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DOCUMENT RESUME ED 330 558 SE 052 068 TITLE The State of Mathematics Achievement in Idaho: The Trial Stw..e Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievemenr; Calculators; *Educational Assessment; Family Environment; =Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Sollng; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS *Idaho; 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 and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In Idaho, 2,716 students in 101 public schools were assessed. This report describes the mathematics proficiency of Idaho eighth-graders, compares their overall performance to students in the West region of the United States and the nation (using data from the NAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, parents' educational level, and gender). To provide a context for the assessment data, participating students, their mathematics teachers, and principals completed questionnaires which focused on: instructional content (curriculum coverage, amount of homework); delivery of math instruction (availability of resources, type); use of calculators; educational background of teachers; and conditions facilitating math learning (e.g., hours of television watched, absenteeism). On the NAEP math scale, Idaho students had an average proficiency of 272 compared to 261 nationwide. Many fewer students (Idaho-15%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of "CS A It! vement in IDAHO The Trial State Assessment at Grade Eight THE NATION'S REPORT I CARO 1 .1.k . lif:t v . p cliqt r t** U S DEPARTMENT OF EDUCATION ,)n.e 01F (ILA shone( Reiear, and ,mtrovement DU4ATIONAL RE SOURCES INFORMATION CENTf R ifRIC1 tpe:nA ekx mem! has Slept, frprMuCrd SS f,vw, fru'', the person or orpanaat.oe 0,,WmatN r kcmor 4'01311{1es NI.P been made to .rnprore reprocucbcvl cp.tahtt Pont% wp* dr op,n.ons stated .r.1,1,4 OM ,,,t.^1 ,,of mecessivov epresent ottoai 01 RI r pot.cy 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 Natioaal Asscssment of Educational Progress tNAEP), is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1%9. assessments have been conducted periodically in reading, mathematics. science. writing, history/geography, and other fields. By making objective information on student performance available to policymakers at the national, state. and local levels. NAEP is an integral part of our nation's esaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally nundated project of the National Center for Education Statistics. the U.S. Department of Education. The Commissioner of Education Statistics is responsible. by law. for carrying out the NAEP project through competitive awards to qualified organitations. NAEP reports directly to the Commissioner. who is also respoasible kir providing continuing reviews. including validation studies and solicitation of public comment. on NAEP's conduct and usefulness. In 1988. Congress created the National Assessment Governing Board t NAGB) to formulate policy guidelines for NAEP. The board is responsible hir selecting the subject areas to be assessed, which may include adding to those specified by Congress: identifying appropriate achievement goals for each age and grade: developing assessment obiectives; developing test specifications: designing the assessment methodology; developiq, guidelines and standards for data analysis and for reporting and disseminating results; developing standards and pi-ocedures for interstate. regional. and national comparisons: improving the form and use of the National Aissessment: and ensunng that all items selected for usc in the National Assessment are free from racial. cultural. gender. or regional bias. The National Assessment Governing Board Richard A. Boyd. Chairman Executive Director Martha Holden Jennings Foundation Cleveland. Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.t).C,E.S Saratoga Springs. New York Franck' Alexander Associate Superintendent California Department of Education Sacramento, California David P. Battini High School History Teacher Cairo-Durham High School Caito. NC% York ParrLs C. Battle Teacher Horace Mann Elementary School Miami, Florida Mary R. Blanton Attorney Cromwell. Porter. Blanton & Blanton Salisbury. North Carohna Boyd W. Koehlie Attorney Gauss. Klyn. & Bochlie Pella. Iowa Linda R. Bryant 'Teacher Greenway Middle School Teacher Center Pittsburgh. Pennsylvania Honorable Michael N. Castle Governor of Delaware Carvel State Office Building Wilmington, Delaware Honorable Naomi K. Cohen State of Connecticut !louse of Representatives .egislative Office Building Uri ford. Connecticut Chester E. Finn. Jr. Professor of Education and Public Policy Vanderbilt Unisersity Washington. D.C. Michael S. Clode Wyonnng State Board of Education Saratoga. Wyoming Christine Johnson Principal Abraham Lincoln High School Denver, Colorado John l Indley Principal South Colby Elementary School Port Orchard. Washington Carl J. Rimer Director of Schools The Lutheran Church International t'onter St. Louis, Missouri Missouri Synod Mark D. Musick President Southern Regional Education Board Atlanta. Georgia Honorable Carolyn Pollan Arkansas House of Representat Foil Smith, Arkansas yes, Matthew W. Prophet, Jr. Superintendent Portland Oregon School Distnct Portland. Oregon Honorable William T. Randall Commissioner of Education State Department of Education Denver. Colorado Dorothy K. Rkh President Home and School Institute Special Projects Officc Washington, D.C. Honorable Richard W kiley Attorney Nelson. Mullins. Riley and Scarborough Columbia. South Carolina Thomas Topazes Attorney Law Offices of Frank Rogolienski Coronado, California Herbert J. Walberg Professor of Educatioo University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and Improvement (Fx-Officio) Department of Education Washington. D.C. Roy Truby Executive Director, NAGB Washington. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement in IDAHO The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education 1 kt U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson S 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 catering information, please contact the assessment division of your State Department of Education. For ordering information on the composite repon 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 ImpaDvement U.S. Department of Education 555 New Jersey Avenue, IM 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 perfonned for the National Center for Education Statistics, Office of Educational Research and Improvement, by Educational Testing Service. Educational Testing Service is an equal opportunity/affinnative action employer. Educational Timing Service, ETS, and are registered trademarks of Educational Testing Ser fice. (1 Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of Idaho 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Idaho Public Schools? 1 7 Chapter 1. Students' Mathematics Performance 1 I hAels of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race. Ethnicity 24 Type of Community 27 Parents Education evel 29 Gender 31 Content Area Performance THE 1990 NAL:T*1121AL sATI: ASSESSMENT rs0 111 PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics? 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Delivered/ 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used/ 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics? 67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the I lame 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 1HE 1990 NAEP TRIAL STATE ASSESSMENT Idaho THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congress passed new legislation tOr the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history a provision authorizing voluntary state-by-state assessmmts on a trial basis, in addition to continuing its primary mission, the national ls,cssments that NAEP has conducted since its inception. As a result of the legislation, tho 1990 NAFP program included a Trial State Assessment Program in eighth-gade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-gxade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's sta.ff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMEN1 Idaho In Idaho, 101 public schools participated in the assessment, The weighted school participation rate was 97 percent, which means that all of the eighth-grade students in this sample of schools were representative of 97 percent of the eighth-grade public-school students in Idaho. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 1 percent of the eighth-gxade public-school population was classified as Limited English Proficient (LEP), while 6 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment, To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The studert5 who were excluded from the assessment because they were categorized as l IT or had an In" represented 0 percent and 2 percent of the population, respectively. In total, 2,716 eighth-grade Idaho 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-grade public-school student population in Idaho. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from Idaho on the NAE P mathematics scale is 272. This proficiency is higher than that of students across the nation (261). Average proficienc} on the NALP scale 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 greater detail, NAFP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAY!) scale. 9 2 .[HE 1990 NAEP TRIAL STATE ASSI'..SSM ENT Idaho In Idaho, 100 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in Idaho (15 percent) and 12 percent in the nation appear to have acquired reasoning and pnesblem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in Idaho performed higher than students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the Idaho eighth-grade student population defined by race ethnicity, type of community, parents' education level, and geader. In Idaho: White students had higher average mathematics proficiency than did Hispanic or American Indian students. Further, a greater percentage of White students than Hispanic or American Indian students attained level 300. The results by type of community indicate that the average mathematics performance of the Idaho students attending schools in areas classified as "other- was higher than that of students attending schools in extreme rural areas. In Idaho, the average mathematics proficiency of eighth-grade public-school students having at least one parent who gaduated from college was approximately 27 points higher than that of students whose parents did not graduate from high school. The results by gender show that there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in Idaho. In addition, a geater percentage of males than females in Idaho attained level 300. Compared to the national results, females in Idaho performed higher than females across the country; males in Idaho performed higher than males across the country. THE 1990 NAEP TRIAL STATE ASSESSMENT 3 Idaho A Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information about student achievement. Some of the salient results for the public-school students in Idaho are as follows: More than half of the students in Idaho (67 percent) were in schools where mathematics was identified as a special priority. This is about the same percentage as that for the nation (63 percent). In Idaho, 69 percent of the students could take an algebra course in eighth ga-ade for high-school course placement or credit. About the same percentage of students in Idaho were taking eighth-gxade mathematics (47 percent) as were taking a course in pre-algebra or algebra (50 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 gxeatest percentage of eighth-grade students in public schools in Idaho spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes dail) . Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 4 FIE 1990 NAEP 1 RIAL Si AIL ASSESSMIA I Idaho .....