 ( 2.4) 24$ ( 32) 18 ( 2.8) 251 ( 3.3) 26 ( 7.2) 444 ...) 27 ( 6.9) 226 ( 22)f 24 ( 2.7) 224 ( 2.3) 18 ( 4.2) .44 10 ( 1.8) .44 9 ( 4.9) .. 12 ( 4.6) 4. ( .44) 18 ( 5.3) 44 18 ( 5.4) .4. ., 20 ( 9.4) et. ( tee 18 ( 2.9) 238 ( 3.4) 17 ( 3.3) 245 ( 4.4)1 State Nation RACE/ETHNICITY White State Nation Made State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban 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 i 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accuraw determination of the variability of this estimated mean proficiency. *** Sample SIM is insufficient to permit a reliable estimate (fewer than 62 students). 106 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A8 I Teachers' Reports on the Emphasis Given To (cmtinued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111100 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL, fiertentage and Pteliciency Percentage and Prcaciency Percentage and Proficiency Percentage and Proficiency State 17 ( 2.7) 48 ( 3.1) 48 ( 2.4) 19 ( 1.9) 263 ( 5.0) 251 ( 2.8) 273 ( 2.4) 236 ( 2.3) Nation 14 ( 22) 53 ( 44) 48 ( 3.6) 20 ( 3.0) 269 ( 4.3) 261 ( 2.9) 275 ( 2.5) 243 ( 3.0) PARENTS EDUCATION NS nen-graduate State 11 ( eqi 2.5) 48 ( 231 ( 4.8) 4.7) 37 ( 251 ( 3.8) 4.7) 21 ( «it 3.4) ***) Nation 9 ( ( 3.0) 53 ( 240 ( 7.7) 82) 28 ( .44 ( 5.2) 29 ( 6.9) .4*) NS graduate State 18 ( 3.9) 50 ( 4.5) 37 ( 3.8) 22 ( 3.1) 248 ( 5.2)1 237 ( 4.5) 261 ( 3.6) 235 ( 4.0) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 261 ( &O)1 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Soma college State 17 ( 32) 47 ( 3.9) 48 ( 3.7) 17 ( 3.0) 287 ( 6.8) 258 ( 4.8) 276 ( 3.4) ..... ( .....i) Nation 13 ( 2.5) ***) 57 ( 270 ( 5.8) 3.7) 48 ( 278 ( 4.8) 3.0) 17 ( .-4,.. ( 3.1) .÷..) College graduate State 20 ( 3.4) 48 ( 3.7) v.6 ( 2.7) 15 ( 2.0) 281 ( 5.2) 271 ( 2.7) 2b4 ( 2.7) 240 ( 4.4) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 18 ( 2.4) 282 ( 4.5) 275 ( 3.8) 288 ( 3.0) 249 ( 4.0) GENDER Mal. State 18 ( 2.9) 47 ( 3.3) 45 ( 2.7) 18 ( 1.9) 264 ( 6.0) 253 ( 3.7) 273 ( 2.8) 236 ( 2.8) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.6) 275 ( 5.8) 260 ( 3.5) 276 ( 3.2) 243 ( 3.0) Female State 17 ( 2.7) 50 ( 3.2) 48 ( 2.7) 19 ( 2.3) 262 ( 5.4) 248 ( 2.6) 273 ( 2.4) 235 ( 3.1) Nation 16 ( 2.4) 53 ( 4.5) 48 ( 3.6) 18 ( 2.9) 263 ( 4.4) 262 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 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 relithle estimate (fewer than 62 students). 4.. THE 1990 NAEP TRIAL STATE ASSESSMENT 107 California TABLE A9 I Teachers' Reports on the Availability of i Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1060 NAEP TRIAL I Get AU the Resources I I Get Most of the I Get Some or None of STATE ASSESSMENT Need Resources I Neuf the Resources I Need TOTAL Permits's and Paladin:3r Percentage and Proilciency Percentage and Proficiency State 14 ( 2.1) 53 ( 3.7) 34 ( 3.6) 253 ( 3.4) 260 ( 2.1) 253 ( 2.4) Nation 13 ( 2.4) 58 ( 4.0) 31 ( 4.2) 265 ( 42) 265 ( 2.0) 261 ( 2.9) RACE/ETHNICITY White State 14 ( 22) 56 ( 4.0) 30 ( 4.2) 264 ( 4.0) 274 ( 1.9) 270 ( 2.5) Nation 11 ( 2.5) 58 ( 4.6) 30 ( 4.6) 275 ( 3.5)1 270 ( 2.3) 267 ( 3.3) Sink Siate lb ( 4.8) eta ( 43 ( 8.0) 240 ( 4.6) 39 ( 9.1) 4.4 ( .44) Nation 15 ( 4.2) 52 ( 8.6) 33 ( 72) 241 ( 5.3)1 242 ( 2.4) 236 ( 4.9) Hispanic State 13 ( 2.7) 50 ( 43) 37 ( 4.5) 235 ( 3.8)1 238 ( 2.4) 236 ( 2.3) Nation 23 ( 7.6) 44 ( 4.9) 34 ( 7.7) 248 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 Asian State 16 ( 42) 4.4 52 ( 4.8) 274 ( 4.1) 32 ( 3.8) 270 ( 4.9) Nation 19 ( 8.6) 4.4 ( .41 37 ( 7.7) ..4 44 (12.7) .41 TYPE OF COMMUNITY Advantaged urban State 60 ( 8.8) 29 ( 7.0) 279 ( 5.2)1 278 ( 5.3)1 Nation 38 ( 92) 272 ( 84)1 59 ( 8.9) 286 ( 1.3)1 3 ( 3.1) .... Disadvantaged urban State 9 ( 4.8) ( .44) 59 ( 8.5) 243 ( 5.4)1 31 ( 7.4) 235 ( 3.2)1 Nation .4. 40 (13.1) 251 ( 5.4)1 50 (144) 253 ( 54)1 ..)ther State 17 ( 32) 50 ( 4.9) 33 4.7) 249 ( 3.7)1 257 ( 2.4) 256 ( 3.1)i Nation 11 ( 2.9) 58 ( 5.4) 31 ( 5.6) 265 ( 3.9)f 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. '1" Sample size is insufficient to permit a rebable estimate (fewer than 62 students). 108 I THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE , ) I Teachers' Reports on the Availability of (continued) Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL I Get All the Resources I I Oat Most of the I Get Some or None of STATE ASSESSal.ENT Need Resources I Need the Resources I Need TOTAL PerCatitige end Proackncy Percentell, end Pronclency Pertentage and Proficiency State 14 ( 2.1) 53 ( 3.7) 34 ( 3.6) Nation 253 ( 13 ( 3.4) 2.4) 260 ( se 1 2.1) 4.0) 253 ( 31 ( 2,4) 4,2) 285 ( 4.2) 265 ( 2.0) 281 ( 2,9) PARENTS EDUCATION NS non-graduate State 14 ( 3.6) 51 ( 239 ( 4.8) 3.4) 36 ( 239 ( 4.9) 3.3) Nation 8 ( 2.6) 54 ( 5.7) 38 ( 8,3) ( #44 ) 244 ( 2.7) 243 ( 3.5)1 NS graduate State 14 ( 2.8) ( 4.9) 35 ( 4.8) V011 ( 1141 247 ( 2.8) 244 ( 32) Nation 1 0 ( 2.5) 54 ( 4.9) 35 ( 4.9) 253 ( 4.8)1 2$6 ( 1.9) 258 ( 2.8) Some colleste State 14 ( 2.4) 53 ( 4.5) 32 ( 4.7) 259 ( 4.5) 287 ( 2.9) 280 2.4) Nation 13 ( 3.3) 62 ( 4.3) 25 ( 4.1) 289 ( 2.5) 267 ( 3.8) College graduate State 12 ( 2.0) 54 ( 4.4) 34 ( 4.1) 269 ( 4.5) 276 ( 2.3) 286 ( 3.3) Nation 15 ( 2.9) 56 ( 4.9) 30 ( 5.1) 276*( 5.4)1 276 ( 2.2) 273 ( 3.7) GENDER Male State 13 ( 2.1) $2 ( 3.9) 34 ( 3.9) 252 ( 3.7) 263 ( 2.6) 254 ( 2.6) Nation 13 ( 2.6) 57 ( 4.0) 50 ( 4.0) 2134 ( 5.0)1 285 ( 2,6) 284 ( 3.3) Fernat State ( 2.2) 53 ( 3.7) 33 ( 3.6) 255 ( 4.0) 257 ( 2.1) 252 ( 2.8) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 266 ( 3.9) 254 ( 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 -- thc 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 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 California 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 Never TOTAL Percentage and Proficiency Percentage and Profidency Pen:entail* and Proficiency State 69 ( 3.1) 32 ( 2.9) 9 ( 1.8) 259 ( 2.0) 254 ( 2.8) 250 ( 6.3)1 Nation 50 ( 4.4) 43 ( 4.1) ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 5.4)1 RACE/ETHNICITY White State 66 ( 3.7) 27 ( 3.2) 8 ( 2.3) 272 ( 2.2) 270 ( 3.1) 270 ( 4.6)1 Nation 49 ( 4.6) 43 ( 4.5) 8 ( 2.3) 265 ( 2.7) 271 ( 2.2) 285 ( 4.9)1 Black State 59 233 ( 8.8) ( 4.2) 24 ( 4.9) ( *44 17 ( 9.4) .44) Nation 47 ( 8 1) 45 ( 7.0) 9 ( 4.1' 240 ( 3.4) 238 ( 4.0) ***) Hispanic State 50 ( 4.2) 41 ( 4.6) 8 ( 1.8) 236 ( 2.1) 239 ( 1.9) Nation 64 ( 7.2) 32 ( 6.9) 4 ( 1.4) 246 ( 2.5) 247 ( 6.3)1 Asian State 64 ( 4.0) 29 ( 3.8) 8 ( 2.3) 275 ( 3.3) 271 ( 5.8) 4" ( *") Nation 60 -* ( 8.2) 37 114-0 ( 7.9) ( ) 4 ( "I ( 2.7) "41 TYPE OF COMMUNITy Advantaged urban State 73 282 ( 7.9) ( 4.2)1 15 ( 4.8) ...) 