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DOCUMENT RESUME ED 330 559 SE 052 069 TITLE The State of Mathematics Achievement in Illinois: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NCTE 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 s!-ate reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/TechLical (143) EDRS PRICE MF01/PC06 Plus lostage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Yathematics Instruction; Mathematics Skills; .,:athematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television viewing IDENTIFIERS *Illinois; National Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers ane operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In Illinois, 2,683 students in 101 public schools were assessed. This report describes the mathematics proficiency of Illinois eighth-graders, compares their overall performance to students in the Central 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/ethnioitY, 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, Illinois students had an average proficiency of 260 compared to 261 nationwide. Many fewer students (Illinois-12%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJVCRW) NATIONAL CENTER FOR EDUCATION STATISTICS 1/47, CI) (4/4461 eV're 4.4 The SUM If M h A M in ILLINOIS The Trial State Assessment at Grade Eight r. py 7:7 qt 30, sv- r.14,P seo age U S DEPARTMENT OF EDUCATION du, Fit'Sra't P Arnd 1,coorP,enl f rut. TIONAL f.i SOuRCE S iN ORMAT ION CE TF RI RICI , le)k ,,ment PIA new, ,Pprodu e.11 as e.1.0 OVSC,r, 0, 0f Qan,tatiOn ,,,,prial.no har,wes NAO. !Wen rwoduk t,of, clwatt, S staftv0 do( ,,ent essa,ov ,..peSer,1 si posq,0,, Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD. the National Assessment of Educational Progress (NAEP). is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1969. assessments have been conducted periodically in reading. mathematics, seience. writing. history/geography. and other fields. By making objective information on student performance available to policymakers at the national. state, and local levels. NAL!' is an integral pan of our nation's evaluation of the condition and progress of education. Only information related to academie achievement is collected under this program. NAEP guarantees the privacy of individual students and their NAEP is a congressionally mandated project of the National Center for Education Statistics the U.S. Department of Education. The Commissioner of ilddcation Statistics is responsible. by lass. for carrying out the NAEP project through competitive awards to qualified organi/ations. NALP reports directly to the Commissioner. who is also responsible for providing continuing reviews. includ.ng validation studies and solicitation or public comment. on NAFP's conduct and usefulness. In 1988. Congress created the National Assessment Governing Board NAGBi to formulate policy guidelines for NAEP The hoard is responsible for selecting the subjeo areas to he assessed, which may include adding to those specified by Congress: identifying appropriate achievement goals for each age and grade: developing assessment obiectives; developing test specifications, designing the assessment methodology: developing guidelines and standards for data analysis and En reporting and disseminating results: d:veloping standards anti procedures for interstate, regional, and national comparkons: improving the form and ti.e of the National Assessment; and ensuring that all items selected for use in the National Assessment are free from racial, cultural, gender. or regional bias. The National Assessment Governing Board Richard A. Boyd, Chairman Executive Director Martha Holden knnings Foundation Cleveland. Ohio Phyllis Williamson Aldrkh Curriculum Coordinator Saratogy-Warren Saratoga Springs. New York Francie Alexander Associate Superintendent California Depanment of Education Sacramento. California David P. Battini High School History Teacher Cairo-Durham High School Cairo. New York Parris C. Battle Teacher Horace Mann Elementary School Flohda Mary R. Blanton Attorney. Cromwell. Porter. Blanton & Blanton Salisbury. North Carolina Floyd W. Bottitie Attorney Gaass. Klyn. & Boeh lie Pella. Iowa Linda R. Bryant Teacher Cireenway Middle School Teacher Center Pittsburgh. Pennsylvania Honorable Michael N. Castle Uovernor ot Delaware Carvel State Office Building Wilmington. Delaware Honorable Naomi IX. Cohen State of Connecticut House of Representatives l.egislative Office Building Hartford. Connecticut Chester F. Finn. Jr. Professor of Education and Public Policy Vanderbilt University. Washington. Michwel S. Glode Wyoming State Board of Education Saratoga, Wyoming Christine Johnson Principal Abraham Lincoln High School Denver, t 'coloristic+ John lindley Principal Sot, h Colby Elementary School ri in Orchard, Washington Carl J. Maser Director of Schools The Iaitheran Church - Missouri Synod International Center St. Louis. Missouri Mark D. Musick President Southern Regional Education Board Atlanta. Georgia Honorable Carolyn Pollan Arkansas House of Represemitiscs Fon Smith. Arkansas Matthew W. Prophet, Jr. Superintendent Portland Oregon School District Portland, Oregon Honorable William T. Randall Commissioner of Education State Department of Education Iknver. Colorado Dorothy K. Rich President Home and Sehool Institute Special Projects Office Washington. D.C. Honorable Richard W. Riley Attorney Nelson. Mullins. Riley, and Scarborough Columbia. South Carolina Thomus Topazes Attorney l.aw Offices of Frank Rogoitenski t'otonado. California Herbert .J. Walberg Professor of Education University of Illinois Chicago. Illinois Assistvnt Secretary lor Educational Research and Improvement (Ex Officio> S. Department of Education Washington. DC Roy Truhy Executive Director. NAGB Washington. DC NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement in ILLINOIS The Trial State Assessment at Grade Eight THE NATIONS REPORT CARO Report No. 21-ST-02 June 1991 "repared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department ot Education U.S. Department of Educaticn Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). library of Congress, Catalog Card Number: 91-61478 ISBN: 0-88685-14-9 The work upon which this publication is based was performed for the National Center for Education StltiniCs, Office of Educational Research and Improvement, by Educational Testing Service. Educational Testing Service is an equal opportunity/affirmative action employer. Educational Testing Service, ETS, anda sre registered trademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY INTRODUCTION 7 Overview of the 1990 Trial State Assessment This Report 9 Guidelines for Analysis 11 Profile of Illinois 14 Fighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Illinois Public Schools? Chapter 1. Students Mathematics Performance 1 S .evels of Mathematics ProticiencN 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race Ethnicity 24 'type of Communit -17 Parents' Education I..evel 29 Gender 1,1 Content Area Performance 11 THE 1990 VAEP /CAL STATt. ASSESS1EN1 PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Arc Students Taught in Mathematics' Curriculum Coverage 41 Mathematics hiomework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Delivereir 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groupy 54 Lsing Mathematical Objects is Materials tor Mathematics Instruction Summary 59 Chapter 5. How Arc Calculators Used' 60 The Availabilit of Calculators 62 The Use of Calculators 63 When To I. 'se a Calculator 64 Summary 66 Chapter 6. Who is Teaching Eighth-Grade Mathematics' 67 Lducational Background 6g Sumrnar 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and 'teaching 73 Amount of Reading Materials in the Home 74 flours of 1 elevision Watched per Day Student Absenteeism 76 Students' Perceptions of Mathematics 7S Summary 79 PROCEDURAL APPENDIX s DATA APPENDIX 9' IN 1 IlL 1990 NAFP TRIAL SI ATI% ASSLSSML\ Illinois THE NATION'S REPORT CARD EXECUTIVE SUMMARY In I9SS. Congress passed new legislation for the National Assessment of- I'dueational Progess (NAI.PI, which included for the first time in the project's histol) -- a provision authorizing oluntars state-b> -state assessments on a trial basis. in addition to continuing its prima) mission, the natio:t.. as .,.:ssments that NAI P has conducted since it. inception, /1. a result of the legislatioi.. the 1990 N Al' progam included a lrial State Assessment Program in eighth-grade matheinatics. National assessments in mathematics, reading. writing, and science k etc condueted simultaneousl 199(1 at grades four. eight. and twele. I or the Trial State Assessment, eighth-grade public-school students k ere assessed in each of .17' states. the District of Columbia. and two territories in rehniarN 1990. The sample was carefull designed to represent the eighth-grade pubht.-school population in a state ill- territor. Within each selected school, students were randoml chosen to participate in the program. I oeal school district personnel administered all assessment sessions, and the contractor's staff monitored 50 rrcent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniforml. The results ot the monitoring indicated a high degee of qualit and uniformit across sessions. H11. 1990 \AIT RI Al StAll ASSISSMI Illinois In Illinois, 101 public schools participated in the assessment. The weighted school participation rate was 96 percent, which means that all of the eighth-grade students in this sampk of schools were representative of 96 percent of the eighth-grade pubfie-sehool students in Illinois. In each school. a random sample of students was sdected to participate in the assessment. As estimated by the sample, 1 percent of the eighth-gade public-school population was classified as limited Fng lish Proficient (l IT). while 9 percent had an Individualized klueation Plan (lIT). An IFP 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 wen: permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to he categorized as I ,imited Frig lish Proficient or had to have an Individualized Fducation Plan and (in either ease) be judged incapable of participating in the assessment. The stutko:s who were excluded from the assessment because the were categorized as I IP or had an IF P represented I percent and 5 percent of the population. respectivel. In total. 2,00 eighth-grade Illinois public-school students were assessk..d. The weighted student participation rate was 96 percent. This means that the sample of students who took part in the assessment was representative of 96 percent of the eligible eighth-grade publie-schooI student population in Illinois. Students' Mathematics Performance The average proficiene of eighth-grade public-school students from Illinois On the NAV mathematics scale is 260. This proficiency is no difkrent from that of students across the nation (261). Average proficiene on the !S AFP seak provides a global view of eighth grader.,' 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 i...Teater detail. NAI:1' used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-gade students to ddine the skills, knowledge, and understandings that characterize lour levels of mathematics performance -- levels NO, 250, 300, and 350 on the NAFP scale, 9 1 I. I 99 o \ 41.1) i RIM. St Al F ASSESSMIA I Illinois In Illinois, 96 percent of the eighth fgr iders, 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 Illinois (12 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 -- Numners and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in Illinois performed comparably to students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the Illinois eighth-grade student population defined by race ethnicity type of communit , parents' education level, and gender. In Illinois: 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 geater percentage of White students than Black or Hispanic students and about the same perc...ntage of White as Asian students attained level 300. The results h type of communit indicate that the average mathematics performance of the Illinois students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas. extreme rural areas, or areas classified as "other". In Illinois. the average mathematics proficiency of eighth-gade public-school students having L4t least one parent who gaduated from college was approximatel> 31 points higher than that of students whose parents did not gradiwte from high school. The results by gender show that there appears to be no difference in the average mathematics proficiency of eighth-gade males and females attending public schools in Illinois. In addition. there was no difference between the percentages of males and females in Illinois who attained level 300. Compared to the national results. females in Illinois performed no differently from females across the country: males in Illinois performed no differently from males across the country. , 1 HE 190 \ AI P IRIAI SI Al I. ASSI-SSMIA1 3 Illinois A Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, hut it becomes more usefUl for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers. and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education. illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information about student achievement. Some of the salient results for the public-school students in Illinois are as follows: About three-quarters of the students in Illinois (75 percent) were in schools where mathematics was identified as a special priority. .1-his is about the same percentage as that for the nation (63 percent ). In Illinois, 75 percent of the students could take an algehi a course in eighth gxade for high-school course placement or credit. A geater percentage of students in Illinois were taking eighth-gade mathematics (63 percent) than were taking a course in pre-algebra or algebra (34 percent). Across the nation. 62 percent were taking eighth-gade mathematics and 34 percent were taking a course in pre-algebra or algebra. According to their teachers, the geatest percentage of eighth-grade students in public schools in Illinois spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent 30 minutes doing mathematics homework each da>. Across the nation, teachers reported that the largest rercentage of students spent either 15 or :10 minutes doing mathematics homework each day . while students reported either 15 or 30 minutes daily. . Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heav 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 1 'M. 1990 \ MT HUAI Si AI F. ASSESSMFA Illinois In Illinois, 18 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 28 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 Illinois, 19 percent of the students never used a calculator to work problems in class, while 49 percent almost always did. In Illinois, 45 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's deigee. This compares to 44 percent for students across the nation. More than half of the students (65 percent) had teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in Illinois 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 Illinois (12 percent) watched one hour or less of television each dly: 14 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. 4 Afto 1HE 199U AIP TRIAL SI AT . ASSESSMEN1 5 Illinois THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Eclucational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon Qdifornia Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshim Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands IP THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Illinois This report describes the performance of the eighth-grade public-school students in Illinois and consists of three sections: This Introduction provides backp-ound information about the Trial State Assessment and this report. It also provides a profile of the eighth-gi-ade public-school students in Illinois. Part One describes the mathematics performance of the eighth-gade public-school students in Illinois, the Central rcOon, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics pelicies and instruction in schools in Illinois, the Central region, and the nation. Overview of the 1990 Trial State Assessment In 198g, Congi-ess passed new legislation for the National Assessment of rducational Progress (NAYP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survej instrument .1br the eighth grade and shall conduct a demonstration of the instrument in /990 in States which wish to participate, with the purpose qf determining whether such an assessment yields valid. reliable State representative data. (Section 406 (1)(21(C7) 0) of the General Education Provisions Act, as amended by Pub. L. 100-297 ( 20 1 S.C. 1221e-1 ( 2 )( C )( i) ) As a result of the legislation. the 1990 NAFP program included a Trial State Assessment Progam in eighth-gade mathematics. National assessments in mathematics, reading, %citing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. I.or the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's stall- 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 &give of quality and uniformity across sessions. 8 HE 1990 NAEP TRIAL STATE ASSESSMENT Illinois The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patterned after the consensus process described in Public I,aw 98-511, Section 405 (F), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation tha tuthorized 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 NMI' 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 Illinois, in the Central region, and for the nation. Results also are provided for goups of students defined by shared characteristics race ethnicit), type of community, parents' education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for Illinois are based only on the students included in the Trial State Assessment Progam. However, the results for the nation and the re0on of the country arc based on the nationally and regionally representative samples of public-school students who were assessed in January or Februar) as part of the 1990 national NAIT progam. Use of the re&nal and national results from the 1990 national NAIT program was necessar) because the voluntary nature of the Trial State Assessment Program did not guarantee representativt. national or regional results. since not every state participated in the progam. National Council of leachers of Mathematics. Curriculum and 1. valuati,,n Standards Itr 5(hool kfathern ti(.s (Reston, VA: National Council of 'teachers of Mathematics, 1989). .4 . TIM 1990 NAEY TRIAL STATE ASSESSMEN*1 9 Illinois 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 Illinois. 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 gxoup live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are in professional or managerial positions. Disadvantaged Urban: Students in this group live in metropilitan 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 Ey: outside metropolitan statistical areas, live in areas with a population below ROM and attend schools where many of the students' parents are farmers or farm wo kers. 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 h) each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school. some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. 10 1 HE 1990 NAEP TRIAL. STATE ASSESSMENT Illinois GENDER Results are reported separately for males and females. REGION The United States has been divided into four regions: Northeast, Southeast, Central, and West. States included in each region are shown in Figure 1. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the st#te is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURE 1 I Regions of the Country THE NATION'S REPORT CARD NORTHEAST SOUTHEAST CENTRAL WEST _ Connecticut Alabama Illinois Alaska Delaware Arkansas Indiana Arizona District of Columb.a 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 Maxico Pennsylvania Tennessee Ohio Oklahoma Rhode island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Txu Virginia Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT II Illinois Gni': :lines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported arc necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard e,ror of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistically significant), the report describes the grout) 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 he about the same or widely discrepant. The reader is cautioned to rel on the results of the statistical tests -- rather than on the apparent magnitude of the difference between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular group had higher ( or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain the value zero, When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups. the confidence interval included zero, and thus no difference could be assumed between the groups. When three or more groups are being compared. a I3onferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendk. 12 THE 19O NAEP TRIAL STATE ASSESSMENT Illinois It is also important to note that the confidence intervals pictured in the figures in Part Onc of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. lowever, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-goup percentages reported in the text and used in all statistical tests are based on unrounded estimates (i,e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Ilence, the percentage for a combined gsoup (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groAi, that were combined. Sitnilarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not he consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). I 1111 .'. 