=11.1. In Idaho, 8 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 40 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 Idaho, 27 percent of the students never used a calculator to work problems in class, while 43 percent almost always did. In Idaho, 27 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 (63 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 Idaho 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 witn 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 Idaho (19 percent) watched one hour or less of television each day; 7 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. THE 14440 NAEP TRIAL STATE ASSESSMENT 5 Idaho THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progrtss (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Idaho This report describes the performance of the eighth-grade public-school students in Idaho and consists of three sections: This Introduction provides background information about the Trial State Assessment and this report. It also provides a profile of the eighth-grade public-school .,tudents in Idaho. Part One describes the mathematics performance of the eighth-grade public-school students in Idaho, the West region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Idaho, the West region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress rissed new legislation for the National Assessment of Educational Progress (NAFP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survey instrument for the eighth grade and shall conduct a demonstration of the instrument in 1990 in States which wish to participate, with the purpose of determining whether such an assessment yields valid, reliable State representative data. (Section 406 (i)( )(C)(1) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 L.S.C. 1221e-1(i)( 2)(C)(i))) As a result of the legislation, the 1990 NAFP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eig,hth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed LO ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 8 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho The Trial State Assessment was based on a set of mathematics objectiveS newly developed for the program and pat':rned after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized 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 Coiicil of Chief State School Officers in mid-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,' the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-grade public-school students in Idaho, in the West region, and for the nation. Results also are provided for groups of students defined by shared characteristics -- race/ethnicity, type of community, parents' education level, and gender. Defmitions of the subpopulations referred to in this report are presented below. The results for Idaho are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nationally and regionally representative samples of public-school students who were assessul in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAEP program was necessary because the voluntary nature of the Trial State Assessment Program did not guarantee representative national or regional results, since not every state participated in the program. National Council of Teachers of Mathematics, Curriculum and Evaluatiwt Standards for School Alathematks (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 9 Idaho 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 criteiia 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 Idaho. TYPE OF COMMUNITY Results are provided for four mutually exclusive community types -- advantaged urban, disadvantaged urban, extreme rural, and other -- as defined below: Advantaged Urban: Students in this group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are in professional or managerial positions. Disadvantaged Urban: Students in this gi-oup live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are on welfare or are not regularly employed. Extreme Rural: Students in this group live outside metropolitan statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas c_her than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. 10 1 'HE 1990 NAEP TRIAL Si ATE ASSESSMENT Idaho 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 Wasnington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURE 1 I Regions of the Country DIE NATION'S REPORT CARO _ NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Alabama Illinois Alaska Delaware Arkansas Indiana Arizona District of Columbia Flock la Iowa California Maine Georgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana New Jersey North Carolina Nobraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohio Oklahoma Rhode island Virginia South Dakota Origon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming 4 THE 1990 NAEF TRIAL STATE ASSESSMENT 11 Idaho Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific backgound question in a particular way. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As such, they are subject to a musure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report arc based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistically significant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) -- regardless of whether the sample means or sample proportions appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the difference is not statistically significant), the means or proportions are described as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the apparent magnitude of the difference between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. When three or more groups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendix. 12 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparin.g 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, ir several places in this Arport, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each al, the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported i. the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT 13 Idaho Profile of Idaho EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-gade public-school students in Idaho, the West re&n, 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 Idaho Eighth-Grade Public-School I Students PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Idaho West Nation r-- DEMOGRAPHIC SUBGROUPS RacWEthnicity Percentage Percentage Percentage White 90 ( 0.8) 83 ( 1.9) 70 ( 0.5) Black 0 ( 0.1) ( 2.0) 16 ( 0.3) Hispanic 6 ( 0.6) 21 ( 1.5) 10 ( 0.4) Asian ( 0.3) 4 ( 1.3) 2 ( 0.5) Amencan Indian 2 ( 0.4) 4 ( 2.3) 2 ( 0.7) Type o Community Advantaged urban 4 ( 0.1) 14 ( 8.5) 10 ( 3.3) Disadvantaged urban 3 ( 0.1) 19 ( 7.5) 10 ( 2.8) Extreme rural 27 ( 1.9) 10 3.8) 10 ( 3.0) Other 67 ( 1.8) 58 (10.1) 70 ( 4.4) Parents' Education Did not finish high school 6 ( 0.5) 10 ( 1.3) 10 ( 0.8) Graduated high school 19 ( 0.7) 19 ( 2.5) 25 ( 1.2) Some education atter high school 22 ( 0.9) 18 ( 1.2) 17 ( 0.9) Graduated college 46 ( 1.3) 42 ( 4.0) 39 ( 1.9) Gender Male 52 ( 1.2) 55 ( 2.1) 51 ( 1.1) Female 48 ( 1.2) 45 ( 2.1) 49 ( 1.1) The standard errors cf the esumated stausucs appear in 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. 20 14 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Idaho schools and students sampled for the 1990 Trial State Assessment. In Idaho, 101 public schools participated in the assessment. The weighted school participation rate was 97 percent, which means that all of the eighth-grade students in this sample of schools were representative of 97 percent of the eighth-grade public-school students in Idaho. TABLE 2 Profile of the Population Assessed in Idaho EIGHTH-GRADE PUBUC SCHOOL PARTICIPATION Weighted school participation rate before substitution Weighted school participation rate after substitution Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of substitute schoois participating Total number of participating schools 97% 97% 108 2 101 4 0 101 EIGHTH-GRADE PUBIJC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students selected to participate in the assessment Number of students withdrawn trom the assessment Percentage of students who were of Limited English Proficiency Percentage of students excluded from the assessment due to Lim:ted English Proficiency Percentage of students who had an Individualized Education Plan Percentage of students excluded from the assessment due to Individualized Education Plan status Number of students to be assessed Number of students assessed 96% 3,031 123 1% 0% 6% 2% 2,830 2,710 r THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Idaho In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 1 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 6 percent had an Individualized Education Plan (IEP). 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 were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 0 permnt and 2 percent of the population, respectively. In total, 2,716 eighth-grade Idaho 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-grade public-school student population in Idaho. 16 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho THE NATION'S REPORT CARO PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Idaho Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAEP mathematics scale, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficiency of eighth-grade public-school students in Idaho. Chapter 1 compares the overall mathematics performance of the students in Idaho to students in the West region and the nation, lt also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 summarizes the students' overall mathematics performance for subpopulations defined by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 17 CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-gyade public-school students from Idaho on the NAFP mathematics scale is 272. This proficiency is higher than that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School Mathematics Proficiency NAEP Mathematics Scale 200 225 250 275 300 500 Average Proficiency 14$ Idaho West Nation 261 261 ( ( 0.1) 2.6) 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. I Differences reported are statistxally different at about the 95 permnt 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 interesi 13 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho LEVELS OF MA1 HEMATICS PROFICIENCY Average proficiency on the NALP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAFP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-pade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 3(X), and 350 on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are given in Figure 3. It is important to note that the definitions of these levels are based solely on student performance on the 1990 mathematics assessment. The levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In Idaho, 100 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in Idaho (15 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). CONTENT AREA PERFORMANCE As previously indicated, the questions comprising the Trial State Assessment covered five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Figure 5 provides the Idaho West region, and national results for each content area. Students in Idaho performAi higher than students in the nation in all of these five conten! areas. " A, 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 19 Idaho FIGURF 3 1 Levels of Mathematics Proficiency THE NATION'S REPORT anti LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problemS with and without regrouping. Using a calculator, they can extend these abilities to multipliCation and division problems. These students can identify SolutionS to one-step word problems and select the greatest four-digit number in a list. In measurement, these students can read a ruler as well as common weight and graduated Scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In mita analysts, they are able to read Simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numerical sentences and extend simple pattern sequences. LEVEL 250 Simple Multiplicative Reasoning and 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 place value, "even," "factor," and "multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and probability. In algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions. 