12 ( *** ( 6.4) .44) Nation 39 (22.9) ( *441 41 273 (17.9) ( 6.0)1 20 (12,2) Disadvantaged urban State 55 (10.1) 41 (10.7) 3 ( 2.3) 241 ( 4.0)1 243 ( 7.7)1 Nation 70 (11.7) 21 ( 9.0) 9 ( 8.5) 248 ( 4.8)1 249 ( 8.7)1 Other State 60 ( 4.4) 33 ( 4.2) 7 ( 2.4) 257 ( 2.3) 256 ( 3.4) 251 ( 7.3)1 Nation 50 ( 4.4) 44 ( 4.5) 6 ( 1.8) 260 ( 2.4) 264 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Interest, the value for the entire population is within 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). 110 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE AICIa I Teachers' Reports on the Frequency of Small (continued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 199O NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Profickincy Percentage and Proficiency Percentage and Proficiency State 59 ( 3.1) 32 ( 2.9) 9 ( 1.8) 259 ( 2.0) 254 ( 2.8) 250 ( 6.3)1 Nation 50 ( 4.4) 43 ( 4.1) 6 ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 5.4)) PARENTS' EDUCATION NS non-graduate State 56 ( 5.0) 39 ( 52) ( 1.8) 240 ( 3.3) 243 ( 3.7) 0111IP *V* ) Nation BO ( 244 ( 6.4) 3.2) 39 ( 244 ( 6.5) 3.2)1 1 ( i.4) NS graduate State 55 ( 244 ( 4.0) 2.8) 38 ( 247 ( 4.1) 2.3) 8 ( 4.1H. 2.2) Nation 49 ( 4.8) 45 ( 5.1) 8 ( 2.5) 252 ( 2.8) 257 ( 2.7) Some college State 65 ( 4.1) 26 ( 3.6) 9 ( 2.8) 285 ( 2.8) 281 ( 4.4) ( Nation 51 ( 5.2) 42 ( 5.1) 266 ( 3.1) 268 ( 3.2) College graduate State 64 ( 3.5) 26 ( 3.0) 9 ( 2.3) 273 ( 2.5) 272 ( 3.7) 261 ( 6.9)1 Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 276 ( 3.0) 285 ( 4.9)1 GENDER Male State 57 ( 3 6) 34 ( 3.4) 9 ( 2.0) 262 ( 2.5) 255 ( 2.8) 252 ( 13.7)1 Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 265 ( 3.1) 278 ( 5.3)1 Female State 62 ( 3.1) 30 ( 3.1) 8 ( 1.9) 256 ( 2.0) 253 ( 3.2) 247 ( 7.2)1 Nation SO 1 4.7) 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.6)1 The standard errors of the esumated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within r 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 111 California TABLE MOb I Teachers' Reports on the Use of Mathematical i Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency Parcantelpt and Proficiency Rercenlage and Proficiency State 35 ( 3.8) 58 ( 3.7) ( 1.2) 252 ( 2.5) 257 ( 1.9) 269 ( 7.2) Nation 22 ( 3.7) 68 ( 3.9) ( 2.6) 254 ( 3.2) 263 ( 1.9) 282 ( 5.9)1 RACE/ETHNIC1TY Whit. State 36 ( 4.9) 57 ( 4.9) 7 ( 1.5) 267 ( 2.9) 272 ( 1.8) 285 ( 6.3)1 Nation 17 ( 4.0) 72 ( 4.2) 10 ( 2.7) 261 ( 3.o)( 289 ( 2.1) 288 ( 6.2)1 Black State 39 ( 7.4) 51 ( 6.7) 10 ( 3.3) 228 ( 4.4) Nation 22 ( 5.9) 70 ( 8.3) 8 ( 3.9) 233 ( 5.9)1 241 ( 2.9) Hispanic State 34 ( 231 ( 3.9) 2.8) 80 ( 239 ( 3.7) 1.9) ...) Nation 39 ( 7.5) 5.5 ( 7.3) 7 ( 2.6) 247 ( 3.8) 245 ( 3.8)1 Mien State 31 ( 4.9) 59 ( 4.8) 263 ( 4.9)! 275 ( 3.4) Nation 42 ( ( 6.5) .4-41 52 ( 5.7) 6 ( 42) TYPE OF COMMUNITY Advantaged urban State 33 ( 282 ( 9.2) 6.9)1 57 ( 272 ( 9.4) 3.5)1 10 ( f.. ( 3.9) Nation 23 (4.4) 4,4-*) 83 (11.5) 278 ( 5.6)1 15 ( 9.3) ** ) Disadvantaged urban State 42 ( 9.6) 237 ( 3.8)1 55 ( 244 ( 9.0) 6.6)1 ***) Nation 39 (11.4) 247 ( 7.5)1 59 (12.1) 253 ( 7.0)1 Other State 35 ( 4.6) 59 ( 4.8) 252 ( 3.1) 257 ( 2.1) ft* -*) Nation 19 ( 4.3) 72 ( 5.0) 9 ( 3.3) 253 ( 3.9)1 263 ( 2.2) 281 ( 7.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample Stze IS insufficient to permit a reliable estimate (fewer than 62 students). 112 4 -.1 1 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE AlOb I Teachers' Reports on the Use of Mathematical (continued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Lass Than Once a Week Never TOTAL Percentage mid Proficiency Percentage and Proficiency Percentage and Proficiency State SS ( 3.8) 58 ( 3.7) 7 ( 1.2) 252 ( 2.5) 257 ( 1.9) 269 ( 7.2) Nation 22 ( 3.7) 69 ( 3.9) 9 ( 2.6) 254 ( 3.2) 263 ( 1.9) 282 ( 5.9)1 PARENTS EDUCATION NS non-graduate State 38 ( 5.2) 56 ( 5.2) 6 ( 2 7) 234 ( 3.9) 243 ( 2.9) Nation 25 ( 5.6) 66 ( 7.2) 9 ( 6.5) 243 ( 2.2) ( HS graduate State 35 ( 4.3) 61 ( 42) 4 ( 1.0) 240 ( 3.2) 247 ( 2.3) 4" ( 4") Nation 23 ( 4.8) 70 ( 5.3) 7 ( 2,8) 248 ( 4.0)1 255 ( 22) '44 ( 4") Some college State 36 ( 4.7) 59 ( 5.1) 4 ( 1.2) 255 ( 3,4) 267 ( 2.4) Nation 18 ( 261 ( 4.0) 4.4)1 73 ( 269 ( 4.3) 2.3) 9 ( 44 2.4) 441 College graduate State 35 ( 4.7) 55 ( 4.5) 10 ( 1,9) 267 ( 3.5) 272 ( 2.0) 282 ( 7.8)1 Nation 20 ( 3,9) 69 ( 3.7) 11 ( 2.5) 266 ( 3.5)1 274 ( 2.2) 297 ( 4.2)1 GENDER Male State 33 ( 3.6) 60 ( 3,7) 8 ( 1.2) 254 ( 2.8) 259 ( 2.2) 270 ( 8,5) Nation 22 4.1) 69 ( 4.1) 8 ( 2.0) 255 ( 4.1) 266 ( 2.1) 287 ( 7.2)1 Female State 37 ( 4.1) 56 ( 3.9) 7 ( 1.3) 250 ( 2.8) 255 ( 2.2) 267 ( 6.9) Nation 21 ( 36) 69 ( 4.2) 10 ( 3,3) 254 ( 3.3) 262 ( 1,9) 278 ( 6.0)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students), THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Cahfornia TABLE Al la 1 Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Ono* a Week or Less TOTAL Percentage and Proficiency Percentage and Prolloiency Percentage and Proficiency State 04 ( 3.2) 27 ( 2.8) 9 ( 2.1) 259 ( 1.8) 254 ( 2$) 250 ( 5.4)1 Nation 62 ( 3.4) 31 ( 3.1) 7 ( 1.8) 261 ( 1.8) 254 ( 2.9) 260 ( 5.1)1 RACE/ETHNICITY White State 62 ( 3.9) 28 ( 3.9) 10 ( 2$) 274 ( 1.9) 268 ( 2.4) 263 ( 6.0)1 Nation 64 ( 3.7) 28 ( 32) 8 ( 2.3) 272 ( 1.9) 264 ( 3.4) 264 ( 5.4)1 Black State 70 ( 5.6) 232 ( 3.6) 21 ( 4.6) **a ( 9 ( 4.5) *** ( Nation 56 ( 7.7) 244 ( 4.0) 41 ( 7.9) 233 ( 3.9)1 2 ( 1.4) *es ( Hispanic State 61 ( 4.2) 31 ( 3.4) 8 ( 2.0) 238 ( 2.0) 238 ( 2.6) te. ( Nation 81 ( 6.8) 32 ( 5.3) 8 ( 2.3) 251 ( 3.1) 240 ( 4.3)1 Asian State 76 ( 4.1) 9 ( 3.2) 275 ( 2.8) ( Nation 83 ( 6.9) 10 ( 3.2) 7 ( 5.1) 284( 7.0)1 '04 ( *") TYPE OF COMMUNITY Advantaged urban State 62 ( 6.6) 33 ( 6.8) 5 ( 2.5) 282 ( 3.8)1 271 ( 5.6)1 ft 41-*) Nation 63 (15.9) 23 ( 5.2) 14 (14,13) 283 ( 7.3)1 ( Disadvantaged urban State 61 ( 9,0) 29 ( 6.2) 10 ( 3.9) 244 ( 6.3)1 239 ( 7.7)1 Nation 66 (10.7) 31 (11,1) 4 ( 2.2) 252 4.7)1 243 ( 8.0)1 Other State 61 ( 5.0) 26 ( 4.6) 12 ( 3.8) 257 ( 2.2) 258 ( 2.7)1 250 ( 0.2)1 Nation 63 ( 3.9) 31 ( 3$) 6 ( 1.9) 267 ( 2.3) 255 ( 3.1) 257 ( 5.8)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent cvrtainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 8" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I t) 114 THE 1990 NAEP TRIAL STATE ASSESSMENT Ca lifbrnia TABLE Al la I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Almost Every Day Several About Once a Week or STATE ASSESSMENT Times a Week Less TOTAL and Proficiency and Proficiency Percentage mid Proficiency State 64 ( 3.2) 27 ( 2.8) 9 ( 2.1) 259 ( 1.8) 254 ( 2.5) 250 ( 5.4)1 Nation 62 ( 3.4) 31 ( 3.1) ( 1.8) 267 ( 1.8) 254 ( 2.9) 260 ( 5.1)1 PARENTS EDUCATION NS non-graduate State 62 ( 5.7) 31 ( 4.8) 239 ( 3.1) 243 ( 3.5) Nation 67 ( 245 ( 5.5) 3.2) *4. 