1990 NAEP 1 RIAI. STATE ASSESSMENT 13 Illinois Profile of Illinois EIGHTH-GRADE SCHOOL AM) STUDENT CHARACTERISTICS Table I provides a profile of the demographic characteristics of the eighth-grade public-school students in Illinois, the Central 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 Illinois Eighth-Grade Public-School I Students PERCENTAGE OF STUDENTS 1990 NAEP TRIAL. STATE ASSESSMENT Illinois Central Nation DEMOGRAPHIC SUBGROUPS Raciathnkiiy Percentage Portontage Percentage White 67 ( 1.9) 79 ( 2.8) 70 ( 0.5) Rack 17 ( 1.9) 13 ( 3.2) 16 ( 0.3) Hispanic 12 ( 1.4) 5 ( 1.0) 10 ( 0.4) Asian 3 ( 0.5) ( 0.4) 2 ( 04) American Indian ( 0.2) 1 ( 0.4) 2 ( 0.7) Type of Community Advantaged urban 21 ( 3.7) 3 ( 3.1) 10 ( 3.3) Disadvantaged urban 21 ( 3.2) 10 ( 4.3) 10 ( 2.8) Extreme rural 14 ( 3.3) 8 ( 8.0) 10 ( 3.0) Other 43 ( 5.1) 79 ( 7.7) 70 ( 4.4) Parents Ecksoation Did not finish high school 8 ( 0.8) 7 ( 0.9) 10 ( 0.6) Graduated high school 25 ( 1,5) 33 ( 2.1) 25 ( 1.2) Some education after high school 19 ( 0.9) 19 ( 0.9) 17 ( 0.9) Graduated college 39 ( 1.8) 35 ( 1.8) 39 ( 1.9) Gondor Male 52 ( 1.1) SO ( 1.4) Si ( 1.1) Female 48 ( 1.1) 50 ( 1.44 49 ( 1.4) The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages for Race!Ethnicity may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Illinois schools and students sampled for the 1990 Trial State Assessment. In Illinois, 101 public schools participated in the assessment. The weighted school participation rate was 96 percent, which means that all of the eighth-grade students in this sample of schools were representative of 96 percent of the eighth-grade public-school students in Illinois. TABLE 2 f Profile of the Population Assessed in Illinois EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution Weighted schoOl participation rate atter substitution Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating schools 78% 98% 107 2 82 21 19 101 EIGHTH-ORADE PUBUC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students selected to participate in the assessment Number of students withdrawn from the assessment Percentage of students who 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 ot students excluded from the assessment due to individualized Education Plan status Number of students to be asseSsed Number of students assessed 96% 3,087 103 1% 1% 9% 5% 2,813 2,683 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Illinois In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample. I percent of the eighth-gade public-school population was classified as Limited English Proficient (LEP). while 9 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to he eligible for special education, that typically sets forth goals and objectives for the student and describes a progam 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 he 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 I peicent and 5 percent of the population, respectively. In total, 2,683 eighth-grade Illinois public-school students were assessed. The weighted student participation rate was 96 percent. This means that the sample of students who took part in the assessment was representative of 96 percent of the eligible eighth-gade public-school student population in Illinois. TIIP. 1990 \ALP TRIAL Si ATE ASSESSNIEVI Illinois THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Illinois Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations, Measurement; Geometry: Data Analysis, Statistics, and Probability; and Mgebra and l'unctions. Students' overall performance in these content areas was summarized on the NMI) mathematics scale, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficienc of eighth-grade public-school students in Illinois. Chapter I compares the overall mathematics performance of the students in Illinois to students in the Central reon and the nation. It also presents the students average proficiency separately for the five mathematics content areas. Chapter 2 summarizes the students` overall mathematics performance for subpopulations defined by race ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. THE 1990 NALP TRIAL STATE ASSESSMENT 17 Illinois CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from Illinois on the NAEP mathematics scale is 260. This proficiency is no different from that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency NAEP Mathematics Scale 200 225 250 275 300 500 1111 REPORT Average Proficiency 4.- 1+4 Illinois 200 ( 1.7) Moo. Central 265 ( 2.0) Nation 211 ( 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 Oifferences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 18 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois LEVEIS OF MATHEMATICS PROM:TEMA' Average proficiency on the NAFP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the pecifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, \ALP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to defme the skills, knowledge, and understandings that characterize four levels of mathematics performance levels 200, 250, 300, and 350 on the \ALP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, matherwies 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 fbur levels of mathematics proficiency are Oven in Figure 3. It is important to note that the definitions of these levels are based solely on student performance on the 1990 mathematics assessment. Fhe levels are not judgmental standards of what ought to be achieved at a particular gade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In Illinois, 96 percent of the eighth gaders, 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 Illinois (12 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals. percents, elemental-) geometric properties, and simple algebraic manipulations (level 300). CONTENT AREA PERFORMANCE As previousl) indicated, the questions comprising the Trial State Assessment covered five content areas -- Numbers and Operations; Measurement; Geometr); Data Analysis. Statistics, and Probability: and Algebra and Functions. Figure 5 provides the Illinois. Central region. and national results for each content area. Students in Illinois performed comparably to students in the nation in all of these five content areas. TIIL 1990 AU' I RIM- SI AIL ASSESSNIEM 19 P, Illinois FIGt RI 3 I Levels of Mathematics Proficiency 11110 ME NATION'S REPORT CARO LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships invokang whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-step word problems and Select the greatest four-digit number in a list. In measurement, these students can read a rL'ar as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of corns. In geometry, these students can recognize simple figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these Students can recognize translations of word problems to numerical sentences and extend simple pattern sequences. 1 LEVEL 250 Simple Multiplicative Reasoning and Two-Step Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-Step addition and subtraction problems involving money. Using a calculator. they can identify solutions to other 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 pface 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 Oar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to undertand the relationship between proportion and probability In algebra. they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions. 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois FIGURF 3 1 Levels of Mathematics Proficiency (continued) I THE NATION'S REPORT CARO LEVEL 300 Reasoning and Problem Solving Involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations 4 Students at this level are able to represent, interpret, and perform simple operations With fractions and decimal numbers. They are able to locate fractions and decimals on number lines. simplify fractions, and recognize the equivalence between common fractions and decimals, including pictorial representations They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expressions, including those With exponents and negative integers. in measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and uSe proportional relationships to solve routine problems involving Similar triangles and scale drawings. in geometry. they have some mastery of the definitions arid properties of geometric figures and solids. in data analysis, these Students can calculate averages, select and interpret data from tabular displays. pictographs. and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open linear sentences and inequalities by Substitution, and checking and graphing an interval representing a compound inequality when it is described in words. They can determine and apply a rule for simple functional relations and extend a numerical pattern. Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to include some properties Of exponents, They can recognize scientific notation on a calculator and make the transition between scientific notation and decimal notation. In measurement. they can apply their knowledge of area and perimeter of rectangles anc triangles to solve problems. Tney can tind the circumferences of circles and the surface areas of solid figures In geomet y. they can apply the Pythagorean theorem tO Solve problems involving indirect .leasureMent. These students also can apply their i,nowledge of the propertes of geometric fig 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 identity art 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. "1 W. 1990 \ MT RIM. SI AI I: ASSESSME\ I 21 Illinois FIGURE 4 I Levels of Eighth-Grade Public-School Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation NE RATION'S REPORT pa" CARD 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within : 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. r, 0 22 THL 1990 NAEP TRIAL STATE ASSESSMENT Porcontage O ( 0.1) ( 0.2) ( 0.2) 12 ( 1.1) 12 ( 2.5) 12 ( 1.2) 64 ( 2.1) 70 ( 3.2) 64 ( 1.6) 96 ( 0.8) 98 ( 0.9) 97 ( 0.7) Illinois THE NATION'S REPORT CARO FIGURE 5 I Eighth-Grade Public-School Mathematics Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation NUMBERS AND OPERATIONS MEASUREMENT GEOME1RY P'411 1.04010.011 1^11"4 DATA ANALYSIS, STATISTICS, AND PROBABILITY I011801.41 .-.1"11 ALGEBRA AND FUNCTIONS 11.1,1NA, F=4"0.4 0 200 225 250 275 Avorage Proficiency 285 ( 1.7) 270 ( 2.7) 286 ( 1.4) 256 ( 2.0) 283 ( 3.4) 258 ( 1.7) 256 ( 1.7) 282 ( 3.1) 259 ( 1.4) 262 ( 2.0) 265 ( 3.2) 282 ( 1.8) 260 ( 1.7) 283 ( 2.1) 260 ( 1.3) 300 500 Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within / 2 standard errors of the estimated mean (95 percvnt confidence interval, denoted by 0+4). If the confidence intervals for the populations do not overlap, there is a statistically significant diflerence between the populations. THE 1990 AEI) TRIAL STATE ASSESSM EN 1 23 Illinois 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 subtri-oups of the student population defined by race,,ethnicity, type of community, parents education level, and gender. RACEJERIMCITY. The Trial State Assessment results can be compared according to the different racial ethnic goups when the number of students in a racial ethnic group is sufficient in size to he reliabl> reported (at least 62 students). Average mathematics performance results for White, Black, Hiswanic, and Asian students from Illinois are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficienc) than did Black or Hispanic students and about the same mathematics proficienc) as did Asian students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Black or Hispanic students and about the same percentage of White as Asian students attained level 300. 24 THE 1990 NAEP TRIAL sAE ASSESSMEN1 Illinois FIGURE 6 I Average Eighth-Grade Public-School i Mathematics Proficiency by Race/Ethnicity NAEP Mathematics Scat* 0 200 225 250 275 WC SOO Itt 1113011 Average Profit:low PPil 11,4001 III 1twol 1-4"1 Illinois White 271 ( 1.4) Black 233 (3.8) Hispanic ( 13) Asian Stai 4.1) Central White 272 ( 2.6) Black 232 ( Se)1 Hispanic ( i Asian Nation White 21* ( 1.5) Black 2.3) Hispanic 213 ( 21) Asian ( 5.5)1 The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. s" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 25 Illinois TIE WONT REPOITI FIGURE 7 I Levels of Eighth-Grade Public-School CARD I Mathematics Proficiency by Race/Ethnicity LEVEL 300 Slat White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian LEVEL 250 Nato White Black H ispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian LEVEL 200 State White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by I-+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because few students attained that level. Interpret with caution the nature of the Ftample does not allow accurate determination of the variability of this evtimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r*, 100 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 ( 1.5) 1 ( 0.8) 2 ( 0.8) 24 ( 5.2) 14 ( 2.8) 1 ( 1.0)1 *el ( 441 15 ( 1.5) 2 ( 1.3) 3 ( 1.1) 31 ( 6.2)1 78 ( 1.6) 27 ( 6.0) 31 ( 3.9) 88 ( 5.1) 78 1 3.1) 23 ( 4.7)1 vat 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) 80 ( 5.6P 99 ( 0.3) 88 ( 2.4) ( 3.6) 99 ( 1.6) 100 ( 0.4) 91 ( 4.4)1 KIM *** ) REX '1 ) 09 ( 0.4) 89 ( 3.1) 93 ( 1.6) 97 ( 2.6)1 Illinois TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, disadvantaged urban areas, extreme rural areas, and areas classified as "other". (These are the "type of community" groups in Illinois with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Illinois students attnding schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural areas, or areas classified as "other". FIGURE 8 Average Eighth-Grade Pub Ic-School Mathematics Proficiency by Type of Community 200 NAEP Mathematics Scala 225 250 275 300 500 A. 11mpowal P41 P-4.1 WOO Avorago Proficiency Illinois Advantaged urban 211 ( 2.8) Disadvantaged urban ( SA) Extreme rural 2114 ( 3.6)1 Other 213 ( 2.2) Central Advantaged urban mar ( '41 Disadvantaged urban 236 ( 3.8$ Extreme rural Ma* 1141 Other SIB ( 3.4) Nation 0-4- Advantaged urban lin ( 3.8$ Disadvantaged urban NI ( 3.5)I Extreme rural ( 4.1$ Other MI ( 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 i-m), If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- tht nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 27 Illinois FIGURE 9 LEVEL 300 State Adv. urban Dlsadv. urban Ext. rural Other Region Adv. urban Dqsadv. urban Ext. rural Other Ration Adv. urban Disadv. urban Ext. rural Other LEVEL 250 State Adv. urban Disadv. urban Ext. rural Other Ragion Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban Dtsadv. urban Ext. rural Other LEVEL 200 State Adv. urban Disadv. urban Ext. rural Other Region Adv. urban Dlsadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community THE NATIONS REPORT CARD Now 0 20 40 60 80 Percentage at or Above Proficiency Levels he 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 confider= interval, denoted by H-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 1. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 26 ( 3.0) 2 ( 1.0) 10 ( 2.3)1 10 ( 1.6) 1 ( 1 .0)1 * ) 13 ( 2.9) 26 ( 4.8)1 ( 2.1)1 6 ( 2.3)1 12 ( 1.2) 85 ( 3.0) 34 ( 6.3) 70 ( 5.3)1 68 ( 3.1) 11111 ) 31 ( 8.7)1 mm ( ) 73 ( 4.2) ( 4.6)t 48 ( 5.0)1 58 ( 6.2)1 64 ( 2.3) 100 ( 0.5) 00 ( 3.6) 99 ( 1.0)1 98 ( 0.7) MIR ) 92 ( 3.0)1 *** .) 99 ( 0.9) 100 ( 0.0) 95 ( 1.5)1 97 ( 2.8)1 97 ( 1.0) 100 "1 01 &i 28 THE 1990 NAEP TRIAL STATE ASSESSMEN1 Illinois 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 Illinois, the average mathematics proficitley of eighth-grade public-school students having at least one parent who gxaduated from college was approximately 31 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, about the same percentage of students in Illinois (39 percent) and in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 8 percent for Illinois and 10 perctnt for the nation. FIGURE 10 I Average Eighth-Grade Public-School i Mathematics Proficiency by Parents' Education NAEP Mathematics Scala 0 200 225 250 275 300 500 Average Proficiency Illinois 1.4.01 HS non-graduate 20 ( 2.9) M4 H S graduate 221 ( 1.8) Some college Xi ( 1.2) 1.4.4 College graduate 273 ( 2.1) Central HS non-graduate IOW ( 1404 S graduate 211 ( 2.5) Some college fa0 3.05) College graduate 34) Nation P41 HS non-graduate 243 ( 2.0) HS graduate X14 ( 1.5) 144 Some college ass( 1.7) 144 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 1+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Illinois 111E NATION'S 'WORT FIGURE 11 I Levels vf 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. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. 0 20 40 60 80 Percentage at or Above Proficincy Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within I 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by t44). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 2 ( 1.1) 5 ( 1.0) 9 ( 2.3) 21 ( 2.1) ( 8 ( 3.9) 14 ( 3.4) 17 ( 3.7) 1 ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.9) 42 ( 4.4) 56 ( 2.4) 88 ( 2.7) 78 ( 2.7) wito .) 06 ( 4.1) 75 ( 5.1) 79 ( 3.9) 37 ( 4.6) Se ( 2.7) 71 ( 2.6) 73 ( 2.0) 01 2.8) 94 1.3) 98 (1.1) 98 0.5) ass ) 00 (1.2) 100 0.0) 911 0.9) 98 1.9) 97 0.8) 99 0.7) 99 0.7) 100 THE 1990 NAEP TRIAL STATE ASSESSMENT n...111Nm GENDER Illinois 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 Illinois. Compared to the national results, females in Illinois performed no differently from females across the country; males in Illinois performed no differently from males across the country. FIGURE 12 I Average Eighth-Grade Public-School I Mathematics Proficiency by Gender NAEP Mathematics Scale 200 225 250 275 300 500 Averaw Proficiency P.1 PM Illinois Male Female ( ( 2.0) 13) Central 1Smot Male ( 3.3) P.P1 Female ( 2.6) Nation PM Male 302 ( 1.5) 1.1 Female ( 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 t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by P4-1). 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 Illinois who attained level 200. The percentage of females in Illinois who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in Illinois 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 Illinois FIGURE 13 1 Levels of Eighth-Grade Public-School i Mathematics Proficiency by Gender LEVEL 300 State Male Female Region Male Female Nation Male Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female THE NATKRil P.11 proseri pm.lomurrotti fwimommommi Its 1.011 Percentage 12 ( 1.5) 11 ( 1.3) 14 ( 4.8) 9 ( 2.3) 14 ( 1.7) 10 ( 1.3) 63 ( 2.5) 65 ( 2.5) 69 ( 3.3) 71 ( 4.0) 64 ( 2.0) ( 1.8) t-9.11 96 ( 1.0) ORM 96 ( 0.7) pu 99 ( 0,8) 96 ( 1.2) erg 97 ( 0.9) 1. 97 ( 0.8) 0 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by P-4-1). If the confidence intervals for the populations do not overlap, there is a stausucally significant difference between the populations. Proficiency level 350 is not presented tri this figure because so few students attained that level. C.) 32 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois In addition, there was no difference between the percentages of males and females in Illinois who attained level 100. The percentage of females in Illinois who attained level 300 was similar to the percentage of females in the nation who attained level 300. Also, the percentage of males in Illinois who attained level 300 was similar to the percentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race 'ethnicity, type of community, parents' education level, and gender. THE 3990 NALP TRIAL STATE ASSESSMEN 33 Illinois TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS HMO NAEP TRIAL STATE ASSESSMENT Numbers and Operatiem Maasuremen Geometry 1 Data Analysis' Statistics, and Probability Algebra and IOTA: Proadancy Pro fleloney Pro Ilekney Prni Odom Prodebncy State 265 ( 1.7) 256 2.0) 256 ( 1.7) 262 ( 2.0) 260 ( 1.7) Region 270 ( 2.7) 263 3.4) 262 ( 3.1) 265 ( 3.2) 263 (2.1) Natlor 266 ( 1.4) 258 1.7) 259 ( 1.4) 262 ( 1.8) 200 ( 1.3) RACEATHNICITY White State 275 ( 1.5) 270 ( 1.7) 205 ( 1.5) 275 ( 1.8) 270 ( 1.5) Region 276 ( 2.9) 271 ( 37) 288 ( 3.0) 273 ( 3.1) 266(2.3) Nation 273 ( 1.6) 257 ( 2.0) 267 ( 1.5) 272 ( 1.8) 268 ( 1.4) Black State 242 ( 3.8) 219 ( 4.8) 234 ( 3.8) 228 ( 4.2) 236 ( 3.8) Region 241 ( 8.5)1 223 ( 3.5)1 231 ( 42)1 225 ( 7.0)1 231 ( 1.0)1 Nation 244 ( 3.1) 227 ( 3.6) 234 ( 2.8) 231 ( 3.8) 237 ( 2.7) Hispanic State Region 241 ( ..* 32) 228 ( +111. ( 3.7) OM) 235 ( Me* 3.5) 44) 231 ( .4* ( 4.5) 237 ( 44, ( 4.2) .41 Nation 24$ ( 2.7) 238 ( 3.4) 243 ( 32) 239 ( 3.4) 243 ( 3.1) Adan State Region 283 ( 4.8) ...) 276 ( 4.. 7.7) ...) 274 ( 3.9) 279 ( 5.7) 41111 279 ( 4.3) Nation 285 ( 5.9)1 27$ ( 6.3)! 275 ( 5.9)1 282 ( 6.9)1 278 ( 6-7)1 TYPE OF COMMUNITY Advirtsitud urban State 285 ( 2.9) 279 ( 3$) 278 ( 2.8) 279 ( 2.4) Region 4410 diM) Nation 283 ( 3,2)1 281 ( 3.2)1 277 52)1 285 ( 4,8)1 277 ( 4.8)! Disadvantaged ban State 244 ( 5.0) 225 ( 5.4) 234 ( 4.3) 231 ( 6.7) 236 ( 4.6) Region 245 ( 2.2)1 228 ( 5.9)1 236 ( 8.7)! 231 ( 5.0)1 234 ( 4.7)1 Nation 255 ( 3.1 )! 242 ( 4,9)1 248 ( 3.7); 247 ( 4.5)1 247 1 3.2)! Extreme rural State 269 ( 34)1 264 ( 42)1 268 ( 2.8)i 266 ( i.2)t 263 ( 4.1)1 Region 44* ( 41,. ( .441 AIM ( Nation 258 ( 4.3)1 254 ( 4.2)1 253 ( 4.5)3 257 ( 5.0)! 256 ( 4.8)1 Other State 268 ( 2.2) 280 ( 2.8) 257 ( 2.3) 265 ( 2.5) 263 ( 2.3) Region 273 ( '3.5) 286 ( 4.3) 264 ( 3.7) 267 ( 4.1) 265 ( 2.8) Nation 266 ( 1.9) 257 ( 2.4) 259( 1.7) 281 ( 22) 281 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 3 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). 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE 3 I Eighth-Grade Public-School Mathematics ("mtinued) I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT U4STINWS and OPeraIkIlls Geometry Data AnalYilli' Statistics, and Probability Algebra and TOTAL Prolkiesmy Proacieney Prandeney Prolielencly Wolk:low State 265 ( 1.7) 256 ( 2.0) 256 ( 1.7) 262 ( 2.0) 260 ( 1.7) Region 270 ( 2.7) 263 ( 3.4) 262 ( 3.1) 265 ( 3.2) 263 ( 2.1) Nation 266 ( 14) 258 ( 1.7) 250 ( 14) 262 ( 41.8) 260 ( 1.3) PARENTS' EDUCATION NS non-graduate State Region 247 ( 3.3) 11.1 235 ( *114 4.2) 240 tey " 239 ( 4.3) 41 243 ( 444 3.2) *41 Nation 247 ( 2.4) 237 ( 3.8) 242 ( 21) 240 ( 3.1) 242 ( 3.0) HS graduate State 250 ( 1.8) 246 ( 2.1) 247 ( 1.8) 254 ( 2.0) 251 ( 1.8) Region 209 ( 2.5) 255 ( 3.8) 257 ( 3.4) 260 ( 3.2) 25a ( 3.4) Nation 259 ( 1.8) 24$ ( 2.1) 252 ( 1.6) 253( 2.2) 253( 2.0) Some college State 268 ( 1.7) 258 ( 2.1) 257 ( 2.0) 265 ( 2.1) 201 ( 2.2) Region 275 ( 3.2) 270 ( 5.7) 264 ( 4.0) 273 4.7) 266 ( 3.7) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 263 ( 2.2) College graduate State 277 ( 2.3) 271 ( 2.7) 267 ( 2.0) 275 ( 2.6) 273 ( 14) Region 277 ( 4.2) 270 ( 4.4) 270 ( 4.3) 273 ( 4.5) 271 ( 3.1) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 27$ ( 2.2) 273 ( 1.7) GENDER Mate State 265 ( 2.0) 259 ( 2.3) 256 ( 2.0) 261 ( 2.3) 258 ( 2.0) Region 271 ( 3.9) 267 ( 4.8) 264 ( 3.7) 26.5 ( 3.4) 263 ( 2.2) Nation 286 ( 2.0) 262 ( 2.3) 260 ( 1.7) 262 ( 2.1) 260 ( 1.6) Female State 265 ( 1.7) 253 ( 2.3) 256 ( 1.8) 282 ( 2. 262 ( 4.7) Region 270 ( 2.7) 259 ( 3.4) 260 ( 3.1) 265 ( 4.0) 262 ( 2.8) Nation 266 ( 1.4) 253 ( 1.8) 258 ( 1.5) 261 ( 1.9) ( 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. Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Illinois THE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, wadi 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 progams. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information on student achievement. It is important to note that the NAEP data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. THE 1990 NA,EP TRIAL STATE ASSFSSMENT 4 37 Illinois 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, NMI' data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home 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. 