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho FIGURE 3 I Levels of Mathematics Proficiency (continued) I ME NATION'S REPORT CARD LEVEL 300 Reasoning and Problem Solving Involving Fractions, Decimals, Percents, Elamentary Geometric Properties, and Simple Algebraic Manipulations Students at this level are awe 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 fradtions and decimals, including pictorial representations. They can interpret the meaning of percents less than and greater than 100 and apply Me concepts of percentage$ to solve simple problems. The Se Students demonstrate some evidence of using mathematical notation to interpret expreSsions, including fhoSe With exponents and negative integers. in measurement, these students can find the perimeters and areas of rectangles, recOgnize relationships among Common units of measure, and use proportional relationships to Solve routine problems involving similar triangles and scale drawings. In geometry, they have Some mastery of the definitions and properties of geometric figureS and Solids. In data analysis, thesE Students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to Open linear sentences and inequalities by substitution, and checking and graphing an interval representing a compound inequality when it is described in words. They can determine and apply a rule for simple functional relations and extend a numerical pattern. 11.01.0..1. LEVEL 350 Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of number and algebraic understanding to include some properties of exponents. They can recognize scientific notation on a calculator and make the transition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles to solve problems. They can find the circumferences of circles and the surface areas of solid figures In geometry, they can apply the Pythagorean theorem to solve problems involving indirect measurement. These students also can apply their knowledge of the properties of geometric figures to solve problems. Such as determining the slope ot a line. In data analysis, these students can compute means tt .1 frequency tables and determine the probability of a simple event. in algebra, they can identify an equation describing a linear relation provided in a table and solve literal equations and a system of two linear equations. They are developing an understanding of linear functions and their graphs, as well as functional notation, including the composition of functions. They can determine me nth term of a sequence and cive counterexamples to disprove an algebraic generalization. THE 1990 NAEP TRIAL S'IAIE ASSESSMENT 21 Idaho 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 0 20 40 60 80 ( 0.1) 0 ( 0.4) O ( 0.2) 15 ( 0.9) 12 ( 2.4) 12 ( 1.2) 79 ( 1.0) 63 ( 2.8) 64 ( 1.6) 100 ( 0.2) 97 ( 1.0) 97 ( 0.7) 00 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 04-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 22 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho THE NATION'S REPORT FIGURE 5 I Eighth-Grade Public-School Mathematics CARO Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation NUMBERS AND OPERATIONS MEASUREMENT GEOMETRY 1-4110w4 P-4104 Peg 1"".."4.4.0101 10411 MI DATA ANALYSIS, STATISTICS, AND PROBABILITY ALGEBRA AND FUNCTIONS P4 tP*-1 /111 PM 044 200 225 250 275 Average Proficiency 274 ( 0.8) 264 ( 2.6) 288 ( 1.4) 270 ( 1.0) 258 ( 3.0) 258 ( 1.7) 289 ( 0.8) 260 ( 2.6) 259 ( 1.4) 274 ( 0.9) 262 ( 3.6) 262 ( 1.8) 269 ( 0 9) 259 ( 2 4) 260 ( 1.3) 300 500 Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent cvrtainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence inter% al, denoted by P+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT 23 Idaho CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY The Trial State Assessment results can be compared according to the different racial/ethnic groups when the number of students in a raciaLethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Hispanic, and American Indian students from Idaho are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Hispanic or American Indian students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Hispanic or American Indian students attained level 300. 24 THE 1990 NAEP TRIAL STATE ASSESSMENT FIGURE 6 I Average Eighth-Grade Public-School Mathematics Proficiency by Race/Ethnicity NAEP Mathematics Scale 0 200 225 250 275 300 500 Average Pronciency 1.-411111 HI Idaho White 274 ( 0.7) Hispanic 20 ( 2.4) Amencan Indian 3111 ( 4.8) West White Ste 3.2) Hispanic aU ( 3.7) American Indian ( Nation White , ( 1.5) Hispanic 213 ( 2.8) American Indian 20 ( 5,3)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 H-I). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). ME 1990 NAEP TRIAL STATE ASSESSMENT 25 Idaho TIE NATION'S REPORT FIGURE 7 Levels of Eighth-Grade Public-School CARD Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Hispanic Amer. Indian Rogion White Hispanic Amer. Indian Nation White Hispanic Amer. Indian LEVEL 250 State White Hispanic Amer. Indian Region WMe Hispanic Amer. Indian Nation White Hispanic Amer. Indian LEVEL 200 Stat. White Hispanic Amer. Indian Region White Hispanic Amer. Indian Nation White Hispanic Amer. Indian 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certsinty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence 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. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. **8 Sample sire is insufficient to permit a reliable estimate (fewer than 62 students). 100 1 4,, 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 ( 0.9) 3 ( 1.4) 5 ( 3.8) 18 ( 3.2) 3 ( 1.6) **) 16 ( 1.5) 3 ( 1.1) 1 ( 2.3)1 e2 ( 0.9) 50 ( 4.7) 53 ( 8.8) 74 ( 3.3) 41 ( 5.4) sota 74 ( 1.8) 41 ( 4.5) 45 (16.0)1 100 ( 0.2) 97 ( 1.7) 95 ( 2.1) 90 ( 0.8) 93 ( 2.0) ) 90 ( 0.4) 93 ( 1.6) 07 ( 8.7)1 Idaho TYPE OF COMMUNITY Figure 8 and Figure 9 present fa, mathematics proficiency results for eighth-grade students attending public schools in areas classified as "other" and extreme rural areas. (These are the "type of community" groups in Idaho with studrnt samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Idaho students attending schools in areas classified as "other" was higher than that of students attending schools in extreme rural areas. FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community NAEP Mathematics Scal 0 200 225 250 275 300 500 Away* Profickocy 1114""I MMI Idaho Extreme rural Other SID ( 1.1) 273 (1.0) West Extreme rural Other 211. 34) Nation Extreme rural tee ( 4.in Other 211 C 1.0) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of Mterest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-4.4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 27 1.111=11.1011111,. FIGURE 9 LEVEL 300 State Ext. rural Other Region Ext. rural Other Nation Ext. rural Other LEVEL 250 State Ext. rural Other Region Ext. rural Other Nation Ext. rural Other LEVEL 200 State Ext. rural 100 ( 0.2) Other 99 ( 0.3) Region Ext. rural 98 ( 1.3)1 Other 90 ( 1.7) Nation Ext. rural 97 ( 2.8)) Other 97 ( 1.0) Idaho Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community DIE NATION'S REPORT CARD 77 ( 1.9) BO ( 1.3) 52 (12.8)1 82 ( 5.0) 58 ( 6.2)1 64 ( 2.3) 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 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. Ink ,1 28 THE 1990 NAEP TRIAL STATE ASSESSMEN1 Idaho PARENTS' EDUCATION LEVEL Previous NAEP fmdings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In Idaho, the average mathematics proficiency of eighth-grade public-schooI students having at least one parent who graduated from college was approximately 27 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, a larger percentage of students in Idaho (46 percent) than in the nation (39 percent) had at least one parent who gaduated from college. In comparison, the percentage of students wl,o reported that neither parent graduated from high school was 6 percent for Idaho and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School Mathematics Proficiency by Parents' Education NAEP Mathematics Seale 0 200 225 250 275 300 500 Average Prof Icfancy Mal III PON4 111 Idaho KS non-graduate 014 HS graduate Some college College graduate P401 1.4041 Welt HS non-graduate I-4S graduate Some college College graduate Nation HS non-graduate Nas HS graduate tal Some college eel College graduate The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. r't ; 4) THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Idaho DIE NATION'S firORT FIGURE 1 1 I Levels of Eighth-Grade Public-School WIRD I Mathematics Proficiency by Parents' Education LEVEL 300 Stat. HS non-grad. HS graduate Some college College grad. Pollan HS non-grad. HS graduate Sane college College grad. Nation MS non-grad. HS graduate Soma college College grad. LEVEL 250 stets HS non-grad. HS graduate Some college College grad. Rogion 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. Roo/ On HS non-grad. HS graduate Some college College grad. finnan HS non-grad. HS graduate Some college College grad. 0 20 40 50 BO Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 2 ( 1.5) ( 1.6) 14 ( 1.9) 21 ( 1,7) 2 ( 2.3) 2 ( 1.3) 15 ( 2.8) 21 ( 35) 1 ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.0) 52 ( 4.4) SS ( 3.0) 96 ( 2.1) 1111 ( 1.3) 44 ( 6.8) 51 ( 4.4) 75 ( 4,1) 79 ( 3.6) 37 ( 4.6) 56 ( 2.7) 71 ( 2.6) TS ( 2.0) 1110 ( 2,0) 99 ( 0.3) 100 ( 0.0) 100 ( 0.2) ( 3.2) 97 ( 1,6) 99 ( 0.7) 99 ( 0.7) SS ( 1,9) 97 ( 0.8) Se ( 0.7) ( 0.7) 100 30 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho GENDER As shown in Figure 12, there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in Idaho. Compared to the national results, females in Idaho performed higher than females across the country; males in Idaho performed higher than males across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by H-4). If the confidence intervals for the populations do not overlap, there is a Fiatistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in Idaho who attained level 200. The percentage of females in Idaho who attained level 200 was greater than the percentage of females in the nation who attained level 200. Also, the percentage of males in Idaho who attained level 200 was greater than the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASSESSMENT 3 1 Idaho FIGURE 13 1 Levels of Eighth-Grade Public-School Mathematics Proficiency by Gender LEVEL 300 State Mate Female Raglan Male Female Nation Male Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 Stit Male Female Region Male Female Nation Male Female 0 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 17 ( 1.3) 12 ( 1.0) 13 ( 3.1) 11 ( 2.2) 14 ( 1.7) 10 ( 1.3) 110 ( 1.4) 79 ( 1.2) 05 ( 4.1) 61 ( 3.2) 04 ( 2.0) 64 ( 1.8) 100 ( 0.3) 99 ( 0.3) 97 ( 1.2) 90 ( 1.0) 97 ( 0.9) 97 ( 0.8) Idaho In addition, a greater percentage of males than females in Idaho attained level 300. The percentage of females in Idaho who attained level 300 was similar to the percentage of females in the nation who attained level 300. Also, the percentage of males in Idaho who attained level 300 was similar to the percentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Idaho TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Numbers and °partitions Measurement Geometry Data Analysis, Statistics, and Probability Algebra and noctions TOTAL Prollciencx Pro Ociency Proficiency Proficiency Proficiency State 274 ( OA) 270 ( 1.0) 289 ( 0.8) 274 ( 0.9) 269 ( 09) Region 204 ( 2.6) 258 ( 3.0) 260 ( 2.8) 262 ( 3.8) 259 ( 2.4) Nation 208 ( 1.4) 256 ( 1.7) 259 ( 1.4) 262 ( 1.8) 260 ( 1.3) RACE/ETHNICITY White State 278 ( 0.7) 273 ( 4.0) 271 ( 0.8) 277 ( 0.9) 272 ( 0.9) Region 271 ( 3.2) 267 ( 3.9) 267 ( 3.0) 272 ( 4.4) 207 ( 2.8) Nation 273 ( 1.6) 287 ( 2.0) 267 ( 1.5) 272 ( 1.8) 268 ( 1.4) Hispanic State 25$ ( 2.8) 248 ( 3.6) 248 ( 246 ( 3.4) 244 ( 2.9) Region 248 ( 3.5) 239 ( 4.2) 245 ( 4.4) 240 ( 4/) 243 ( 4.0) Nation 248 ( 2.7) 238 ( 3.4) 243 ( 3.2) 232 ( 3.4) 243 ( 3.1) AMfiCall Indian State 257 ( 5.7) 251 ( 5.9) 254 ( 5.1) 252 ( 6.0) 252 ( 5.4) Region ( Mrs) 44elt *Mt) Nation 249 ( 7.8)1 247 ( 6.8)1 248 ( 8.6)1 242 ( 5.2)1 242 ( 4.9)1 TYPE OF COMMUNITY Extrwno rural State 272 ( 1.1) 267 ( 1.8) 267 ( 1,5) 271 ( 1,3) 265 ( 1$) Region 254 ( 8.6)1 254 ( 4.6)1 252 ( 9.4)1 253 ( 8.8)1 251 ( 8.5)1 Nation 258 ( 4,3)1 254 ( 4.2)1 253 ( 4.5)1 257 ( 5.0)1 258 ( 4.8)1 Oiltor State 275 ( 1.2) 270 ( 1.3) 269 ( 1.1) 274 ( 1.3) 270 ( 11) Region 262 ( 3.6) 255 ( 4.2) 258 ( 3.4) 259 ( 4.2) 258 ( 3.5) Nation 268 ( 1.9) 2$7 ( 2.4) 2$9 ( 1.7) 251 ( 2.2) 261 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 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. 6** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 0 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Idew TABLE 3 I Eighth-Gt.: liblic-School Mathematics (amtinued) Content Area Oerformance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1900 /MEP TRIAL STATE ASSESSMENT Numbers and Operations Mnasurnment ennenntry Data Malys's, andsdns, and Probability .. NiMbraRinctionar TOTAL Pro &fancy 274 ( 0.11) 264 ( 2.0 28(14 ) Proficiency 270 ( 1.0) 258 (3.0) 258 ( 1.7) Proficiency 240 DA) 240 2.6) 254 1.4) Proficiency 274 262 SA 262 IA Prolloiescy 250209 280 13 State Region Nation PARENTS EDUCATION NS nen-graduate State 256 ( 2.4) 244 ( 4.1) 253 ( 2,3) 254 ( 3.8) 249 ( S.9) Region 2415 ( 4.2) 242 ( 8.2) 244 ( 240 ( 02) 245 ( 5.1) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2, 240 ( 3.1) 242 ( 3.0) $5 iyaduate State 265 ( 1.6) 261 ( 2.1) 261 ( 1.6) 263 ( 1.4) 256 ( 1.8) Region 254 ( 2.5) 245 ( 3.0) 251 ( 3.6) 249 ( 3.2) 250 ( 2.4) Nation 259 ( 1.8) 24$ ( 2.4) 252 ( 14) 253 ( 22) 253 ( 2A) Soma college State 277 ( 1.7) 273 ( 2.1) 271 ( 1.4) 278 ( 1.5) 273 ( 1.6) Region 272 ( 2.7) 268 ( 5.3) 264 ( 3A) 271 ( 4.2) 264 ( 3.2) Nation 270 ( 1.5) 284 ( 2.7) 262 ( 2.0) 269( 2.4) 263 ( 2.2) College graduat State 202 ( 1.0) 279 ( 1.6) 275 ( 1.1) 263 ( 1.4) 277 1.3 Region 275 ( 2.7) 271 ( 3.0) 271 ( 2.3) 270 ( 4.3) 272 2.6 Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 276 ( 2.2) 273 ( 1.7) GENDER Male State 275 ( 1.0) 274 ( 1.3) 271 ( 1.2) 275 ( 1.1) 206 ( 1.0) Region 264 ( 3.8) 263 ( 3.5) 261 ( 3.4) 264 ( 4.1) 260 ( 3.3) Nation 266 ( 2.0) 262 ( 2.3) 200 ( 1.7) 262 ( 2.1) 260 ( 1.6) Female State 273 ( 0.9) 267 ( 1.3) 267 ( 1.0) 273 ( 1.0) 270 ( 1.2) Region 263 ( 24) 252 ( 2.9) 259 ( 2.9) 200 ( 4.0) 259 ( 2.8 Nation 206 ( 1.4) 253 ( 1.6) 258 ( 14) 261 ( 1A) 200 ( 14) The standard errors of the estimated stittistiCs 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. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 THE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students parth in the 1990 Trial State Assessment, their mathematics teachers, and the principals c 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-gade 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 NAEP TRIAL STATE ASSESSMENT 37 Idaho 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 fmdings 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 mon- hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an 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 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho 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 refonns that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.3 This chapter focuses on curricular and instructional content issues in Idaho 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 arc as follows: More than half of the eighth-pude students in Idaho (67 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 2 Curus McKnight, et al., The Underachieving Curriculum Assessing U.S. School Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign, IL: Stipes Publishing Company, 1987). Lynn Steen. Ed. Everybody Coun's A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Press, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Idaho In Idaho, 69 percent of the students could take an algebra course .in eighth grade for high school course placement or credit. Many of the students in Idaho (86 percent) were taught mathematics by teachers who teach only one subject. About three-quarters (70 percent) of the students in Idaho 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 Idaho Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1690 NAEP TRIAL STATE ASSESSMENT Idaho West Nation _ Percentage of eighth-grade students in public sCh0Ois that identified mathematics as receiving special emphasis in school-wide goals and objectives, instruction, in-service training, etc. Percentage of elOth-grade public-school students who are offered a course In algebra for high school course placement or credit Percentage of eighth-grade students in pubhc schools who are taught by teachers who teach oniy mathematics Percentage of eighth-grade students in public SOMAS who are assigned to a mathematics class by their ability in mathematics Percentage of eighth-grade students in public schools who receive fotr or more hours of mathematics instruction per week Percentage Percentage Percentage 67 ( 1.3) 01 ( 8.6) 63 5.9) 89 ( 1.1) 92 ( 4.7) 78 ( 4.6) de ( 1.8) 98 ( 1.6) 91 ( 3.3) 70 ( 2.0) ( 8.3) 63 ( 4.0) 29 ( 1.2) 25 ( 5.9) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho CURRICULUM COVERAGE To place students' mathematics proficiency in a cuniculum-related context, it is necessary to examine the extent to which eighth graders in Idaho are taking mathematics courses. Based on their responses, shown in Table 5: About the same percentage of students in Idaho were taking eighth-grade mathematics (47 peroent) as were taking a course in pre-algebra or algebra (50 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in Idaho who war enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class i They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Idaho West Nation what kind of mathematics class are you7 taking this year? Eighth-grads mathematics Pre-algebra Algebra Percentage end Prolidency Percentage Ind Proficiency Percentage and Proficiency 47 ( 1.1) et3 ( 2.7) 82 ( 2.1) 284 ( 0.7) 252 ( 2.4) 251 ( 1.4) 32 ( 1.2) 15 ( 2.7) 19 ( 1.9) 271 ( 1.1) 206 ( 3.6) 272 ( 2.4) 18 ( 1.1) 17 ( 1.8) 15 ( 12) 301 ( 12) 299 ( 4.5) 290 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Idaho Further, from Table A5 in the Data Appendix:' A somewhat greater percentage of females (52 percent) than males (48 percent) in Idaho were enrolled in pre-algebra or algebra courses. In Idaho, 51 percent of White students, 37 percent of Hispanic students, and 34 percent of American Indian students were enrolled in pre-algebra or algebra courses. Similarly, 52 percent of students attending schools in areas classified as "other" and 49 percent in schools in extreme rural areas were enrolled in pre-algebra or algebra courses. MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to the;r teachers, the greatest percentage of eighth-grade students in public schools in Idaho spent either 15 or 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes daily. Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix): In Idaho, 4 percent of the students spent no time each day on mathematics homework, compared to I percent for the nation. Moreover, 2 percent of the students in Idaho and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulauons race,ethnicity, type of community, parents' education level, and gender. gay 42 THE 1990 NAEP TRIAL STATE ASSESSMENT The irsults by race/ethnicity show that 2 percent of White students, 1 percent of Hispanic students, and 0 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 4 percent of White students, 9 percent of Hispanic students, and 5 percent of American Indian students spent no time doing mathematics homework. In addition, 2 percent of students attending schools in areas classified as "other" and 2 percent in schools in extreme rural areas spent an hour or more on mathematics homework daily. In comparison, 4 percent of students attendhig schools in areas classified as "other" and 4 percent in schools in extreme rural areas spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSL1ENT Idaho West Nation I Percentage and ProOdency Percentage and Proadoncy Percentage and ProOdency About how much time do students spend on mathematics homework each day? None 4 ( 0$) 1 ( 0.3) 1 ( 0.3) 245 ( 2.7) ( 441 114 ( 041 15 minutes 43 ( 1.4) 42 ( 6.7) 43 ( 42) 269 ( 1.0) 258 ( 4.2) 256 ( 2.3) 30 minutes 43 ( 1.5) 43 ( 6.2) 43 ( 4.3) 273 ( 1.1) 264 ( 4.7) ( 2.6) 46 minutes ( 1.1) 9 ( 2.3) 10 ( 1.9) 285 ( 3,8) 270 ( 6.5)1 272 ( 5.7)1 An hour or more 4 ( 0.9) 278 ( 5.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 43 TABLE 7 I Students' Reports on the Amount of Tune They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSUENT Idaho Wost Nation About how much time do you usually spend each day on mathematias homework? Pirawdage and Pre Odom Ihreantse and Prilloleasp Parceidap and Mielliddegv Nom 14 ( 0.8) 12 ( 1.7) 272 ( 1.9) 254 ( 4.2) 2591 ("2.81 16 minutes 29 ( 1.1) 31 ( 4.5) 31 ( 2.0) 274 ( 1.1) 263 ( 18) 264 ( 1.9) 30 mintatos 28 ( 1.1) 2$ ( 1.7) 32 ( 1.2) 271 ( 1.3) 261 ( 2.9) 263 ( 1.9) 45 Wades 14 ( 0.8) 15 ( 1.6) 15 ( 1.0) 271 ( 1.9) 267 ( 4.2) 208 ( 1.9) An hour or more 15 ( 0.7) 14 ( 1.7) 12 ( 1.1) 269 ( 1.7) 261 ( 4.3) 258 ( 11) 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 stant4ard errors of the esumate for the sample. And, according to the students (Table 7 and Table A7 in the Data Appendix): In Idaho, some of the students (14 percent) reported that they spent no time each day on mathematics homework, compaird to 9 percent for the nation. Moreover, 15 percent of the studerts in Idaho 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 14 percent of White students, 18 percent of Hispanic students, and 30 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 14 percent of White students, 12 percent of Hispanic students, and 12 percent of American Indian students spent no time doing mathematics homework. 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho In addition, 14 percent of students attending schools in areas classified as "other" and 17 percent in schools in ext:eme =al areas spent an hour or more on matheimtics homework daily. In comparison, 15 percent of students attending schools in areas classified as "other" and 12 percent in schools in extreme rural areas spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the 'National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement.' Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. 5 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston. VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 45 Idaho The responses of the assessed students' teachers to the topic emphasis questions for each content area were combined to create a new variable. For each question in a particular content area, a value of 3 was given to "heavy emphasis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 46 THE 1990 NAEr TRIAL STATE ASSESSMENT Idaho TABLE 8 I Teachers' Reports on the Emphasis Given to 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Idaho West 'teflon Percentage wd loseacteney Percentage and Prole:honey Percadage and Preltdeney Teacher °emphases" categories by content areas Numbers and Operations Heavy emphasis 46 ( 1.8) 42 ( 1.4) 49 ( 3.8) 271 ( 1.1) 257 ( 3.8) 260 ( 1.8) Little or no emphasis 11 ( 0.7) 13 ( 2.1) 15 ( 2.1) 292 ( 2.7) 291 ( 6.6) 287 ( 3.4) Measurement Heavy emphasis 10 ( 1.1) 11 ( 2.8) 17 ( 3.0) 266 ( 2.5) 251 ( 7.7)1 250 ( 5.6) Little or no emphasis 41 ( 1.2) 38 ( 5.3) 33 ( 4.0) 276 ( 2.1) 275 ( 0.3) 272 ( 4.0) Geometry Heavy emphasis 14 ( 0.7) 24 ( 6.3) 2$ ( 3.8) 269 ( 2.2) 260 ( 2.8)! 260 ( 32) Little or no emphasis 34 ( 1.5) id ( 4.5) 21 ( 3.3) 288 ( 1.7) 277 (114)1 264 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 9 ( 0.8) 14 ( 3.7) 14 ( 2.2) 273 ( 3.3) 264 (10.8)1 269 ( 4.3) Little or no emphasis 70 ( 1.3) 54 ( 8.3) 53 ( 4.4) 273 ( 1.1) 282 ( 4.9) 281 ( 29) Algebra and Functions Heavy emphasis 58 ( 1.5) 43 ( 5.6) 46 ( 3.8) 281 ( 0.9) 277 1 52) 275 ( 2.5) Little or no emphasis 13 ( 02) 23 ( 5.1) 20 ( 3.0) 243 ( 2.4) 243 ( 4.2)1 243 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not isicluded. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 Idaho SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The infomiation on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: More than half of the eighth-grade students in Idaho (67 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Idaho, 69 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. About the same percentage of students in Idaho were taking eighth-grade mathematics (47 percent) as were taking a course in pre-algebra or algebra (50 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 Idaho spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. In Idaho, some of the students (14 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 15 percent of the students in Idaho 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 instnictional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 48 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho CHAPTER 4 rex° -2X-.9 IUI 1111111111111111111 111111111111111111111M111 111111111111111111111 II 11111111.1111111111111Mall 111111111W-11-111111.111111 1111111111, U 111111181111 MINS 1111111111ININME AV 11111111111 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 i ssessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. ° National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA; National Council of Teachers of Mathematics, 1991). r , THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Idaho From Table 9 and Table A9 in the Data Appendix: In Idaho, 8 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 40 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures xere 13 percent and 31 percent, respectively. In Idaho, 7 percent of students attending schools in areas classified as "other" and 12 percent in schools in extreme rural areas had mathematics teachers who got all the resources they needed. By comparison, in Idaho, 44 percent of students attending schools in areas classified as "other" and 31 percent in schools in extreme rural areas were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had mathematics achievement levels similar to those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of i Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NW TRIAL STATE ASSESSMENT Idaho West Nation Which of the following statements ts true about how well supplied you 8re 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 resources I need. I get same or none of the resources I need. Percentage Percentage Percentage and and and Proficiency Proficiency Proficiency 8 ( 1.7) 15 ( 5.2) 13 ( 2.4) 271 ( 2.8)1 281 ( 5.9)1 265 ( 4.2) 52 ( 1.9) 62 ( 3.8) 56 ( 4.0) 272 ( 1.3) 286 ( 4.1) 285 ( 2.0) 40 ( 1.1) 23 ( 8.1) 31 ( 4.2) 271 ( 1.0) 257 ( 3.7), 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 populatian of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.7 Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: About half of the students in Idaho (55 percent) worked mathematics problems in small groups at least once a week; some never worked mathematics problems in small groups (12 percent). The largest percentage of the students (64 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; some never used such objects (16 percent). In Idaho, 75 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 one-quarter of the students (29 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (38 percent). 7 Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Currkuium Eighty-second Yearbook of the National Society for the Study of Education (Chicago, IL: UMversity of Chicago Press, 1983). THE 1990 NAEP TRIAL STATE ASSESSMENT 51 TABLE 10 1 Teachers' Reports on Patterns of Mathematics i Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1990 NAEP TRIAL STATE ASSESSMENT Idaho West Nation , About how often do students work problems in small groups? At least ones a week Less than once a west( Never About how often do students use objects I like rulers, counting blocks, or geometric 1 solids? At toast one* a week Loss than once a weak Now Percentage end Profidency 55 ( 2.2) 272 ( 1.0) 33 ( 2.3) 271 ( 1.2) 12 ( 0-9) 272 ( 2.9) Percenlage Pontentage and end lintlidency Proficiency 57 ( 8.9) 262 ( 4.2)1 39 ( 7.6) 206 ( 4.5) 3 ( 2.2) ***) 50 ( 4.4) 200 ( 2.2) 43 ( 4.1) 244 ( 2.3) 5 ( 2.0) 277 ( 5.4)1 Percentage Percentage Percentage and and and Proficiency Prolleiency Proficiency 20 ( 1.2) 274 ( 1.5) 64 ( 1.1) 270 ( 0.8) 16 ( 0.6) 276 ( 2.0) 34 ( 8.2) 256 ( 4.9)1 57 ( 6.4) 265 ( 4.0) MN) 22 ( :1,7) 254 ( 3.2) 69 ( 3.9) 263 ( 1.9) ( 2.6) 282 ( 9-9)) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 52 THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE 1 1 I Teachers' Reports on Materials for I Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Idaho West Nation Plecentage Percentage Percentage About how often dO students do problems and and and from textbooks? Prefidenoy Preadency Picliciency Almost every day 75 ( 1.9) 55 ( 8.0) 62 ( 3.4) 274 ( 0.8) 270 ( 3.3) 267 ( 1.8) Several times a week 22 ( 1.8) 36 ( 51) 31 ( 3.1) 285 ( 1.9) 256 ( 5.2) 254 ( 2.9) About once a week or loss 3 ( 0.5) v.* 9 ( 4.9) ( 7 ( 1.6) 2430 ( 5.1)1 About how often do students do problems Percentage Percentage Percentage on worksheets? and and and Proficiency PnIficiorcy Proficiency AI lust several tknes a week 29 ( 2.0) 25 ( 5.2) 34 ( 3.5) 255 ( 1.5) 258 ( 4.3)t 255 ( 2.3) About once a week 34 ( 1.2) 34 ( 4.6) 33 ( 3.4) 270( 1.1) 256 ( 4.1 ) 210 ( 2.3) Less Man weekly 3$ ( 2.0) 41 ( 5.8) 32 ( 3.6) 27$ ( 12) 274 ( 42) 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. 1 Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). The next section presents the students' responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT 53 Idaho COLLABORATING IN SMALL GROUPS In Idaho, 41 percent of the students reported never working mathematics problems in small groups (see Table 12); 29 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 1990 MEP TRIAL STATE ASSESSMENT Idaho West Nation . Percentage and Pnancisnay Percentage arid Praidway Percentage owl Praia:no How often do you work in small groups in your mathematics class? AI WM ono a wit* 29 ( 1.0) 35 ( 4.6) 28 ( 2.5) 271 ( 1.2) 266 ( 4.2) 258 ( 2.7) Less trian once a week 29 ( 1.0) 29 ( 2.8) 23 ( 1.4) 274 ( 1.2) 271 ( 11) 267 ( 2.0) Nw 41 ( 1.1) 36 ( 4.6) 44 ( 2.9) 271 ( 1.1) 256 ( 2.0) 261 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Examining the subpopulations (Table Al2 in the Data Appendix): In Idaho, 29 percent of students attending schools in areas classified as "other" and 33 percent in schools in extreme rural areas worked in small groups at least once a week. Further, 29 percent of White students, 37 percent of Hispanic students, and 36 percent of American Indian 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 (30 percent and 29 percent, respectively). THE 3990 NAEP TRIAL STATE ASSESSMENT Idaho USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used inathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: About half of the students in Idaho (45 percent) never used mathematical objects; 21 pexcent used these objects at least once a week. Mathematical objects were used at least once a week by 20 percent of students attending schools in areas classified as "other" and 24 percent in schools in extreme rural areas. Males were as likely as females to use mathematical objects in their mathematics classes at least once a week (23 percent and 19 percent, respectively). In addition, 20 percent of White students, 28 percent of Hispanic students, and 19 percent of American Indian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1) NAEP TRIAL STATE ASSESSMENT Idaho Weal Nation How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Al lust once a weak LAMS than mai a week Pan:whip and Prollalancy 21 ( 1.3) 289 ( 1.6) 34 ( 1.1) 274 ( 1.1) 4$ ( 0.9) 271 ( 1,1) Parcantar Plavantage and and Proficiency Proficiency 30 ( 3.5) 260 ( 4.0) 2$ ( 1.8) 289 ( 2.7) ( 3.3) 258 ( 2.8) 2$ ( 1.8) 256 ( 2.6) 31 ( 1.2) 269 ( 1$) 41 ( 2.2) 259 ( 1.8) The standard errors of the estimated statistics appear m parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standarderrors of the estimate for the sample. G THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Idaho MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in Idaho 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): Many of the students in Idaho (83 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 83 percent of students attending schools in areas classified as "other" and 87 percent in schools in eXtrerne rural areas. TABLE 14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS ANO AVERAGE MATHEMATICS PROFICIENCY 1060 NAEP TRIAL. STATE ASSESSMENT . Idaho 1 West _ Nation . How often do you do maihemattcs problems from textbooks in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Proedeno Almost every day 83 ( 0.9) 71 ( 3.5) 74 ( 1.9) 274 ( 0.7) 267 ( 2.4) 267 ( 1.2) Several tknes a week 11 ( 0.6) 15 ( 1.5) 14 ( 0.8) 263 ( 1.8) 251 ( 2.4) 252 ( 1.7) About once a week or fess ( 0.6) 14 ( 3.1) 12 ( 1.1) 247 ( 3.6) 242 (11.2)1 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be sakl 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. Cl 56 T; iE 1990 NAEP TRIAL STATE ASSESSMENT Idaho And, for the frequency of worksheet usage (Table 15 and Table A IS in the Data Appendix): About one-quarter of the students in Idaho (27 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 24 percent of students attending schools in areas classified as "other" and 27 percent in schools in extreme rural areas. TABLE 15 I Students' Reports on the Frequency of I Mathematks Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY rMO NAEP TRIAL STATE ASSESSMENT Idaho West Nation How often do you do mathematics problems on worksheets in your mathematics class? Penuntage and Pranaionay Pereatill Old lArseldeaay ParCentage and Preadwacy At least several times a %wok 27 ( 1.7) 35 ( 4.0) 38 ( 24) 263 ( 1A) 250 ( 4.2) 253 ( 22) About once a week 26 ( 1.0) 23 ( 2.6) 25 ( 1.2) 270 ( 1.3) 262 ( 2.1) 281 ( 1.4) Less than woeMy 47 ( 1.5) 41 ( 4.1) 37 ( 2.5) 278 ( 1.1) 270 ( 3,4) 272 ( 1.9) The standard errors of the estimated StatirtiCS appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population i- 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. G THE 1990 NAEP TRIAL STATE ASSESSMENT 57 TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Idaho West nation =1111NIMMIIIIP Patterns of classroom instruction Permintop Saahmts Tenho* feramtags Similefts Taman MonamMags IMMO TmmWwwis Percentage of students who work mathematics problems in small groups At least once a week 29 ( 1.11) 55 ( 22) 35 ( 4.8) 57 ( 8.9) 28 ( 2.5) 50 ( 4.4) Less than once a week 29 ( 1.0) 33 ( 2.3) 29 ( 2.8) 39 ( 7.6) 28 ( 1.4) 43 ( 4.1) Never 41 ( 1.1) 12 ( 0.8) 36 ( 4,6) 3 ( 2.2) 44 ( 2.9!. 8 ( 2.0) Percentage of students who use objects like riders, countkv blocks, or geometric solids At least once a week 21 ( 1.3) 20 ( 1.2) 36 ( 3.5) 34 ( 8.2) 28 ( 1.8) 22 ( 3.7) Less than once a week 34 ( 1.1) 64 ( 1.1) 28 ( 57 ( 64) 31 ( 12) 69 ( 3.9) Never 4,5 ( 0.9) 16 ( 0.8) 36 ( 3.3) 8 ( 3.0) 41 ( 2.2) 9 ( 2.6) Materials for mathematics Percentage Pommy* Pondmilage instruction Shawl* Tamehms SWIM' Tanctims Shmimbi Tomblin Percentage of students wIro use a mathematics textbook Almost every day 83 ( 0.9) 75 ( 1.9) 71 ( 3.5) 55 ( 6.0) 74 ( 1.9) 62 ( 3.4) Several times a week 11 ( 0.6) 22 ( 1i) 15 ( 1S) 36 ( 5.1) 14 ( 0,8) 31 ( 3.1) About once a week or less ( 0.6) 3 ( 0.5) 14 ( 3.1) 9 ( 4.9) 12 ( 1.8) 7 ( 1.8) Percentage of students who use a mathematics worksheet At least several times a week 27 ( 4.7) 29 ( 2.0) 35 ( 4.0) 25 ( 5.2) 38 ( 2.4) 34 3.8) About once a week 26 ( 1.0) 34 ( 1.2) 23 ( 2.61 34 ( 4.6) 25 ( 12) 33 ( 3.4) Less than weekly 47 ( 1.5) 3$ ( 2.0) 41 ( 4.1) 41 ( 5.6) 37 ( 2.5) 32 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 58 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho 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 i)ractices are emerging, they are not yet commonplace. According to the students' mathematics teachers: About half of the students in Ida..o (55 percent) worked mathematics problems in small groups at least once a week; some never worked in small groups (12 percent). The largest percentage of the students (64 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and some never used such objects (16 percent). In Idaho, 75 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 one-quarter of the students (29 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (38 percent). And, according to the students: In Idaho, 41 percent of the students never worked mathematics problems in small groups; 29 percent of the students worked mathematics problems in small grows at least once a week. About half of the students in Idaho (45 percent) never used mathematical objects; 21 percent used these objects at least once a week. Many of the students in Idaho (83 percent) worked mathematics probh-Ans from textbooks almost every day, compared to 74 percent of students in the nation. About one-quarter of the students in Idaho (27 percent) used worksheets at least several times a week, compared to 38 percent in the nation. THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Idaho CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculatorg are important tools for mathematics and students need to be able to use them wicriy. 