6 ( 2.1) HS graduate State 58 ( 4.3) 32 ( 3.6) 10 ( 2.8) 246 ( 2.7) 245 ( 3,0) Nation 61 ( 4.4) 34 ( 3.7) 6 ( 1.5) 257 ( 2.5) 250 ( 2.9) Some college State 66 ( 3.6) 26 ( 3.4) 9 ( 2.8) 264 ( 2.4) 263 ( 4.1) IP** ) Nation 68 ( 42) 26 ( 3.7) 6 ( 1.9) 272 ( 2.7) 258 ( 5.2) College graduate State 67 ( 3.3) 25 ( 2.9) 9 ( 2.4) 273 ( 2.1) 269 ( 3.4) 265 ( 8.1)i Nation 61 ( 281 ( 4.0) 2.2) 31 ( 265 ( 3.9) 3.1) 8 ( 0- 3.1) GENDER Male State 64 ( 3.4) 28 ( 3.0) 9 ( 2.2) 260 ( 2.1) 257 ( 3.1) 255 ( 6.0)1 Nation 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2.1) 256 ( 3.6) 261 ( 6.7)! Female State 64 ( 3.3) 27 ( 2.9) 9 ( 2.3) 257 ( 1.9) 251 ( 2.6) 245 ( 5.9)1 Nation 65 ( 266 ( 3.6) 1.8) 28 ( 253 ( 3.3) 2.5) 7 ( .. 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 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). THE 1990 NAEP TRIAL STATE ASSESSMENT 115 California TABLE Al lb I Teachers' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week I About Once a Week Less than Weekly Percentage and Percentage and Percentage sod TOTAL Proficiency Prvechnicy Prodatency State 35 ( 3.1) 31 ( 2.9) 34 ( 2.9) 253 ( 2.6) 288 ( 3.0) 260 ( 2.9) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 260 ( 2.3) 274 ( 2.7) RACE/ETHNICITY Mite State 34 ( 3.7) 30 ( 3.3) 36 ( 3.3) 288 ( 3.0) 273 ( 2.9) 273 ( 3.0) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 284 ( 2.7) 279 ( 2.9) Black State 32 ( 7.2) 27 ( 7.2) 41 ( 9.7) tmVi 0*4(444) Nation 45 ( 7.5) 31 ( 7.6) 23 ( 8.3) 232 ( 3.1)1 243 ( 2.3)1 248 ( 7.0)1 Hispanic State 40 ( 4.1) 32 ( 4.1) 28 ( 3.6) 235 ( 1.9) 235 ( 3.4) 241 ( 3.1) Nation ( 7.7) 26 ( 5.3) 33 ( 7.5) 242 ( 3.2)1 244 ( 5.1)1 257 ( 2.3)1 Asian State 28 ( 5.0) 30 ( 4.1) 42 ( 4.5) 288 ( 5.4); 272 ( 5.2) 276 ( 3.9) Nation 37 ( 8.3) 35 ( 9.7) .44 ( 27 (10.4) TYPE OF COMMUNITY Advantaged urban State 33 ( 8.9) 33 ( 6.4) 34 ( 9.5) 268 ( 6.611 283 ( 8.811 284 ( 6.6)1 Nation 59 (13.9) 273 ( 3.4)1 20 ( 6.0) ..) Of* ( **V Disadvantaged urban State 45 ( 7.4) 25 ( 8.6) 30 ( 7.0) 242 ( 6.3P 228 ( 3.3)1 252 ( 7.2P Nation 50 (13.9) 22 (11.2) 28 (10.7) 237 ( 258 ( 8.3)1 263 ( 4.1)1 Other State 32 ( 4.4) 33 ( 4.0) 34 ( 4.2) 251 ( 2.8) 254 ( 4.1) 261 ( 3.2) Nation 30 ( 4.4) 35 ( 4.3) 36 ( 4.2) 256 ( 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 naturc of the sample does not allow accurate determination of the variability of this estimated mean proficiency *** Sample sire is insufficient to permit a reliable estimate (fewer than 62 students). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE Al lb I Teachers' Reports on the Frequency of (cmtinued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Saveral Times a Weak About Once a Week Loss than Waitdy TOTAL Percentage and Proadency Percentage and Proficianblf Percentage and Preaching! State 35 ( 3. 31 ( 2.9) 34 ( 2.9) 253 ( 2.6) 260 ( 3.0) 260 ( 2.9) Nation 34 ( 3.8) 33 ( 3M 32 ( 3.6) 256 ( 2.3) 210 ( 2.3) 274 ( 2.7) PARENTS' EDUCATION KS non-graduate State 42 ( 5.1) 29 ( 5.0) 237 ( 3.1) 251 ( 4.1) Nation 35 ( 6.0) 29 ( 6.3) 36 ( 6.0) 239 ( 3.5) 250 ( 43)1 NS graduate State 35 ( 42) 32 ( 4.3) 33 ( 4.4) 243 ( 2.7) 243 ( 3.9) 247 ( 3.4) Nation 35 ( 5.3) 36 ( 4S) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 263 ( 3.4) Some college State 37 ( 3.7) 28 ( 3.3) 35 ( 3.9) 262 ( 3.8) 265 ( 3.6) 264 ( 3.6) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 266 ( 42) 278 ( 2.6) College graduate State 31 ( 3.7) 33 ( 2.9) 36 ( 3.0) 269 ( 32) 272 ( 3.3) 273 ( 4.0) Nati on 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Male State 35 ( 3.3) 31 ( 3.3) 34 ( 3.0) 256 ( 3.0) 258 ( 3.4) 262 ( 3.3) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 261 ( 2.8) 275 ( 3.2) Female State 35 ( 3.3) 31 ( 2.9) 34 ( 3.0) 250 ( 2.5) 255 ( 3.4) 259 ( 3.1) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 117 California TABLE Al2 I Students' Reports on the Frequency of Small i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency Percentage end Proficiency Percentage and Proficiency State 35 ( 2.0) 25 ( 1.2) 40 ( 2.0) 256 ( 2.0) 280 ( 1.8) 254 ( 1.7) Nation 28 ( 25) 28 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 261 ( 1.6) RACE/ETHNICITY White State 35 ( 3.0) 27 ( 2.0) 38 ( 2.7) 273 ( 2.0) 272 ( 2.0) 268 ( 2.1) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 268 ( 3.1 ) 272 ( 1.9) 270 ( 1.7) Slack State 35 ( 4.7) 33 ( 4.9) *4-8 Nation 28 ( 3.0) 24 ( 3.6) 48 ( 4.7) 234 ( 3.0) 245 ( 4.6) 234 ( 3.1) Hispanic State 35 ( 2.2) 21 ( 1.6) 44 ( 2.3) 235 ( 2.3) 241 ( 2.6) 237 ( 1.7) Nation 37 ( 5.2) 22 ( 3,6) 41 ( 5,0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) Asian State 32 ( 4.0) 26 ( 3,1) 42 ( 3.3) 270 ( 5.0) 274 ( 4.0) 272 ( 3,6) Nation 28 ( 6.4) ( 32 ( 4.0) 40 ( 6.2) 4.**) TYPE OF COMMUNITY Advantaged urban State 33) 7.1 ) 28 ( 4.4) 38 ( 5.3) 282 ( 5.9)1 278 ( 2.8)1 274 ( 4.7)1 Nation 27 (13.9) ..) 33 ( 4.5) 286 ( 5.4)1 40 (13.4) 279 ( 3.5p Disadvantaged urban Stite 39 ( 7.0) 24 ( 2.9) 38 ( 8.0) 240 ( 4.7)1 250 ( 5.9)1 238 ( 4.1)1 Nation 31 ( 5.7) 20 ( 2.8) 49 ( 6.3) 245 ( 4.0)i 267 ( 6.4)1 245 ( 3.7)1 Other State 38 ( 2.9) 25 ( 37 ( 2.8) 256 ( 2.6) 259 ( ) 254 ( 2.6) Nation 27 ( 2.6) 28( 1.7) 45 ( 3.3) 260 ( 3.3) 264 ( 2.1) 262 ( 2.2) The standard errors of the estimated statistics appear m parentheses. It can be said with about 95 percent oertainty that, for each population of interest, the value for the entire population is within 7 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency '1" Sample Size Is insufficient to permit a reliable estimate (fewer than 62 students). 118 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE Al2 I Students' Reports on the Frequency of Small ("nitinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Levet Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 35 ( 2.0) 25 ( 1.2) 40 ( 2.0) 256 ( 2.0) 260 ( 1.8) 254 ( 1.7) Nation 28 ( 2.5) 28 ( 1.4) 44 ( 2.9) 2$8 ( 2.7) 207 ( 2.0) 261 ( 1.6) PARENTS' EDUCATION KS non-graduate State 35 ( 4.5) 20 ( 2.6) 45 ( 4.1) 234 ( 3.4) 44 ( 4141 243 ( 3.0) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4.5) 242 ( 34) 244 ( 3.0) 242 ( 2.7) HS graduate State 32 ( 2.7) 28 ( 1.8) 41 ( 2.5) 247 ( 3.1) 245 ( 3.6) 244 ( 2.0) Nation 28 ( 3.0) 28 ( 1.8) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some college State 33 ( 3.3) 28 ( 2.4) 39 ( 3.5) 266 ( 2.1) 263 ( 3.4) 262 ( 2.8) Nation 27 ( 3.9) 27 ( 2.4) 48 ( 3.8) 265 ( 3.6) 268 ( 3.3) 266 ( 2.1) College graduate State 37 ( 2.8) 27 ( 1.9) 38 ( 2.8) 271 ( 2.7) 274 ( 2.5) 269 ( 2.7) Nation 28 ( 3.0) 28 ( 1.9) 44 ( 3.6) 270 ( 2.7) 278 ( 2.8) 275 ( 22) GENDER Male State 34 ( 2.2) 25 ( 1.6) 41 ( 2.3) 260 ( 2.5) 260 ( 2.5) 256 ( 2.2) Nation 31 ( 2.9) 28 ( 1.7) 41 ( 2.9) 259 ( 3.3) 268 ( 22) 262 ( 1.8) Female State 36 ( 2.2) 25 ( 1.7) 39 ( 2.4) 253 ( 2.0) 261 ( 2.4) 253 ( 1.9) Nation 26 ( 2.4) 27 ( 1.8) 47 ( 3.2) 257 ( 2.8) 266 ( 1.7) 260 ( 1,8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 7i- 2 standard errors of the estimate for the sample. *" Saw). site is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 119 