38 TUE 1990 NAEP TRIAL STATE ASSESSMENT Illinois CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs. This chapter focuses on curricular and instructional content issues in Illinois public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: About three-quarters of the eighth-grade students in Illinois (75 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curtis McKnight, et al.. The Underachieving Curriculum Assessing U.S. School Mathematks from an International Perspective. A National Report on the Second International Mathematics Study (Champaign, IL: Stipes Pubhshmg Company, 1987). Lynn Steen, Ed. Everyht,...:, ,-ounts A Report to the Nation on the future oj Mathemaths Lducation (Washington. I)C: National Academy Press. 1989). 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Illinois In Illinois, 75 percent of the students could take an algebra course in eighth grade for high school course placement or credit, About three-quarters of the students in Illinois (78 percent) west taught mathematics bi teachers who teach only one subject. More than half (64 percent) of the students in Illinois 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 Illinois I Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1960 NAEP TRIAL STATE ASSESSMENT Illinois Central Nation Percentage of eighth-grade students in public schools that identified mathematics as receiving special emphasis in school-wide goats and objectives, instruction, in-service training, etc. Percentage of eighth-grade public-school students who are offered a course in algebra for high school course placement or credit Percentage of eighth-grade students In public schools who are taught by teachers 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 Ponortaipo Paramtage Pargentage 75 ( 4.3) 79 (13.8) 63 ( 5.9) 75 ( 3.0) 00 (15.4) 7$ ( 4.6) 78 ( 4.0) 87 ( 7.8) 91 ( 3.3) 84 ( 3.2) 00 ( 5.7) 03 ( 4.0) 23 ( 4.3) 25 ( 8.6) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in Illinois are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in Illinois were taking eighth-grade mathematics (63 percent) than were taking a course in pre-algebra or algebra (34 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taldng a course in pre-algebra or algebra. Students in Illinois who were enrolled in pre-algebrd or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1800 NAEP TRIAL STATE ASSESSMENT Motels Central Nation Percentage and Proficiency Percentage and Proficiency Percentage and ProNciency What land of mathematics class are you taking this year? Eighth-grade mathematics 53 ( 2.4) 58 ( 4.8) 62 ( 2.1) 251 ( 1.7) 255 ( 3.1) 251 ( 1.4) Pre-algebra 18 ( 2,0) 22 ( 4.3) 19 ( 1.9) 268 ( 3.7) 276 ( 3.1)t 272 ( 2.4) Algebra 16 ( 1.3) 15 ( 2.8) 15 ( 1.2) 290 ( 2.6) 289 ( 5.4) 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics COUTses. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. o THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Illinois Further, from Table A5 in the Data Appendix:4 About the same percentage of females (36 percent) and males (31 percent) in Illinois were enrolled in pre-algebra or algebra courses. In Illinois, 35 percent of White students, 32 percent of Black students, 23 percent of Hispanic students, and 64 percent of Asian students were enrolled in pre-algebra or algebra courses. Similarly, 46 percent of students attending schools in advantaged urban areas, 26 percent in schools in disadvantaged urban areas, 30 percent in schools in extreme rural areas, and 30 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 repot' the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectivel). According to their teachers, the greatest percentage of eighth-gade students in public schools in Illinois spent either 15 or 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 largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes (Jail). Further. as reported h) their teachers (Table 6 a'id Table A6 in the Data Appendix): In Illinois, 1 percent of the students spent no time each day on mathematics homework. compared to 1 percent for the nation. Moreover. 5 percent of the students in Illinois and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. 4 For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations -- race ethnicit,, type of community. parents education level, and gender. 42 THE 1990 NAEP '1-R1AL STATE ASSESSNIE\ Illinois The results by race/ethnicity show that 5 percent of White students, 8 pexcent of Black students, 3 percent of Hispanic students, and 3 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 1 percent of White students, 2 percent of Black students, 1 percent of Hispanic students, and 0 percent of Asian students spent no time doing mathematics homework. In addition, 5 percent of students attending schools in advantaged urban areas, 5 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 6 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 3 percent of students attending schools in advantaged urban areas, I percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 0 percent in schools in areas classified as "other" spent 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 1900 NAEP TRIAL STATE ASSESSMENT Control Nihon -- ^ -.. - --* About how much time do students spend Pwcantige Percentage Percentage on mathematics homework each day? None and Praedanay ( 0.8) 1+0 ( 041 and Pnolidency 1 ( 0.8) 4.**) and ProOdenow I ( 0.3) 16 rolnutos 35 ( 4.1) 34 ( 7.1) 43 ( 4.2) 257 ( 2.9) 255 ( 4.7) 258 ( 2.3) 30 minutes 49 ( 3.9) 48 ( 9.8) 43 ( 4.3) 282 ( 2.9) 272 ( 3.5) 266 ( 2.8) 46 mInutos 10 ( 2.4) 13 ( 8.0) 10 ( 1.9) 271 ( 7.2)1 261 (12.5)I 272 ( 5.7)1 An hour or more 5 ( 1.4) 4 ( 0.9) 273 ( 8.3)1 278 ( 5.1)I The standard errors of the estimated statistics a pear in 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). THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Illinois TABLE 7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Illinois Cwiral Nation About how much time do you usually spend each day on mathematics homework? 15 minutss 30 minutes 45 minutia An hour or mars Ponantap Perosnlage Parcarda. and and ind Pndlidamay Pralkiency 7 ( 1.1) 253 ( 3.4) 29 ( 1.3) 281 ( 2.1) 35 ( 1.1) 284 ( 1.6) 17 ( 02) 250 ( 2.8) 12 ( 0.0) 258 ( 2.1) 7 ( 1.4) ( «to) 34(41) 269 ( 3.5) 32 ( 2.3) 264 ( 3.6) 15 ( 12) 265 ( 4.0) 12 ( 3.4) 282 ( 82)I 9 ( 0.5) 251 ( 2.5) 31 ( 2.0) 264 ( 1.9) 32 ( 1.2) 283 ( 1.9) 18 ( 1.0) 288 ( 1.0) 12 ( 1.1) 25. ( 3.1) The standard errors of the estimated statistics appear in parentheses. It can be said with rbout 95 percent certainty that, for each population of interest, the value for the entire population is within 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). And, according to the students (Table 7 and Table A7 in the Data Appendix): In Illinois, 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, 12 percent of the students in Illinois and 12 percent of students in the nation spent an hour or more each day on mathematics homework. The results by race/ethnicity show that 11 percent of White students, 19 percent of Black students, 13 percent of Hispanic students, and 15 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 8 percent of White students, 3 percent of Black students, 8 percent of Hispanic students, and 0 percent of Asian students spent no time doing mathematics homework. 4 44 THE 1990 NAE.P TRIAL STATE ASSESSMENT Illinois In addition, 8 percent of students attending schools in advantaged urban areas, 17 percent in schools in disadvantaged urban areas, 14 percent in schools in extreme rural areas, and 11 percent in schools in areas classified as "other" spent an hour or mort on mathematics homework daily. In comparison, 5 percent of students attending schools in advantaged urban areas, 6 percent in schools in disadvantaged urban areas, 11 percent in schools in extreme rural areas, and 6 percent in schools in areas classified as "other" spent no time doing mathematics homework. LNSTRUCTIONAL 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 abiut emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. 5 National Council of Teachers of Mathemaucs. Currkulum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathemaucs, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 45 Illinois 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 Alcbra 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 Illinois TABLE 8 I Teachers' Reports on the Emphasis Given to 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 KAEP TRIAL STATE ASSESSMENT Illinois 1 Central Nation , Percemisse and Proficiency Percentage end Proficiency Precentese Proficiency Teachor "emphasis" categories by content areas Numbers and Operations Heavy emphasis 41 ( 4.3) 54 ( 7 2) 49 ( 3.8) 257 ( 2.7) 264 ( 4.3) 260 ( 1.8) Little or no emphasis 15 ( 2$) 13 ( 4$) 15 ( 2.1) 289 ( 4.1) 285 ( 287 ( 3.4) Measurement Heavy emphasis 17 ( 3.4) 18 ( 5.7) 17 ( 3.0) 233 ( 9.0)1 247 (125)1 250 ( 5.6) Little or no emphasis 34 ( 3.4) 42 ( 9.7) 33 ( 4.0) 268 ( 4.5) 270 ( 7.7)1 272 ( 4.0) Geometry Heavy emphasis 29 ( 4.0) 26 ( 7.0) 28 ( 3.8) 258 ( 3.6) 261 ( 7,9)1 260 ( 3.2) Little or no emphasis 26 ( 3$) 35 ( 7 .2) 21 ( 3.3) 255 ( 3.7) 261 ( 9.0)1 264 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 14 ( 3.0) 12 ( 2.5) 14 ( 22) 253 ( 3.3)1 262 ( 7.5) 269 ( 4.3) Little or no emphasis 57 ( 3.8) 57 ( 8.8) 53 ( 4.4) 265 ( 3.2) 264 ( $.6)1 261 ( 2.9) Algebra and Functions Heavy emphasis 55 ( 3.5) 50 ( 7.6) 46 ( 3.6) 272 ( 22) 273 ( 3.6) 275 ( 2.5) Little or RO emphasis 12 ( 2.4) 19 ( 3.9) 20 ( 3.0) 239 ( 5.1)i 242 ( 5$)1 243 ( 3.0) AMIEMININ. 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 mcluded. ! Interpret with caution -- the nature of the sample does not allow accurate deterrnmation of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 Illinois SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are sonic topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: About three-quarters of the eighth-grade students in Illinois (75 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Illinois, 75 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in Illinois were taking eighth-grade mathematics (63 percent) than were taking a course in pre-algebra or algebra (34 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 Illinois spent either 15 or 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 Illinois, relatively few of the students (7 percent) reported that they spent no time each da on mathematics homework. compared to 9 percent for the nation. Moreover, 12 percent of the students in Illinois 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. 45 THE 1990 \ ALP I RIM, Si Al E ASSISSMLM Illinois CHAPTER 4 =Xs -2x-.9 it OU IIIIMM-111-1111111111111 11111111. MIMI, OM 11111111111111111111111F11111 11111111611111111111111 111111-11FMAIIIII 111111 ..IBEF.1111111 "15111111011Mq11111111 111111-&-OW IBM .1011111I MABEE§ 1111MMIIIN aiusuuiuuas 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. ° National Council of Teaesers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). r- THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Illinois From Table 9 and Table A9 in the Data Appendix: In Illinois, 18 percent of the eighth-grade students had mathematics teachers who reported getting ail of the resources they needed, while 28 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 Illinois, 33 percesat of students attending schools in advantaged urban areas, 9 percent in schools in disadvantaged urban areas, 26 percent in schools in extreme rural areas, and 16 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in Illinois, 10 percent of students attending schools in advantaged urban areas, 41 percent in schools in disadvantaged urban areas, iS percent in schools in extreme rural areas, and 29 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had higher mathematics achievement levels than those whose teachers got only some or none of the resouras they needed. TABLE 9 I Teachers' Reports on the Availability of i Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT Winch Central Nation Which of the following statements rs true about how well supplied you are by your school system with the instructional materials and other resources you need to teach your class? I get all the resources I need. I get most of the mascots I need. I get some or none of a resources I need. Percentage Percentage Percentage and gird and Proaciency Po:agency Proldency 18 ( 275 ( 3.9) 3.8)1 ( ( 2.4) «4) 13 ( 265 ( 2.4) 4.2) 64 ( 4.5) 45 ( 7.8) 58 ( 4.0) 263 ( 2.2) 271 ( 2.2)1 266 ( 2.0) 23 ( 4.1) 47 ( 7.3) 31 ( 4.2) 24$ ( 3.5) 259 ( 3.5) 281 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 student0. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois PATTERNS IN CLASSROOM LNSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: About half of the students in Illinois (45 percent) worked mathematics problems in small groups at least once a week; some never worked mathematics problems in small groups (15 percent). The largest percentage of the students (68 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (7 percent). In Illinois, 71 percent of the students were assigned problems from a mathematics textbook almost every day; 3 percent workecl textbook problems about once a week or less. About half of the students (47 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problei,, less than weekly (29 percent). Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and mi. Common Currkulum Eighty-second Yeart)ook of the National Society for the Study of Education (Chicago, IL: University of Chicago Press, 1983). THE 1990 NAEP TRIAL STATE ASSESSMENT 51 Illinois TABLE 10 I Teachers' Reports on Patterns of Mathematics I Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 NAEP TRIAL STATE ASSESSMENT Mine Is Csna1 Nation About how often z'o students wOrk Perorate. and Percentage and Pereenle. and problems in small groups? Peek:tow Prollidany ProlichmeW At least once a week 45 ( 4.3) 50 ( 7.8) 50 ( 4.4) 260 ( 3.5) 258 ( 4.1) 260 ( 22) Less than once a week 40 ( 4.0) 43 ( 8.6) 43 ( 4.1) 263 ( 2.6) 266 ( 4.0)1 264 ( 2.3) Never 15 ( 2.9) 293 ( 3.4) 7 ( 4.3) *04) 8 ( 2.0) 277 ( 5.4)1 About how often do students use objects Percentage Percentage Percentage like rulers, counting blocks, or geometric and and and solids? Proficiency ProAciency Prolkiency At least once a week 26 ( 3.7) 15 ( 5.1) 22 ( 3.7) 254 ( 3.5) 255 ( 4.9)1 254 ( 32) Less than once a week 68 ( 3S) 81 ( 6.0) 69 ( 3.9) 263 ( 2.3) 264 ( 3.3) 263 ( 1.9) Never ( 1.4) 282 ( 8.9)1 4 ( 2.3) *** r**) 9 ( 2.8) 282 ( 5.9)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population if 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 deterrnMation of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r**41 52 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE 11 I Teachers' Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Illinois Central Nation , Percentage Peroermo-- liontentage About how often do students do problems end sod and from textbooks? Proficiency Proficiency Proliclency Nmost every day 71 ( 4.8) 82 ( 5.8) 82 ( 3.4) 267 ( 1.41) 289 ( 3.8) 2157 ( 1.8) Several times it week 28 ( 4.4) 32 ( 42) 31 ( 3.1) 251 ( 3A) 252 ( 5.3) 254 ( 2A) About once a week or less 3 ( 0.9) 14* ( ( 2.7) Mr* ( *11 ( 1.6) 200 ( About how often do students do problems Percontage Percents. Porcadage on worksheets? and end end Proficiency Proficiency Prolidency At least several times a week 47 ( 4.1) 38 ( 8.3) 34 ( 3.6) 253 ( 3.0) 252 ( 5.5)1 256 ( 2.3) About once a week 23 ( 2.8) 23 ( 4.8) 33 ( 3.4) 282 ( 4.3) 281 ( 8.1) ( 2.3) Less than weekly 29 ( 4.2) 39 ( 7.0) 22 ( 3.8) 275 ( 2.8) 278 ( 4.1) 274 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 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 esumate (fewer than 62 students). The next section presents the students' responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT 53 Illinois COLLABORATING IN SMALL GROUPS In Illinois, 43 percent of the students reported never working mathematics problems in small groups (see Table 12); 27 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 I Students' Reports on the Frequency of Small i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1880 NAEP TRIAL. STATE ASSESSMENT Wools Central Nation 1 , Percentage and Pica:king Percentage and Preactency Percentage and Pnradeney How often do you work in small groups in your mathematics class? At WO once a week 27 ( 2.4) 23 ( 4.8) 211 ( 2.5) 258 ( 3.5) 268 ( 8.5) 258 ( 2.7) Lass Om ones a week 30 ( 2.1) 32 ( 3.3) 28 ( 1.4) 271 ( 1.8) 280 ( 3.0) 287 ( 2.0) New 43 ( 2.8) 45 ( 0.3) 44 ( 2A) 258 ( 1.9) 264 ( 3.4) 281 ( 1.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Examining . subpopulations (Table Al2 in the Data Appendix): In Illinois, 25 percent of students attending schools in advantaged urban areas, 26 percent in schools in disadvantaged urban areas, 32 percent in schools in extreme rural areas, and 24 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 25 t of White students, 33 percent of Black students, 28 percent or Hr'i's7lanic students, and 35 percent of Asian students worked mathematics problems in small groups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (28 percent and 26 percent, respectively). eft/ 54 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois USLNG MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: Less than half of the students in Illinois (39 percent) never used mathematical objects; 31 percent used these objects at least once a week. Mathematical objects were used at least once a week by 28 percent of students attending schools in advantaged urban areas, 34 percent in schools in disadvantaged urban areas, 34 percent in schools in extreme rural areas, and 29 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 (33 percent and 28 percent, respectively). In addition, 28 percent of White students, 41 percent of Black students, 34 percent of Hispanic students, and 24 percent of Asian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Illinois Central Nation How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Percentage and Proaciancy Percantage and Proficiency Percentage and Proficien0 At least once a week 31 ( 2.2) 23 ( 2.9) 2$ ( 1.6) 255 ( 24) 260 ( 3,5) 25$ ( 2.6) Less than once a week 31 ( 1.5) 36 ( 24) 31 ( 1.2) 270 ( 1.7) 272 ( 2A) 289 ( 1.5) Now 39 ( 257 ( 2.1) 2.0) 41 ( 2e2 ( 4.6) 2.6) 41 ( 259 ( 2.2) 1.6) The standard errors of the estimated statistics appear in parentheses. It cart be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. G THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Illinois MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in Illinois who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table A 14 in the Data Appendix): About three-quarters of the students in Illinois (71 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 74 percent of students attending schools in advantaged urban areas, 63 percent in schools in disadvantaged urban areas, 79 percent in schools in extreme rural areas, and 71 percent in schools in areas classified as "other". TABLE 14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Illinois How often do you do mathematics problems from textbooks in your mathematics class? Percentage and Pronciency Pegg:~ and Pgvidency Poroontop good Proadonoy Almost every day 71 ( 2.5) 74 ( 4.7) 74 ( 1,0) 266( 1.7) 271 ( 2.2) 287 ( 1.2) Several times a week 10 ( 1.3) 15 ( 1.6) 14 ( 0.8) 248 ( 3.0) 250 ( 4.2) 252 ( 1.7) About once a week or less 13 ( 1.8) 11 ( 4.3) 12 ( 1.8) 248 ( 3.7) 250 ( 4.7)1 242 ( 4.5) The stantiard 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. G 56 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois And, for the frequency of worksheet usage (Table 15 and Table A 15 in the Data Appendix): Less than half of the students in Illinois (40 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 44 percent of students attending schools in advantaged urban areas, 41 percent in schools in disadvantaged urban areas, 29 percent in schools in extreme rural areas, and 43 percent in schools in areas classified as "other". TABLE 15 I Students' Reports on the Frequency of i Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 19S0 NAEP TRIAL STATE A1SESSMENT Illinois Central Nation Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency How often do you do matiematics problems on worksheets in your mathematics class? At least several Hines a week 40 ( 3.0) 36 ( 6.0) 3,3 ( 2.4) 256 ( 2.1) 257 ( 4.9) 253 ( 22) About once a week 22 ( 1.3) 23 ( 2.3) 25 ( 1.2) 257 ( 2.0) 284 ( 2.8) 261 ( 1.4) Less than weekly 37 ( 3.0) 40 ( 5.6) 37 ( 2.51 268 ( 2.7) 273 ( 4,0) 272 ( 1.9) The standard errors of the esumated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. 44.0 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 Illinois TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS MO KAEP TRIAL STATE ASSESSMENT Illinois Centrai Nation Patterns of classroom instruction Penmen' Students Machete Parcentwp Students Teachers Pelventap Students Tudors Percentage of students who work mathematics problems in small groups At least once a week 27 ( 2.4) 43 ( 4.3) 23 ( 4.8) 50 ( 7.8) 28 ( 2.5) SO ( 4.4) Less than once a week 30 ( 2.1) 40 ( 4.0) 32 ( 3.3) 43 ( 8.6) 2$ ( 1.4) 43 ( 4.1) Never 43 ( 2.8) 15 ( 2.9) 45 ( 6.3) 7 ( 4.3) 44 ( 2.9) 5 ( 2.0) Percentage of students who use objects Hke Tidos, counting blocks, or goametric solids Al least once a week 31 ( 22) 26 ( 3.7) 23 ( 2.9) 15 ( 5.1) 28 ( 1.8) 22 ( 3.7) Less than once a week 31 ( 1.5) 68 ( 3.9) 36 ( 2.5) 81 ( 6.0) 31 ( 12) 69 ( 3.9) Never 39 ( 2.1) 7 ( 1.4) 41 ( 4.6) 4 ( 2.3) 41 ( 2.2) 9 ( 2.6) Materials for mathematics instruction Pertentago Students Teachers Percentage Students Teachers Percentage Students Teachers Percentage of students who use a mathematics textbook Almost every day 71 ( 2.5) 71 ( 4.6) 74 ( 4.7) 82 ( 51) 74 ( 1.9) 62 ( 3.4) Several times a week 16 ( 1.3) 26 ( 4.4) 15 ( 1.6) 32 ( 42) 14 ( 0.8) 31 ( 3.1) About once a week or less 13 ( 1.8) 3 ( 0.9) 11 ( 4.3) 8 ( 2.7) 12 ( 1.8) 7 ( 111) Percentage of students who use a mathematics workshoet At least several times a week 40 ( 3.0) 47 ( 4.1) 36 ( 6.0) 38 ( 8.3) 38 ( 2.4) 34 ( 3.8) About once a week 22 ( 1.3) 23 ( 2.8) 23 ( 2.3) 23 ( 4.8) 25 ( 1.2) 33 ( 3.4) Less than weekly 37 ( 3.0) 29 ( 4.2) 40 ( SA) 39 ( 7.0) 37 ( 24) 32 ( 3.6) The standard errors of the estimated CAUSIICS appear in 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 Illinois 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: About half of the students in Illinois (45 percent) worked mathematics problems in small groups at least once a week; some never worked in small groups (15 percent). The largest percentage of the students (68 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 Illinois. 