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.8 The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. 8 National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Table 17 provides a profile of Idaho eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 30 percent of the students in Idaho had teacher3 who allowed calculators to be used for tests. A greater percentage of students in Idaho than in the nation had teachers who permitted unrestricted use of calculators (28 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of Idaho Policies on I Calculator Use PERCENTAGE OF STUDENTS , 1000 NAEP TRIAL STATE ASSESSMENT Idaho West Nation _ Percentage of eighth-grade students in public schools whose teachers permit the unrestricted use a calculators Percentage of eighth-grade students In public schools whose teachers permit the use of calculators for tests Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned by the school Percentage Percentage Ponlentage 28 ( 2.0) 20 ( 4.0) 18 ( 3.4) 30 ( 14) 48 ( $.8) 33 ( 4.5) 50 ( 2.0) 72 ( 7.4) 56 ( 4.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of unerest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Idaho THE AVAILABILITY OF CALCULATORS In Idaho, most students or their families (99 percent) owned calculators (Table 18); however, fewer students (42 percent) had teachers who explained the use of calculators to them. Fmm Table A18 in the Data Appendix: In Idaho, 42 percent of White students, 45 percent of Hispanic students, and 42 percent of American Indian students had teachers who explained how to use them. Females were as likely as males to have the USC of calculators explained to them (42 percent and 42 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WM NAEP TRIAL STATE ASSESSMENT Idaho West Nation Do you or your family own a calculator? Yes No Does your mathematics teacher explain how to use a calculator for mathematics problems? Vas No Percentage Percentage Pommies* and and and Proficiency Proficiency lonsliciency 90 ( 0.3) 96 ( 0.6) 97 ( 0.4) 272 ( 0.7) 263 ( 2.8) 263 ( 1.3) Ot ) 3 ( OA) 234 ( 3.8) Percentage Percentage Percentage end and and Proliciency Proficiency Proficiency 42 ( 1.1) 59 ( 3.4) 49 ( 2.3) 268 ( OS) 280 ( 2.7) 255 ( 1.7) 58 ( 1.1) 41 ( 3.4) 51 ( 2.3) 274 ( 0.9) ( 3.0) 200 ( 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 141 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho THE USE OF CALCULATORS As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important *ills and content. As part of the Trial State Assessment, studf.ms were asked how frequently (never, sometimes, almost always) they used calm. is for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In Idaho, 27 percent of the students never used a calculator to work problems in class, while 43 percent almost always did. Some of the students (16 percent) never used a calculator to work problems at home, compared to 26 percent who almost always used one. Less than half of the students (38 percent) never used a calculator to take quizzes or tests, while 19 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calculator 1 for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Idaho West Nation 1 Percentage and Proadency Percerdage and Prenctemy Percentage and Pretidency How often do you use a calculator for the following tasks? Working problems in class Almost always 43 ( 1.1) 53 ( 2.1) 48 ( 1.5) 266 ( 1.0) 255 ( 2.6) 264 ( 1.5) Never 27 ( 1.2) 14 ( 2.4) 23 ( 1.9) 279 ( 1.3) 265 ( 3.0) 272 ( 1.4) Doing problems at home Almost always 26 ( 1.0) 29 ( 1.7) 30 ( 1.3) 272 ( 1.3) 283 ( 3.3) 261 ( 1.8) Never 18 ( 0.9) 19 ( 1.8) 19 ( 0.9) 273 ( 1.8) 258 ( 3.7) 263 ( 1.8) Taking quizzes or tests Almost always 19 ( 0.9) 25 ( 1.6) 27 ( 1.4) 269 ( 1.5) 259 ( 3.9) 253 ( 2.4) Never 38 ( 12) 22 ( 3.0) 30 ( 2.0) 280 ( 1.1) 270 ( 3.3) 274 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within Ti 2 standard errors of the estimate for the sample. The percentages may not total 100 percent bevause the "Sometimes" category is not included. THE 1990 NAEP TRIAL STATE ASSESSMENT 63 Idaho WHEN TO USE A CALCULATOR Part of the Trial State Assessment was nesignal to investigate whether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive itcms across the two sections. However, because of the sampling methodology used as pall of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who Lsed the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. C 64 THE 1990 NAEP TRIAL STATE ASSESSMENT The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: About the same percentage of students in Idaho were in the High group as were in the Other group. A smaller percentage of males than females were in the High group. In addition, 48 percent of White students, 53 percent of Hispanic students, and 27 percent of American Indian students were in the High group. TABLE 20 Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY tin MEP TRIAL STATE ASSESSMENT Idaho West Nation Parcaidage and Prof Manny Paraledage and Pralidency Parcodaga and Prafidency "Calculator-use- group High 48 ( 1.3) ( 2.6) 42 ( 13) 276 ( 0.9) 273 ( 2.7) 272 ( 1.6) Other 52 ( 1.3) 62 ( 2.6) 58 ( 1.3) 286 ( 1.3) 258 ( 2.8) 255 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard error: of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 Idaho SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instructional time to teaching students how to perform routine calculations by hand. Using calculators to replace this time-consuming process would create more instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 30 percent of the students in Idaho had teachers who allowed calculators to be used for tests. A greater percentage of students in Idaho than in the nation had teachers who permitted unrestricted use of calculators (28 percent and 18 percent, respectively). In Idaho, most students or their families (99 percent) owned calculators; however, fewer students (42 percent) had teachers who explained the use of calculators to them. In Idaho, 27 percent of the students never used a calculator to work problems in class, while 43 percent almost always did. Some of the students (16 percent) never used a calculator to work problems at home, compared to 26 percent who almost always used one. Less than half of the students (38 percent) never used a calculator to take quizzes or tests, while 19 percent almost always did. 171. 66 l'HE 1990 NAEP TRIAL STATE ASSESSMENT Idaho 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 Idaho, 27 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 tht., nation More than half of the students (63 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. Many of the students (80 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (xea!on, VA: National Council of Teachers of Mathematics, 1991). ",I r) THE 1990 NAEP TRIAL STATE ASSESSMENT 67 TABLE 21 I Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 10 NAEP TRIAL STATE ASSESSMENT Idaho Poroweage Pereardags ntrige Percentage of students whose mathematics teathers reported having the following degrees SaChe lor's degree 73 ( 14) OS ( 5.2) SO ( 4 .2) Master's or specialist's degree 27 ( 1.0) 32 ( 52) 42 ( 42) Doctorate or professional degree 0 ( 0.0) ( 0.0) 2 ( 1.4) Pwcentage of student, whose mathematics teachers have the **owing types of teaching certificates that art recognired by Idaho No regular certification 3 ( 0.4) 8 ( 2.4) 4 ( 1.2) Regular certification but less than the highest available 34 ( 1$) 20 ( 3.3) 29 ( 4.3) Highest certification available (permanent or long-term) 93 ( 14) 74 ( 3.3) Percentige of students whose mathematics teachers have the following types of teaching certificates that are rwcognized by Idaho Mathematics (middle school or secondary) 80 ( 1.0) fie ( 3.0) $4 ( 2.2) Education (elementary or middle school) 17 ( 0.9) 9 ( 24) 12 ( 24) Other 2 ( 0.3) 2 ( 1.3) 4 ( 1.5) 1 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 standarderrors 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 Idaho Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In Idaho, 34 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. Relatively few of the eighth-grade public-school students in Idaho (10 percent) were taw:4A mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and I Graduate Fields of Study PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Idaho West Nation What was your undergraduate major? Percentage Percentage Percentage Mathematics 34 ( 1.9) 31 ( 5.9) 43 ( 3.9) Education 47 ( 2.0) 34 ( SAS) 35 ( 3.8) Other 19 ( 1.2) 35 ( cc 22 ( 3.3) What was your graduate major? Percentage Percentage Percentage Mathematics 10 ( 1.8) 19 ( 4.7) 22 ( 3.4) Education 45 ( 1.9) 38 ( 4.5) 38 ( 34) Other or no graduate levei study 46 ( 1.4) 45 ( 5.4) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within .i. 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 69 Idaho Teachers' responses to questions concerning their in-service training for the year up to the Thal State Assessment (Table 23) show that: In Idaho, 36 percent of the eieith-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Some of the students in Idaho (19 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, I I percent of the students had mathematics teachers who spent no time on similar in-service training. TABLE 23 J Teachers' Reports on Their In-Senrice Training PERCENTAGE OF STUDENTS 1999 NAEP TRIAL STATE ASSESSMENT Idaho West NOW During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? None Ono to 15 hours le hours or mars Poetontago Percents. Pereentege 19 ( 1.0) 11 ( 3.0) 11 ( 2.1) 45 ( 2.0) 45 ( 7.0) Si ( 4.1) 38 ( 2.0) 44 ( SA) 39 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample, 70 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho SUMMARY Recent results trom international studies have shown that students from the United States do not compare favorably with students from othes nations in mathematics and science achievement." Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In Idaho, 27 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 stutients (63 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 Idaho, 34 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. Relatively few of the eighth-grade public-school students in Idaho (10 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. 10 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). 11 Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement NA EP's 1990 Assessment of the Nation and the Thal Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). 76 THE 1990 NAEP TRIAL STATE ASSESSMENT 71 Idaho In Idaho, 36 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Some of the students in Idaho (19 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. P'n: ''"' i I 72 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho 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 ;tate Assessment were asked a series of questions about themselves, their parents or guardiails, and home factors related to education. THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Idaho 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 !inning and schooling. Students participating in the Trial State Assessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports on Types of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ROO NAEP TRIAL STATE ASSESSMENT Idaho West Nation _ Does your family have, or receive on a regular basis, any of the following items: more then 2$ books, an encyclopedia, newspapers, magazines? Zero to two types Three types Far types and Progidensy Parcaniap and Progdancy Parcallieg* and givadancy 18 ( 0.9) 24 ( 1.8) 21 ( 1.0) 258 ( 1.9) 245 ( 4.1) 244 ( 2.0) 31 ( 1.4) 30 ( 1.0) 270 ( 1.2) 258 ( 2.4) 258 ( 1.7) 53 ( 1.2) 45 ( 1.9) 48 ( 1.3) 277 ( 0.8) 273 ( 3.2) 272 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The data for Idaho reveal that: Students in Idaho who had all four of these types of materials in the home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT A smaller percentage of Hispanic and American Indian students had all four types of these reading materials in their homes than did White students. About the same percentage of students attending schools in areas classified as "other" as in extreme tural 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 Tii State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 AMP TRIAL STATE ASSESSMENT Idaho West Nation Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency How much television do you usually watch each day? One how or less 19 ( 0.9) 14 ( 1.8) 12 ( 0.8) 278 ( 1.1) 269 ( 3.6) 269 ( 2.2) Two hours 26 ( 1.1) 20 ( 1.6) 21 ( 0.9) 276 ( 1.3) 26S ( 3.6) 286 ( 1.8) Three hours 24 ( 0.8) 20 ( 1-2) 22 ( 0.8) 272 ( 1.2) 262 ( 22) 268 ( 1.7) Four to Nye hours 24 ( 1.0) 29 ( 1.7) 2$ ( 1.1) ( 1.