California AMP.I.PIMPM.11111111110111%. TABLE A13 I Students' Reports on the Use of Mathematics 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never _ TOTAL Perceritage and Proficiency Percentage and Proficiency Percentage and Proficiency State 32 ( 2.0) 28 ( 1.3) 40 ( 1.9) 253 ( 1.9) 264 ( 1.9) 254 ( 1.4) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.6) 269 ( 1.5) 253 ( 1.8) RACE/ETHNICITY White State 30 ( 2.4) 31 ( 1.8) 39 ( 2.3) 268 t 2.4) 276 ( 2.0) 270 ( 1.7) Nation 27 ( 1M) 33 ( 1.6) 40 ( 2.5) 266 ( 2.8) 275 ( 1.6) 268 ( 1.8) Black State 33 ( 4.3) 22 ( 3.5) 45 ( 4.4) ( 232 ( 3.7) Nation 27 ( 3.3) 27 ( 3.2) 46 ( 4.5) 234 ( 3.7) 248 ( 4.5) 232 ( 2.6) Hispanic State 34 ( 2.2) 24 ( 1.7) 43 ( 2.4) 23$ ( 2.4) 241 ( 2.5) 235 ( 1.7) Nation 38 ( 4.2) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) Asian State 35 ( 3.8) 29 ( 2.8) 36 ( 3.8) 269 ( 4.3) 279 ( 3.5) 268 ( 3.4) Nation 30 ( 3.2) 38 ( 4.7) ) 0" TYPE OF COMMUNITY Advantaged urban State 28 ( 4.8) 34 ( 3.4) 37 ( 4.9) 274 ( 5.8)1 283 ( 4.1)1 276 ( 3.5)1 Nation 36 (10.3) 33 ( 4.8) 32 (11.1) 278 ( 284 ( 3.2)1 281 ( 5.9)1 Disadvantaged urban State 35 ( 5.5) 26 ( 2.9) 39 ( 4.9) 241 5.7)1 244 ( 5.7)1 240 ( 3.7)1 Nation 35 ( 6.6) 19 ( 2.1) 46 ( 6.4) 249 ( 5.3)1 256 ( 5.7)1 246 ( 4.8)1 Other State 35 ( 3.0) 28 ( 1.7) 37 ( 2.9) 253 ( 2.4) 264 ( 2.2) 253 ( 2.6) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 256 ( 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. 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. *0* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 120 j () THE 1990 NAEP TRIAL STATE ASSESSMENT Cabfornia TABLE A13 I Students' Reports on the Use of Mathematics (continued) i Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1980 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week flew TOTAL Poramtage and ProSclency Percentage and Penedency Percentage and Prottchncy State 32 ( 2.0) 28 ( 1.3) 40 ( 1.9) 253 ( 1.9) 264 ( 1.9) 254 ( 1.4) Nation 28 ( 1.6) 31 ( 1.2) 41 ( 22) 258 ( 2.6) 299 ( 1.5) 259 ( 1.6) PARENTS EDUCATION HS non-graduate State 31 ( 2.8) 24 ( 2.7) 45 ( 3.3) 235 ( 3.7) 243 ( 4.7) 241 ( 2.6) Nation 27 ( 4.2) 26 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) HS graduate State 34 ( 2.8) 28 ( 2.5) 38 ( 2.5) 242 ( 22) 253 ( 3.1) 241 ( 2.4) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 21) Some collage State 31 ( 3.3) 28 ( 25) 42 ( 2.7) 262 ( 3.4) 268 ( 3.6) 261 ( 2$) Nation 29 ( 2.6) 38 ( 2.3) 35 ( 2.6) 281 ( 3.5) 274 ( 22) 263 ( 2.1) Cottage graduate State 32 ( 2.4) 30 ( 1.5) 38 ( 2.3) 268 ( 2.8) 278 ( 2.3) 269 ( 1.9) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.6) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Mate State 34 ( 2.1) 28 ( 1.4) 38 ( 1.8) 255 ( 2.4) 266 ( 2.1) 254 ( 2.0) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 31 ( 2.3) 27 ( 1.9) 43 ( 2.4) 251 ( 2.4) 261 ( 2.3) 253 ( 1.8) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 268 ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Interest, the value for the entire population is within -t. 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Califorrjg TABLE A14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1990 MEP TRIAL About Once a Weak or STATE ASSESSMENT Almost Every Day Several Times a Week Less , TOTAL Percentage and Proficiency Percentage and Protidesicy Percentage and Proficiency State 69 ( 2.0) 17 ( 1.4) 14 ( 1.5) 262 ( 1.3) 247 ( 2,5) 240 ( 2.8) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 4.5) RACE/ETHNICITY White State 73 ( 2.7) 15 ( 1.6) 12 ( 2.2) 274 ( 1.4) 266 ( 2.9) 259 ( 3.1) Nation 76 ( 2.5) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 2.2) 252 ( 5.1)1 Slack State 71 ( 3.8) 14 ( 2$) 237 ( 2.8) INF* ( firt.) Nation 71 ( 2.8) 15 ( 1.7) 14 ( 3.2) 240 ( 2.9) 232 ( 3.1) 223 ( 6.1)1 Hispanic State 61 ( 2.5) 21 ( 1.8) 18 1, 1.9) 242 ( 1.4) 230 ( 2.9) 225 ( 2.5) Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 22A 1 3.4) Asian State 75 ( 3.0) 277 ( 2.5) 18 ( 2.3) *. 7 ( 2.1) Nation 79 ( 4.9) 289 ( 5.0)1 13 ( 3.4) .. 8 ( 2.6) TYPE OF COMMUNITY Advantaged urban State 73 ( 6.6) 20 ( 4.9) 7 ( 2.9) 282 ( 4.0)1 267 ( 5.8)1 Nation 73 (11.1) 13 ( 1.7) 14 (10.4) 286 ( 4.6)1 esi Disadvantaged urban State 65 ( 6.7) 18 ( 5.3) 248 ( 4.4)) Nation 69 ( 2.8) 15 ( 25) 15 ( 2.2) 253 ( 3.7)1 243 ( 4.4)1 235 ( 6.5)1 Other State 67 ( 17 ( 1,8) 16 ( 1.8) 262 ( 1.7) 245 ( 3.7) 243 ( 4.0) Nation 75 ( 2.2) 14 ( tO) 1e ( 1.9) 267 ( 1.6) 252 ( 2.6) 239 ( 4.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with 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), 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Cahfornia TABLE AI4 I Students' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Less TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Profidency State SS ( 2.0) 17 ( 1.1) 14 ( 1.5) 262 ( 1.3) 247 ( 2.5) 240 ( 2.8) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) 267 ( 12) 252 ( 1.7) 242 ( 44) PARENTS EDUCATION HS non-graduate State 82 ( 2.5) 19 ( 1.9) 19 ( 2.3) 245 ( 2.4) Nation 64 ( 3.4) 18 ( 2.0) 18 ( 3.1) 245 ( 2.3) MP* ) HS graduate State 63 ( 3.4) 20 ( 2.2) 17 ( 2.8) 251 ( 1.7) 236 ( 3.7) 232 ( 3.8) Nation 71 ( 3.6) 16 ( IA) 13 ( 2.8) 258 ( 1.6) 249 ( 32) 239 ( 3.4)1 Some college State 71 ( 2.9) 17 ( 2.3) 12 ( 1.9) 266 ( 2.0) 258 ( 4.1) Nation 80 ( 270 ( 2.0) 1.9) 11 ( **. 1.2) 9 ( 411-* 1.7) m ) College graduate State 75 ( 2.4) 15 ( 1.5) 1 0 ( 1.7) 275 ( 1.8) 264 ( 3.3) 255 ( 4.9) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 260 ( 2.8) 257 ( 6.4)1 GENDER Male State 68 ( 2.0) 18 ( 1.3) 15 ( 1.5) 263 ( 1.7) 252 ( 2.9) 241 ( 3.2) Nation 72 ( 2.4) 16 ( 1.2) 12 ( 2.1) 268 ( 1.6) 252 ( 2.5) 242 ( 6.1) Female State .70 ( 2.3) 17 ( 1.4) 13 ( 1.7) 261 ( 1.4) 242 ( 3.4) 239 ( 3.6) Nation 76 ( 1.8) 13 ( 1.0) 11 ( 1.6) 265 ( 1.3) 250 ( 25) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the alue 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 California TABLE A15 I Students' Reports on the Frequency of 1 Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 103 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Lass Thaa. Wesidy TOTAL Percentage and Pro fidency Percentage and Proficiency Percentage and Prolidency State 44 ( 2.4) 24 ( 1.2) 33 ( 2.3; 249 ( 1.9) 257 ( 1.8) 266 ( 2.0) Nat Ion 38 ( 24) 25 ( 1.2) 37 ( 2.5) 253 ( 22) 261 ( 1.4) 272 ( 1.9) RACE/ETHNICITY White State 38 ( 3.4) 25 ( 1.9) 37 ( 3.1) 268 ( 2.1) 270 ( 2.4) 275 ( 2.1) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 262 ( 2.5) 289 ( 1$) 277 ( 2.0) Slack State 50 ( 4.8) 25 3.8) 24 ( 3.8) Nation 232 ( sa ( 3.4) 3.8) 32 ( 2.7) ( 20( 3.1) 232 ( 4.3) 241 ( 2.9) 241 ( 4.4) Hispanic State 53 ( 2.7) 21 ( 1.8) 26 ( 2.3) 232 ( 1.9) 238 ( 2.2) 244 ( 2.6) Nation 44 ( 4.1) 25 ( 3.4) 32 ( 43) 238 ( 3.9) 247 ( 3.3) 248 ( 3.3) Asian State 32 ( 3.6) 24 ( 32) 43 ( 4.1) 283 ( 4.1) 266 ( 4.7) 281 ( 3.4) Nation 32 ( 5.4) 51 ( 5.9) ( ) TYPE OF COMMUNITY Advantaged urban State 38( 272 ( 8.1) 3.5)1 *** 45 ( 282 ( 7.7) 5.7)1 Nation 50 ( 271 ( 9.0) 3.3)1 19 ( ( 4,9) ***) 31 ( 299 ( 93) 5.3)1 Disadvantaged urban State 55 ( 4.6) 24 ( 2.8) 21 ( 3.6) 237 ( 4.6)1 246 ( 5.1)' 251 ( 6.3)1 Nation 37 ( 5.8) 23 ( 3.6) 41 ( 8.7) 240 ( 4.8)1 253 ( 4.1)1 255 ( 4.2)1 Other State 42 ( 2.7) 25 ( 1$) 33 ( 2.5) 249 ( 2.5) 258 ( 2.9) 264 ( 2.4) Nation 36 ( 2.9) 26 ( 12) 38 ( 2.9) 252 ( 3.0) 261 ( 2.1) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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). 