71 percent of the students were assigned problems from a mathematics textbook almost every day; 3 percent worked textbook problems about once a week or less. About half of the students (47 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (29 percent). And, according to the students: In Illinois, 43 percent of the students never worked mathematics problems in small groups; 27 percent of the students worked mathematics problems in small poups at least once a week. Less than half of the students in Illinois (39 percent) never used mathematical objects; 31 percent used these objects at least once a week. About three-quarters of the students in Illinois (71 percent1 worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. Less than half of the students in Illinois (40 percent) used worksheets at least several times a week, compared to 38 percent in the nation. THE 1990 NAEP TRIAL SI All ASSESSMENT 59 Illinois 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 he used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks.' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. National Assessment of Educational Progress, Mathernatks Objectives 1990 Assessment (Princeton, NJ: Educ:ational Tesung Ser.% ice. 1988). National Council ofleachers of Mathematics, Curriculum and Evaluation Standardk for School Mathematics (Reston, A: National Council of Teachers of Mathematics, 1989). 1;5 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois Table 17 provides a profile of Illinois eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 36 percent of the students in Illinois had teachers who allowed calculators to be used for tests. About the same percentage of students in Illinois and in the nation had teachers who permitted unrestricted use of calculators (23 percent and 18 percent, respectively). TABLE 17 1 Teachers' Reports of Illinois Policies on I Calculator Use PERCENTAGE OF STUDENTS MO NAEP TRIAL. STATE ASSESSMENT Illinois Central 1 Nation , _ Percentage of elghth-grade students in public schools whose teachers permit the unrestricted use of calculators Percentage of eighth-grade students in public schools whose teachers permit the use of calculators for tuts Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned by the school Persentspo Percentsge Portents's 23 ( 3.0) 27 ( ISA) 18 ( 3.4) 30 ( 4.3) 44 ( 7.9) 33 ( 44) 70 ( 34) 55 ( 8.2) 50 ( 4.8) 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 61 Illinois ME AVAILABILITY OF CALCULATORS In Illinois, most students or their families (98 percent) owned calculators (Table 18); however, fewer students (59 percent) had teachers who explained the use of calculators to them. From Table A 18 in the Data Appendix: In Minois, 56 percent of White students, 66 pement of Black students, 69 percent of Hispanic students, and 61 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 60 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One 7ERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - ION NAEP TRIAL STATE ASSESSMENT Illinois Central Nation Do you or your family own s calculator? Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes II *ventage and laisnay OS ( 03) 261 ( 1.7) 2 ( 0.3) 234 ( 4.5) Parawdap and Pralicionay 59 ( 2.5) 258 ( 1.9) 41 ( 2.5) 284 ( 2.1) Ihretentage Parentage and and Prallalancy Prokisnay 98 ( 0.8) 206 ( 2.5) 2 0.6) a? " M 1.31 3 ( 0.4) 234 ( 3.8) Parandame Pereentage and and *adding Proficiency 58 ( 4.9) 263 ( 3.9) 44 ( 4.9) 209 ( 3.4) 49 ( 2.3) 258 ( 1.1) ( 2.3) 296 ( 1.5)' The standard errors of the estimated statistics appear in parentheses. It can be raid with about 95 percent certainty that, for each population of interest, :hit value for the entire population is within * 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois ME USE OF CALCULATORS As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment, emlents were asked how frequently (never, sometimes, almost always) they used lators for working problems in class, doing problems tAt home, and taking quizzes or tests. As reported in Table 19: In Illinois, 19 percent of the students never used a calculator to work problems in class, while 49 percent almost always did. Some of the students (15 percent) never used a calculator to work problems at home, compared to 35 percent who almost always used one. About one-quarter of the students (29 percent) never used a calculator to take quizzes or tests, while 24 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 NAEP TRIAL STATE ASSESSMENT NUM' Central Nation How often do you use a calculator for Me following WO? Working problIMS ill class Almost always Neveff Doing problems at home Almost alwaye Never Taidng quiazos or tests Almost always Nowa' Peroffintsp and 9/90delesp ParMIRINIM ang Pnalkimag 14.149111911 , sod PrellohNey 40 ( 1.14 233( 2.1) 19( 1.7) Nil( 12) 01 ( SA) 200 ( 2.0) 10 ( *0) 270 41 334 13( 272( 1 1.9) 1.4) 3511.3) 35 ( 2.2) 30 ( 1.3) 281 ( 23) 293 ( 2.11) 261 ( 11) 15 ( 13) 19( 2.1) 1$ 0.9) 263 ( 2.3) 263( $.3) *93 ( 11) 29 ( 4.6) 27( 1.4) 23424 21 220 ( c0) 263( 24) 'I. 291 2T/ 22( 41) 30( LO 271( 14) 274 ( 13) .1.11111111 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 uSometimes" 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 63 Illinois 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 helpfiil and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and sonic took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used tht calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the cakulator 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 Illinois The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: About the same percentage of students in Illinois west in the High group as were in the Other group. A smaller percentage of males than females were in the High g;oup. In addition, 50 percent of White studems, 43 percent of Black students, 35 percent of Hispanic students, and 54 percent of Asian students were in the High group. TABLE 20 f Students' Knowledge of Usim Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO MAEP TRIAL STATE ASSESSMENT Illinois Conk* Nation Pervantaga and lindiatanay Parcentsga and anallkdency ftrosadage and PridkiewAY "Calculator-use" group High 47 ( 15) 48( 1.8) 42 ( 1.3) 288 ( 1.8) 272 ( 34) 272 ( 1.8) Mir 53 ( 1.5) 54 ( 1.8) 58 ( 1.3) 252 ( 2.1) ( 2.7) 255 ( 14) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 Illinois 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 instmctional 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, 36 percent of the students in Illinois had teachers who allowed calculators to be used for tests. About the same percentage of students in Illinois and in the nation had teachers who permitted unrestricted use of calculators (23 percent and 18 percent, respectively). In Illinois, most students or their families (98 percent) owned calculators; however, fewer students (59 percent) had teachers who explained the use of calculators to them. In Illinois, 19 percent of the students never used a calculator to work problems in class, while 49 percent almost always did. Some of the students (15 percent) never used a calculator to work problems at home, compared to 35 percent who almost always used one. About one-quarter of the students (29 percent) never used a calculator to take quizzes or tests, while 24 percent almost always did. 7 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has become an issue of increasing importance to federal, state, and local governments. As part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.' Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In Illinois, 45 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. More than half of the students (65 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 (73 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 67 Illinois TABLE 21 I Profile of Eighth-Grade Public-School 1 Mathematics Teachers PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMEXT Illinois Contra Nation Percentage of students whose mathematics teachers reported having the following degrees Pommes!, Pemintaile Pargengais Bachelor's degree 55 ( 4.7) 48 ( 9.1) 50 ( 4.2) Master's or specialist's degree 45 ( 4.7) 48 ( 8.5) 42 ( 4.2) Doctorate or professional degree 0 ( 0.5) 4 ( 22) 2 ( 1.4) Percentage of students %lame mathematics teachers haw the following types of teadiing certificates that are recognized by Illinois No regulor certification 0 ( 2.8) 4 2.7) 4 ( 1.2) Regular certification but less than the highest available 29 ( 4.0) 25 72) 21) ( 4.3) Highest certification availeble (permanent or long-term) 05 ( 4.5) 7.1 7.3) 00 ( 4.3) Percentage of students whose mathematics teachers haw the following typal of teaching certificates that are recognized by Illinois Mathematics (middle school or secondary) 73 ( 3.0) 77 ( 4.5) 84 ( 2.2) Education (elementary or middle school) 26 ( 3.4) 17 ( 7.5) 12 ( 2.0) Other ( 0.0) 7 ( 4.8) 4 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. 68 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that. . In Illinois, 30 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 Illinois (15 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 1 Teachers' Reports on Their Undergraduate and Graduate Fields of Study PERCENTAGE OF STUDENTS _. . 1990 MEP TRIAL STATE ASSESSMENT Illinois Central Nation _ 1=11111111011=11ft=1.1.11(111111=aawa. What was your undergraduate major? Percentage Perceester Percents** Mathematics 30 ( 3.8) 57 ( 7.1) 43 ( 3.9) Education 49 ( 4.1) 29 ( 0.4) 35 ( 3.8) Other 21 ( 4.2) 14 ( 5.4) 22 ( 3.3) What was your graduate major? Percentage Percentage Percentage Mathematics 15 ( 13) 34 ( 9.1) 22 ( 3.4) Education P) ( 4A) 34 ( 0.2) 33 ( 3,5) Other or no gratkude Wel study 48 ( 4.3) 32 ( 0.0) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL. STATE ASSESSMENT 69 Illinois Teachers' responses to questions concerning their in-service training for the year up to the Tiial State Assessment (Table 23) show that: In Illinois, 24 percent of the eighth-grade public-school stuiients had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Some of the students in Illinois (18 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. TABLE 23 f Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS _ MO NAEP TRIAL STATE ASSESSMENT Illinois Central Won _ During the last year, how much time in total have you spent on in-service educ.ation in mathematics or tire teaching of mathematics? None Ono to 15 hours 15 haws or more Percents. Percentage Percentage 18 ( $5 ( 24 ( 3.5) 4.0) 3.3) 71 28 SA 5.0 11 ( St ( ( 2.1) 4.1) 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement.' Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and tenitories are described, variatio: 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 bc effective teachers; however, it is likely that relevant mining and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In Illinois, 45 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. More than half of the students (65 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 Illinois, 30 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 Illinois (15 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 Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). " Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematks Achievement NA EP's 1990 Assessment of the Nation and the Trial Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). P.: 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 71 Illinois In Illinois, 24 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics c - the teaching of mathematics. Across the nation, 39 percent of the stunts had teachers who spent at least that much time on similar types of in-service training. Some of the students in Illinois (18 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. 72 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois CHAPTER 7 The Conditions Beyond School that Facilitate Mathematics Learning and Teaching Because students spend much more time out of school each day than they do in school, it is reasonable to expect that out-of-school factors greatly influence students' attitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, encouragement, and participation in student learning experiences are powerful influences. Together, teachers and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment and mathematics proficiency, students participating in the Trial State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education. THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Illinois AMOUNT OF READING MATERIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students participatingin 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 NAEP TRIAL STATE ASSESSMENT Costa NOW Does your family have, or receive on a regular basis, any of the following item more than 25 books, an encyclopedia, newspapers, magazines? Zero to two typos Ttw typos For typos illaroastsle mut Pergessio sod Prilklasw 0401101111401 111 ( 1A) Pa t 2.0 4$ 250 ( /4) ( $.4) $1 ( $58 ( 4.1) 13) SI ( 22) NI t SM so 1 Si ( 14) 50 ( 13) ( 13) 2415 ( 1.7) 272 ( 2.1) 272 ( 13) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percem certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The data for Illinois reveal that: Students in Illinois who had all four of these types of materials in the home showed higher mathematics proficiency than did students with zero to two types of materials. This i3 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 Iliktois A smaller percentage of Black and Ifispanic students and about the same percentage of Asian students had all four types of these reading materials in their homes as did White students. A greater percentage of students attending schools in advantaged urban areas than in disadvantaged urban areas or arras classified as "other" and about the same percentar of students in schools in advantaged urban areas as in extreme rural areas had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent 1 Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Central Nation How much television do you usually Pertardalp Personlana Percentage aid and and watch each day? Prolidancy 12 ( 0.8) 270 ( 24) Praildanay 14 ( 1.0) 270 ( 3.5) PrallkiNICY 12 ( 0-8) He ( 2.2) One hour or toss Two hours 23 ( 1.1) 22 ( V) 21 ( 0.0) 203 ( 2.3) 274 ( 3.2) 288 ( 1.8) Throe hours 24 ( 0.8) 25 ( 2.4) 22 ( 0.8) 285 ( 1.7) 271 ( 4.0) 205 ( 1.7) Four to flys haws 29 ( 1.2) 27 ( 3.0) 28 ( 1.1) 257 ( 1.5) 281 ( 2.9) 200 ( 13) Six hours or mon 14 ( 1.0) 14 ( 1.15) 10 ( 1.0) 242 ( 2.8) 247 ( 3.4) 243 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 75 Illinois From Table 25 and Table A25 in the Data Appendix: In Illinois, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Some of the eighth-grade public-school students in Illinois (12 percent) watched one hour or less of television each day; 14 percent watched six hours or more. A greater percentage of males than females tended to watch six or more hours of television daily. However, a smaller percentage of males than females watched one hour or less per day. In addition, 10 percent of White students, 27 percent of Black students, 17 percent of Hispanic students, and 4 percent of Asian students watched six hours or more of television each day. In comparison, 12 percent of White students, 9 perccnt of Black students, 9 percent of Hispanic student's, and 23 percent of Asian students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix: In Illinois, average mathematics proficiency was lowest for students who missed three or more days of school. About half of the students in Illinois (47 percent) did not miss any school days in the month prior to the assessment, while 21 percent missed three days or more. ln addition, 21 percent of White students, 16 percent of Black students, 27 percent of Hispanic students, and 10 percent of Asian students missed three or more days of school. 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois Similarly, 21 percent of students attending schools in advantaged urban areas, 23 percent in schools in disadvantaged urban areas, 21 percent in schools in extreme rural areas, and 20 percent in schools in areas classified as "other" missed thme or mole days of school. TABLE 26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP 1 rt 4 "TATE ASSESSMENT Nino* Porcontago and Prelicktney Peroonlass and Pividency Paraimempr and lonsidincy How many days of school did you miss last month? None 47 ( 1.0) 47 ( 1.7) 45 ( 1.1) 264 ( 1.9) 209 ( 2.5) 205 ( Ono or two days 32 ( 1.0) 30 ( 2.0) 32 ( 0.9) 261 ( 2.1) 271 ( 3.4) 206 ( 1.5) Throe days or more 21 ( 0.6) 23 ( 23 ( 1.1) 253 ( 2.2) 252 ( 3.3) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 93 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. r-- THE 1990 NAEP TRIAL STATE ASSESSMENT 77 Illinois 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." 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: / like mathematics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people we mathematic. 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 sty lent "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly wee" were given a value of 1 (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded undecidea," "disagree," or "strongly disagree" were givt n a value of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception index according to whether they tended to strongly agree with the statements (an index of 1), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statemmts (at index of 3). Table 27 pr t. vides the data for the students' attitudes toward mathematics as defmed by their perception index. The following results were observed for Illinois: Average mathematics proficiency was lowest for students who were in the "undecided, disagree, strongly disagree" category. About one-quarter of the students (27 percent) were in the "strongly agree" category (perception index of 1). This compares to 27 percent across the nation. Some of the students in Illinois (20 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). 2 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 78 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE 27 I Students Perceptions of Mathematics 11110 NAEP TRIAL STATE ASSESSMENT PERCENTAGE OF STUDENTS AND AVF.RAGE MATHEMATICS PROFICIENCY SWdont perception Index* groups Orwell Wee ("perception Index" of 1) AM* ("perception Index" of 2) Undecided, dieefwe, dm* *agree ("perception index" of 3) Poramings frokolocar 27 11 250)02 I 111 20( 1.1) 253 ( 2.2) ParamMos Parambi. and and Poiltiono Prablimo 27 1.3) 271 ( ta) 2: IV) 2:50 2N 11.1i The standard errors of the estimated SIAtisties appear in parentheses. It can be said with about 95 percent oertainty dutt, for eacb population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sampk. 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 Illinois 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 =sults 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 Illinois Some of the eighth-grade public-school students in Illinois (12 percent) watched one hour or less of television each day; 14 percent watched six hours or more. Average mathematics proficiency was lowest fbr students who spent aix hours or more watching television each day. About half of the students in Illinois (47 percent) did not miss any school days in the month prior to the assessment, while 21 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. About one-quarter of the students (27 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was lowest for students who were in the "undecided, disagree, strongly disagree" category. 80 ME 1990 NAEP TRIAL STATE ASSESSMENT Illinois THE NATION'S REPORT CARO 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 Educational Testing Service. The development of the Trial State Assessment Program benefitted from the involvement of hundreds of representatives from State EdUcation Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the program. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The first step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. THE 1990 NAEP TRIAL STATE ASSESSMENT 81 Illinois The blocks were then assembled into assessirmt 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 west given five minutes to complete each of the background questionnahts and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required approximately 55 minutes of student thne. In accordance with the BIB desigp, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with evexy other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets war spiraled or interleaved in a systematic sequence so that each booklet appeared an appropriate nuraber of times in the sample. The students within an assessment session west 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 nr-nber of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State A ssessment Program were developed using a broad-based consensus process, as described in the introduction to this report.' The assessment framework consisted of two dimen&ions: mathematical content areas and abilities. The five content areas assessee were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure A 1). The thrt.t 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. 1RT provides a common scale on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. his common scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. Nauonal Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Pnnceton, Educational Testing Service, 1988). 82 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois This Content area focuSes on students' understanding of numberS (whole numbers, fractions, decimals, integers) and their application to real-world situations, as well as computational and estimation situations. Understanding numerical relationships as expressed in ratios, proportions, and percents is emphasized. Students' abilities in estimation, mental computation, use of calculators, generalization of numerical patterns, and verification of results are also included. Fasurement 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. Que aeons are included that require an abffity to read instruments using metric, customary, or nonstandard units, with emphasis on precision and accurecy Questions requiring estimation, measurements, and applications of measurements of length, time, money, temperature, mass/weight, area, volume, capacity, and angles are also included in this content area. Geometry This content area focuses on students' knowledge of geometric figures and relationships and on their skills in working with this knowledge. These skills are important at all levels of schooling as well as in practical applications. Students need to be able to model and visualize geometric figures in one, two, and three dimensions and to communicate geometric ideas. In addition, students should to able to use informal reasoning to establish geometric reiationships. 