$) 263 ( 2.9) 260 ( 1.7) Slxhotasormora ( 0.0) 16 ( 2.0) 18 ( 113) 256 ( 2.7) 24$ ( 2.6) 245 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. r L.: I. f THE 1990 NAEP TRIAL STATE ASSESSMENT 75 Ida Ito From Table 25 and Table A25 in the Data Appendix: In Idaho, 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 Idaho (19 percent) watched one hour or less of television each day; 7 percent watched six hours or more. A greater percentage of males than females tended to watch six or more hours of television daily. However, a somewhat smaller percentage of males than females watched one hour or less per day. In addition, 6 percent of White students, 12 pescent of Hispanic students, and 10 percent of American Indian students watched six hours or more of television each day. In comparison, 19 percent of White students, 14 percent of Hispanic students, and 20 percent of American Indian 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 Idaho, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in Idaho (43 percent) did not miss any school days in the month prior to the assessment, while 21 percent missed three days or more. In addition, 21 percent of White students, 23 percent of Hispanic students, and 26 percent of American Indian students missed three or more days of school. 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Similarly, 23 percent of students attending schools in areas classified as "other" and 17 percent in schools in extreme rural areas missed three or more days of school. TABLE 26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1850 NAEP TRIAL Sn'..TE ASSESSMENT How many days of school did you miss last month? Ono or two days Three days or mars Panantaaa and londidancY 43 ( 1.0) 273 ( 1.1) 36 ( 1.0) 273 ( 1.1) 21 ( 1.0) 267 ( 13) Paramtais Pamela.* and and PreNdenay PraNdangy 43 ( 2.7) 2013 ( 3.5) 30 ( 1.4) 265 ( 3,0) 27 ( 1.6) 250 ( 3.1) 45( 1.1) 265 ( 1.6) 32 ( OA) 20$ ( 1.5) 23 ( 1.1) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 77 Idaho STUDENTS' PERCEPTIONS OF MATHEMATICS 4ording to the National Council of Teachers of Mathemat.. ;arning mathematics should requirr 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: I like mathematics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for solving everyday problems. A student "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly agree" were given a value of I (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's responses wen averaged over the five statements. The students were then assigned a percrption index according to whether they tended to strongly agree with the statements (an index of 1), tended to agree with the stlitements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statements (an index of 3). Table 27 provides the data for the students' attitudes toward mathrnatics as defined by their perceetion index. The following results were observed for Idaho: Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. About one-quarter of the students (29 percent) were in the "strongly agree" category (perception index of I). This compares to 27 percent across the nation. About one-quarter of the students in Idaho (22 percent), compared to 24 percent across the nation, were in thL "undecided, disagree, or strongly disagree" category (perception index of 3). i 2 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 75 fl Li THE 1990 NAEP TRIAL STATE ASSESSMENT TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ._-------..---.- MO NW TRIAL STATE ASSESSMENT Idaho West Nation Student 'perception mdex" groups Pernagdap and Prnicknig Ponstall and dralkienny PonsmOopo Pand rolidanso Strongly agr 29 ( 0.9) 27 ( 1.0) 27 ( 1.3) ("perception index" of 1) 251 ( 1.1) 273 5.4 271 ( 1.9) *O 40 ( 1.0) 411( 1.5) 49 ( I.0) ("perception index" of 2) 271 ( 0.11) 252 ( 2A) 262 ( 1.7) Undecided, disagree, strongly disagree 22 ( 1.1) 25 ( 2.1) 24 ( 1.2) ("perception index" of 3) 200 ( 1.5) 249 ( 2.9) 251 ( 14) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. The data related to out-of-school factors show that: Students in Idaho who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. THE 1990 NAEP TRIAL STATE ASSESSMENT 79 Idaho Some of the eighth-grade public-school students in Idaho (19 percent) watched one hour or less of television each day; 7 percent watched six hours or more. Average mathematics proficiency was lowesl for students who spent six hours or more watching television each day. Less than half of the students in Idaho (43 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 (29 percent) were in the "strongly agree" category relating to Audents' perceptions of mathematics. Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. 80 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Thal State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon which the assessment was based, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Educational Testing Service. The development of the Trial State Assessment Program beL-fitted 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 incomelete 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 Idaho The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting Oa general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required approximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets were spiraled or interleaved in a systematic sequence so that each booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as described in the incroduction to this report.' The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure A I). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Pmblem 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 Letermine the percentages of students who gave various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on students' performance on the set of mathematics items they received. IRT provides a common scale on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This common scale makes it possible to report on relationships between students' characteristics (Lased on their responses to the background questions) and their overall performance in the assessment. National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princvton, Educational Tesung Service, 1988). 82 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho FIGURE Al I Content Areas Assessed Numbers and Operations This content area focuses on students' understanding of numbers (whole numbers, fractions, decimals, Integers) and their apphcation 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 numeneal patterns, and verification of results are also includer.:. 11.11.easurement 110. This content area focuses on students' ability to describe real-world objects using numbers. Students are asked to identify attributes, select appropriate units, apply measurement concepts, and communicate measurement-related ideas to others. Questions are included that require an ability to read instruments using metric, customary, or nonstandard units, with emphasis on precision and accuracy. Questions requiring estimation, measurements, and applications of measurements of length, time, money, temperature, 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 be able to use informal reasoning to establish geometric relationships. Data Analysis, Statistics, and Probability This content area focuses on data representation and analysis across all disciplines and reflects the importance and prevalence of these activities in our society. Statistical knowledge and the ability to interpret data are necessary skills in the contemporary world. Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysis. Algebra and Functions This content area is broad in scope, covering algebraic and functional concepts in more Informal, exploratory ways tor the eignth-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 mears 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. 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 83 Idaho FIGURE A2 I Mathematical Abilities The following three categories of mathematical abilities are not to be construed as hierarchical. For example, problem solving Involves interactions be4Ween ConCeptual knowledge Oe procedural skills, but what is considered complex problem solving at one grade level may bt onsIderee conceptual understanding or procedural knowledge at another. CFnceptual Understanding Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts; can use and interrelate models, diagrams, and varied representations of concepts; can identify and apply principles; know and can apply facts and definitions: can compare, contrast, and integrate related concepts and principles; can recognize, interpret, and apply the signs, symbols, and terms used to represent concepts; arid can interpret the assumptions and relations involving concepts In mathematical settings. Such understandings are essential to performing procedures in a maaningful way and applying them in problem-solving situations. Procedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to select and apply appropriate procedures correctly, verify arid Justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors inherent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have been created as tools to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncomputational skills such as rounding and ordering. Problem Solving In problem solving, students are required to use their reasoning and analytic abilities when they encounter new situations. Problem solving includes the ability to recognize and formulate prehlems; 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. 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho 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 04o-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 defme levels at the extremes would therefore have been highly speculative. To defme 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 criteri, for selecting these "benchmark" items were as follows: To defme performance at level 200, items were chosen that were answered cormtly by at least 65 percent of the students whose proficiency was at or near 200 on the sca.le. 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. no ) TH E 1990 NAEP TRIAL STATE ASSESSMENT 85 Idaho 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 perfolming at each level. Each of the four proficiency levels was defmed by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter I provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.' Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were gAren to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and the 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. a Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho FIGURE A3 f Example Items for Mathematics Proficiency Levels Level 20o: Simple Addnive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 /77 Dab Cal 0 bleu bb 7. UAW Mot dub lags Mar a ohs mac aim sot siwas dams, bah oi ball so thaws Owe. If du Us sha sae bad a las Amu. wihke las siD Mass tas lessee ha bete 0 The bat wish cis soak bsik Ms ins wick the ma bias Tts Us iwcii ohs nib* bias 0 Us cart *A lEICAMPLE 2 11101Gla OF MOW ACM) AT ?AMWAY RAMS Mas %se SW lbws lbw Gras Wei Ompefesit IL How way buss of mops wilts picind ca Thunder, ss OD 60 0 7D so GD 90 0 I doWs blew. THE 1990 NAEP TRIAL STATE ASSESSMENT Grade 4 Overall Percentage Percentage Coned re UM 65 91 Correct 73% ftw Anchor Levels: MI MO loo Grade 4 Overall Percentage Corre,.. I% Percentage Correct for et4 :MAWS: 222 212 2QS1 2114 75 91 100 Grade a Overall Percentage Percentage Correct 2QQ 2N 76 87 COMICt 89% for Anchor Levels: 212Q /IQ 96 100 87 Idaho FIGURE A3 I Example Items for Mathematics Proficiency Levels (=timed) Level Mk Simple Multiplicative Reasoning and Two-Step Problem Solving EXAMPLE I 7. 