124 ./ THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A 15 I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1 1990 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week About Once a Week Less Than Weekly TOTAL Percentage and Proficiency Percentage aid Proficiency Percentage and Proficiency State 44 ' 24 ( 1.2) 33 ( 2.3) 249 ( 1.9) 257 ( 1.8) 266 ( 2.0) Nation 38 ( 2.4) 25 ( 1.2) 37 ( 2.5) 253 ( 2.2) 261 ( 1.4) 272 ( 1.9) PARENTS EDUCATION KS nengraduate State 50 ( 4.1) 24 ( 3.0) 26 ( 3.4) 232 ( 2.3) 250 ( 3.8) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) KS graduate State 45 ( 3.4) 25 ( 2.7) 31 ( 3.4) 241 ( 2.6) 242 ( 2.5) 253 ( 2.9) Nation 40 ( 32) 29 ( 22) 32 ( 3.6) 247 ( 2.7) 256 ( 2.5) 262 ( 2.2) Some college State 42 ( 2.8) 23 ( 2.2) 34 ( 2.7) 258 ( 3.2) 259 ( 32) 271 ( 2.5) Nation 34 ( 3.4) 26 ( 2.2) 40 ( 3.6) 259 ( 2.3) 289 ( 2.8) 271 ( 2.8) Collage graduate State 40 ( 3.4) 25 ( t.6) 36 ( 32) 265 ( 2.8) 271 ( 2.8) 278 ( 2.7) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 284 ( 2.6) 273 ( 2.5) 285 ( 2.3) GENDER Male State 45 ( 2.7) 24 ( 1.4) 31 ( 2.4) 252 ( 2.2) 257 ( 2.2) 266 ( 2.6) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 263 ( 2.3) 274 ( 2.4) Female State 42 ( 2.5) 24 ( 1.6) 34 ( 2.6) 246 ( 1.9) 256 ( 2.4) 265 ( 2.1) 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 population is within t 2 standard errors of the estimate for the sample. *1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 125 California TABLE A18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Own a Calculator Teacher Bcpia Ins Calculator Use Yes No Yes -. No TOTAL Percentage and Proficiency 97 ( 0.4) 257 ( 1.2) 97 ( 0.4) 263 ( 1.3) 99 ( 0.3) 271 ( 1.4) 98 ( 0.3) 270 ( 1.5) 98 ( 1.1) 233 ( 3.1) 93 ( 1.5) 237 ( 2.8) 94 ( 0.9) 237 ( 1.5) 92 ( 1.2) 245 ( 2.7) 97 ( 1.1) 273 ( 2.8) 99 ( 0.9) 282 ( 5.3)) 98 ( 0.8) 278 ( 3.3)1 99 ( 1.0) 281 ( 3.8)1 96 ( 12) 243 ( 4.1)1 94 ( 1.2) 250 ( 3.5)1 97 ( 0.5) 257 ( 1.8) 97 ( 0.5) 263 ) 1.7) Parcentage and Proficiency 3 ( 04) 232 ( 3.8) 3 ( 0.4) 234 ( 3.8) 1 ( 0.3) it** ( 1144 2 ( 0.3) ( 44) 2 ( 1.1) 7 ( 1.5) .41 8 ( 1.2) 3 ( 1.1).) 1 ( 0.9) *0-4 ( *44 ) 2 ( 0.8) 00 1 ( 1,0) ..) 4 ( 1.2)) 6 ( 1.2) ...) 3 ( 0.5) - 0.0) 3 ( 0.5) 233 ( 5.4) Parcentarge and Proacioncy 58 ( 1.8) 254 ( 1.3) 49 ( 2.3) 258 ( 1.7) 58 ( 2.2) 269 ( 1.5) 46 ( 2.6) 266 ( 1.8) 61 ( 3.8) 232 ( 3.5) 53 ( 4.9) 235 ( 3,6) 61 ( 2.8) 235 ( 1.6) 63 ( 4,3) 243 ( 3.4) 50 ( 3.8) 267 ( 3.0) 52 ( 4.8) ..) 56 ( 3.2) 277 ( 2.8)i 45 (12.2) 276 ( 2.5)1 81 ( 3.9) 237 ( 3.9)1 57, ( 7.5) 247 ( 4,1)1 63 ( 2.7) 253 ( 1.8) 50 ( 2.7) 258 ( 2,1) Porcatag and Profit:Wm 42 ( 1.8) 261 ( 1.7) 51 ( 2.3) 2661 1.5) 42 ( 2.2) 274 ( 2.1) 54 ( 2.6) 273 ( 1.8) 39 ( 3.8) 238 ( 4.7) 47 ( 4.9) 239 ( 2.7) 39 ( 2.8) 240 ( 2.2) 37 ( 4.3) 245 ( 2.9) 50 ( 3.6) 276 ( 3.4) 48 ( 4.8) . 44 ( 3.2) 279 ( 5.2)1 55 (12.2) 285 ( 6.4)1 39 ( 3.9) 250 ( 5.5)1 47 ( 7.5) 251 ( 3.8)1 37 ( 2.7) 281 ( 2.4) 50 ( 2.7) 266 ( 2.0) State Nation RACE/ETHNICITY Mite State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban 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 &low accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 126 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A18 (continued) Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT Own a Calculator Teacher Explains Calculator Use Yes No Yes , No - TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage end Proficiency State 97 ( OA) 257 ( 1.2) 3 ( 232 ( 0.4) 3.8) 58 ( 254 ( 1.8) 1,3) 42 ( 261 ( 1.8) 1.7) Nation 97 ( 0.4) 3 ( 0,4) 49 ( 2.3) $1 ( 2.3) 263 ( 1.3) 234 ( 3.8) 256 ( 1.7) 2661 1.5) PARENTS EDUCATION NS non-graduate State 93 ( 1.7) 57 ( 14) 43 ( 3.4) 240 ( 2.2) 236 ( 2.6) 245 ( 3.0) Nation 92 ( 1.6) 8 ( 1S) 53 ( 4.8) 47 ( 4.6) 243 ( 2.0) 242 ( 2.9) 243 ( 25) HS graduate State 96 ( 0.7) 2 ( 0.7) 61 ( 3.0) 39 ( 3.0) 245 ( 1.7) 243 ( 2.1) 247 ( 2.6) Nation 97 ( 0.6) 3 ( 0.6) 54 ( 3.0) 45 ( 3.0) 255 ( 1.5) ( 252 ( 1.9) 258 ( 2.0) Some college State 97 ( 0.8) 3 ( 0.8) 59 ( 2.8) 41 ( 2.8) 263 ( 1.9) 260 ( 2,1) 267 ( 3.2) Nation 96 ( 0.9) 4 ( 0.9) 48 ( 32) 52 ( 32) 268 ( 1.8) Hs.) 265 ( 2.4) 268 ( 2.2) Co4 logo graduate State 99 ( 0.4) 1 ( 0.4) 58 ( 2.3) 42 ( 2.3) 272 ( 1.7) 4" ( "4) 268 ( 1.8) 276 ( 2.3) Nation 99 ( 0.2) 1 ( 02) 46 ( 2,6) 54 ( 2.6) 275 ( 1.6) 268 ( 2.2) 280 ( 1.9) GENDER Mate State 97 ( 0.5) 3 ( 0.5) 58 ( 2.0) 42 ( 2.0) 258 ( 1.6) "4 ( ) 255 ( 1.6) 262 ( 2.4) Nation 97 ( 264 ( 0.5) 1.7) 3 ( *44 ( 0.5) 444) 51 ( 258 ( 2.6) 2.1) 49 ( 269 ( 2.6) 2.1) FINTIade State 97 ( 0.51 3 ( 0.5) 58 ( 2.2) 42 ( 2.2) 256 ( 1.3) 252 ( 1.5) 259 ( 1.7) Nation 97 ( OS) 3 ( 0.5) 47 ( 2.5) 53 ( 241 262 ( 1.3) *44 ( 258 ( 1.7) 263 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 s'andard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (.ewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 127 California TABLE A19 1 Students' Reports on the Use of a Calculator i for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1900 NAEP TRIAL STATE ASSESSMENT "Ming Prnbillms In Clan Doing Problems at Home Taking Quizzes or Tests Almost Always 4 Never Almost Always Never Almost Always Never TOTAL Percentage and Proficiency Percentage Mid Proficiency Percentage and Proficiency Percentage and Proficiency Percentage arid Proficiency Percentage and Proficiency State 48 ( 1.8) 19 ( 1.8) 33 ( 1.5) 16 ( 1.1) 23 ( 1.5) 30 ( 1.7) 250 ( 1.7) 264 ( 2.1) 257 ( 1.7) 259 ( 2.3) 253 ( 2.9) 266 ( 1.4) Nation 43 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) RACE/ETHNICITY White State 45 ( 2.1) 18 ( 2.5) 37 ( 2.1) 16 ( 1.8) 24 ( 2.1) 34 ( 2 5) 285 ( 2.0) 274 ( 2.7) 270 ( 1.8) 271 ( 2.9) 271 ( 3.3) 278 ( 1.7) Nation 46 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 25 ( 1.8) 32 ( 2.3) 262 ( 1.7) 278 ( 1.3) 270 ( 1.7) 269 ( 2.3) 263 ( 2.6) 279 ( 1.2) Black State 59 ( 230 ( 4.4) 4.0) 13 ( NMI ( 2.7) Mt* ) 35 ( *4, 3.4) 29 ( 5.0) 24 ( 3.0) Nation 57 ( 3.2) 20 ( 3.9) 31 ( 2.9) 18 ( 1.9) 38 ( 3.3) 24 ( 3.1) 232 ( 2.4) 249 ( 4.0) 233 ( 3.3) 248 ( 5.5) 230 ( 3.8) 251 ( 4.1) Hispanic State 48 ( 2.3) 19 ( 1.6) 29 ( 1.8) 18 ( 1.4) 24 ( 1.8) 25 ( 1.9) 232 ( 1.7) 246 ( 2.5) 237 ( 2.3) 239 ( 3.0) 232 ( 2.6) 248 ( 1.9) Nation 51 ( 2.9) 16 ( 3.5) 28 ( 3.2) 21 ( 2.1) 26 ( 2.7) 22 ( 3.1) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1) 237 ( 3.2) 256 ( 4.2) Asian State 37 ( 263 ( 2.8) 3.8) 26 ( 280 ( 2.9) 4.7) 33 ( 270 ( 3.1) 4.4) 18 ( 2.4) 18 ( 2.9) **,.) 