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 visuai exploration of data. and the development and evaluation of arguments based On data analysis. Algebra and Functions This content area is broad in scope, covering algebraic and functional concepts in more informal, exploratory ways for the eighth-grade Trial State Assessment. Proficiency in this concept area requires both manipulative facility and conceptual understanding: it involves the ability to use algebra as a means of representation and algebraic processing as a problem-solving tool. Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. THE 1990 NAEP TRIAL STATE ASSESSMENT 83 Illinois FIGURE A2 f Mathematical Abilities The following three categories of mathematical abilities are not to tz :onstrued as hierarchical. For example, problem solving involves interactions between conceptual kn edge and procedural skills, but what is considered complex problem solving at one grade level may be considered conceptual understanding or procedural knowledge ai 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 definition: can compare, contrast, and integrate related Concepts and principles: can recognize, interpret, and apply the signs, symbols, and terms used to represent concepts: and can interpret the assumptions and relatiuns involving concepts in mathematical settings. Such understandings are essential to performing procedures in a meaningful way and applying them in problem-solving situations. Frocedural 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 methcds, and extend or modify procedures to deal with factors inherent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have Peen 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 analvf,i; 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. THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois A scale ranging from 0 to 500 was created to report performance for each content area. Each content-area scale was based on the distribution of student performance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In contrast, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics items from the 1990 assessment that discriminated well between adjacent levels. The Liiteria for selecting these "benchmark" items were as follows: To define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To define performance at each of the higher levels on the scale, items were chosen that were: a) answered correctly by at least 65 percent of students whose proficiency was at or near that level; and b) answered incorrectly by a majority (at least 50 percent) of the students performing at or near the next lower level. The percentage of students at a level who answered the item correctly had to be at least 30 points higher than the percentage of students at the next lower level who answered it correctly. n 0 TIIE 1990 NAEP TRIAL STATE ASSISSMENT 85 Illinois Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.2 Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: cuniculum, instructional practices, teacher qualifications, educational standards and teform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and the use of various instructional approaches. Because of the nature of the sampling for the Trial State Assessment, the responses to the mathematics teacher questionnaire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. fl I 86 THE 1990 NAEP TRIAL STATE ASSESSMENT illinois FIGURE A3 Dump le Items for Mathematics Proficienq Levels Level 200: Simple Additive Reasoning and Problem Solving aids Whole Numbers EXAMPLE 'I CAN alb der:" ramOr 0 Oleos Ise 7. Lae hiIs sows eta lei dem Mews lave of WI so &ors ems V sho Alb ssob Iwo WM es kiwi of hie Aiwa. Ikea loos st,kusb se ki 0) The Us with es mamas bdis 0 no boo Ober 0 The boo wet Ms Mew Wm lbo ail EXAMPLE 2 1001 11004 MO= AT trauma MOO Ma 'No Vot 100. Oip Oreo Welk CI= =Oimpeasie 11. lew wry boom al ammo woo *boil 00 11bowert 0 IS 0 60 0 70 0 SO 0 90 0 I doo's bow. VIE 1990 NAEP TRIAL STATE ASSESSMENE Grade 4 Onwall POCONO. Correct 73% Pecontage Correct for Anchor Levels: XS IS MI Me 05 91 100 -- Grade 4 Mersa Pircentapo coma 90% Percentage Car .43# `td Moho( Levels: MI *iLdi 222 TS 91 100 C_ Grade 9 04M11 Pilf0010041 Coma, 84% Percentage Correct for Anchor live* 2211 21111 El) TS 87 90 100 87 [ Level 250: Simple Multiplicative Reasoning and Two-Step Problem Solving I Illinois FIGURE A3 I &ample Items for Mathematics Proficiency Levels (continued) EXAMPLE 1 7. What is the value of n + S when an 3 ? Answer EXAMPLE 2 114t COLOR SLIMY MILTS 14111 KMMIair111 no ;Me obra shaft da woks oi mon of bat coin. On di anis klow, Nuke r arch irspb to itharsto Liar be As able. UM orcb rbr anis papb Wilk& mama bar NW. Oa yar we rho cabana as sbis park& 0 Vas 0 No EXAMPLE 3 6. Kathleen ts packing baschalb tato ham. Each halt, Als 6 baseballs. She dm 24 balk. Which number macaw will help hee and out how sassy bow sla will soot CD - 24 + 6 w 0 tll) 24 + 6 0 op 24 - 0 CO 1 don't faro. Grade 8 Overall Percentage Correct 75% Percentage correct for Anchor Levels: 200 Ma 2§2 28 00 05 08 Grade Overail Percentage Correct 73% Percentage Correct for Anchor Lave's: 21/0 121 110 21 08 92 92 Grade Omrall Percentage Correct 77% Percentage Correct for Anchor Levels: 122 aRQ alQ 37 71 95 103 88 ME 1990 NAEP TRIAL STATE ASSESSMENT Illinois FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 300: EXAMPLE Ressoning and Problem SoMng involving Fractions, Decimals, Percents, Elementary Geometric Propedies, and Simple Algebraic Manipulations I. Which ei the foliewieg Amy the node et iligpieg ***ewe nue& era the bee 2 EXAMPLE 2 A le Ow ameig nem *et das**1424*I. be IS lee *14 tepeeesest by iisra;* mtle3 tubes hew IS tie sew sash wed, * beim toss hob trait be eigneeeniAs by seals medal bow soy saes bight AI mg tee the eidembeeer so We gimlet& Yes 0 Ne Grade 8 Metall Percentage Correct: 80% Percentage Correct for Anchor Levels: 22Q aig 204 33 49 77 90 Grade 12 Overall Percentage Correct: 75% Percentage Carect for Anchol 244 222 ZI4 46 79 95 Grate 8 OVVIIII Percentage Correct: 59% Percentage Correct for Anchor 221 224 IN IT 40 as 99 r)4 ME 1990 NAEP TRIAL STATE ASSESSMENT 89 Illinois FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability EXAMPLE pp 610stiao 16-17 Mee a she NW% SUM da-iliswra If this patent of ciet4.1.411ameissest bow may eses will k In lle 1000a4pw0 EXAMPLE 2 It. Isigan flaw Tao lama yaor wow c.ufI ala 16. Monger Grade 5 Overall Percentage Correct 34% Percentage Correct for Anchor Levels: AM 3112 Zia 13 19 53 85 Grade 12 Oman Percentage Cars* 40% Percentage COMBO for Anchor Levels: 222 222 22 40 90 Grade 5 04mM Percentage Correct: 15% Percentage Urrect kw Anchor Levels: VS E2 1 4 25 74 Grado 12 Overall Percentage COMM 27% Percentage Correct for Mellor Levels: k22 21/Q 114 3 22 74 90 ThE 19 90 NAM" TRIAL STATE AUESSAIENT Illinois SCHOOL CHARACTERISTICS A11) POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative 3amples 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 Varizbility The statistics reportfA NAEP (average proficiencies, percentages of students at or above particular scale-scote levels, and percentages of students responding in certain ways to background questiors) are estimates of the corresponding information for the population of eighth-grade studenis i 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 ever) eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAEP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like almost all estimates based on assessment measures, NAEP's total group and subgroup proficiency estimates are subject to E. second sollwe 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 subgroup proficiency might have been obtained. Thus. a second source of uncertainty arises because each student was administered a subset of the total pool of questions. C THL 1990 \ AEP TRIAL STATE ASSESSMENT 91 Illinois In additioa to reporting estimates of average profieiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a background question in a certain way or the proportion of students in certain racial/ethnic groups) reflect only sampling error. NAFP uses a methodology called the jackknife procedure to estimate these standard errors. Drawing Inferences from the Results One or the goals of the lrial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and terntor} based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples to make inferences about the popul... ton. '1 he use of confidence intervals. based on the standard errors, provides a way to make inferences about the populatum 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 94 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 -t 2 standard errors of the sample mean. As an example. suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence ilnerxal for the population quantity would he as killows: lean I 2 standard errors 256 i 2 - ( 256 2.4 256 - 2 4 and 256 + 2 4 1516. 254 hus. one ui eonclUde Nnh 95 percent certainty that the average proficiency for the entire population of eighth-grade students in puNie schools in that state is between 253.6 and 25S.4. Siumihsi L'ontidenue interxals can be eonstruded tor percentages. provided that the percentages are not OA itt'ffidr lwge (greater than 90 percent t u extremely ( Ie.s.s than 1(1 percent/ For extreme percentages. confidence intervals constructed in the above manner ma not be appropriate and pn,ieduies foi obtaining act.urale confidence intervals :tic quite eomplicated. 1111 lioyo \ Ali' 1 121A1 SI All ASSISS%11 \I Illinois Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the oserall results, this report presents outcomes separatel 16r a variety of important sullgrour.. Many of these subgroups are defined by shared characteristics of students. such as their gender. race ethnicit. and the type of community in which their school is located. ()tiler subgroups are defined by students' TeNponses to background questions such as . thorn how nuich time do rola spend each dar on 'mathematics homescork'' Still other subgroups are defined by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As all example. one might be interested in answering the question- Do students who reported so.ndang -11 minute% or more doing ?mathematics homeworA each day exhibit /ugher taerage mathontaties proficient.). than students who reported .spending MItillfr.s OP frs.0 ansWer the question posed ;those. one lxvns bs comparing the average mathematics proficiency for the Iwo gnmps being anals /ed. If the mean for the group who reported spend* 45 minutes or more tm mathematics homework is higher. one may he tempted to conclude that that group does have higher aelnevement than the group who reported sfmiding IS Minutes of less on homework. I Ioweser. es en though the means differ. there Ina\ be no real difference m performant'e between the tko groups in the population because of the uncenamts associated with the estimated as erage proficienc of the groups in the sample Remember that the intent is to make a statement about the entire population, not bout the 'Nut ieular sample that was assessed I he data from the sample are used to maise interemes about the population as a %%bole \s dist missed in fly pre ions section. each esninated sample Mean proticiencs for proportion) has a degree of uneertaints associated with tt It is therefore possible that it all student. in Ow populatitm had been assessed, rather than a sample of student., or if the assessinent had leen repeAtcd with a different saillple of students 01 a different but cquis.dent, set of questions. the performances of sariolls group. NAOUlti hase been different I hills, dettnimimnmt hether there is a tea/ dine! ence behsecti the mean proficiencs tor pioportion of tcrlain attribute) Ita Isto groups in the population. ttne must obtain an estmiate of the degree ol uneertaifil Associated \N 'oh the difference betSs veil the proticieno means oi proportions of those !Joni,s tor the sampk: I Ins estimate of the degree of Whet-taint -- called /he ocohhit,leHot ot the (/ifference belscen the giOUps -- is obtained hs taking the squale of cad, gioup's staildand ernor summing these squared standard error's. and then taking the square root of tins sum. uumiuLin to the manner iii \s Inch the standard error tor an mdisidual proup !Dean of rfoPornon used. the ttan,./ard etror of the (id/creme Can be used to help determine liethei thileientes betsseen groups in the popillation me real I he differelh-e betssvtil tilt mean proficiencs or proportion of the two groups t 2 standard eltOtS of the tillfrrenCe repiesents all appre \inmate t)5 percent confidence filter\ al If the resulting intersal inclutks /ero. one should conclude that there is insufficient es idence to clami I real difference bettsecn ilroups in the population II the intersal does nt: Contain tea), the difference betst tell giolips is staltsocalh signal«int (different at the If5 Josef liii 1,0911 \I l' I II \I 51 \II ss! ss Illinois As an example, suppose that one were interested in determining whetherthe average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a particular states public schools. Suppose that the sample estimates of the mean proficiencies and standard errors for females and males were as follows: Group Average Proficiency Standard Error Female 259 2.0 Male 255 .01 2.1 The difference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is \ 2.62 + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.S and 4 + 5.S = -1.S, 9.S "The value zero is within this confidence interval, which extends from -1.S to 9.S (i.e zero is between -1.S and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report, when the mean proficienc) or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiene) than a second group. the 95 percent confidence interval for the difference between groups did not contain zero When a statement indicates that the average proficiency or proportion of some attribute was about the same for two goups, 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 he slight may represent a statisticall) significant difference in the population because of the maimitude of the standard errors. ConverseI), a difference that appears to be large ma) not he statistically significant. 3 '1 he procedure described above (especiall the estimation of the standard error of the difference) is, in a strict sense. onl appropriate %Allen the statistics being compared come from independent samples. i'or certain comparisons in the report, the groups vkere not independent In those cases, a different itrid more appropriate) estimate of the standard error of the difttiernt. sk as used r ) 94 THE 1990 \ AEP TRIAI. SIAM ASSESSMENT Illinois The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significance is being performed. However, in each chapter of this report, many different groups are being compared (i.e., multiple sets of confidence intervals are being analyzed). When one considers sets of confidence intervals, statistical theory indicates that the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. 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 NAFP are statistics and therefore are subject to a certain degree of uncertaint!.. In certain cases. typically when the standard error is based on a small number of studmts. 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 an 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 proficienc and background variables were tabulated and reported for groups defined b race ethnicity and type of school community, as well as by gender and parents' education level. NAY P collects data for five racial ethnic subgroups (White. Blaek. Hispanic, Asian Pacific Islander. and American Indian Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged ('rhan. Extreme Rural, and Other Communities). However, in many states or territories, and for some re0ons of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and or background variable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subinoup. a minimum sample size of (12 students was required. This number was determined by computing the sample size required to detect an effect site of .2 with a probability of .1i or greater. 1 iiL 1990 ALP TRIAL Si Al 1 ASSLSSMEM 95 Illinois The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or territory, divided by the standard deviation of the p:oficieney 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 num'er of students being taught by teachers with master's &gees in mathematics might be described as "relatively few" or -almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms tin the mapitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage Description of Text in Report p -,- 0 None 0 <. p L 10 Relatively few 10 -.: p f: 20 Some 20 -... p ....: 30 About one-quarter 30 --. p f.,. 44 Less than half 44 .- p -'_:: 55 About half 55 ., p f:. 69 More than half 69 -. p ..., 79 About three-quarters 79 - p -.:.. 89 Many 89 .,_ p p ,----- 100 100 Almost all All 1 r I 1 111 1990 \ NLP 1 RIM. Si ME ASSI-SSMIA I Illinois THE NATION'S REPORT CARD DATA APPENDIX l'or each of the tables in the main hody of the report that presents mathematics proficiency results. this appendix contains corresponding data for each level of the four reporting suhpopulations race ethn.:it. tpe of communit. parents' education level. and gender. THI, 1990 \MT I RIM. S I Al I. ASSI.SSMIA I 97 Illinois TABLE AS 1 Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY -r- 1990 NAEP TRIAL Eighth-grade STATE ASSESSMENT Mailie macs iste-einelwa Alvan _. TOTAL and Proficiency 83 ( 24) 251 ( 1.7) 62 ( 2.1) 251 ( 1.4) 63 ( 3.0) 261 ( 1.6) 59 ( 2.5) 259 ( 1.6) 84 ( 4.2) 227 ( 2.6) 72 ( 4.7) 232 ( 3.4) 73 ( 2.9) 232 ( 3,4) 75 ( 4.4) 240 ( 2.4) 31 ( 5.1) 50 ( 6.0) 265 ( 3.9)I 55 ( 9.4) 269 ( 2.5)1 72 ( 5.2) 229 ( 4.8) 85 ( 6.0) 240 ( 4.0)' 68 ( 9.4) 269 ( 4.1)1 74 ( 4.5) 249 ( 3.1)! 67 ( 3.7) 255 ( 2.2) 61 ( 2,2) 251 ( 2.0) Percentage and Proficiency 18 ( 2.0) 288 ( 31) 19 ( 1.9) 272 ( 2.4) 18 ( 2.5) 279 ( 1.9) 21 ( 2.4) 277 ( 2.2) 20 ( 4.1) 232 ( 5.4)1 15 ( 3.0) 245 ( 8.4) 12 ( 2.1) ( 13 ( 3.9) 27 ( 6.8) ( 21 ( 6.5)) 22 I 5.1) 283 ( 4.4)1 22 ( 7.9) *.*) 14 ( 4,4) 237 ( 8.0)1 16 ( 4.1) ( 4*. ) 25 (10.4) 276 ( 3.3)1 14 ( 5.0) ( 14 ( 2.4) 271 ( 2.8)1 20 ( 2.1) 272 ( 2.8) Percentage and Proficiency 16 ( 1.3) 290 t 2.6) 15 ( 1.2) 200 ( 2.4) 10 ( 1.7) 300 ( 2.4) 17 ( 1.5) 300 ( 2.3) 12 ( 1.8) 9 1 22) ( 0.1 11 ( 1.8 ) 044 fr0.11) 6 ( 1.6) 41 37 ( 6.9) *** ) 41 ( 7.4) grity 25 3.7) S07 ( 4.3)1 21 ( 4.4) 12 ( 2.4) 202 ( 9.5)1 14 ( 3.3) 287 ( 4,.2)1 5 ( 2.3) ft* ) 7 ( 2.2) * ) 18 ( 2.0) 288 ( 44)1 18 ( 1.4) 294 ( 2.7) State Nation RACE/ETHNICITY WNte State Nation Blade State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Diudvantaged urban State Nation Extreme rural State Nation Other State Nat ion 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). e 95 THE 1990 NAE13 TRIAL STATE ASSESSMENT Illinois TABLE AS I Students' Reports On the Mathematics Class (continued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY /01111111111. 1990 NAEP TRIAL STATE ASSESSMENT EIghthirade Mathematics Pre-algebra Algebra TOTAL Pinon lap and Preaching Periontago and Pivackincy Porsitalop and Prellelency State 18 ( 2.0) 16 13) 251 ( 1.7) 266 ( 3.7) 2.13) Nation 62 ( 2.1) 19 ( 1.9) 15 1.2) 251 ( 1.4) 272 ( 2.4) 296 ( 2.4) PARENTS' EDUCATION NS noe-gradilate State 75 ( 241 ( 3.9) 2.8) 15 ( Ipe 2.6) 8 ( 2.6) Nation 77 ( 241 ( 3.7) 2.1) 13 ( 3.4) 3 ( 1.1) 0.01 113 graduate State 74 ( 2.8) 12 ( 2.0) 11 ( 1.6) 247 ( 1.9) 259 ( 4.9) 275 ( 5.1) Nation TO ( 2.6) 18 ( 2.4) 8 ( 1.1) 249 ( 1.0) 268 ( 3.5) 277 ( 5.2) Some college State 05 ( 2.9) 20 ( 2.9) 13 ( 1.7) 255 ( 1.7) 269 ( 4.3) 289 ( 5.0) Nation 60 ( 1) 21 ( 2.9) 15 ( 1.9) 2:67 2 1) 270 ( 2.6) 295 ( 3.2) College gradate State 5". 32) 22 ( 2.7) 23 ( 2.1) 2b1 ( 2.6) 276 ( 3.8) 299 ( 2.9) Nation ( 2.7) 21 ( 2.3) 24 ( 1.7) 259 ( 1.5) 278 ( 2.8) 303 ( 2.3) GENDER Male State 65 ( 2.4) 17 ( 1.8) 14 ( 1.6) 250 ( 2.0) 270 ( 3.7) 295 ( 3.4) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 12) 252 ( 1.6) 275 ( 2.9) 2902.5) ( Female State 62 ( 3.0) 19 ( 2.7) 17 ( 1.6) 252 ( 1.8) 268 ( 42) 285 ( 2.9) Nation 01 ( 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 Vitt 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 percent..ges 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). 1 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Illinois 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 - None 15 Mtnutes 30 Minutes 7 45 Minutes An Hour or Mare TOTAL Percentage and Proficiency 1 ( 0.6) ( 44-.) 1 ( 0.3) e.e ( eee) 1 ( 0.5) ( 1 ( 0.3) ( 2 ( 1.3) ( *.) 1 ( 0.7) **. ( 1 ( 0.7) ( ...) 1 ( 0.8) ( *) 0 ( 0.0) ( 0 0.0) ( ...) 3 ( 2.6) e" ( *") 1 ( 0.9) ( eee) ( 0.0) eee e) 0 ( 0.0) e" ( ***) 0 ( 0.0) ..* ( ) 0 ( 0.2) ..) 1 ( 0.4) *** ( ***) Percentage aid Preficiency 35 ( 4.1) 257 ( 2.9) 43 ( 42) 258 ( 2.3) 38 ( 4.9) 285 ( 2.6) 39 ( 4.5) 288 ( 2.2) 21 ( 6.1) 226 ( 6.9)1 55 ( 7.8) 232 ( 3.1) 36 ( 7.2) 237 ( 4.7)1 46 ( 7.8) 245 ( 3.0)1 17 ( 5.8) ( 34 ( 9.1) 275 ( 3.5)1 61 (11.3) 273 ( 3.1)1 29 1 8.5) 237 (13,1)i 41 (12.6) 236 ( 2.1)1 39 (15.7) 261 ( 3.4)1 68 (14.9) 253 ( 5.4)1 34 ( 6.3) 255 ( 3.1 )1 37 ( 4.3) 256 ( 3.1) Percentage mid Proficimicy 49 ( 3.9) 262 ( 2.9) 43 ( 4.3) 268 ( 2.6) 47 ( 4.5) 272 ( 2.2) 45 ( 5.1) 270 ( 2.7) 50 ( 8.1) 239 ( 6.1)1 40 ( 6.7) 248 ( 5.3) 51 ( 8.1) 232 ( 52)1 34 ( 6.8) 251 ( 4.2)1 65 ( 9.8) ( ...) 37 ( 8.8) *4 53 ( 8.5) 279 ( 3.8)1 32 ( 8.6) ( 53 ( 9.6) 235 ( 6.8)i 36 ( 9.4) 253 ( 9.0)1 61 (15.7) 267 ( 6.0)1 14 (10.9) ( 46 ( 5.2) 263 ( 3.7) 49 ( 5.1) 265 ( 2.5) Percentage and Proficiency 10 ( 2.4) 271 ( 7.2)1 10 ( 1.9) 272 ( 5.7)1 9 ( 2.1) 291 ( 4.4)1 11 ( 2.4) 277 ( 7.8)1 19 ( 8.0) ( 3 ( 1.2) ( 10 ( 4.0) ( *.) 13 ( 2.9) ( ..) 14 ( 5.9) 10 ( 5.4) ( ...) 6 ( 2.4) eee eee/ 5 ( 3.4) eee ( eee) 12 ( 5.6) 248 (12.9); 12 ( 5.9) eee ( tee) 0 ( 0.0) ea. ( aee) 8 ( 5.6) ( 14 ( 4.4) 281 ( 5.0)1 10 ( 2.4) 276 ( 8.6)1 Percentage and Proficiency 5 ( 1.4) 273 ( 8.3)1 4 ( 0.9) 276 ( 5.1)1 5 ( 1.4) 287 ( 5.7)1 4 ( 0.9) 279 ( 5.8)1 8 ( 3.7) .14 2 ( 0.8) *** ( el 7 ( 2.1) **. 4,4,4) 3 ( 2.3) 24 (102) ( es" 1 eee) 0 ( 0.0) ...) ( 10 6.2) 0 ( 0.0) ...) *.. ( 4 ( 1.1) 282 (11.6)1 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 Extreme rural State Nation Other State Nation '1 he standard errors of the estimated statisties appear in parentheses. it can be said with about 95 percent certainty that, for each population of intere7t, 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 esumated mean proficiency. *** Sample size ts Insufficient to permit a reliable estimate (fewer than 62 students). CJ 100 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A6 (continued) Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each May PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 13 Minutes 30 Minutes 45 Minutes An How or Mora TOTAL Percentage and Prone:tang ( 0.6) it44 ( «p) ( 0.3) ( 0.5) 4" ( 444) 1 ( 0,8) ( ( 0.6) es. 1 ( 0.5) 2 ( 1.1) 1 ( 0.5) H.