33 ( 277 ( 3.8) 2.9) Nation 35 ( 8.3) ***) 29 ( 5.8) 30 ( 8.3) 23 ( 4.4) 4.14) 23 ( 5.8) 48 ( ( 8.4) 404) TYPE OF COMMUNITY Advantaged urban State 52 ( 4.7) 14 ( 3.8) 48 ( 4.6) 10 ( 1.8) 33 ( 5.5) 23 ( 4.6) 272 ( 5.0)1 ( ') 279 ( 4.0)1 "'" ( "') 281 ( 7.4)1 279 ( 3.7)1 Nation 51 ( 5.4) 23 (10.7) 32 ( 6.1) 15 ( 2.4) 31 ( 3.8) 28 ( 9.8) 270 ( 4.7)1 ( ") 274 ( 4.9)1 *** ( 444) 281 ( 7.6)1 285 ( 4.2)1 Disadvantaged urban State 45 ( 3.7) 18 ( 3.8) 28 ( 2.8) 15 ( 2.0) 18 ( 2.5) 32 ( 4.8) 236 ( 3.9)1 ( 4") 244 ( 5.0)1 ' ( ') *** ( "4) 253 ( 5.0)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 1 5.4)1 246 1 52)1 254 1 4.6)1 240 1 4.9)1 263 ( 5.0)1 Other State 44 ( 2.6) 20 ( 2.1) 29 ( 1.7) 18 ( 1.5) 22 ( 1.9) 32 ( 2.1) 249 ( 2.1) 207 ( 2.5) 255 ( 2.2) 260 ( 2.8) 252 ( 3.2) 266 ( 2.0) Nation 48 ( 1.9) 22 ( 2.0) 32 ( 1,7) 18 ( 1.1) 27 ( 1.8) 29 ( 2.1) 254 ( 2.1) 272 ( 1.8) 283 ( 2.3) 263 ( 2.8) 253 ( 2.7) 275 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 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. **a Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 128 THE 1990 NAEP TRIAL STATE ASSESSMENT California .../11 TABLE A 19 I Students' Reports on the Use of a Calculator (continued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT - Working Problems In Class Doing Problems at Nome Taking QUIrns or Tests Almost Always Never Almost Always Never Almost Always Never TOTAL Percentage and Proficient* Pen:entity* and Proficiency Percentage and Pro kidney Percentage end Prolidency flareardage and Pro! lektocy Percentage and 91'01k:ism State ( 1.6) 19 ( 1.8) 33 ( 1.5) 16 ( 1.1) 23 ( 1.5) 30 ( 1.7) 250 ( 1.7) 204 ( 2.1) 251 ( 1.7) 259 ( 2.3) 253 ( 2.0) 288 ( 1.4) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 281 ( 1.5) 283 ( 1.8) 214 ( 24) 274 ( 1.3) PARENTS EDUCATION it$ non-graduate State 48 ( 234 ( 3.7) 2.3) 23 (( 2.8) *41 27 ( 240 ( 2.5) 3.3) Imp* sim) 22 ( to.t. 2.0) ***) 30 ( 252 ( 3.8) 3.3) Nation 54 ( 3.3) 19 ( 3.8) 26 ( 3.1) 22 ( 2.0) 32 ( 3.0) 24 ( 3.2) 240 ( 2.3) 244 ( 3.8) 244 ( 4.2) 237 ( 2.3) 251 ( 4.8) HS graduate State 44 ( 240 ( 2.8) 2.2) 18 ( 248 ( 2.3) 2.9) 31 ( 246 ( 3.1) 2.7) 17 ( 247 ( 2.2) 3.8) 23 ( 239 ( 24) 3.9) 2$ ( 253 3.0) 2.4) Nation 52 ( 2.5) 20 ( 2.4) 29 ( 1.9) 18 ( 1.5) 26 ( 1.8) 27 ( 22) ( 1.4) 265 ( 2.7) 250 ( 2.4) 256 C 2.4) 240 ( 2.8) 265 ( 2.0) Son* college State 49 ( 2.8) 17 ( 2.6) 34 ( 2.4) 15 ( 1.9) 23 ( 2,0) 30 ( 2.9) 257 ( 2.4) 271 ( 4.2) 260 ( 2.9) 261 ( 4.0) 259 ( 4,0) 270 ( 3.5) Nation 46 ( 2.8) 26 ( 2.8) 28 ( 2.0) 20 ( 1.9) 2$ ( 2.4) 35 ( 24) 258 ( 2.1) 272 ( 2.5) 207 ( 3.0) 268 ( 3.2) 255 ( 3.0) 275 ( 2.0) College graduate State 43 ( 2.1) 20 ( 2.3) 37 ( 2.3) 17 ( 1.7) 24 ( 2.4) 33 ( 2.0) 263 ( 2.7) 277 ( 2.7) 268 ( 2.8) 275 ( 3.3) 269 ( 4.5) 278 ( 1.9) Nation 45 ( 1.9) 25 ( 2.4) 33 ( 2.0) 16 ( 1.4) 26 ( 1.6) 33 ( 2.7) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 268 ( 2.8) 285 ( 2.0) GENDER Male State 47 ( 1.6) 18 ( 1.6) 34 ( 1.7) 18 ( 1.1) 22 ( 1.7) 29 ( 1.9) 251 ( 2.0) 268 ( 3.0) 259 ( 2.2) 262 ( 2.6) 255 ( 3.5) 268 ( 2.1) Nation 50 ( 1.7) 20 ( 2.0) 29 ( 1.6) 19 ( 1.3) 27 ( 1,5) 26 ( 2.1) 2S5 ( 1.9) 275 ( 22) 264 ( 2.8) 263 ( 2.5) 258 ( 3.0) 277 ( 1.9) Female State 45 ( 2.0) 20 ( 1.9) 33 ( 2.0) 15 ( 1.5) 25 ( 1.7) 31 ( 1.9) 248 ( 1.9) ( 2.2) 256 ( 22) 256 ( 2.9) 252 ( 3.0) 284 ( 1.8) Nation 46 ( 2.0) 26 ( 2.1) 32 ( 1.6) 18 ( 12) 27 1.8) 33 ( 2.1) 252 ( 1.7) 269 ( 1.8) 259 ( 1.7) 283 ( 2.1) 251 ( 2.4) 271 ( 1,5) 4. The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 129 California TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL "Calculator.Use" STATE ASSESSMENT High Group Other "Calculator-Use" Group TOTAL Percentage and Proficiency Percentage and Pftlikktfley State 43 ( 1.1) 57 ( 1.1) 265 ( 1.7) 248 1.3) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACE/ETHNICITY White state 47 ( 1.7) 53 ( 1.7) 276 ( 2.2) 264 ( 1.7) Nation 44 ( 1.4) 56 ( 1.4) 277 ( 1.7) 263 ( 1.7) Stack State 38 ( .4* ( 5.2) 62 ( 224 ( 5.2) 4.7) Nation 37 ( 3.4) 83 ( 3.4) 248 ( 3.9) 231 ( 3.0) Hispanic State 38 ( 2.1) 62 ( 2.1) 245 ( 2.3) 231 ( 1.7) Nation 36 ( 4.2) 64 ( 4.2) 254 ( 4.6) 238 ( 3.0) Asian State 50 ( 2.9) 50 ( 2.9) 279 ( 3.1) 262 ( 3.4) Nation 50 ( 4.8) 50 ( 4.8) *4 I TYPE OF COMMUNITY Advantaged urban State 55 ( 1.9) 45 ( 1.9) 284 1 4.7)1 268 ( 3.9)1 Nation 50 ( 3.8) 50 ( 3.8) 288 ( 4.9)i 275 ( 4.4)1 Disadvantaged urban State 37 ( 2.4) 63 ( 2.4) 252 ( 4.5)1 237 ( 4.7)1 Nation 38 ( 4.2) 62 ( 4.2) 262 ( 5.6)1 244 ( 3.9)1 Other State 41 ( 1.4) 69 ( 1.4) 263 ( 2.4) 249 ( 1.9) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is svithin t 2 standard errors of the estimate for the sample. Interpret with caution -- the nature or the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11100 NAEP TRIAL "Calculator-Use" "Calculator-Use STATE ASSESSMENT Nigh Group Other Group , TOTAL Percentage and Prone:fancy Pisrcentage and Proficiency State 43 ( 1.1) 57 ( 1.1) 265 ( 1.7) 248 ( 1.3) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) PARENTS' EDUCATION NS non-graduate State 41 ( 3.5) 59 ( 3.5) 244 ( 4.1) 235 ( 3.3) Nation 34 ( 3.3) 68 ( 3.3) 248 ( 4.4) 242 ( 2.4) NS graduate State 37 ( 3.3) 63 ( 3.3) 255 ( 2.6) 237 ( 2.3) Nation 40 ( 2.2) 60 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some College State 45 ( 2.4) 55 ( 2.4) 268 ( 2.4) 257 ( 3.1) Nation 48 ( 2.2) 52 ( 2.2) 277 ( 2.6) 258 ( 2.5) College graduate State 49 ( 1.9) 51 ( 1.9) 277 ( 2.5) 264 ( 1.8) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER Male State 40 ( 1.5) 60 ( 1.5) 267 ( 2.5) 249 ( 1.6) Nation 39 ( 2.0) SI ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 47 ( 1.9) 53 ( 1.9) 263 ( 1.5) 247 ( 1.9) Nation 45 ( 1.8) 55 ( 1.8) 269 ( 1.7) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within I 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 131 Ca r a TABLE A24 I Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types --. Four Types TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 32 ( 12) 31 ( 1.0) 47 ( 1.4) 242 ( 1.4) 258 ( 1.6) 39 ( 1.6) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) RACE/ETHNICITY White State 17 ( 1.4) 30 ( 1.5) 53 ( 1.5) 257 ( 1.9) 271 ( 2.1) 276 ( 1.8) Nation 16( 1.1) 29 ( 1.3) 56 ( 1.5) 251 ( 2.2) 288 ( 1.5) 276 ( 1.7) Slack State 29 ( 4.4) 33 ( 4.7) 38 ( 3.8) 237 ( 4.3) Nation 31 ( 1.9) 38 ( 22) 33 ( 2.4) 232 ( 3.2) 233 ( 3.9) 245 ( 3.3) Hispanic State 49 ( 1.5) 30 ( 1.4) 20 ( 1.3) 231 ( 1.8) 237 ( 1.9) 250 ( 2.8) Nation 44 ( 3.0) 30 ( 2.4) 26 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) Asian State 39 ( 3.7) 32 ( 2.4) 28 ( 3.5) 260 ( 3.6) 273 ( 3.3) 286 ( 3.9) Nation *** *** ***) 38 ( 42) **. TYPE OF COMMUNITY Advantaged urban State 33 ( 3.3) 54 ( 3.6) 41+0. 114- 272 ( 2.7)1 285 ( 4.4)I Nation 13 ( 3.8) 61 ( 4.9) t ( ***) 287 ( 3.6)I Disadvantaged urban State 43 ( 3.6) 31 ( 2.8) 26 ( 4.4) 235 ( 4.1)1 242 ( 5.1)1 252 ( 4.5)1 Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.6) 243 ( 2.9)1 247 ( 3.7)1 257 ( 4.9)i Other State 33 ( 1.8) 30 ( 1.4) 38 ( 1.9) 244 ( 1.8) 256 ( 2.5) 267 ( 2.1) Nation 22 ( 15) 30 ( 1.3) 48 ( 1 .5) 244 ( 2.6) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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). r7 132 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A24 I Students' Reports on Types of Reading (continued) 1 Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Far Types , TOTAL Percentage and Proncleney Percentage end Pro Rdency Percentage end Proficiency State 32 ( 1.2) 31 ( 1.0) 37 ( 1.4) 242 ( 1.4) 256 ( 1.6) 269 ( 1.6) Nation 21 ( 4.0) 30 ( 4.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) PARENTS' EDUCATION HS non-graduate State 61 ( 2.8) 26 ( 2.2) 13 ( 1.8) 238 ( 2.4) 240 ( 3.5) ye. ( ...) Nation 47 ( 4,0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 246 ( 3.3) HS graduat State 34 ( 2.1) 35 ( 2.3) 31 ( 22) 238 ( 2.9) 247 ( 2.3) 250 ( 2.4) Nation 26 ( 2.2) 33 ( 1.9) 40 ( 1.7) 246 ( 2.2) 253 ( 2.7) 260 ( 2.1) Some college State 23 ( 2.0) 37 ( 2.5) 40 ( 2.8) 250 ( 3.0) 2FX) ( 2.7) 271 ( 2.6) Nation 17 ( 1.5) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduate State 16 ( 1.6) 27 ( 1.4) 56 ( 1.7) 256 ( 2.6) .t " f 2 5) 276 ( 2.0) Nation 10 ( 0.8) 1.8) 62 ( 2.0) 254 ( 2.8) 2.5) 280 ( 1.8) GENDER Male State 34 ( 1.4) 291 1.2) 38 ( 1.6) 243 ( 2.0) 258 ( 2.1) 271 ( 2.1) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Female State 30 ( 1.6) 33 ( 1.6) 37 ( 2.0) 240 ( 1.9) 255 ( 1.8) 267 ( 1.7) Nation 22 ( 12) 29 ( 1.4) 49 ( 1.9) 244 ( 2.2) 258 ( 1.9) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± ". standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 133 California TABLE A25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One Hour or Less Tito Hours Three Hours Four to Five Hours - Six Hours or More _ TOTAL Percenbsge and Pro edam Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 16 ( 0.9) 24 ( 0.9) 23 ( 1.0) 26 ( 1.0) 11 ( 0.7) 266 ( 2.1) 259 ( 1.7) 257 ( 1.8) 251 ( 1$) 244 ( 2.7) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 ( 1.1) 16 ( 1.0) 269 ( 22) 268 ( 1.8) 265 ( 1.7) 200 ( 1.7) 245 ( 1.7) RACE/ETHNICITY Whits State 19 ( 1.4) 27 ( 1.1) 24 ( 1.6) 22 ( 1.1) 8 ( 0.8) 280 ( 2.3) 272 ( 1.8) 270 ( 2.2) 266 ( 2.0) 261 ( 3.5) Nation 13 ( 1.0) 23 ( 1.2) 24 ( 1.1) 27 ( 1.4) 12 ( 1.2) 276 ( 2.5) 275 ( 2.2) 272 ( 1.9) 267 ( 1.7) 253 ( 2.6) Black State 8 ( 2.8) 18 ( 2.7) 14 ( 2.2) 31 ( 3.6) 28 ( 3.0) *44 ( ) *411 ( *** ) frb* ***) Nation 13 ( 1.7) 17 ( 2.1) 32 ( 1.8) 32 ( 22) 239 ( 7.0) 239 ( 5.0) 239 ( 4.0) 233 ( 2.5) Hispanic State 14 ( 1.1) 21 ( 1.5) 24 ( 1.7) 30 ( 1.7) 12 ( 1.1) 241 ( 3.8) 238 ( 2.4) 238 ( 2.5) 233 ( 1.8) 232 ( 3.7) Nation 20 ( 2.5) 19 ( 2.1) 31 ( 3.1) 17 ( 1.7) **4 245 ( 3.2) 242 ( 5.6) 247 ( 3.5) 236 ( 3.8) Asian State 20 ( 2.5) 25 ( 2.7) 22 ( 3.0) 23 ( 3.0) 270 ( 42) 273 ( 4.2) 273 ( 4.5) Nation 18 ( SO) 24 ( 42) 22( 31) 23 ( 041 ( 4.7) GSM ) 13 ( -** 4.0) TYPE OF COMMUNITY Advantaged urban State 21 ( 3.1) 25 ( 2.9) 25 ( 3.0) 22 ( 2.5) 288 ( 4.3p 283 ( 4.1)' 260 ( 3.3)1 267 ( 4.9), Nation 18 ( 1.4) **4 ) 25 ( a.* ( 4.3) ) 21 ( ( 1.8) *44.) 30 ( 4.3) *.k.) 6 ( 2.0) Disadvantaged urban State 1 1 ( 1.5) 44(4*) 26 ( 241 ( 2.0) 5.4)! 21 ( 244 ( 2.9) 4.2)1 30 ( 238 ( 2.1) 4.3)1 12 ( 2.0) Nation 9 ( 12) ...) 17 ( 250 ( 3.1) 4.0p 19 ( 255 ( 2.1) 5.0)1 34 ( 251 ( 2.4) 4.7)1 20 ( 238 ( 32) 4.5)I Other State 17 ( 1.0) 24 ( 1.5) 23 ( 1.4) 26 ( 1.5) 10 ( 0.5) 265 ( 2.7) 259 ( 2.4) 256 ( 2.8) 252 ( 2.0) 244 ( 3.7) Nation 12 ( 1.0) 21 ( 1.0) 23 ( 1.2) 27 ( 1.2) 17 ( 14) 268 ( 2.6) 269 ( 2.3) 285 ( 2.1) 259 ( 2.2) 248 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample sin is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A25 I Students' Reports on the Amount of Time Spent (continued) I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT One Hour or Less Two Hours Three Hours Four to Five Hours _ , Six Hours or Moro TOTAL Percentage and ProGclency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 18 ( 0.9) 24 ( 0.9) 23 ( 1.0) 26 ( 1.0) 11 ( 0.7) 266 ( 2.1) 259 ( 1.7) 257 ( 1.8) 251 ( 1.5) 244 ( 2.7) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 ( 1.1) 16 ( 1.0) 269 ( 2.2) 26$ ( 1.8) 265 ( 1.7) 260 ( 1.7) 245 ( 1.7) PARENTS EDUCATION HS noniraduate State ) 23 ( ( 3.0) 25 ( 242 ( 3.1) 4.0) 32 ( 236 ( 3.5) 3.6) 10 ( ( 2.1) *441 Nation 12 ( 4.1.* 2.2) 20 ( 3.4) ( 28 ( 244 ( 2.9) 32) ( .41 HS graduate State 12 ( et. 1.5) 24 ( 246 ( 2.1) 2.8) 26 ( 247 ( 2.2) 3.1) 26 ( 243 ( 1.9) 2.8) 12 ( ORM ( 1.9) Oen Nation 8 ( 1.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 19 ( 1.6) 249 ( 4.7) 257 ( 2.8) 259 ( 32) 253 ( 2.5) 248 ( 3.0) Some college State 19 ( 1.8) 22 ( 1.9) 23 ( 2.0) 25 ( 2.6) 269 ( 3.7) 265 ( 32) 267 ( 3.0) 257 ( 3.4) 4141 ( 114.* Nation 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 20 ( 1.4) 27 ( 1.3) 21 ( 1.5) 24 ( 1.4) 9 ( 1.0) 281 ( 2.7) 275 ( 2.2) 273 ( 2.7) 263 ( 2.1) 254 ( 4.9) Nation 17 ( 1.3) 22 ( 1.6) 23 ( 1.1) 25 ( 1$) 12 ( 1.1) 282 ( 2.6) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 3.2) GENDER Male State 14 ( 1.1) 24 ( 1.0) 23 ( 1.3) 27 ( 1.3) 12 ( 1.0) 265 ( 3.6) 263 ( 2.5) 258 ( 2.5) 254 ( 1.7) 246 ( 3.8) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 28 ( 1.3) 17 ( 1.5) 269 ( 3.3) 267 ( 2.6) 267 ( 2.2) 262 ( 2.1) 248 ( 2.5) Female State 19 ( 1.2) 24 ( 1.2) 23 ( 1.1) 24 ( 1.5) 10 ( 1.0) 267 ( 2.1) 256 ( 1.9) 256 ( 2.4) 247 ( 2.3) 242 ( 4.2) Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 1.6) 15 ( 1.2) 269 ( 2.8) 269 ( 2.2) 264 ( 1.8) 258 ( 1.9) 241 ( 22) ,11wr. 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 f2 students). t) THE 1990 NAEP TRIAL STATE ASSESSMENT 135 California TABLE A26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 t4AEP TRIAL STATE ASSESSMENT None One or Two Days Thrite Days or More TOTAL Ponvontags and Proadoney Patentage and Proadenav Parcentagn and Prolickney State 39 ( 0.9) 33 ( 1.1) 25 ( 1.3) 263 ( 1.6) 259 ( 1.6) 240 ( 1.6) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 256 ( 1.5) 250 ( 1.9) RACE1ETHNIC1TY White State 39 ( 1.3) 35 ( 1.3) 27 ( 1.6) 275 ( 2.2) 275 ( 1.8) 261 ( 2.0) Nation 43 ( 1.2) 34 ( 1.2) 23 ( 12) 273 ( 1.8) 272 ( 1.7) 258 ( 2.1) Slack State 42 ( 237 ( 4.0) 4.7) ) 26 ( 3.6) «b..) Nation 58 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 31 ( 1.9) 34 ( 2.0) 35 ( 2.6) 241 ( 2.5) 240 ( 2.2) 231 ( 2.1) Nation 41 ( 3.3) 32 ( 22) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) Asian State 59 ( 276 ( 3.0) 3.3) 27 ( 272 ( 2.9) 3.8) 15 ( 2.4) fp.) Nation 82 ( 5.6) 11 ( 4.9) 287 ( 4.7)1 TYPE OF COMMUNITY Advantaged urban State 39 ( 1.9) 38 ( 2.7) 22 ( 2.1) 282 ( 3.3)1 280 ( 4.2)1 267 ( 4.9)1 Nation 47 ( 2.3) 38 ( 2.6) IS ( 3.7) 284 ( 4.4)1 279 ( 4.5)1 Disadvantaged urban State 38 ( 3.9) 31 ( 3.0) 31 ( 3.4) 248 ( 4.4)1 245 ( 5.3)1 233 ( 4.8)1 Nation 42 ( 3.3) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 256 ( 4.2)1 238 ( 6.3)1 Other State 39 ( 1.4) 32 ( 1.3) 28 ( 1.6) 263 ( 2.3) 258 ( 2.0) 245 ( 2.1) Nation 4,5 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 266 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 4: 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow amurate determination of the variability of this estimated mean proriciency. *** Sample me is insufficient to permit a reliable estimate (fewer than 62 students). 