* ( 1P4 ) 0 ( 0.3) 4** Olt* ) 1 ( 0.6) 1 ( 0.3) *4.) 1 ( 0.5) 4" ( 4") 1 ( 0.4) 4" ( 444) Percentage and Proficiency 35 ( 4.1) 257 ( 2.9) 43 ( 4.2) 256 ( 2.3) 39 ( 6.3) 240 ( 4.7)1 49 ( 0.3) 240 ( 2.8) 40 ( 5.5) 252 ( 3.1) 43 ( 5.2) 249 ( 3.1) 36 ( 4.7) 263 ( 3.0) 44 ( 5.4) 265 ( 2.6) 31 ( 4.3) 266 ( 3.4) 40 ( 4.7) 205 ( 2.5) 36 ( 4.5) 256 ( 3.3) 44 ( 4.4) 257 ( 2.9) 33 ( 4.1) 259 ( 2.9) 41 ( 4.4) 255 ( 2.3) Percentage and Proficiency 49 ( 3.9) 262 ( 2.9) 43 ( 4.3) 296 ( 2.6) 50 ( 6.4) 243 ( 4.4) 40 ( 6.1) 246 ( 3.7) 48 ( 5.4) 254 ( 3.2) 44 ( 5.8) 255 ( 2.7) 46 ( 4.2) 265 ( 2.8) 43 t 5.8) 270 ( 3.6) 50 ( 4.3) 275 ( 2.6) 44 ( 4.1) 277 ( 3.0) 48 ( 4.2) 263 ( 3.1) 43( 4.3) 288 ( 2.9) 50 ( 4.0) 281 ( 3.0) 43 ( 4.7) 2$4 ( ,2.8) Parentage and Proficiency 10 ( 2.4) 271 ( 72)1 10 ( 1.9) 272 ( 5.7)1 ( 2.7) ( 1.7) 444 ( *It* ) a ( 2.4) 9 ( 3.1) 4" ( 4") 11 ( 3.6) .44(m) ( 2.1) 0441 12 ( 2.5) 264 ( 9.0)1 1 I ( 2.3) 287 ( 6.1)1 10 ( 2.4) 276 ( 7.2)1 ( 1.9) 273 ( 7.3)1 11 ( 2.7) 265 ( 8.1)1 11 ( 2.0) 272 ( 5.7)1 Percentage aid Proficiency 5 ( 1A) 273 ( 6.3)1 4 ( 0.9) 278 ( 5.1)1 4 ( 1.9) 0.11 4 ( 1.3) .41 4 ( 1.4) ( 3 ( 1.0) 5 ( 2.3) ***) 4 ( 1.0) 45411 6 ( 1.8) 444(44*) 5 ( 1.3) "4 ( 4") 5 ( 1.3) 279 ( 7.7)1 6 ( 1.5) 444 ( 4") ( 444) State Nation PARENTS' EDUCATION NS non-graduate State Nation HS graduate State Nation Some college State Nation College graduate State Nation GENDER Male state Nation Femal State Nation The standard errors of the estimated statirics appear in 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 sue is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 101 Illinois TABLE A7 I Students' Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Wailes 45 Minutes An Hour or More TOTAL Portioning' and Prefidonni 7 ( 1.1) 253 ( 3.4) 9 ( 0.6) 251 ( 2.6) ( 1.5) 261 ( 3.9) 16 ( 10) 258 ( 3.4) 3 ( 1.0) 4.1 7 ( 1.5) ( **a) ( 2.2) ( 941 12 ( 1.8) 0.0) ) 4 ( 2.0) .44(m) 5 ( 1.4) 8 ( 2.5) ( a") ( 1.5) 12 ( 3.7) 11 ( 2.6) *44(44*) 8 ( 2.3) ( 2.1) ( "a) 9 ( 1.0) 250 ( 3.8) Percentage end Proficiency 29( 13) 261 ( 2.1) 31 ( 2.0) 264 ( 1.9) 30 ( 1.8) 270 ( 1.6) 33 ( 2.4) 270 ( 1.9) 26 ( 2.7) 232 ( 42)1 26 ( 2.5) 241 ( 3.8) 23 ( 2.6) 237 ( 5.5) 27 ( 3.0) 246 ( 3.6) 26 ( 8.8) 22 ( 4.8) mm 32 ( 3.2) 277 ( 3.0) 41 (12.5) 276 ( 3.0)1 24 ( 2.6) 236 ( 6.0) 24 ( 3.3) 253 ( 4.9)1 24 ( 3.8) 263 ( 4.2)1 36 ( 4.6) 260 ( 34)1 30 ( 2.2) 264 ( 3.0) 30 ( 1.8) 263 ( 2.3) Pennniage and Proficiency 35 ( 1.1) 264 ( 1.6) 32( 1.2) 263( 1$) 36 ( 1.5) 274 ( 1.7) 32 ( 1.3) 270 ( 2.1) 31 ( 1.9) 237 ( 5.1) 33 ( 2.7) 237 ( 3.5) 36 ( 3.0) 240 ( 3.2) 30 ( 2.6) 248 ( 3.4) *or. 31 ( 5.6) et,* Imi) 41 ( 2.6) 285 ( 3$) 31 ( 6.6) 280 ( 4.6)1 36 ( 2.5) 242 ( 5.6) 31 ( 3.0) 247 ( 4.7)1 31 ( 4_2) 264 ( 5.4)i 31 ( 2.9) 255 ( 5.1)1 34 ( 1.6) 266 ( 2.2) 32 ( 1.3) 284 ( 2.3) Perceniag" and Pro &Ana 17 ( 0.7) 259 ( 2.6) 10 ( 1.0) 286(1.9) 16 ( 1.0) 273 ( 2.1) 15 ( 0.9) 277 ( 2.2) 20 ( 1.7) 231 ( 8.0) 18 ( 2.3) 240 ( 2.6) 22 ( 2.1) 233 ( 4.4) 17 ( 2.1) 241 ( 4.3) 18 ( 3.9) 14 ( 1.6) 284 ( 4.7)I 12 ( 3.3) *v.) 18 ( 1.9) 235 ( 6.6) 20 ( 1.9) 250 ( 4.8)i 20 ( 3,1) 18 ( 3.8) 4*0(4.4) 18 ( 1.2) 260 ( 2.8) 15 ( 1,1) 267 ( 2.1) Parasitic. and ~dem 12 ( 0.9) 256 ( 2.7) 12 ( 1.1) 258 ( 3.1) 11 ( 1.1) 271 ( 33) 11 ( 1.3) 268 ( 3.3) 19 ( 2.4) 233 ( 4.0) 16 ( 1.9) 232 ( 3.7) 13 ( 1.7) 14 ( 1.7) 4*. ( 15 ( 4.7) 25 ( 6.2) 4-» 8 ( 15) ( «Hi) ( 3,4) ( 17 ( 1.8) 231 ( 4$) 14 ( 2.2) 14 ( 3,4) 444(444) ( 2.7) ( 11 ( 1,4) 259 ( 4.6) 13 ( 1.1) 258 ( 3.6) State Nation RACE/ETHNICITY Whits State Nation Oink State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantagal urban State Nation Disadvantaged titan State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of th 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). 1 ,^ 102 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE A7 I Students' Reports on the Amount of Time They (continued) Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes An flour or More TOTAL Pirsentoga and Proilaiency Percontage and Proeckincy Percentage aryd ProAdoncy Pimento' and Prodding Paraming and Prakiency State ( 1.1) 29 ( 1.3) 35 ( 1.1) 17 ( 0.7) 12 ( 0.9) 253 ( 3A) 281 ( 2.1) 284 ( 1.8) 259 ( 2.6) 258 ( 2.7) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 16 ( 1.0) 12 ( 1.1) 251 ( 2.8) 204 ( 1.9) 263 ( 1.9) 266 ( 1.9) 258 ( 3.1) PARENTS EDUCATION HS Gon-graduate State 9 (( 2.4) 27 (( 3.7) «11 36 ( 245 ( 3.6) 3.5) 16 ( 2.4) 11 ( 2.3) Nation 17 ( **It ( 3.0) Orel 26 ( 248 ( 3.3) 4.0) 34 ( 248 ( 4.4) 2.6) 12 ( ( 2.5) 10 ( 2.2) *01 NS graduate State 9 ( 1.8) 30 ( 2.1) 33 ( 2.1) 16 ( 1.7) 11 ( 1.4) 253 ( 1.6) 254 ( 2.4) 247 ( 4.6) 245 ( 4.8) Nation 10 ( 1.7) 33 ( 2.2) 31 ( 1.9) 16 ( 1,4) 11 ( 1.5) 246 ( 42) 259 ( 32) 254 ( 2.4) 256 ( 2.8) 244 ( 3.4) Some college State 8 ( 1.8) ..**) 32 ( 265 ( 2.1) 2.3) 30 ( 266 ( 1.7) 2.8) 17 ( 257 ( 1.5) 3.7) 14 ( 257 ( 2.0) 4.1) Nation 9 ( 1.2) 30 ( 2.7) 36 ( 2.1) 14 ( 1,8) 11 ( 1.5) /* ) 288 ( 3.0) 266 ( 2.6) 274 ( 3.5) College graduate State ( 0.8) 28 ( 1.8) 36 ( 1.4) 19 ( 1.2) 12 ( 1.2) 271 ( 3.0) 278 ( 2.4) 274 ( 3.4) 270 ( 3.7) Nation ( 0.9) 31 ( 3.4) 31 ( 2,0) 18 ( 1,2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Male State 8 ( 1.2) 31 ( 1.4) 34 ( 1.8) 16 1,1) 12 ( 1.1) 254 ( 4,4) 261 ( 2.5) 265 ( 2.1) 255 ( 4.1) 259 ( 3.2) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 288 ( 2.4) 205 ( 3.0) 258 ( 4.1) Female State 6 ( 12) 27 ( 1.7) 38 ( 1.6) 19 ( 1.2) 13 ( 1.1) 252 ( 3.9)1 260 ( 2.5) 263 ( 2.8) 292 ( 2.3) 254 ( 3.2) Nation ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 248 ( 4,1) 283 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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 proficency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 103 Illinois TABLE AS I Teachers' Reports on the Emphasis Given To 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measurement Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Norinehme and ftWklemw 41 ( 4.3) 257 ( 2.7) 49 ( 3-8) 280 ( 1.8) 37 ( 5.0) 267 ( 2.1) 48 ( 3.71 267 ( 2_2) 50 ( 8.7) 239 ( 4.4) 54 ( 7.9) 243 ( 4.3) 55 ( 7.3) 234 ( 5.2) 47 ( 8.7) 246 ( 4.6) 44 (12.1) 4.) 28 ( 6.7) 270 ( 8.0)1 2$ (13.0) ( 57 ( 9.8) 238 ( 8.9)1 48 (12.1) 255 ( 6.3)1 32 (14.8) 261 ( 5.8)1 53 (12.4) 257 ( 7.1)1 43 ( 5.8) 261 ( 2.6) 52 ( 4.1) 260 ( 2.3) Pimmniop ProlkUncy 15 ( 2.5) 284 ( 4.1) 15 ( 2.1) 287 ( 3.4) 16 ( 2.8) 297 ( 3.3) 16 ( 2.4) 289 ( 3.5) 4144k ) 9 ( 4.4) *I» 8 ( 2.2) ( *ft) 25 ( 7.0) ( 30 ( 7.3) 303 ( 4.4)1 16 ( 4.2) ( 9 ( 4.5) **. 9 ( 4.0) ***) 4 ( 25) 15 ( 3.4) 286 ( 4.2)1 16 ( 2.7) 286 ( 3.6) Nmatage and Proft.Mmy 17 ( 3.4) 210 ( 9.0p 17 ( 3.0) 250 ( 5.8) 12 ( 3.7) 284 ( 8.8)1 14 ( 3.4) 259 ( cu)! 2$ ( $.0) 200 ( 5.3)1 25 ( 7.4) 228 ( 2.8)1 30 ( 7.2) 208 ( 6.8)t 23 ( 4.1) v.* 17 *it.) t *qui) wt. 28 ( 9.6) 196 ( 6.0)1 39 (10.3) 238 ( 8.4)1 18 (17.7) * .41 MD* ) 13 ( 2.9) 250 (11.1) 16 ( 3.9) 253 ( 7.1)1 P.rcesag, esW Nolidomy 34 ( 3.4) 26$ ( 4.5) 33 ( 4.0) 272 ( 4.0) 36 ( 3.9) 276 ( 3.5) 36 ( 4.7) 277 ( 4.3) 28 ( 8.3) 221 ( 9.4)1 23 ( 5.7) 238 ( 8.1)1 21 ( 5.5) ( ) 34 ( 5.8) 255 ( 4.4)1 28 ( 8.7) 44 8.9) *0. ( ***) 51 ( 7.3) 268 ( 8.5)1 ( 84) «Hi 15 ( 7.1) 229 (22.3)! 21 ( 8.5) 44. ***) 33 ( 0.2) 281 (11.0)1 32 (11.7) 285 ( 9.1)1 38 ( 5.5) 264 ( 5.1)1 34 ( 5.3) 270 ( 4.8) Nmoontw wad Prolkismy 4.0) 25$ 3.0) 2$ 3.8) 260 ( 3.2) 29 ( 4.0) 288 ( 3.2) 27 ( 4.4) 265 ( 3.3) 29( 9.1) 232 ( 6.3)! 33 ( 7.9) 242 ( 5.8)t 30 ( 5.9) 231 ( 5.4)! 27 ( 6.8) *** t ***) 33 ( 5.8) ( Mt* ) ***) 33 ( 9.3) 272 ( 5.3)1 38 ( 9.4) 287 ( 4.9)1 19 ( 7.4) 222 ( 83)1 33 (11.8) 248 ( 6.2)1 36 (18.9) 283 ( 5.4)1 9 ( 8.1) gm 32 ( 5.7) 258 ( 4.2) 28 ( 4.8) 280 ( 3.9) %maw kvildency 26 ( 33) 255 ( 3.7 ) 21 ( 3.3) 284 ( 5.4) 27 ( 4.0) 264 ( 3.0) 22 ( 3.4) 273 ( 53) 16 ( 4.5) 24 ( 7.3) 233 ( 4.7)! 33 ( 8.7) 229 ( 8.7)1 18 ( 5.5) ( .**) 20 ( 3.5) 285 ( 8.0)! 13 ( 3.2) 041 26 ( 7.5) 234 (10.5)! 18 ( 7.6) 35 (10.4) 255 ( 5.2)1 18 ( 7.9) ( 28 ( 6.1) 255 ( 3.9)1 24 ( 4.3) 285 ( 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 Extreme tura) 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 prqflciency. I'S* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). .) 104 THE 2990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A8 I Teachers' Reports on the Emphasis Given to (cwitinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measurement Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Lit 'le or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage aid Proficiency Percentage Proficiency Peecentage end Proficiency Percentage and Proficiency Percentage mid Proficiency Percentage and Profit:law State 41 ( 4.3) 15 ( 2.5) 17 ( 3.4) 34 ( 3.4) 29 ( 4.0) 26 ( 3.5) 257 ( 2.7) 289 ( 4.1) 235 ( 9.0)1 268 ( 4.5) 258 ( 3.0) 255 ( 3.7) 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 ( 5.6) 272 ( 4.0) 260 ( 3.2) 264 ( 5.4) PARENTS EDUCATION HS nen-graduate State 51 ( 241 ( 7.1) 5.5) 11 ( 3.0) 4,4-1 20 ( ( 5.8) .41 32 ( 5.4) 25 ( 4.9) 37 ( 243 ( 6.1) 5.4)1 Nation ( 8.9) 22 ( 5.3) 25 ( 5.3) 251 ( 3.4) *** ) NS graduate State 44 ( 5.4) 20 ( 5.2) 30 ( 4.4) 31 ( 5.3) 29 ( 5.7) 150 ( 3.0) 233 (10.2)1 252 ( 5.4) 251 ( 4.2)1 245 ( 3.5)1 Nation 55 ( 4.8) 11 ( 2.8) 17 ( 3.9) 27 ( 5.0) 27 ( 4.5) 24 ( 5.1) 259 ( 2.9) 251 ( 6.1)t 253 ( 4.7)1 255 ( 4.2) 248 ( 4.8)1 Some college State 43 ( 4.7) 14 ( 2.6) 32 ( 4.4) 27 ( 4.0) 23 ( 3.5) 264 ( 2.7) *4 *IN) 263 ( 5.1) 257 ( 4.1) 254 ( 5.6) Nation 47 ( 4.4) 17 ( 3.3) 12 ( 2.7) 39 ( 5.5) 27 ( 5.0) 23 ( 4.1) 265 ( 2.6) 284 ( )1 279 ( 4.5) 262 ( 4.8)i 270 ( 4.7) College graduate State 34 ( 4.2) 22 ( 4.0) 14 ( 3.4) 39 ( 4.1) 30 ( 4.9) 25 ( 3.1) 267 ( 3.2) 298 ( 4.1)1 249 (13 1)1 282 ( 4.7) 270 ( 3.4) 270 ( 4.0) Nation 44 ( 4.1) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 269 ( 2.6) 298 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 6.4) GENDER Male State 40 ( 4.4) 15 ( 2.5) 17 ( 3,8) 33 ( 3.5) 28 ( 41) 28 ( 4.3) 254 ( 3.2) 292 ( 5.2) 240 (10.5)1 270 ( 5.4) 258 ( 4.2) 258 ( 4.2) Nation 48 I 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 261 ( 2.5) 287 ( 4.4) 258 ( 6.7) 275 ( 4.8) 263 ( 3.8) 266 ( 6.8) Female State 41 ( 4.6) 15 ( 2.8) 17 ( 3.3) 35 ( 3.6) 31 ( 4.1) 25 ( 3,0) 259 ( 2.7) 287 ( 4.0) 230 ( 9.0)1 265 ( 4.6) 258 ( 3,9) 2551 4.1) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 260 ( 2.0) 286 ( 3,3) 241 ( 5.4) 268 ( 4.1) 256 ( 3,3) 283 ( 5.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages may not total 100 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). 'ME 1990 NAEP TRIAL STATE ASSESSMENT 105 Illinois TABLE A8 I Teachers' Reports on the Emphasis Given To ("mtinued) i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 !MEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra and Furor lions Heavy Emphasis time Of No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 14 ( 3.0) 57 ( 3.8) 55 ( 3.5) 12 ( 2.4) 253 ( 6.3)1 265 ( 32) 272 ( 2.2) 239 ( 5.1)1 Nation 14 ( 22) 53 ( 4.4) 46 ( 3.6) 20 ( 3.0) 269 ( 4.3) 261 ( 2,9) 275 ( 2.5) 243 ( 3.0) RACE/ETHNICITY Whits State 12 ( 3.2) 59 ( 42) 56 ( 3.8) 12 ( 2.9) 272 ( 52)1 ;.76 ( 2.6) 280 ( 2.2) 246 ( 4.9)1 Nation 14 ( 2.4) 53 ( 5.0) 48 ( 42) 18 ( 2.8) 276 ( 4.1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) Black State 25 ( 223 ( 9.3) 9.8)1 49 228 ( 9.0) ( 4.9)1 54 ( 247 ( 7.7) 5.4) 8 ( 2.1) Nation 14 ( 3.4) 53 ( 82) 39 ( 7.1) 27 ( 6.9) 225 ( 4.3) 253 ( 6.3) 220 ( 2.2)1 Hispanic State 12 ( 3.5) 57 ( 6.3) 44 ( 8.3) 20 ( 6.4) ( 234 ( 7.0) 244 ( 3.8) Nation 15 ( 4.1) ***) 56 246 ( 6.3) ( 4.4) 46 ( 257 ( 5.9) 4.0)1 18 ( 42) 0.4) Asian State 15 ( 6.8) 65 ( 5.8) 80 ( 62) 3 ( 22) 1111.0 "4-.1 ( Nation ( 35 ( 7.1) 61 ( 4-** ( 8.1) 9 44 ( 4.9) ( .41 TYPE OF COMMUNITY Advantaged urban State 5 ( 3.0) *..) 59 288 ( 7.8) ( 5.5)1 52 ( 290 ( 6.5) 3.6)1 5 ( 1.9) Nation 11 ( 6.6) 65 (19.4) 41 ( 8.9) 18 ( 5.3) *ft ( ) 284 ( 7.4)1 296 ( 7,9)1 Disadvantaged State 16 ( 6.8) 59 ( flA) 43 ( 8.6) 15 ( 6.2) 213 ( 5.6)1 235 ( 9.4)1 252 ( 6.7)1 225 ( 8.9)I Nation 34 (11.4) 53111.8) ( 236 ( 8.2)i 254 ( 6.3)1 Extreme rural State 0 ( 0.0) 84 ( 8.6) 41 (155) 18 (11.9) 268 ( 5.0)1 274 ( 4.4)1 ( +ft ) Nation 5 ( 5.4) 65 (16.9) 33 ( 8.1) 42 (16.0) 254 ( 6.7)1 241 ( 5.9)1 Other State 18 ( 51) 48 6.1) 64 ( 5.2) 11 ( 2.8) 265 ( 5.2)1 268 ( 3.6) 270 ( 2.8) 244 ( 9.0)I Nation 15 ( 2.9) 53 ( 5.2) 47 ( 4.3) 17 ( 3.3) 267 ( 4.7) 260 ( 3.4) 276 ( 2.8) 245 ( 4,4)1 The standard errors of the estimated statistics appear in 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 doet not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insuMcient to permit a reliable estimate (fewer than 62 students). 4. 106 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE AS I Teachers' Reports on the Emphasis Given To (cmtinued) i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Data Analysts, Statistics, and Probability Aigebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Uttle or No Emphasis TOTAL Percentage and Prefidency Percentage and Proficiency Percentage and Proficiency Percentege and Proficiency State 14 ( 3.0) 57 ( 3.8) 55 ( 35) 12 ( 2.4) 253 ( 6.3)! 265 ( 3.2) 272 ( 2.2) 239 ( 5.1)! Nation 14 ( 2.2) 53 ( 4.4) 48 ( 3.6) 20 ( 3.0) 289 ( 4,3) 261 ( 2.9) 275 ( 2.5) 243 ( 3.0) PARENTS EDUCATION 1121 non-graduate State 9 ( 2.3) 62 ( 241 ( 5.1) 5.0) 46 ( 251 ( 6.8) 4.2) 20 ( ( 5.8) 114,11) Nation 9 ( ob,fr. 3.0) 41 53 ( 240 ( 7.7) 6.2) 23 ( we* ( 52) .41 29 ( 6.9) NS gracksate State 15 ( 3-8) 57 ( 5.4) 51 ( 5.2) 15 ( 3.8) 252 ( 6.7)1 256 ( 3.7) 263 ( 2$) 232 ( 5.7)t Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.8) 261 ( 6.0)1 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Some college State 16 ( 3.8) 54 ( 4.9) 56 ( 3.8) 12 ( 2.3) 283 ( 5.3)1 288 ( 3.6) 270 ( 3.0) Nation 13 ( 2.5) .**) 57 ( 270 ( 5.8) 3.7) 46 ( 278 ( 4.8) 3.0) 17 ( 3.1) College gractuato State 13 ( 32) 58 ( 3.9) 59 ( 3.9) 7 ( 1.4) 262 ( 8.1)1 281 ( 3.3) 284 ( 2.8) 248 ( 6.8) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.0) 18 ( 2.4) 282 ( 4$) 275 ( 3.8) 288 ( 3.0) 249 ( 4.0) GENDER Male State 14 ( 3.2) 57 ( 4.4) 54 ( 3.9) 12 ( 2.4) 254 ( 6.1)1 268 ( 3.6) 271 ( 2.7) 237 ( 4.6)1 Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.6) 275 ( 5.8) 260 ( 3$) 278 ( 3.2) 243 ( 3.0) Female State 14 ( 2.8) 58 ( 3.6) Se ( 3.7) 11 ( 2.7) 252 ( 7.1)! 265 ( 3.3) 272 ( 2$) 241 ( 6.6)l Nation 10 ( 2.4) 53 ( 4.5) 46 ( 3.6) 16 ( 2.9) 263 ( 4.4) 282 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 pernt certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is Insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 107 Illinois TABLE A9 I Teachers' Reports on the Availability of i Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ..mi 11,NMIM11.11.11=1I1k=411, 1000 NAV TRIAL I Get All the Resources I 1 Clet Most of the I Get Sante or None of STATE ASSESSMENT Need Resources 1 Need the Resources I Need TOTAL and Roadway Percentage and Proficiency thwesatage and Proficiency State 18 ( 3.9) 54 ( 4.5) 28 ( 4.1) 275 ( 3.6)1 283 ( 2.2) 248 ( 3.5) Nation 13 ( 2.4) Se ( 4.0) 31 ( 42) 265 ( 4.2) 266 ( 2.0) 261 ( 2.9) RACE/ETHNIC1TY White State 22 ( 4.9) 57 ( 5.0) 21 ( 3.7) 278 ( 3.3)1 272 ( 1.8) 262 ( 2.7) Nation 11 ( 2.5) 58 ( 4.6) 30 ( 4.8) 275 ( 3.5)1 270 ( 2.3) 267 ( 3.3) Black State SO ( 9.4) 42 (10.1) **I 235 ( 6.6) 226 ( 3.4)1 Nation 15 4.2) 52 ( 6.6) 33 ( 7.2) 241 ( 5.3)1 242 ( 2.4) 236 ( 4.9) Hispanic State 11 ( 4.0) 46 ( 8.8) 43 ( 8.6) ) 235 ( 4.6)1 234 ( 3.7)1 Nation 23 ( 7.6) 44 ( 4.9) 34 ( 7.7) 246 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 Asian State .. ...) 40 ( 9.3) .. ...) 33 (12.2) Nation 37 ( 7.7) .. ...) 44 (12.7) ..) TYPE OF COMMUNITY Advantaged urban State 33 ( 9.1) 57 ( 9.0) 10 287 ( 3A)1 278 ( 2.9,1 Nation 38 ( 9.2) 272 ( 8.5)1 59 ( 8.9) 286 ( 1.3)1 3 ( 3.1) .. 4.) Disadvantaged urban State 9 ( 6.3) ...) 50 ( 9.1) 235 ( 7.6) 41 ( 8.6) 237 ( 5.4)1 Nation 40 (13.1) 50 (145) 251 ( 54)1 253 1 5.5)1 Extreme rural State 26 (17.3) 262 (11.6)1 59 (11.2) 269 ( 1.9)1 15 (13.0) .. ...) Nation 2 ( 2.6) 54 (10.4) 43 (10.3) 411.4 ) 260 ( 8.8)1 257 ( 5.0)1 Other State 16 ( 5.2) 56 ( 6.6) 29 ( 5.8) 277 ( 3.8)1 263 ( 2.9)1 254 ( 3.0) Nation 11 ( 2.9) 58 1 5.4) 31 ( 5.6) 265 ( 3.9)1 264 ( 2.1) 263 ( 4.2) The standard e,Tors 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 tbe entire population is within 7: 2 standard errors of the estimate for the sample. ! Interpret with caltion 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 82 students). 1 108 THE 1990 NAEP TRIAL 5LATE ASSESSMENT Illinois TAbE A9 I Teachers' Reports on the Availability of (continued) I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL I Get NI the Resources I I OM Most of the I Got Soma or None of STATE ASSESSMENT Need Resources I Need the Resources I Need TOTAL Poroonlaso and "roadway 18 ( 3.9) state 275 ( 3.6)1 Nation 13 ( 2.4) 265 ( 42) PARENTS' EDUCATION HS non-graduate State 14 (( 4.1) .41 Nation 8 ( ,* ( 2.0) .41 $45 iradiata State 14 ( 33) 200 ( 4.4); Nation 10 ( 2.5) 253 ( 4.8)1 Some college State 29 ( 4.7) 273 ( 3.8)1 Nation college graduate 13 ( 3.3) State 23 ( 4.8) 288 ( 3.5)1 Nation 15 ( 2.9) 276 ( 5.4); GENDER Male State 19 1 3.9) 274 ( 4.8)1 Nation 13 ( 2.6) 204 ( 5.0)1 Female State 18 ( 4.1) 275 ( 2.9)1 Nation 13 ( 2.4) 266 ( 3.9) Porantoyo and 'roadway 54 445) 263 2.2) 58 4.0) 285 2.0) 45 ( 5.8) 245 ( 3.3) 54 ( 5.7) 244 ( 2.7) 57 ( 5.5) 255 ( 2.6) 54 ( 4.9) 258 ( 1.9) 53 ( 5.0) 263 ( 2.2) 82 ( 4.3) 269 ( 2.5) 58 ( 4.8) 274 ( 2.3) 56 ( 4.9) 276 C 2.2) 55 ( 4.6) 282 ( 25) 57 ( 4.0) 265 ( 2.8) 53 ( 4.7) 263 ( 2.1) 55 ( 4.4) 264 ( 2.0) Poroodogo and . "madam 28 ( 4.1) 248 3.5) 31 42) 261 2.9) 41 ( OA) 237 ( 4.1)! 38 ( 8.3) 243 ( 3.5); 29 ( 5.1) 243 ( 33) 35 ( 4.9) 256 ( 2.8) 27 ( 4.3) 255 ( 3.6) 25 ( 4.1) 287 ( 3,8) 21 ( 3.6) 258 ( 4.8) 30 ( 5.1) 273 ( 3.7) 28 ( 4.0) 248 ( 3.6) 30 ( 4.0) 264 ( 3.3) 29 ( 4.5) 247 ( 3.9) 32 ( 4.7) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 109 Mhwis TABLE AlOa I Teachers' Reports on the Frequency of Small 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT - At Least Once a Week Less Than Once a Week Nwer TOTAL Panxidape Pratt-40w Parcantaga and Poraantaga and Milldam" State 45 ( 4.3) 40 ( 4.0) 15 ( 2.9) 200 ( 3.5) 263 ( 2.8) 263 ( 3.4) Nation 50 ( 4.4) 43 ( 4.1) 6 ( 2.0) 260 ( 22) 204 ( 2.3) 277 ( 5A)I RACE/ETIINICITY White State 40 ( 4.7) 42 ( 4.8) 18 ( 3.4) 274 ( 2.7) 270 ( 2.2) 269 ( 2.9) Nation 49 ( 4.8) 43 ( 4.5) 6 ( 2.3) 265 ( 2.7) 271 ( 22) 285 ( 4.9)1 Black State 63 ( 8.8) 24 ( 3.7) 13 ( 4.7) 233 ( 6.0) 241 ( 4.9) ( Nation 47 ( 8.1) 45 ( 7.0) C ( 4.1) 240 ( 34) 238 ( 4.0) Hispanic State 49 ( 8.8) 46 ( 9.0) 5 ( 2.0) 232 ( 8.1)1 239 ( 5.7)1 ( "41 Nation 84 ( 7.2) 246 ( 2.5) 32 ( 61) 247 ( 8.3)1 4 ( 1.4) ( 4) Asian State 63 (10.8) ee. 28 ( 9.7) .411 ( "") Nation 60 ( 9.2) 37 ( 7.9) 4 ( 2.7) *** ( "") TYPE OF COMMUNITY Advantaged urban State 46 ( 8.1) 40 ( 6.5) 14 ( 5.0) 283 ( 3.8)1 281 ( 4.9)1 274 ( 6.9)1 Nation 39 (22.9) *Yr* ( *4 41 (17.9) 273 ( 6.0)1 20 (12.2) 4.**) Disadvantaged urban State $5 ( 9.9) 27 ( 8.9) 18 ( 8.3) 229 ( 7.0)1 239 ( 8.0)1 256 ( 9.9)1 Nation 70 (11.7) 21 ( 9.0) 9 ( 8.5) 248 ( 4.8)1 249 ( 8.7)1 Extreme rural State 48 (14.1) 28 (12.4) 26 (11.7) 263 ( 8.4)1 268 ( 4.2); 263 1 ?AP Nation 35 (14.6) 58 (17.1) 255 ( 55)1 258 ( 5.9)1 Other State 39 ( 6.9) 49 ( 65) 12 ( 3.8) 265 ( 3.6)1 262 ( 3.4) 260 ( 8.4)1 Nation 50 ( 4.4) 44 ( 4.5) 8 ( 1.8) 260 ( 2.4) 264 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 41 110 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE Al Oa I Teachers' Reports on the Frequency of Small (wntinued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week _ Never TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Prodelancy State 43 ( 4.3) 40 ( 4.0) 15 ( 2.9) 260 ( 3.5) 283 ( 2.8) 283 ( 3.4) Nation 50 ( 4.4) 43 ( 4.1) ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 5.4)) PARENTS' EDUCATION HS non-graduate State 46 ( 238 ( 12) 62)1 38 ( 248 ( 6.5) 4.4) .44 ( Nation 60 ( 6.4) 39 ( 6.5) 1 ( 1.4) 244 ( 3.2) 244 ( 3.2)1 VISA HS graduate state 44 ( 5.7) 39 ( 52) 18 ( 3.9) 251 ( 3.7) 252 ( 2.9) 260 ( 3.9)1 Nation 49 ( 252 ( 4.8) 2.8) 43 ( 257 ( 5.1) 2.7) 6 ( fik. ( 2.5) Some college State 38 ( 4.0) 46 ( 4.4) 16 ( 3.3) 264 ( 3.$) 265 ( 2.0) 283 ( 5.1) Nation 51 ( 266 ( 52) 3.1) 42 ( 268 ( 5.1) 32) ( 2.3) 44.,t) College graduate State 48 ( 4.7) 38 ( 4.0) 14 ( 3.0) 273 ( 32) 276 ( 3.1) 272 ( 4.2)1 Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 276 ( 3.0) 285 ( 4.9)1 GENDER Male State 44 ( 4.6) 41 ( 4.2) 16 ( 3.2) 260 ( 4.2) 264 ( 2.7) 264 ( 3.9)1 Nation 50 ( 4.5) 42 ( 4.0) ( 2.1) 261 ( 3.0) 285 ( 3.1) 278 ( 5.3)1 Female State 47 ( 4.3) 39 ( 4.0) 15 ( 2.7) 261 ( 3.3) 262 ( 2.7) 282 ( 3.4) Nation 50 ( 4.7) 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.8)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. **6 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT Ill Illinois TABLE AlOb I Teachers' Reports on the Use of Mathematical 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 NAEP TRIAL STATE ASS1DSSMENT At Least Owe a Week Less than Once a Week Never TOTAL Percentage and forallaiancy Paraentage ind Prolinanay Pansentage and Proildancy State 2. ( 3.7) 69(3.9) 7 ( 1.4) 254 ( 3.5) 253 ( 2.3) 282 ( 8.9)! Nation 22 ( 3,7) 09 ( 3.9) 9 ( 2.6) 254 ( 3.2) 253 ( 1.9) 282 ( 5.9)I RACE/ETHNICITY Whits State 23 ( 4.1) so( 4.2) 8 ( 1.5) 267 ( 2.7) 271 ( 1.9) 290 ( 0.0) Nation 17 ( 4.0) 72 ( 4.2) 10 ( 2.7) 261 ( 3.8)1 26S ( 2.1) 288 ( 6.2)1 State 25 ( 84) 225 ( 6.4) 69 ( 6.7) 238 ( 5.0) ( 3.2) *go ( Nation 22 ( 5.9) 70 ( 6.3) 8 ( 3.9) 233 ( 5.9)1 241 ( 2.9) Hispanic State 40 ( 7.2) 58 ( 7.4) 2 ( 1.0) 230 ( 52)1 238 ( 5.7)1 Nation 39 ( 7.5) 55 ( 7.3) 7 ( 2.6) 247 ( 3.8) 245 ( 3.0)1 ( ***) Asian State 38 (13.1) 0,44) 54 (12.1) /414 4,44) ( 42) ( "") Nation 42 ( 6.5) 111 52 ( 5.7) *41 6 ( 42) .44) TYPE OF COMMUNITY Advantaged tirban State 25 ( 9.1) 85 ( 9.2) 10 ( 3.3) 274 ( 4.5)1 282 ( 3.7)1 Nation 23 (14.4) 63 (11.5) 15 ( 9.3) 278 ( 5.8)1 Disadvantaged urban State 39 ( 9.6) 58 ( 9.1) 3 ( 2.0) 229 ( 7.3)1 238 ( 6.9)1 Nation 39 (11.4) 59 (12.1) 2 ( 1.8) 247 ( 7 4)1 253 ( 7.0)1 414 it,* ) Extreme rural State ( 7.4) 90 ( 7.5) 1 ( 1.2) IN11, *IN ) 265 ( 4.0)i Nation 27 (14.9) *64) 85 (14.6) 262 ( 2.8)1 8 ( 3.9) Other State 28 ( 0.1) 06 ( 0.1) 8 ( 2.3) 259 ( 3.8)r 263 ( 2.3) 278 (10.9)1 Nation 19 ( 4.3) 72 ( 5.0) ( 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 vaiue 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). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE MOb I Teachers' Reports on the Use of Mathematical (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1990 NAEP TRIAL STATE ASSESSMENT Al Lust Once a Week Less Than Once a Week Never TOTAL Percentage and ProlIclency Percentage and Proadency Percentage and ProlldineY State 26 ( 3.7) 68 ( 3.9) 7 ( 1A) 254 ( 3.5) 203 ( 2.3) 282 ( 0.9)4 Nation 22 ( 3.7) 09 ( 3.9) 0 ( 2.6) 254 ( 3.2) 203 ( 1.9) 282 ( 5.9)1 PARENTS EDUCATION KS non-graduate State 28 ( 5.4) 69 ( 5.4) 3 ( 1.5) 247 ( 3.8) Nation 25 ( ...m. ( 5.6) .....) 06 ( 243 ( 72) 2.2) 9 ( ( 6.5) 441 KS graduate State 27 ( 249 ( 4.5) 3.1) 68 ( 254 ( 4.7) 2.6) 5 ( 1.6) *el Nation 23 ( 246 ( 4.8) 4.0)1 70 ( 255 ( 5.3) 21) *** ( 2.8) ***) Some college State 27 ( 4.4) 66 ( 4.5) 8 ( 2.2) zao ( 3.4) 285 ( 2.1) Nation 18 ( 4.0) 73 ( 4.3) 9 ( 2.4) 261 ( 4.4)4 289 ( 2.3) Ilt4^1 114-11 College graduate State 22 ( 3.8) 70 ( 4.1) 8 ( 1.5) 267 ( 35) 274 ( 2.5) 297 ( 6.6) Nation 20 ( 3.9) 69 ( 3.7) 11 ( 25) 366 ( 3.5)1 274 ( 22) 297 ` 4.211 GENDER Male State 25 ( 4.0) 69 ( 4.1) 8 ( 1.4) 253 ( 4.3) 264 ( 2.6) 287 ( 8.2)1 Nation 22 ( 4.1) 02 ( 4.1) 8 ( 2.0) 255 ( 4.1) 265 ( 2.1) 287 ( 7.2)1 Female State 26 ( 3.8) 66 ( 4.0) 7 ( 1.6) 255 ( 3.3) 263 ( 2.4) 279 ( Nation 21 ( 3.6) 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 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). I 7 S THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Illinois TABLE Alla I 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 We* About Onoe a W eek or Less TOTAL and Pre lidency 71 ( 4.8) 287 ( 1.8) 82 ( 3.4) 267 ( 1.8) 76 ( 4.8) 274 ( 1.7) 64 ( 3.7) 272 ( 1.9) 57 ( 9.8) 240 ( 5.0)! 56 ( 7.7) 244 ( 4.0) 63 ( 9.0) 243 ( 4.0) 61 ( 6.8) 251 ( 3.1) 78 ( 7.0) ( ) 83 ( 6.9) 284 ( 7.0)1 65 ( 8.0) 287 ( 3.0)1 63 (15.9) 283 ( 7.3)1 73 ( 9.4) 248 ( 5.1)1 68 (10.7) 252 ( 4.7)i 90 ( 7.5) 266 ( 4.0)1 50 (10.6) 268 ( 4.0)1 68 ( 7.9) 267 ( 2.0) 63 ( 3.9) 287 ( 2.3) Percentsse and Prondenay 28 ( 44) 251 ( 3.9) 31 ( 3.1) 254 ( 2.9) 22 ( 4.5) 265 ( 3.4)i 28 ( 32) 264 ( 3.4) 39 ( 9.4) 229 ( 5.9)1 41 ( 7.9) 233 ( 3.9)1 36 ( 9.0) 223 ( 5.8)1 32 ( 53) 240 ( 4.3)1 19 ( 6.7) 10 ( 3.2) 33 ( 7.3) 272 ( 6.3)1 23 ( 5.2) 44, ( 24 ( 9.2) 210 ( 4 0)1 31 (11.1) 243 ( 8.0)1 ( .4) 40 (10.0) 247 ( 7.6)1 29 ( 7.7) 256 ( 3.7)1 31 ( 3.5) 255 ( 3.1) Paradise and Preaciency 3 ( Oda) ( *44) ( 1.8) 260 ( 5.1)1 2( 1.1) .41 8 ( 2.3) 284 ( 5.4)1 4 ( 1.8) .0* ( «4) 2 ( 1.4) 1- 2 ( 0.6) ( 04.) 8 ( 2.3) *** ".) 3 ( 2.1) .44 ( .40) 7 ( 5.1) *4* ( 0-4e. 14 (14.6) ( ".) 4 ; 2.2) ( 0 ( 0.0) 10 ( 7.3) 0.4 ***) 3 ( 1.9) *4.0 6 ( 1.9) 257 ( 5 itp State Nation RACE/ETHNICITY White State Nation Mad( State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation 1 he standard errors of the estimated statistics appear in parentheses It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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 esumate (fewer than 62 studemz). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE Al la I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 101110 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week - About Once a Week or Lass TOTAL and Prafidanay Parosidasa and Pralidenay Pansenlage and Prolkdency State 71 ( 4-6) 20 ( 4A) 3 ( 0.9) 26? ( 1.8) 251 ( 3.9) ( ***) Nation 62 ( 3.4) 31 ( 3.1) ( 1.8) 26? ( 1.8) 254 ( 2.9) 200 ( 5.1)1 PARENTS' EDUCATION NS non-graduate State 75 ( 5.6) 247 ( 3.1) 21 ( 5.1) *iv) 4 ( 2.3) ..**) Nation 67 ( 5.5) 245 ( 3.2) 27 ( 5.2) *4. ( ( 2.1) ( ***) KS graduate State 71 ( 5.8) 26 ( 5A) 3 ( 1.1) 258 ( 2.1) 242 ( 4.0)1 *** ( Nation 61 ( 4.4) 257 ( 2.5) 34' ( 3.7) 250 ( 2.9) ( 1.5) .-619 Some college State 69 ( 5.7) 28 ( 5.6) 3 ( 1.0) 268 ( 2.0) 255 ( 3.7)1 Nation 68 ( 4.2) 26 ( 3.7) 6 ( 1.9) 272 ( 2.7) 258 ( 5.2) College graduate State 73 ( 4.2) 25 ( 4.2) 2 ( 1.0) 278 ( 2.0) 264 ( 4.4) *** f Nation 61 ( 4.0) 281 ( 2.2) 31 ( 3.9) 265 ( 3.1) 8 ( 3.1) ..**) GENDER Male State 70 ( 5.3) 27 ( 5.1) 267 ( 2.2) 2F0 ( 3.9)1 Nation 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2.1) 256 ( 3.6) 261 ( 6.7)1 Female State 73 ( 4.1) 2661 1.8) 25 ( 4.0) 251 ( 4.4) 2 ( 0.9) Nation 65 ( 3.6) 28 ( 3.3) 7 ( 2.2) 266 ( 1.8) 253 ( 2.5) *** ( The standard errors of th: 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 3990 NAEP TRIAL STATE ASSESSMENT 315 Illinois TABLE Al lb I Teachers' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week LOSS than %olds . _ TOTAL Percentage and Proficiency Peroentage and Pradelley Percentage and Proficiency State 47 ( 4.1) 23 ( 2.6) 29 ( 4.2) 253 ( 3.0) 262 ( 4.3) 275 ( 2.8) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.8) 256 ( 2.3) 280 ( 2.3) 274 ( 2.7) RACEJETNICIrf White State 42 ( 4.4) 24 ( 2.8) 34 ( 4.6) 265 ( 2.2) 270 ( 4.2) 260 ( 2.4) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Bieck State 59 ( 8.1) 232 ( 5.4) 26 ( 7.7) 236 ( 5.9)1 15 ( 5.0) .**) Nation 45 ( 7.5) 31 ( 7.6) 23 ( 6.3) 232 ( 3.1)1 243 ( 2.3)1 248 ( 7.0)# Hispanic State 64 ( 6.9) 19 ( 4.2) 18 ( 5.8) 229 ( 4.9)1 It**) HIP Nation 41 ( 7.7) 26 ( 5.3) 33 ( 7.5) 242 ( 3.2)1 244 ( 5.1)1 257 ( 2.3)1 Asian State 45 (12.4) 23 ( 7 2) 32 ( 9.1) fgt. 11,4Hb Nation 37 ( 6.3) 35 ( 9.7) ( 27 (10.4) ( wik.) TYPE OF COMMUNITY Advantaged urban State 52 ( 7.3) 16 ( 5.7) 32 ( 8.7) 272 ( 4.7)1 288 ( 5.5)1 293 ( 8.1)l Nation 59 (13.9) 273 ( 3.4)1 ( OHM ) imm.) Disadvantaged trban State 60 (10.1) 22 ( 6.9) 18 ( 8.4) 225 ( 5.9)1 251 ( 8.7)1 256 ( 4.0)1 Nation 50 (13.9) 22 (11.2) 28 (10.7) 237 ( 2.4)1 258 ( 8.3)1 263 ( 4.1)1 Extreme nral State 35 (11,8) 37 (15.1) 260 ( 4.7); 287 ( 3.9)1 Nation 27 (14.3) ,.) 49 (12.7) 258 ( 6.7)1 24 (10.1) ( Other State 47 ( 6.7) 22 ( 4.3) 31 ( 7.1) 257 ( 2.6)1 280 ( 3.8)1 273 ( 4.6)! Nation 30 ( 4.4) 35 ( 4.3) 36 ( 4.2) 258 ( 3.3) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is wu.hm ± 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. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 316 THE 3990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A 1 lb I Teachers' Reports on the Frequency of (continued) i Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week Abcr.tt Once a Week Less than Weekly MINIMIRS=11==MIM..61111.. gm& and Prolialom per01111111, and Prod/alum Pataantage and Prelidency State 47 ( 4.11 23 ( 2.8) 29 ( 41) 253 ( 3.0) 262 ( 4.3) 275 ( 2.6) Nation 34 ( 16) 33( 3.4) 32 ( 3.6) 256 ( 2.3) 200 ( 2.3) 274 ( 2.7) PARENTS EDUCATION 1411 non-graduate State 4$ ( 236 ( 6.0) 5.2) 25 ( 4.3) ( 021 27 ( 6.8) .44) Nation 35 ( 6.0) 29 ( 6.3) 35( 6.9) 239 ( 3.5) 11** 011.0 250 ( 4.5)1 NS graduate State 54 ( 54) 20 ( 34) 26 ( 5.0) 24? ( 24) 256 ( 4.5)1 264 ( 3.7) Nation 35 ( 5.3) 36 ( 4.5) 30 ( 4.8) 250 ( 3.6) 250 ( 2.7) 263 ( 3.4) Sono college State 47 ( 4.2) 24 ( 3.2) 29 ( 4.5) 258 ( 2.7) 264 ( 3.7) 274 ( 3.0) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 266 ( 4.2) 278 ( 2.6) College graduate State 42 ( 4.3) 25 ( 3.9) 33 ( 4.5) 265 ( 3.1) 272 ( 5.2) 286 ( 3.1) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2.0) GENDER Male State 50 ( 4.4) 22 2.9) 28 ( 4.2) 253 ( 3.2) 265 ( 4.8) 276 ( 2.8) Nation 35 ( 4.4) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 261 ( 2.8) 275 ( 3.2) Female State 45 ( 4.1) 24 ( 3.1) ( 4.3) 254 ( 3.0) 280 ( 4.7) 274 ( 3 3) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It. can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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. 11" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 117 Illinois TABLE Al2 I Students' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Pre Wow Percentage Percentage and and Preiciency Preacitatcy State 27 ( 2.4) 30 ( 2.1) 43 ( 2.8) 256 ( 3.5) 271 ( 1.9) 256 ( 1.9) Nation 28 ( 2.6) 28 ( 1.4) 44 ( 2.9) 256 ( 2.7) 267 ( 2.0) 261 ( 1.6) RACE/ETIINICITY White State 25 ( 2.7) ( 2.7) 41 ( 3.1) 270 ( 2.6) 277 ( 1.9 267 ( 1.6) Nation 27 ( 2.9) 29 ( 1.7 44 ( 3.5) 263 ( 3.1) 272 ( 1.9 270 ( 1.7) Black State 33 ( 4.8) 17 ( 2.5 SO ( 3.0) 227 ( 4.9)1 240 ( 4.3 234 ( 4.3) Nation 28 ( 3.0) 24 ( 3.6 48 ( 4.7) 234 ( 3.0) 245 ( 4.6) 234 ( 3.1) Hispanic State 28 ( 3.8) 23 ( 2.7 49 ( 4.3) 230 ( 4.9) 249 ( 3.4' 232 ( 4.0) Nation 37 ( 52) 22 ( 3.6 41 ( 5.0) 242 ( 3.9) 250 1 3.4) 240 ( 2.8) Asian State 35 ( .3) 23 ( 4.5) .44) ***) Nation 32 ( 4.0) ( .41 40 ( 6.2) TYPE OF COMMUNITY Advantaged urban State 25 ( 5.6) 36 ( 4.7) 36 ( 5.1) 279 ( 3.3)1 239 ( 3.0) 276 ( 3.9)1 Nation 27 (13.9) *44 33 ( 4$) 236 ( 5.4)1 40 (13.4) 279 ( 3.5)1 Disadvantaged urban State 26 ( 4.1) 19 ( 2.6) 55 ( 4.4) 227 ( 5.3)1 249 ( 5.8)1 236 ( 5.5) Nation 31 ( 5.7) 20 ( 2.8) 49 6.3) 245 ( 4.0)1 - ( 6.4)1 245 ( 3.7)1 Extreme rural State 32 ( 7.6) ( 8.7) 37 ( 7.9) 281 ( 9.8)1 271 ( 5.7)1 261 ( 3.7)1 Nation 34 (10.8) 27 ( 3.8) 39 (11.6) 249 ( sa)! 264 ( 3.5)1 256 ( 6.2)1 Other State 24 ( 4.1) 33 ( 3.2) 42 ( 5.0) 262 ( 3.8)1 267 ( 2.5) 259 ( 2.9) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 264 ( 2.1) 262 ( 2.2) The standard errors of the estimated statistics appear in parentheses. 11 can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this esumated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). j ti 118 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A 12 I Students' Reports on the Frequency of Small (continued) 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL 1 STATE ASSESSMENT At Least Once a Week i Less Than Once a Week Never TOTAL pansentage and Praildancy and Prallaioncy Pannodap and "Widow State 27 ( 2.4) 30 ( 2.1) 241.9i 258 ( 3.5) 271 ( 1.9) 25043 Nation 28 ( 2.5) 28 ( 1.4) 44 ( 2A) 25$ ( 23) 297 ( 2.0) 281 ( 1.8) PARENTS' EDUCATION 115 non-grecksate State SI ( 235 ( 4.3) 5.4) 22 ( 3.5) .41 48 ( 241 ( 4.4) 3.0) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4.5) 242 ( 3.4) 244 ( 3.0) 242 ( 2.7) Pin graduate State 23 ( 2.2) 30 ( 3.1) 47 ( 3.4) 245 ( 3.6) 280( 21) 250 ( 2.1) Nation 28 ( 3.0) 28 ( 1.8) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some college State 24 ( 3.5) 30 ( 2.8) 45 ( 3.6 257 ( 4.8) 272 ( 2.7) 259 ( 2.1 Nation 27 ( 3.9) 27 ( 2.4) 46 ( 3.8 265 ( 3.6) 268 ( 3.3) ( College graduate State 30 ( 3.1) 32 ( 2.7) 38 ( 3.3 270 ( 3.8) 282 ( 2.0) 269 ( 2.4 Nation 28 ( 3.0) 28 ( 1.0) 44 ( 3.6) 270 ( 2.7) 278 ( 2.8) 275 ( 2.2) GENDER Male State 28 ( 2.1) 30 ( 2.3) 44 ( 2.8) 254 ( 3$) 272 ( 2.3) 258 ( 2.3) Nation 31 ( 2.9) 28 ( 1.7) 41 ( 2,9) 259 ( 3.3) 268 ( 2.6) 262 ( 1.8) Female State 28 ( 3.2) 28 ( 2.4) 43 ( 3.2) 258 ( 4.8) 269 ( 2,1) 258 ( 2.0) Nation 26 ( 2.4) 27 ( 1.8) 47 ( 3,2) 257 ( 2,$) 268 ( 1.7) 260 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample, Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I rs) a 4.4 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Illinois TABLE A13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ MO NAEP TRIAL STATE ASSESSMENT At Least One. a Week Loss Than Once a Week Never TOTAL and Proficiency 31 ( 22) 235 ( 24) 28 ( 1.8) 268 ( 2.13) Pommies, and Pratidency 31 ( 1.5) 270 ( 1.7) 31 ( 1.2) 266 ( 1.5) Pommisp wd Praildeely 38 257 2.1 2.01 41 2.2 2511 1.8) State Nation RACE/ETHNICITY White State 28 ( 2.5) 35 ( 1.6) 37 ( 2.4) 297 ( 2.3) 276 ( 1.7) 270 ( 1.8) Nation 27 ( 1.9) 33 ( 1.6) 40 ( 2.5) 206 ( 2.6) 275 ( 1.6) 268 ( 1.8) Black State 41 ( 4.7) 17 ( 2.3) 42 ( 4.7) 233 ( 5.5) 240 ( 0.5) 229 ( 2.9) Nation 27 ( 3.3) 27 ( 3.2) 419 ( 4.5) 234 ( 3.7) 248 ( 4.5) 232 ( 2.6) Hispanic State 34 ( 3.1) 23 ( 2.4) 43 ( 2.9) 232 ( 5.2) 247 ( 3.5) 232 ( 4.0) Nation 3$ ( 4.2) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) Asian State 24 ( 4.4) , 4.**) 31 ( 5.0) 11141 *41 46 ( SA) ( Nation 32 ( 3.7) *** ( .44) 30 ( 32) ( *Al 38 ( 4.7) TYPE OF COMMUNITY Advantaged urban State 28 ( 5.8) 34 ( 3.6) 39 ( 5.3) 276 ( 4.4)1 287 ( 25) 280 ( 4.8)1 Nation 36 (10.3) 33 ( 4.8) 32 (11.1) 278 ( 6.1)1 284 ( 3.2)1 281 ( 5.9)1 Disadvantaged urban State 34 ( 3.4) 22 ( 1.4) 44 ( 3.5) 235 ( 6.5) 242 ( 4,7) 234 ( 5.6) Nation 35 ( 6.6) 19 ( 2.1) 46 ( 64) 249 ( 5.3)1 256 ( 5.7)1 246 ( 4.8)1 Extreme oval State 34 ( 7.0) 40 ( 3.0) 28(83) 255 ( 5.7)1 272 ( 33)1 205 ( 2.6)1 Nation 21 ( 3.1) 37 ( 4.7) 43 ( 5.0) 202 ( 4.7)1 251 ( 5.2)1 Other State 29 ( 3.9) 31 ( 2.6) 39 ( 3.7) 258 ( 3.8) 270 ( 2.5) 260 ( 2.3) 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 ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature DJ the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a rehable estimate (fewer than 0 students). 120 L.1 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A 13 I Students' Reports on the Use of Mathematics (ccetinued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 /MEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week , Never TOTAL Percentage and PreAciency Percentage and Proedency Percentage and Preadeng State 31 ( 2.2) 31 ; 1.5) 30 ( 2.1) 255 ( 2.5) 270 ( 1.7) 257 ( 2.0) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.8) 269 ( 1.5) 250 ( 1.8) PARENTS' EDUCATION 14S non-graduate State 27 ( 2.9) +.) 25 (( 2.9) 47 ( 235 ( 3.6) 4.3) Nation 27 ( 4.2) 20 ( 2.7) 47 ( 5.0) 227 ( 3-0) 253 ( 3.5) 240 ( 2.3) NS graduate State 31 ( 3.1) 32 ( 2.8) 37 ( 2.8) 246 ( 3.1) 259 ( 2.4) 250 ( 2.0) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some college State 26 ( 2.7) 35 ( 2.6) 39 ( 3.0) 256 ( 3.3) 270 ( 2.0) 281 ( 2.7) Nation 29 ( 2.8) 36 ( 2.3) 35 ( 2.8) 281 ( 3.5) 274 ( 2.2) 283 ( 2.1) College graduate State 32 ( 2.4) 32 ( 2.2) 36 ( 2.5) 265 ( 3.6) 282 ( 2.1) 273 ( 2.3) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.6) 289 ( 3.0) 27$ ( 2.0) 275 ( 2.0) GENDER Male State 33 ( 2.5) 31 ( 1.9) 36 ( 23) 254 ( 3.0) 272 ( 1.9) 257 ( 2.4) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 28 ( 2.2) 31 ( 1.8) 41 ( 2.5) 256 ( 2.7) 268 ( 2.0) 2513 ( 2.3) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.8) 257 ( 3.0) 268 ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *" Sample si2e is insufficient to permit a reliable estimate (fewer than 62 students). " ' THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Illinois TABLE A 14 I Students' Reports on the Frequency of 1 Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Lass TOTAL Percentage aW PireiMentor Parentage and Preliciency Percentage and Prelldency State 71 ( 2.5) 16 ( 1.3) 13 ( 1.8) ( 1.7) 248 ( 3.0) 246 ( 3.7) Nation 74 ( 1.9) 14 ( 0.0) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 4.5) RACEIETHNICITY White State 75 ( 2.?) 14 ( 1.5) 11 ( 2.0) ( 1.4) 263 ( 2.7) 259 ( 3.1) Nation 76 ( 2.5) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 2.2) 252 ( 5.1)1 Mack State 66 ( 4.8) 20 ( 2.5) 14 ( 3.2) 236 ( 4.2) 227 ( 5.2) 223 ( 3.9)1 Nation Ti f 2.8) 15 ( 1.7) 14 ( 3.2) 240 ( 2.9) 232 ( 3.1) 223 ( 8.1)! Hispanic State sa ( 4.4) 25 ( 3.1) 20 ( 3.4) 243 ( 2.8) 224 ( 5.5) 228 ( 6.7)1 Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) Asian State 68 ( 63) 17 ( 1". ( 4.5) -.) Nation 79 289 ( 4.9) ( 5.0)1 13 ( p* ( 3.4) Mr* ( TYPE OF COMMUNITY Advantaged urtan State 74 285 ( 4.9) ( 2,9) 15 ( 270 ( 3.2) 4.3)1 11 ( 4*. 2.1) Nation 73 286 (11.1) ( 4.6)1 13 ( 1.7) 14 (10.4) .44 1,441 Difseaventaged urban State 63 ( 5.7) 19 ( 2.8) 18 ( 4.1) 244 ( 4.4) 223 ( 5.4)1 221 ( 5.5)1 Nation 69 ( 2.8) 15 ( 2.5) 15 ( 2.2) 253 ( 3,7)1 243 ( 4.4)t 235 ( 81,5)1 Extrema rural State 79 207 ( 5.6) ( 3.2)i 11 ( 3.7) 9 ( it** 3.9) Nation 68 (11.3) ( 8.2) 263 ( 4.2)1 RIM ( 4.1 17 Otter State 71 ( 4,6) 16 ( 2.3) 12 ( 3.7) 267 ( 2.2) 253 ( 3.9)1 250 ( 4.4) Nation 75 ( 2.2) 14 ( 1.0) 10 ( 1.9) 267 ( 1.6) 262 ( 2.6) 239 ( 4.3)i The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insuffkient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE AI4 I Students' Reports on the Frequency of (continued) i Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Lass TOTAL Pimento's and Pretielency Percentage and Madsen Percentage and PreAkkocy State 71 ( 2.5) 10 ( 1.3) 13 ( 1.8) 260 ( 1.7) 2411 ( 3.0) 245 ( 3.7) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 44) PARENTS' EDUCATION NS non-graduate State 66 ( 4.3) 19 ( 3.2) 15 ( 2.8) 246 ( 2.8) 04* ( ***) 1144 OM) Nation 84 ( SA) 245 ( 2.3) 18 ( .4* ( 2.0) 044 ( 441 KS graduate State 8111 ( 3.4) 17 ( 1.7) 15 ( 2.6) 257 ( 1.9) 239 ( 3.2) 241 ( 4.7)! Nation 71 ( 3.6) 18 ( 1.8) 13 ( 2.8) 258 ( 1.6) 249 ( 3.2) 239 ( 3.4)! Some college State 71 ( 3.7) 15 ( 2.2) 14 ( 2.7) 26$ ( 1.8) 252 ( 4.4) 250 ( 44)1 Nation 80 ( 2.0) 9 ( 1.7) 270 ( 1.9) ( College graduate State 76 ( 2.2) 13 ( 1.3) 10 ( 15) 277 ( 2.1) 260 ( 3.8) 260 ( 42) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 280 ( 2.8) 257 ( 6.4)! GENDER Maio State 71 ( 2.9) 10 ( 1.4) 13 ( 2.1) 260 ( 1.9) 249 ( 4.0) 245 ( 3.9) Nation 72 ( 2.4) 16 ( 1.2) 12 ( 2.1) 268 ( 1.6) 252 ( 2.5) 242 ( 6.1) Female State 72 ( 2.5) 16( 1.5) 12 ( 1.8) 265 ( 1.8) 2445 ( 3.3) 248 ( 4.6) Nation 76 ( 1.8) 13 ( 1.0) 11 ( 1.6) 265 ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students), 1 2:3 THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Illinois TABLE A15 I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Several Times I About Once a Week a Week Law Than Weekly TOTAL Porosntaga and Pritiaioncy ParsaNdirs and Prwackingi Portaidage and I/Widow State 40 ( 32) 22 37 256 ( 2.1) 257 2A 255 Nation 38 ( 2.4) 25 1.2 $T 2.5 2:0 ( 22) 261 ( 1.4 272 ( 1.9) RACERTHNICITY White State 38 ( 3.5) 22 ( 1.7) 40 ( 3.5) 266 ( 2.0) 269 ( 2.0) 278 ( 1.9) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 262 ( 2.5) 209 ( 1.5) 277 ( 2.0) Black State 45 ( 6.7) 20( 2.5) 2$ ( 6.4) 236 ( 5.4) 232 ( 3.6) 229 ( 4.3)1 Nation 46 ( 32) 32 ( 2.7) 20 ( 3.1) 232 ( 4.3) 241 ( 2.9) 241 ( 4.4) Hispanic State 44 ( 32) 23 ( 2.5) 33 ( 3.2) 234 ( 4.9) 230 ( 3.6) 241 ( 4.1) Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 238 ( 3.9) 247 ( 3.3) 248 ( 3.3) Asian State 42 ( 6.2) 17 ( 3.0) 1HM Nation 32 ( 5.1) 17 ( 3.5) 51 ( .4* ( 5.9) ( TYPE Of COMMUNITY Advantaged urban State 44 ( 5.9) 20 ( 3.0) 36 ( 7.2) - 272 ( 2.8)1 278 ( 4,9)1 298 ( 4.4)1 Nation 50 ( 9.0) 19 ( 42) 31 ( 9.3) 271 ( 3.3)1 299 ( 5.3)1 Disadvantaged urban State 41 ( 5.8) 25 ( 1.9) 34 ( 4.6) 234 ( 8.8)1 236 ( 4.6) 238 ( 6.3) Nation 37 ( 5.8) 23 ( 3.6) 41 ( 6.7) 240 ( 4,8)1 253 ( 4.1)1 255 ( 42)1 Extreme nye! State 29 ( 8.1) 25 ( 4.2) 47 ( 92) 281 ( 8.1)1 260 ( 6.0)1 268 ( 4.2)1 Nation 42 (10.1) 30 ( 4A) 2$ ( 7.5) 249 ( 4.0)1 256 ( 3.4)1 267 ( 7.3)1 Other State 43 ( 5.1) 22 ( 2.6) 34 ( 42) 257 ( 2.7) 260 ( 2.5) 271 ( 3.3) Nation 34 ( 2.9) 26 ( 1.2) 38 ( 2.9) 252 ( 3.0) 261 ( 2.1) 272 ( 111) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "s Sample sax is insufficient to permit a reliable estimate (fewer than 62 students). 124 1 I. THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A 15 I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRW.. STATE ASSESSMENT At Least Savarsi Ulnas a Weak About Ones a Weak - Lass Than Weakly you* State Nation PARENTS' EDUCATION Paroantage and PredIciancy 40 ( SD) 256 ( 2.1) 38 ( 2.4) 2SI ( 2.2) Paroantaga and Prendency 22 ( 1.3) 257 ( 2.0) 25 ( 1.2) 261 (14) Parailfte and Preifelancy 37 ( 3.0) 268 ( 2.7) 37 ( 20) 27 ( 1.9) NS non-graduate State 43 ( 241 ( 3.9) 4.6) 22 (( 3.4) .41 35 ( 244 ( 3.8) 4.5) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 11) 243 ( 2.7) 253 ( 2.8) NS gracksat. State 42 ( 3.9) 22 ( 1.9) 36 ( 3.9) 248 ( 2.1) 248 ( 2.6) 258 ( 2.8) Nation 40 ( 32) 29 ( 2.2) 32 ( 3.6) 247 ( 2.7) 258 ( 2.5) 262 ( 22) Soma cottage State 40 ( 3.8) 24 ( 22) 36 ( 3.6) 200 ( 2.4) 261 ( 3.5) 267 ( 2.6) Nation 34 ( 3.4) 26 ( 2.2) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) Canso* waduate State 38 ( 32) 22 ( 1.41 40 ( 3.5) 267 ( 2.4) 267 ( 2.9) 283 ( 3.5) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 2/3 ( 2.5) 285 ( 2.3) GENDER Mats State 42 ( 3.2) 23 ( 1.6) 35 ( 2.4) 255 ( 2.6) 256 ( 2.3) 270 ( 2.7) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 263 ( 2.3) 274 ( 2.4) Fenster State 39 ( 3.1) 21 ( 1.5) 40 ( 3.3) 257 ( 2.1) 257 ( 2.5) 265 ( 3.1) Nation 37 ( 2.5) 25 ( 1$) 38 ( 2.6) 253 ( 2.1) 269 ( 1.8) 269 ( 2.2) The standard eri.ors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 125 Illinois TABLE Alit Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Own a Calculator Teacher Explains Calculator Use Yes No Yes No a. TOTAL Pen:enter and Proficiency Percentage and Pro/Wool:zit Percentage and Proficiency Percedags and Pre. Idiom State ae ( 0.3) 2 ( 0.3) 89 ( 2.5) 41 ( 2.5) 281 ( 1.7) 234 ( 44) 256 ( 1.9) 284 ( 2.1) Nation 97 ( 0.4) 3 ( 0.4) 49 ( 2.3) 51 ( 2$) 263 ( 1.3) 234 ( 3.8) 258 ( 1.7) 26(1 ( 14) RACE/ETHNICITY White State ( 0.3) 272 ( 1.4) 2 ( 0.3) es* ( 58 ( 3.0) 270 ( 1.8) 44 ( 3.0) 272 ( 1.8) Nation 98 (' 0.3) 2 ( 0.3) 46 ( 2.6) 54 ( 2.8) 270 ( 1.5) 266 ( 1.6) 273 ( 1.8) Black State 97 ( 1.0) 3 ( 1.0) 66 ( 4.5) 34 ( 4.5) .233 ( 3.8) 233 ( 44) 233 ( 3.3) Nation 93 ( 1.5) 237 ( 2.8) ( 1.5) ( *1 53 ( 4.9) 235 ( 3.8) 47 ( 4.9) 239 ( 2.7) His Panic State 95 ( 0.9) $ ( 0.9) 69 ( 3.1) 31 ( 3.1) 237 ( 3.1) *114 { 41 232 ( 3.3) 242 ( 4.8) Nation 92 ( 12) 8 ( 1.2) 63 ( 4.3) 37 ( 4,3) 245 ( 2.7) 243 ( 3.4) 245 ( 2.9) Asian State 98 ( 2.9) 280 ( 4.0) *** ( ***) 39 ( 8.4) ( .41 Nation 99 ( 0.9) 52 ( 4.8) 48 ( 4.8) 282 ( 5.3)1 ( "") TYPE OF COMMUNITY Advantaged urban State 100 ( 0.3) 0 ( 0.3) 70 ( 4.5) 30 ( 4.5) 281 ( 2.9) ( 279 ( 2.9) 286 ( 4.4)1 Nation 99 ( 1.0) 1 ( 1.0) 45 (12.2) 55 (12.2) 281 ( 3.8)1 ( ***) 276 ( 2.5)1 285 ( 64)) Disadvantaged urban State 94 ( 1.4) 237 ( 4.9) 6 ( 1.4) *-.4) 66 ( 3.9) 233 ( 5.1) 34 ( 3.9) 241 ( 6.0)1 Nation 94 ( 1.2) 8 (1.2) 53 ( 7$) 47 ( 7.5) 250 ( 15)1 111.4. 441 247 ( 4.1)1 251 ( 3.6)1 Extreme rural State 98 ( 0.8) 2 ( 0.8) 56 (11.1) 44 (11.1) 264 ( 3.7)1 IV* ) 259 ( 4,4)1 270 ( 2.4)1 Nation 96 ( 1.3) 4 ( 1.3) 42 ( 8.7) 58 ( L7) 257 ( 3.9)1 ( 251 ( 4.8)1 261 ( 4.4)1 Other State 98 ( 0.4) 2 ( 04) 53 ( 3.7) 47 ( 3.7) 263 ( 2.1) 260 ( 2.6) 266 ( 2.6) Nation 97 ( 0.5) 3 ( 0.5) 50 ( 2.7) 50 ( 2.7) 263 ( 1.7) 233 ( 5.4) 258 ( 2.1) 206 ( 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 enure population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample Joes not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I r`,; 126 THE 19911 NAEP TRIAL STATE ASSESSMENT Illinois TABLE Al8 (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 M.... 1000 NAEP TRIAL STATE ASSESSMENT 41 Teacher Explains Calcuator Us Own a Calculator l* as _ Y No - I Yes No TOTAL Percentage and Proficiency Percentap and Pro liciency percompito and Pro fidency Percentage and Proficiency State 98 ( 0.3) 2 ( 0.3) 59 ( 24) 41 ( 2.5) 261 ( 1.7) 234 ( 4.5) 258 ( 1.9) 284 ( 2.1) Nation 97 ( 0.4) 3 ( OA) 49 ( 2.3) 51 ( 2.3) 263 ( 1.3) 234 ( 3.8) 258 ( 1.7) 200 ( 1.5) PARENTS EDUCATION NS non-graduate State 94 ( 1.6) 6( 16) 112 ( 4.2) 38 ( 4.2) 243 ( 24) Ihrft 242 ( 3.3) 243 ( 4.0) Nation 92 ( 1.6) 243 ( 2.0) ( 1.6) e) 53 ( 4.6) 242 ( 2.9) 47 ( 44) 243 ( 2,5) MS graduate State 97 ( 0.7) 3 ( 0.7) 58 ( 2.9) 42 ( 2.9) 252 ( 1.6) 248 ( 2.1) 257 ( 2.1) Nation 97 ( 0.6) 3 ( 0.0) 54 ( 3.0) 46 ( 3.0) 255 ( 14) rrr Fr* ) 252 ( 1A) 258 ( 2.0) Some college State 99 ( 0.4) 262 ( 1.6) 1 0.4) «to 57 ( 32) 261 ( 1.8) 43 ( 32) 265 ( 2.8) Nation 96 ( 0.9) 268 ( 1.8) 4 ( 0.9) 04 .41 48 ( 32) 265 ( 2.4) 52 ( 32) 268 ( 22) Cottage graduate state 99 ( 0.3) 1 ( 0.3) 60 ( 29) 40 ( 2.9) 274 ( 2.1) 271 ( 2.5) 277 ( 2.6) Nation 99 ( 0.2) ( 0.2) 46 ( 2.6) 54 ( 2.6) 275 ( 1,6) 268 ( 2.2) 280 ( 1.9) GENDER Male State 98 ( 0.5) 261 ( 1.9) 2 ( 0.5) ***) GO ( 2.4) 258 ( 2.3) 40 j 2 4) 264 ( 2.4) Nation 97 ( 05) 254 ( 1.7) 3 ( 0.5) .144) 51 ( 2.6) 258 ( 2.1) 46 ( 2.6) 269 ( 2.1) Female State 98 ( 0.5) 261 ( 1.7) 2 ( 04) *se 58 ( 2.9) 258 ( 1.9) 42 ( 2.9) 264 ( 22) Nation 97 ( 04) 3 ( OS) 47 ( 2.5) ( 2.5) 282 ( 1.3) ( 758 ( 1.7) 263 ( 1.6) The standard errors of the estimated statistics appear m parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 127 Illinois ,..,IM?