136 1 i THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A26 I Students' Reports on the Number of Days of (cmtinued) i School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE SSESSMENT A None One or Two Days Three Days or More TOTAL Percentage and Proficiency Percentage and Pronciency Percentage and Prondency State 39 ( 0.9) 33 ( 1.1) 28 ( 1.3) 283 ( 1.6) 259 ( 1.6) 248 ( 1.6) Nation 45 ( 11) 32 ( 0,9) 23 ( 1.1) 265 ( 1.8) 286 ( 1.5) 250 ( 1.9) PARENTS' EDUCATIOR HS non-graduate State 34 ( 3.0) 25 ( 2.1) 41 ( 3.3) 243 ( 3.9) 242 ( 4.4) 236 ( 3.1) Nation 36 ( 3.2) 26 ( 3.1) 38 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) NS graduate State 37 ( 2.6) 33 ( 2.4) 30 ( 2.5) 249 ( 2.3) 248 ( 2.6) 237 ( 3.1) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.8) 249 ( 2.4) Some college State 34 ( 2.2) 41 ( 2.9) 25 ( 2.3) 272 ( 2.8) 264 ( 2.7) 252 ( 3.9) Nation 40 ( 1.8) 37 ( 1.6) 23 ( 1.8) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) College graduate State 44 ( 1.7) 34 ( 1.7) 22 ( 1.5) 275 ( 1.9) 272 ( 2.4) 264 ( 2.5) Nation 51 ( 1.6) 33 ( 1.2) 16 ( 1.3) 275 ( 2.1) 277 ( 1.7) 265 ( 3.1) GENDER Male State 41 ( 1.2) 34 ( 1.3) 25 ( 1.5) 262 ( 2.2) 260 ( 1.9) 249 ( 22) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 1.4) 266 ( 2.0) 267 ( 2.1) 250 ( 2.6) Female State 37 ( 1.6) 32 ( 1.6) 32 ( 1.7) 263 ( 1.9) 259 ( 1.8) 243 ( 1.8) Nation 43 ( 1.4) 32 ( 1.1) 25 ( 1.3) 264 ( 2.3) 2661 1.7) 250 ( 1.8) The standard errors of the estimated staLlstics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 137 California TABLE A27 1 Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Strongly Agree Aire* Undecided, Disagree, Strongly Disagree TOTAL Percentage and Profkiency Percentage and Proficiency Percentage and Proficiency State 25 ( 1.1) 51 ( 0.8) 23 ( 0.9) 258 ( 1.7) 257 ( 1.4) 244 ( 2.0) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) RACE/ETHNICITY White State 28 ( 1.8) 51 ( 1.4) 21 ( 1.2) 280 ( 1.7) 269 ( 1.9) 284 ( 2.3) Nation 28 ( 1.6) 48 ( 1.3) 26( 15) 279 ( 2.0) 272 ( 1.8) 257 2.0) Black State 31 ( 3.2) 48 ( 4.4) 22 ( 3.4) M.* ) 236 ( 4.2) Nation 32 ( 2.5) 52 ( 2.3) 16 ( 1.9) 247 ( 4.1) 233 ( 3.3) 227 ( 4.2) Hispanic State 20 ( 1.4) 52 ( 1.8) 27 ( 1.5) 248 ( 2.3) 239 ( 1.7) 225 ( 2.9) Nation 24 ( 2.5) 48 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 2.2) 236 ( 3.8) Asian State 2.6) 53 ( 2.4) 19 ( 2.2) 284 ( 3.7) 272 ( 3.1) Nation 29 ( 5.5) 53 ( .4* ( 5.6) ***) 17 ( 4.9) *.".) TYPE OF COMMUNITY Advantaged urban State 26 ( 2.1) 51 ( 1.6) 23 ( 2.2) 283 ( 4.1)1 280 ( 3.7)1 267 ( 5.4)1 Nation 17 ( 3.2) 55 ( 2.4) 28 ( 42) 280 ( 4.1)1 *** Disadvantaged urban State 21 ( 4... 2.0) 57 ( 242 ( 2.1) 4.1)1 22 ( 230 ( 1.9) 5.1)1 Nation 26 ( 2.9) 48 ( 2.9) 26 ( 3.2) 260 ( 5.8)1 249 ( 4.6)1 240 ( 45)1 Other State 27 ( 1.7) 49 ( 1.2) 24 ( 1.3) 270 ( 2.0) 256 ( 2.0) 243 ( 2.8) Nation 27 ( 1.4) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. ft can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample Me is insufficient to permit a reliable estimate (fewer than 62 students). 138 4 ' THE 1990 NAEP TRIAL STATE ASSESSMENT California TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19610 NAEP TRIAL STATE ASSESSMENT Strongly Agroo Afro* Undecided, Disagree, Spin* Disagree TOTAL Percentage and Preaching Percantaga and Proliciaeicy Percentage and iNvaciancy State 25 ( 1.1) 51 ( 0.8) 23 ( 0.9) 268 ( 1.7) 257 ( A) 244 ( 2.0) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) PARENTS' EDUCATION HS non-graduate State 19 ( ( 2.1) *44) Si ( 241 ( 2.9) 2.8) 30 ( 231 ( 24) 3.8) Nation 20 ( 2.6) e- ( «is) 50 ( 243 ( 3.3) 2.6) 30 ( 233 ( 3.0) 43) itS graduate State 22 ( 2.0) 53 ( 2.0) 25 ( 2.0) 258 ( Z.0) 244 ( 1.9) 236 ( 3.8) Nation 27 ( 2.1) 47 ( 2.3) 20 ( 2.0) 282 ( 2.7) 255 ( 2.3) 245 ( 2.4) Some college State 31 ( 2.6) 49 ( 2.6) 21 ( 2.3) 272 ( 3.1) 263 ( 2.2) 251 ( 2.7) Nation 28 ( 2.5) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 258 ( 3.2) College graduate State 29 ( 1.6) 52 ( 1.5) 20 ( 1.3) 277 ( 2.4) 272 ( 1.9) 283 ( 2.7) Nation 30 ( 2.3) 51 ( 1.6) 19 ( 1.8) 280 ( 2.4) 274 ( 2.2) 286 ( 2.5) GENDER Male State 26 ( 1.6) 52 ( 1.4) 22 ( 1.2) 270 ( 2.3) 256 ( 1.9) 248 ( 2.5) Nation 28 ( 1.5) 48 ( 1.2) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Female State 25 ( 1.2) 50 ( 1.2) 25 ( 1.2) 286 ( 2.0) 257 ( 1.6) 240 ( 2.6) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 269 ( 2.1) 282 ( 1.8) 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. 88* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). ; 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing Service (EIS), Westat, and National Computer Systems (1sICS). The program benefitted from the contributions of hundreds of individuals at the state and local levels Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Fmally, and most importantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (CCSSO) for its considerable contributions to the program, especially its management of the National Assessment Phuming Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In particular, we aote the significant contributions of Ramsay Se lden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Ratd Garza -- worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people -- from school districts, colleges and universities, and State Education Agencies worked tirelessly to help ETS staff develop the assessment and a framework for interpreting the results. Under the NAEP contract to ETS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mauer), 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 Koff ler, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zaback. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Ku lick, and Phillip Leung collaborated to generate the data and perform analyses. They were Assisted by Drew Bowker, Laura McCain ley, and Craig Pizsuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koff ler 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. 4 U. S. ouvEman PRINTING OFFICE : 1991 0 - 293-275 (BK.4) QL 3 CO 44.1,