//M.Mgm.OwMVM..iMMM,IM/Fn TABLE A 19 I Students' Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT Problems in Class Doing Problems at Horns Taking Quizzes or Tests Mrnost Always Never Almost Always Never Almost Always Never TOTAL Percemay and Prolicisnay 49 C 1.6) 253 ( 2.1) 4$ ( 1.5) 254 ( 1.5) State Nation RACE/ETHNICITY Mtn. State 47 ( 1.9) 266 ( 1.9) Nation 415 ( 1.7) 262 ( 1.7) Slack State 545 ( 3.1) 225 ( 3.7) Nation 57 ( 3.2) 232 ( 2.4) Hispanic State 53 ( 2.9) 229 ( 3.8) Nation 51 ( 2.9) 239 ( 2.8) Asian State 38 ( 54) ( 041 Nation 26 ( 8.3) Ire* ***) TYPE OF COMMUNITY AdvantAgad urban State 58 ( 34) 277 ( 3.0) Nation 51 ( 5.4) 270 ( 4.7)1 Disadvantaged urban State 49 ( 3.4) 227 ( 52) Natior, 52 ( 3.1) 241 ( 3.8)1 Extreme nral State 43 ( 4.1) 255 ( 4.8)1 Nation 48 ( 7.4) 248 ( 4.3)1 Other State 45 ( 2.9) 254 ( 3.2) Nation 48 ( 1.9) 254 ( 2.1) Potently Potenne Percentap Parcents. Perootare and and and and and Prendon Frandsen Prandancer Prone:10w Preldsney 19 1.7 35 ( 1.9) 15 ( 1.3 24 1.4 29 269 12 IV 2.3) 263 ( 2.3 254 2 271 1.7 23 1.9 30 1.3) 19 ( 0.0 27 1.4 30 2.0 272 1.4 261 1.8) 263 ( 1.0 253 2.4 274 1.3) 20 ( 2.0) 275 ( 2.0) 24 ( 2.2) 278 ( 1.3) 17 ( 3.1) 251 1 3.7) 201 3.9) 249 ( 4.0) 15 ( 2.7) 0.1 18 ( 3.5) 252 ( 3.3)1 24 1 6.4) ( ***) 29 ( 5.8) 7 ( 1.8) 23 (10.7) «hi ( «HI 18 ( 3.2) 256 ( 5.4)1 22 ( 4,5) 259 ( 5.4)1 20 ( 4.0) 273 ( 4.4)1 29 ( 6.5) 288 ( 6.1y 24 ( 2.8) 288 ( 2.1) 22 ( 2.0) 272 ( 16) 33 ( 2.5) 274 ( 1.8) 31 ( 1.5) 270 ( 1.7) 40 ( 3.4) 232 ( 4.7) 31 ( 2.9) 233 ( 3.3) 36 ( 2.4) 234 ( 2.8) 26 ( 3,2) 238 ( 4.8) 41 ( 5.2) ees) 30 ( 8.3) 47 ( 3.9) 280 ( 2.8) 32 ( 6.1) 274 ( 4.9)1 32 ( 2.7) 234 ( 5.2) 30 ( 3.3) 246 ( 5.2)1 22 ( 4.8) 262 ( 3.6)1 20 ( 2.5) ," ( *gm) 34 ( 3.1) 264 ( 3.3) 32 ( 1.7) 263 ( 2.3) 16 ( 1.7) 272 ( 2.3) 18 ( 1.2) 209 ( 2.3) 12 ( 2.0) 11111i frikl 18 ( 1.9) 248 ( 5.5) 15 ( 2.0) INF* ( ***) 21 ( 2.1) 244 ( 3,1) 18 ( 4.7) ( 23 ( 4.4) 7 ( 1.4) 15 ( 2.4) gm. ( Ink.) 18 ( 1.8) 244 ( 8.8)1 24 ( 2.3) 254 ( 4.8)1 ( del 23 ( 3.9) 263 ( 4.4)1 17 ( 2.0) 285 ( 2.7) 18 ( 1.1) 283 ( 2.8) 21 ( 1.7) 209 ( 3.0) 25( 1.6) 263 ( 2.6) 35 ( 22) 226 ( 36) 38 ( 3.3) 230 ( 3.6) 24 ( 2.0) 231 ( 4.8) 26 ( 2.7) 237 ( 3.2) 17 ( 3.8) ***) 23 ( 5.8) 27 ( 3.9) 286 ( 3.8) 31 ( 3.8) 281 ( 7.6)1 27 ( 2.8) 225 ( 5.7) 27 ( 2.9) 240 ( 4.9)1 23 ( 5.0) 253 ( 5.7)1 24 ( 8.6) 21 ( 2.1) 255 ( 4.4) 27 ( 1.8) 253 ( 2.7) 12 ( 2.2) 277 ( 1.(1) 32 ( 2.3) 2701 1.2) 22 ( 2.3) 249 ( 4.4) 24 ( 3.1) 251 ( 4.1) 22 ( 2.7) 245 ( 3.8) 22 ( 3.1) 25$ ( 4.2) 25 ( 5.8) 48 ( 8.4) vieft ( *41 17 ( 3.6) 292 ( 4.3)1 28 ( 9.8) 265 ( 4.2)! 24 ( 3.5) 255 ( 52)) 27 ( 4,8) 263 ( 5,0)) 35 ( 5.1) 275 ( 4.6)1 37 ( 8.3) 270 ( 4.0)1 ( 3.0) 270 ( 16) 29 ( 2.1) 276 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent ctrtainty 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. 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). 128 .1 t LJ THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A19 I Students' Reports on the Use of a Calculator (mtinued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1. 1990 NAEP TRIAL STATE ASSESSMENT waildn9CPr°114m$ in lass . Doing Problems at Norm 4 Taking Quizzes or Tests - Almost Always Never Almost I Always ... Never Almost Am ays Never , TOTAL State Nation PARENTS EDUCATtON 143 nongraduate State Nation 148 graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation Promisee Parosnlaes Paromtnee Partatage Parosniser Parconiaes owl and and and and and Prelloisney Pnoildricy Prolicimee Psaildency Prolloisiny Praibienry 41) 1.6 19 1.7 35 ( 1.3 24 1.4 29 1. 253 2.1 269 1.7 261 2.3 263 2.3 254 2.0 271 1.7 48 1.5 23 1.9 30 1.3 10 0.9 27 IA 30 2.0 254 1.5 272 IA 261 1.8) 203 ( 1.41 253 2.4 274 1.3) 53 ( 3.6) 17 ( 3.0) 30 ( 2.9) 18 1 2.6) 23 ( 2.9) 25 2.0) 237 4.1) ' ( ***) 243 SA) 011* 44It eln 54 3.3) 12 ( 3.8) 26 3.1) 22 ( 2.61 32 1 3.8) 24 .34..21 240 2.3) " ( ") 244 3.8) 244 ( 4.2 Wif 2.3) 251 4.8 51 ( 2.1) 19 ( 2.2) 32 ( 2.3) 18 ( 25 ( 1.3) 29 ( 2.1) 245 ( 2.3) 2$3 ( 2.8) 251 ( 2.3) 257 ( 3.5 239 ( 2.9) 2.4) 52 ( 2.5) 20 ( 2.4) 29 ( 1.9) 18 ( 1.5 20 ( 14) 27 2.2) 249 ( 1.4) 265 ( 2.7) 250 ( 24) 250 ( 2.4) 24$ ( 2.8) 285 2.0) 45 ( 2.5) 22 ( 2.5) 31 ( 21) 19 ( 2.1) 23 ( 1.11) 32 2.8) 255 ( 2.8) 269 ( 2.3) 263 ( 2.6) 267 ( 3.3) 257 ( 4.0) 270 2.3) 46 ( 2.8) 28 ( 2.8) 28 ( 2.0) 20 ( 1.9) 28 ( 2.4) 33 2.5) 258 ( 2.1) 272 ( 2.5) 267 ( 3.0) 268 ( 2.2) 255 ( 3.0) 275 ( 2.0) 48 ( 24) 17 ( 2.0) 40 ( 2.7) 12 ( 1.2) 23 ( 2.1) 29 ( 2.3) 208 ( 2.7) 280 ( 2.4) 273 ( 34) 276 ( 2.7) 271 ( 3.8) 281 ( 2.8) 48 ( 1.9) 25 ( 2.4) 33 ( 2.0) 10 ( 1.4) 26 ( 1.8) 33 ( 2.7) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 268 ( 2.6) 285 ( 2.0) 52 ( 1.7) 17 ( 1.7) 36 ( 2.2) 16 ( 1.6 23 1.8) 21 ; 1.1) 255 ( 2.3) 269 ( 2.4) 263 ( 2.8) 263 ( 2.9 253 3.3) 27.' 2.0) 50 ( 1.7) 20 ( 2.0) 29 ( 1.8) 19 ( 1.3 27 1.5) 2. 4 2.1) 255 ( 1.9) 275 ( 2.2) 264 ( 2.8) 263 ( 2.5 250 ( 3.0) 271 ( 1.9) 45 ( 2.1) 20 ( 2.0) 33 ( 2.2) 15 ( 1S) 24 ( 1.8) 31 ( 2.3 252 ( 2.3) 268 ( 1.8) 259 ( 2.4) 264 ( 2.8) 254 ( 2.8) 289 ( 2.1 48 ( 2.0) 26 ( 2.1) 32 ( 1.6) 18 ( 1.2) 27 ( 1.8) 33 ( 2.1 252 ( 1.7) 269 ( 1.8) 259 ( 1.7) 263 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. '0** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL. STATE ASSESSMENT 129 Illinois TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL "Calculator-Use" "Cakitiater-Use" STATE ASSESSMENT High Group Other Group TOTAL Poundage and Pro Wow Perseatage and Prolidanw State 47 ( 1.5) 53 ( 1.5) 268 ( 1.8) 252 ( 2.1) Nation 42 ( 13) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACE/ETHNICITY Whit State 50 ( 1.5) 50 ( 1.5) 277 ( 1.6) 264 ( 1.6) Nation 44 ( 1.4) 56 ( 1.4) 277 ( 1.7) 263 ( 1.7) Mach State 43 ( 5.0) 57 ( 5.0) 239 ( 3.5) 228 ( 3.5) Nation 37 ( 3.4) 63 ( 3.4) 248 ( 3.9) 231 ( 3.0) Hispanic State 35 ( 65 ( 3.2) 245 ( 43) 229 ( 4.1) Nation 36 ( 42) 64 ( 4.2) 254 ( 4.8) 235 ( 3.0) Asian State 54 ( 7.9) 46 ( *fie 7.9) Nation 50 ( 4.8) ( "4) TYPE OF COMMUNITY Advantaged urban State 58 ( 2.6) 42 ( 2.6) 285 ( 3.6) 275 ( 2.4) Nation 50 ( 3.8) 50 ( 3.8) 288 ( 4.9)1 275 ( 4.4)? Disadvantaged urban State 41 ( 3.3) 59 ( 3.3) 243 ( 4.1) 229 ( 5.5) Nation 38 ( 42) 62 ( 4.2) 282 ( 5.6)1 244 1 3.9)1 Extreme rural State 44 ( 2.1) 56 ( 2.1) 270 ( 3.7)1 257 ( 4.0)1 Nation 39 ( 5.6) 61 ( 5.6) 269 1 4.4)1 248 4.3)1 Other State 46 ( 1.6) 52 ( 1.6) 267 ( 2.8) 257 ( 2.0) Nation 42 ( 1.4) 58 ( 14) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable esumate (fewer than 62 students). 4 e CIF 130 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT IGO "Calculator-Use" Grow Other "Calculator-Use" Grow TOTAL Pirs Wan* iserednidis and Prondency State 47 ( 1.5) 53 15) 26$ ( 14) 252 2.1) Nation 42 ( 1.3) 58 (1.3) 272 ( 1.6) 255 ( 1.5) PARENTS' EDUCATION noniraduate State 37 1. 34) ( 34) 24$ ( 4.1) 239 ( 3.8) Nation 34(3.3) 68 ( 3.3) 24$ ( 44) 242 ( 2.4) HS graduat State 44 ( 2.5) 58 ( 25) 258 ( 22) 245 ( 2.8) Nation 40 ( 22) 80 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some college State 49 ( 2.8) 51 ( 2.8) 267 ( 2.9) 257 ( 22) Nation 48 ( 2.2) 52 ( 22) 277 ( 2.8) 258 ( 2.6) College graduat State 52 ( 2.4) 48 ( 2.4) 280 ( 2.4) 264 ( 2.6) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 288 ( 1.9) GENDER Male State 44 ( 1.8) 56 ( 1.8) 267 ( 2.5) 253 ( 2.5) Nation 39 ( 2.0) 81 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 50 ( 2.0) 50 ( 2.0) 268 ( 4.8) 252 ( 2.3) Nation 45 ( 1.8) SS ( 1.8) 269 ( 1.7) 2S4 ( 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 1990 NAEP TRIAL STATE ASSESSMENT 131 noLs TABLE A24 I Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Zero to Two Typos Four Typos TOTAL peromtate /Ad Pro leiwwy Parelatago and Preildency pareetaga and Prellekiney State 16 ( 14 ) 31 ( 1.1) 51 ( 1.4) 243 ( 2A) 256 ( 1.6) 2e4 ( 1.7) Nation 21 ( 1.0) 30 ( 1.0) 415 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) RACE/ETHNiCITY *Me State 13 ( 1.0) 30 ( 1.4) 56 ( 1.6) 257 ( 2.3) 269 ( 14) 278 ( 1.6) Nation 10 ( 1.1) 29 ( 1.3) 56 ( 1.5) 251 ( 2.2) 268 ( 14) 276 ( 1.7) Black Skate 20 ( 2.8) 36 ( 1.9) 44 ( 3.5) 219 ( 3.7) 231 ( 11.6) 240 ( 4.9) Nation 31 ( 1.9) 30 ( 2.2) 33 ( 2.4) 232 ( 3.2) 233 ( 3.9) 245 ( 3.3) Hispanic State 39 ( 4.4) 31 ( 24) 31 ( 3.3) 227 ( 4.4)1 230 ( 3.6) 2413 ( 3.7) Nation 44 ( 3.0) 30 ( 2.4) 26 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) Asian State ( *el 33 ( 4111,1 5.8) *IN ) 44 ( 8.8% ***/ Nation 28 ( 6.0) ( «41 33 ( 5.8) 38 *** ( 4.2) ***) TYPE Of COMMUNITY Advantaged tsban State 12 ( 1.6) 25 ( 2.7) 134 ( 3.6) 271 ( 5.0)1 277 ( 3.1)1 285 ( 2.9) Nation 13 ( *4* ( 3.8) 28 ( 1Htit 2.1) ) 61 287 ( 4.9) ( 3.6)1 Disadvantaged urban State 33 ( 4.5) 34 ( 2.0) 33 ( 3.6) 223 ( 4.8)1 238 ( 5.1) 246 ( 5.6) Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.6) 243 ( 2.9)1 247 ( 3.7)1 257 ( 4.9)1 Extrem nral State 14 ( 2.8) 30 ( 4.0) 56 ( 4.1) 260 ( 5.2)1 270 ( 3.3)1 Nation 17 ( 4.9) 33 ( 3.2) 50 ( 5.1) 253 ( 4.3)I 263 ( 5.6)1 Other State 14 ( 1.8) 34 ( 1.6) 53 ( 22) 251 ( 3.1) 261 ( 2.7) 267 ( 2.1) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 1.5) 244 ( 2.6) 256 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 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). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A24 I Students' Reports OD Types of Reading ("mtinued) Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1900 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Four Types _ . 10TAL Percentage and Proficiency Percentage and Proliciatcy Percentage and Proficiency State 18 ( 1.4) 31 ( 1.1) 51 ( 1.4) 243 ( 2.8) 258 ( 1.8) 268 ( 1.7) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 2.0) 258 ( 1.7) 272 ( 1.5) *ARENTS EDUCATION 143 non.graduate State 39 ( 230 ( 4.0) 4.2) 33 ( 247 ( 3.6) 3.6) 28 ( 3.3) it** Vi Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 248 ( 3.3) NS graduate State 19 ( 1.7) 37 ( 1.9) 44 ( 1.8) 245 ( 3.3) 249 ( 2.3) 258 ( 2.0) Nation 20 ( 22) 33 ( 1.9) 40 ( 1.7) 246 ( 22) 253 ( 2.7) 280 ( 2.1) Sento college State 15 ( 1.9) 30 ( 1.9) 55 ( 2.4) 249 ( 3.0) 260 ( 2.9) 288 ( 1.9) Nation 17 ( 1.5) 32 ( 1.7) SI ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduat State 10 ( 1.0) 28 ( 1.5) 62 ( 1.9) 256 ( 4.8) 2139 ( 2.4) 278 ( 22) Nation 10 ( 0.8) 28 ( 1.8) 82 ( 2.0) 254 ( 2.8) 269 ( 2.5, 280 ( 1.8) GENDER Male State 18 ( 1.6) 32 ( 1.5) 50 ( 1.9) 242 ( 3.1) 258 ( 2.3) 269 ( 2.2) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Female State 18 ( 1.7) 31 ( 1.1) 51 ( 1.6) 244 ( 3.3) 257 ( 2.2) 268 ( 1.6) Nation 22 ( 1.2) 29 ( 1.4) 49 f 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 Mterest, 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 A. 1SMENT 133 Illinois TABLE A25 I Students' Reports on the Amount of Time Spent i Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT One HOUr or Less Tivo Hours Three Hours POW to Fly* Hours Mx Notre or Mors TOTAL Portontage and Mildew Percentage and Pra Adam Parossitaga anti Proaskattey Poroantaga sad NNW/ Pomades. an. P14181C4411CY State 12 ( 0,6) 23 ( 1.1) 24 ( 0.6) 29 ( 1.2) 14 ( 1.0) 270 ( 2.4) 200 ( 2.3) 265 ( 1.7) 251 ( 1.8) 242 ( 2.0) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.6) 28 ( 1.1) 10 ( 1.0) 269 ( 2.2) 266 ( 1.6) 205 ( 1.7) 200 ( 1.7) 245 ( 1.7) RACE/ETHNICITY White State 12 ( 1.2) 24 ( 1.3) 25 ( 1.1) 29 ( 1.4) 10 ( 1.0) 279 ( 2.5) 278 ( 1.5) 274 ( 1.8) 267 ( 1.8) 257 ( 2.7) Nation 13 ( 1.0) 23 ( 12) 24 ( 1.1) 27 ( 1.4) 12 ( 1.2) 276 ( 2.5) 275 ( 22) 272 ( 1.9) 207 ( 1.7) 253 ( 2.4) Slack State 9 ( 1.3) 18 ( 2.2) 20 ( 2.0) 27 ( 1.5) 27 ( 3.0) 237 ( 7.2) 235 ( 3.9) 231 ( 4.2) 226 ( 3.5) Nation 6 ( 0.8) 13 ( 1.7) 17 ( 2.1) 32 ( 1.6) 32 ( 2.2) 239 ( 7.0) 239 ( 5.0) 239 ( 4.0) 233 ( 2.5) Hispanic State 9 ( 1.9) Vi 22 ( 239 ( 2.1) 4.8) 20 ( 243 ( 2.0) 4.8) 31 ( 236 ( 2.5) 4.0) 17 ( 2.0) .41 Nation 20 ( 2.5) 19 ( 2.1) 31 ( 3.1) 17 ( 1.7) 245 ( 3.2) 242 ( 5.8) 247 ( 3.5) 236 ( 3.6) Asian State 23 ( *** 4.7) 30 ( *1111 ( 5.4) * 27 ( 5.9) 16 ( 4.0) ( *in 4 ( 2.4) Nation 18 ( 5.0) .-04) 24 ( *** 4.2) 1111 22 ( 3.1) 23 ( 4.7) s* ( 13 ( ( 4.0) TYPE OF COMMUNITY Advantaged urban State 18 ( 2.5) 2$ ( 1.9) 25 ( 1.8) 22 ( 1.4) 8 ( 2.1) 292 ( 32)1 285 ( 22) 283 ( 2.8) 274 ( 4.0) ( Nation 18 ( 4,14 1.4) 25 ( 4.3) 21 ( ( 1.8) 30 ( 4.3) *iv ( c ) ( to. ( 2.0) Disadvantaged urban State 10 ( 1.1) 15 ( 1.7) 26 ( 2.3) 30 ( 1.4) 19 ( 2.4) ) 242 ( 8.5)1 244 ( 4.4) 235 ( 4.91 221 ( 3.9) Nation 9 ( 1.2) 17 ( 3.1) 19 ( 2.1) 34 ( 2.4j 20 ( 3.2) bdreme rural 250 ( 4.0)1 255 ( 5.0)t 251 ( 4.7)1 238 ( 44)1 State 8 ( 2.1) 19 ( ( 2.5) *41 20 ( 208 ( 3.5) 4.5)! 30 ( 285 ( 2.0) 3.7)1 17 ( 11V1 4.0) **1 Nation 14 ( 3.3) 11.01 19 ( ( 2.6) 23 ( 2.0) 28 ( 258 ( 2.7) 3.8)1 19 ( 3.8) 04..) Other State 11 ( 1.1) 24 ( 2.0) 23 ( 1.0) 29 ( 22) 12 ( 12) 270 ( 2.7) 266 ( 2.1) 265 2.8) 259 ( 2.8) 251 ( 4.7) Nation 12 ( 1.0) 21 ( 1.0) ( 1.2) 27 ( 1.2) 17 ( 1.4) 268 ( 2.6) 269 ( 2.3) 285 ( 2.1) 259 ( 22) 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. I lilterpret with caution -- the nature of the sample does not allow accurate determinatiln of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Illinois TABLE A25 I Students' Reports on the Amount of Time Spent (ccetinued) i Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19S0 NAEP TRIAL STATE ASSESSMENT One Hour or Less Two Hours Three Nours Four to Five Hours Six Hours or More TOTAL Perosnlage and Proficiency Perstentap and Preach/nay Partway/NI and Mildewy Percentage and Prolktency Percentage and Proficiency State 12 ( 0.8) 23 ( 1.1) 24 ( OA) 29 ( 1.2) 14 ( 1.0) 270 ( 2.41 206 ( 2.3) 295 ( 1.7) 257 ( 1.8) 242 ( 2.8) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 ( 1.1) 18 ( 1.0) 2ea ( 2.2) 268 ( 12) 295 ( 1.7) 260 ( 12) 245 ( 1.7) PARENTS EDUCATION HS non-graduat State 9 ( ( 18) "") 20 ( *44 2.7) *44 ) 22 ( 2.9) 29 ( 240 ( 3.2) 4.3) 21 ( 3.5) oimp ) Nation 12 ( ( 2.2) .41 20 ( 3.1) 21 ( 2.8) .9.01 23 ( 244 ( 2.9) 3.2) 20 ( ( 2.4) *01 HS graduate State 9 ( aim ( 1.2) 19 ( 257 ( 1.4) 2.4) 23 ( 257 ( 1.7) 2.2) 34 ( 249 ( 2.1) 2.7) 15 ( 239 ( 1.2) 3.1) Nation 8 ( 1.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 19 ( 1.8) 249 ( 4.7) 257 ( 2.8) 259 ( 3.2) 253 ( 2$) 248 ( 3.0) Some college State 9 ( 12) 25 ( 2.7) 28 ( 2.2) 28 ( 2.2) 11 ( 13) ( 287 ( 4.2) 287 ( 2.5) 260 ( Nation 25 ( 2.4) 23 ( 2.8) 28 ( 22) 14 ( 1.5) GOT ( *41 275 ( 2.7) 289 ( 3.5) 267 ( 2.5) 242 ( 3.4) College graduate State 16 ( 1.6) 25 ( 1.3) 23 ( 1.2) 25 ( 1.7) 11 ( 1.4) 284 ( 2.6) 277 ( 2S) 275 ( 2.4) 269 ( 2.8) 251 ( 4.0) Nation 17 ( 1.3) 22 ( 1.6) 23 ( 1.1) 25 ( 1.5) 12 ( 1.1) 282 ( 2.6) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 32) GENDER Male State 10 ( 1.0) 21 ( 1.4) 23 ( 1.2) 30 ( 1.6) 16 ( 1.4) 271 ( 3.3) 266 ( 3.0) 264 ( 2.2) 258 ( 2.0) 246 ( 3.3) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 28 ( 1.3) 17 ( 1.5) 269 ( 3.3) 287 ( 2.6) 267 ( 2.2) 262 ( 2.1) 248 ( 2$) Female State 14 ( 1.1) 24 ( 1.2) 24 ( 1.2) 27 ( 1.3) 11 ( 1.0) 270 ( 2.9) 287 ( 2.7) 265 ( 2.2) 256 ( 2.3) 236 ( 2.5) Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 1.6) 15 ( 1.2) 289 ( 2.8) 269 ( 2.2) 264 ( 1.8) 258 ( 1.9) 241 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -± 2 standard errors of the estimate for the sample. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Illinois TABLE A26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1890 NAEP TRIAL STATE ASSESSMENT 1 None One or Two Days Three Days or More TOTAL Percents,* and Proficiency Penantage NW Prolkiancy Percentage and PrOlIciency State 47 ( 1.0) 32 ( 1.0) 21 ( 0.8) 284 ( 11) 261 ( 2.1) 263 ( 2,2) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 285 ( 11) 266 ( 1.5) 250 ( 1.9) RAC4ETNNICITY White State 48 ( 1.0) 33 ( 1.1) 21 ( 1.0) 275 ( 1.7) 271 ( 1.8) 264 ( 1.9) Nation 43 ( 1.2) 34 ( 1.2) 23 ( 1.2) 273 ( 1.8) 272 ( 1.7) 268 ( 2.1) !Hack State 51 ( 2.8) 33 ( 2.7) 10 ( 2.2) 237 ( 5.0) 232 ( 4.3) 222 ( 3.8) Nation 56 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 43 ( 3.0) 30 ( 2.9) 27 ( 3.4) 237 ( 3.2) 241 ( 31) 229 ( 5.3) Nation 41 ( 3.3) 32 ( 2.2) 27 ( 2.6) 245 ( 4.8) 250 ( 3.3) 235 ( 3.1) Asian State 62 ( 5.3) 28 ( 5.4) 10 ( 3.4) !NM ( 04. oimp) Nation 62 ( 5.8) 27 ( 5.3) 11 ( 4.9) 287 ( 4.7)1 eq TYPE OF COMMUNITY Advantaged urban State 443 ( 2.3) 33 ( 1.6) 21 ( 2.0) 284 ( 3.0) 281 ( 3.7) 275 ( 4.8)I Naton 47 ( 2.3) 284 ( 4.4)! 38 ( 2.6) 279 ( 44)1 15 ( 3.7) 4.**) Oludvantagad liban State 46(1.9) 31 ( 2.0) 23 ( 2.3) 242 ( 5.7) 2'38 ( 41) 227 ( 5.4) Nation 42 ( 3,3) 20 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 25e ( 4.2)k 238 ( 8.3)1 Extronie rural State 48 ( 2.8) 31 ( 2.8) 21 ( 2.3) 265 ( 4.7)I 209 ( 3.0)1 258 ( 4.7)I Nation 43 ( 44) 32 ( 4.2) 25 ( 3.9) 257 ( 4.1)I 204 ( 5.8)1 Other State 47 ( 1.7) 33 ( 1.3) 20 ( 1.2) 288 ( 2.6) 202 ( 2.7) 258 ( 2.3) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 285 ( 2.2) 206 ( 1.9) 251 ( 2.4) e The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 .1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT /0110. Illinois TABLE A26 I Students' Reports on the Number of Days of ("mitinued) School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Nona Om or Two Das , Throe Days or Moro _ :Tom. Porowitese and Prelkleacy Paresedise and Prelkiancy Parmelee* and tralkiancy State 47 $2 ( 1.0) 21 0.8) 284 1.9 20 C 2.1) 253 2.2) Nation 45 1.1 32 (0.9) 23 1.1) ( 1.$ 260 ( 1.5) 250 ( 1.9) PARENTS' EDUCATION NS noniyaduato State 39 ( 3.0) 35 ( 2.7) 2$ ( 3.2) 248 ( 3.9) 248 ( 3.0) Nation 38 ( 3.2) 26 ( 3.1) 38 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) NS graduate State 48 ( 2.4) 31 ( 2.2) 23 ( 1.7) 253 ( 2.4) 253 ( 2.8) ( 2.9) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.8) 249 ( 2.4) Soma caws* State 44 ( 2.8 33 ( 2.2) 23 ( 1.9) 284 ( 2.3 203 ( 2.8) 280 ( 3.2) Nation 40 ( 1.8 37 ( 1.8) 23 ( 1.8) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) Collage graduate State 51 ( 1.7 33 ( 1.3) 18 ( 1.4) 278 ( 2.4 273 ( 2.9) 285 ( 3.1) Nation 51 ( 1.6 33 ( 12) 18 ( 1.3) 275 ( 2.1 277 ( 1.7) 285 ( 3.1) GENDER Male State 49 ( 1.5) 33 ( 1.4) 18 ( 1.2) 265 ( 2.1) 261 ( 2.9) 251 ( 2.9) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 1.4) 268 ( 2.0) 287 ( 2.1) 250 ( 2.8) Female State 45 ( 1.2) 32 ( 1.3) 23 ( 1.1) 253 ( 2.0) 262 ( 2.2) 255 ( 2.8) Nation 43 ( 1.4) 32 ( 1.1) 25 ( 1.3) 284 ( 2.3) 288 ( 1.7) 250 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). ^..1 c.1 4. THE 1990 NAEP TRIAL STATE ASSESSMENT 137 Illinois TABLE A27 j Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10110 NAEP TRIAL STATE ASSESSMENT , Strongly Agree Air** , Undecided, Disagree, Strongly Meagre* TOTAL Percentage arvd Proficiency Percentage and Proficiency Percentage and Proficiency State 27 ( 1.2) 52 ( 0.8) 20 ( 1.1) 267 ( 2.4) 260 ( 1.7) 253 ( 2.2) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) RACE/ETHNICITY White State 26 ( 1.0) 54 ( 1.0) 21 ( 1.2) 278 ( 2.2) 271 ( 1.6) 264 ( 1.8) Nation 26 ( 1.6) 4$ ( 1.3) 26( 1$) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Mack State 37 ( 3.5) 47 ( 2.4) 16 ( 22) 243 ( 5.8) 230 ( 3.1) 218 ( 4.1) Nation 32 ( 2.5) 52 ( 2.3) 16 ( 1.9) 247 ( 4.1) 233 ( 3.3) 227 ( 4.2) Hispanic State 22 ( 2.3) 53 ( 2.5) 24 ( 2$) 248 ( 4.1) 234 ( 3.2) 231 ( 5.2) Nation 24 ( 2.5) 4$ ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 238 ( 3.8) Asian State 37 ( 5.8) 42 4.3) Nation 29 ( Ct. 5.5) .-*) .4* ( 17 ( * ( 4.9) ***) TYPE OF COMMUNITY Advantaged urban State 27 ( 2.8) 55 ( 2.5) 18 ( 2.3) 289 ( 5.01 280 ( 2.8) 272 ( 3.7)1 Nation ...) 55 ( 280 ( 2.4) 4.1)1 28 ( 4.2) Disadvantaged urban State 28 ( 3$) 50 ( 1.8) 22 ( 2.6) 248 ( 5.6) 234 ( 4.7) 229 ( 6.6)1 Nation 26 ( 2.9) 48 ( 2.9) 26 ( 3.2) 260 ( 5.6)1 249 ( 4.6)1 240 ( 43)1 Extreme rtral State 25 ( 3.1) 53 ( 1.8) 22 ( 3.2) 270 ( 5.2)1 264 ( 4.2)1 260 ( 6.0)1 Nation 34 ( 2.8) 49 ( 2.2) 17 ( 1.4) 270 ( 3.9)1 252 ( 4.1)1 Other State 27 ( 1.2) 52 ( 1.4) 21 ( 1.4) 269 ( 3.2) 262 ( 2.2) 255 ( 2.6) Nation 27 ( 1.4) 48 ( 1.2) 26 ( 1.4) 271 ( 2.4) 2831 2.2) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that. for each population of interest, the value for the entire population is within 2 standard errors of.the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 02 students). 138 THE 1990 NAEP MAL, STATE ASSESSMENT Illinois TABLE A27 I Students' Perceptions of Mathematics (continued) 1 PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT strongly Aciru Affree Undecided, Disagree, Strongly Disagree TOTAL Percentage and Proficiency Pereonie. and Pertentsge and Proficiency State 27 ( 1.2) 52 ( 0.8) 1.1) 267 ( 2A) MO( 1.7 253 2.2) Nation 27 ( 1.3) 49( 'IA 24 1.2) 271 ( 1.9) 262 ( 1.7) 251( 12) PARENTS EDUCATION HS non-graduate State 26 ( 32) 50 ( 3.3) 245 ( 2.6) 24( 22) Nation 20 ( 2.6) **) 50 ( 3.3) 243 ( 22) 30 3.6) 239 ( 4.3) NS graduate State 25 ( 2.0) 50 ( 1.7) 25 ( 1.7) ( 2.9) 253 ( 1.8) 245 ( 3.9) Nation 27 ( 2.1) 47 ( 2.3) 26( 2.0) 262 ( 2.7) 255 ( 2.3) 24$ ( 2.4) Som colleipa State 26 ( 2.4) 53 ( 2.4) 21 ( 1.7) 271 ( 2.7) 260 ( 2.5) 260 ( 2.9) Nation 28 ( 2.5) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 258 ( 32) College graduate State 31 ( 1.8) 53 ( 1.4) 15 ( 1.4) 278 ( 3.4) 273 ( 2.2) 268 ( 3.0) Nation 30 ( 2.3) 51 ( 1.6) 19 ( 1.8) 280 ( 2.4) 274 ( 2.2) 206 ( 2.5) ()ENDER Male State 27 ( 1.4) 52 ( 1.3) 21 ( 1.3) 267 ( 2.6) 261 ( 2.0) 254 ( 2.5) Nation 28 ( 1$) 48 ( 1.2) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Female State 2$ ( 1.6) 52 ( 1.3) 20 ( 1.3) 267 ( 3.0) 260 ( 1.5) 252 ( 2.5) Nation 26 ( 1.7) $0 ( 1.7) 25 ( 1.9) 26a ( 2.1) 262 ( 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. "*" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 .7 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 (ETS), Westat, and National Computer Systems (NCS). 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. rmally, 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 Planning Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In partienlar, we note the significant contributions of Ramsay Selden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through 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 Raul Garza worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGS) and NAGS 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 Mazzeo, with consultation from Engene 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 McCamley, and Craig Pizzuti. 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. U.S. GOVERNMENT PRINTING OFFICE 1991 0 za-rs QL 3 (1114- 14) 1 2 G A