'Mut is the value of + 3 whcn sm 3 t EXAMPLE 2 NAM 00101 OURVIT itotitop hams tt It* Dia SWIM Ilto tale am elan ae seas ti s senoy el belt eels. OA at clear Stew, sat a oink peas Newase as Am fa as talc Laki ma pen el at *en pie web sho saes ben win ad ivy ist der cskolszat so ais souks? 0 Ills 0 Ns EXAMPLE 3 O. Wiles is peals ends& Iwo basso. lack bps holds 4 Nadas. As has 24 bilk Meth swan sans= will kip ea Had est bew wet bean as will else c D 24 - at 24 + 24 + Op 24 o se 0 es I dess's Mow. Grade 8 Merelt Percentage Percentage Correct 2111 28 ee Correct 78% for Anchor Levels: ata 95 08 Grade 8 OderaN Percentage Correct 73% Percentage Correct for Anchor Levels: 292 2C2 21 08 92 92 Grade 8 Oven* Percentage Percentage Correct 37 71 Correct 77% for MOWN Lewis: aaa 95 100 ME 1990 NAEP TRIAL STATE ASSESSMENT Idaho FIGURE A3 Example Items for Mathematics Proficiency Levels (continued) EXAMPLE WbIelt et dr featetat ebowe the mak of NON die abase use& owe the bee It es EXAMPLE 2 110 At Mel wee dbat dot It tegiiitg. a ow II lees toe oloweiesd tau& seia I Wan Wt. Di the esete We Ire Mem weeil be netemegot iv ft Hilt wad towmot tub* MO m f s to if Tat tweets tekeleter ea tide beenteet C) %a 0 Ho THE 1990 NAEP ThIAL STATE ASSESSMENT Grade 5 00,118 Pomade. comet 80% Peroentage Coned for Mchor Lovely aggi 1412 33 49 77 90 Grade 12 Overa8 Paroontoe Correct 75% Percentage WIWI for Anchor Lovely 222 IN 48 79 95 Grade 8 Nora Percentsgo Correct 59% PereentaQ0 COM* f0( Anchor Lave* 214 ass 17 48 58 99 119 Idaho FIGURE A3 L Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability EXAMPLE 1 alleetiolo 16-17 re* so the tolloww4 puns of siot-Issures s e 2 2 $ 1 U. U shLs panels ot ates-kumrs M consiewet. how ISSay dOtl win be WI the 100* 0 100 OD 101 0 196 0 WO 2,3 I EXAMPLE 2 17. tolatet bow you feassi yeas mama so cuessiew 16. /viewer. Grad* 8 OvoreN Porcontago Comet 34% Porcentwo Coned tor Anchor Law*: 2IN 3D2 13 19 53 88 Grads 12 NOMA Peitentage COniet 49% Percentage Correct tor Mchor Laves: Z2Q MI aQ 22 48 90 Grade 8 Oman Peroentaga Correct 15% Percontwo Corroot for Anchor tavola. 20 &IQ 2172 11Q 1 4 28 74 Grat i2 °wag Percents.. Cam* 27% Poroontago Correct for Anchor Lavoie: 2I12 2111 3 22 74 90 MS 1990 NAHA TRIAL STATE ASSESSAERNI" Idaho SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and spezial priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEP's goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or'above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in 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, NAEll's total group and subgroup proficiency estimates are subject to a second source of uncertainty, in addition to sampling error. As p:zviously noted, each student who participx.ed in the Trial State Assessment was administered a subset of questions from the total !,et 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. r,. 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 Idaho In addition to reporting estimates of average proficiencies, proportions of students at or above particulat scale-score levels, and proportions of students fOving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the =certainty 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 of the goals of the Trial State Assessment Peogram is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population means and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small ( less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. 92 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho Analyzing Subgroup Differences in Proficiencies mid Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defined by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As an example, one rmght be interested in answering the question: Do students who reported spending 45 minutes or more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who rt!ported spending 45 minutes or more on mathematics homework is higher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in performance betwefm the two groups in the population because of the uncertainty associated with the estimated average proficiency of the groups in the sample. Remember that the intent is to make a statement about the entire population, not about the particular sample that was assessed. The data from the sample are used to make inferences about the population as a whole. As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have Iscen different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty 2ssociated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard er-or of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the manner in which the standard error for an individual group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups ± 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between groups in the population. If the interval does not contain zero, the difference between groups is statistically significant (different) at the .05 level. THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Idaho As an example, suppose that one were interested in determining whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a particular state's public 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 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 1 2.02 + 2.1: = 2.9 Thus, an approximate 95 percent confidence interval tbr this difference is :Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report. when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the 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 goups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups. the confidence interval included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a statistically significant difference in the population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. The procedure dercrsbed above (especially the estimation of the standard error of the difference) is, in a strict sense, only appropriate when the statistics being compared come from independent samples. i.or certain comparisons in the report, the groups were not independent. In those t;ases, a different and more appropriate) estimate of the standard error (,)f the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho 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 NAEP are statistics and therefore are subject to a certain degree of unct.rtainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol "!". In such cases, the standard errors -- and any confidence intervals or significance tests involving these standard errors -- should be interpreted cautiously. Further details concerning procedures for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgi oup Sample Sizes Results for mathematic: proficiency and background variables were tabulated and reported for groups defined by raceiethnicity and type of school community, as well as by gender and parents' education level. NAEP collects data for five racialethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian./Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not 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 Sins. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probability of .8 or greater. 1 1) THE 1990 NAEP TRIAL STATE ASSESSMENT 95 Idaho The effect size of .2 pertains to the true difference bemeen 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 Iv the standard deviation of the proficiency in the total population. If the true difference between subgioup and total group mean is .2 total-goup standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical report. Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage Description of Text in Report p = 0 None 0 < p S 10 Relatively few 10 < p 5 20 Some 20 < p 5 30 About one-quarter 30 < p 5 44 Less than half 44 < p 5 55 About half 55 < p 5_ 69 More than half 69 < p 5 79 About three-quarters 79 < p 5 89 Many 89 < p < 100 Almost all p = 100 All 90 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho THE NATION'S REPORT CARD DATA APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains corresponding data for each level of the four reporting subpopulations race, ethnicity, type of community, parents' education level, and gender. THE 1990 NAEP TRIAL STATE ASSESSMENT 97 Idaho TABLE A5 I Students' Reports on the Mathematics Class 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pro-algebra Algebra TOTAL Percentage and Proficiency Percentage and Proficiency Percentallit and ProRclency State 47 ( 11) 32 ( 1 2) 18 ( 1.1) 264 0.7) 271 ( 1.1) 301 ( 1.2) Nation 82 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 296 ( 2.4) RACE/ETHNICITY White State 46 ( 1.1) 33 ( 12) 19 ( 1.2) 266 ( 0.7) 272 ( 1.1) 302 ( 1.3) Nation 59 ( 2.5) 21 ( 2.4) 17 ( 1.5) 259 ( 1.6) 277 ( 2.2) 300 ( 2.3) Hispanic State 53 ( 246 ( 3.4) 2.6) 26 ( 2.8) ...) Nation 75 ( 4.4) 13 ( 3.9) 6 ( 1.5) 240 ( 2.4) ** American Indian State 55 ( $.1) 27 ( 5.2) ....) 7 ( 4.0) ( *el Nation 8 ( 7.2) "") 5 ( 2.7) ...) TYPE OF COMMUNITY Factreme rural State ( 3.7) 34 ( 2.9) 15 ( 1.6) 203 ( 2.6) 288 ( 1.4) 295 ( 1.5) Nation 74 ( 249 ( 4.5) 3.1)I 14 ( 5.0) 7 ( 2.2) .. ) Other State 44 ( 1.5) 33 ( 1.8) 19 ( 1.6) 263 ( 1.5) 272 ( 1.4) 302 ( 1.5) Nation 81 ( 2.2) 20 ( 2.1) 16 ( 1.4) 251 ( 2.0) 272 ( 2.8) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within J. 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 r; t 98 THE 1990 NAEP TRIAL STATE ASSESSMENT PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY Eighth-grade Mathematics Idaho TABLE A5 I Students' Reports on the Mathematics Clam (continued) I They Are Taking 1900 NAEP TRIAL STATE ASSESSMENT Pre-algebra Algebra Percentage -----PerPereentage and and and Profkiency Proficiency Proficiency TOTAL State 47 ( 1.1) 32 ( 1.2) 18 ( 1.1) 264 ( 0.7) 271 ( 1.1) 301 ( 1.2) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 296 ( 2.4) PARENTS EDUCATION NS non-graduate state 61 ( 4.8) 9 ( 3.0) 249 ( 2.7) 111- *IN Nation 77 ( 3.7) 13 ( 3.4) 241 ( 2.1) HS graduate State 56 ( 2.8) 32 ( 2.5) 257 ( 1.7) 264 ( 2.2) Nation 70 ( 2.6) 18 ( 2.4) 8 ( 1.1) 249 ( 1.9) 266 ( 3.5) 277 f 5.2) Some college State 46 ( 2.2) 36 ( 2.2) 15 ( 1.5) 270 ( 1.5) 272 ( 1.9) 302 ( 2.2) Nation 60 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2 1, 276 ( 2.8) 295 ( 3.2) Canoga araduate State 41 I .a) 271 t 1.0) 32 ( 1.7) 275 ( 1.3) 25 ( 2.0) 303 ( 1.6) Nation 53 2.7) 21 ( 2.3) 24 ( 1.7) 25i-) ( 1.5) 278 ( 2.8) 303 ( 2.3) GENDER Male State 49 ( 1.5) 31 ( 1.6) 17 ( 1.3) 266 ( 1.0) 273 ( 1.3) 304 ( 1.7) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 2.5) Female state 45 ( 1.5) 33 ( 1.6) 19 ( 1,3) 262 ( 0.9) 269 ( 1.4) 298 ( 1,4) Nation 61 ( 2.6) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear 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 s2.mple. The percentag s may not total 100 percent because a small number of students reported taking other mathematics courses. *" Sample size is insufficient to permit a rehable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Idaho TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ,111.1111.....11111 1290 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes An Hour or More TOTAL State Nation RACE/ETHNICITY Persentage and Prof Molloy 4 ( 0.5) 245 ( 2.7) 1 ( 0.3) tv. 4 ( 0.5) 248 ( 2.8) 1 ( 0.3) v.* ( 11.-** ) ( 0.8) .411 *4,11 ) 5 ( 3.9) 1." ( 0 ( 0.0) --* ***) 4 ( 1.1) ( 0.0) ( 4 ( 0.6) I ( 04) Peiventage and Proficiency 43 ( 1.4) 269 ( 1.0) 43 ( 42) 256 ( 2.3) 43 ( 1.5) 272 ( 1.0) 39 ( 4.5) 286 I 22) 44 ( 4,3) 250 ( 3.9) 48 ( 7,8) 245 ( 3.0)1 49 ( 9.4) 74 (31.9) 41 ( 4.4) 265 ( 1.9) 68 (14.9) 253 ( 5.4)I 44 ( 1.9) 271 ( 1.2) 37 ( 4.3) 258 ( 3.11 Percentage and Proficiency 43 ( 1.5) 273 ( 1.1) 43 ( 4.3) 268 ( 2.8) 43 ( 15) 275 ( 1.1) 45 ( 5.1) 270 ( 2.7) 48 ( 4.5) 249 ( 3.7) 34 ( 8.8) 251 ( 4.2)1 44 ( 8.1) ( 22 (28.2) ( .") 45 ( 5.3) 270 ( 2.5) 14 (10.91 42 ( 2.1) 274 ( 1.4) 49 ( 5.1) 285 ( 2.5) Percentage and Prolktiency 8 ( 1.1) 265 ( 3.8) 10 ( 1.9) 272 ( ( 1.1) 255 ( 3.7) 11 ( 2.4) 277 ( 7.8)i 1 ( 0.6) 13 ( 2.9) ***) ( 05) 4,41 04* ( 9 ( 3.4) 275 ( 2.8)1 8 ( 5.6) ( 0.9) 290 ( 4.7) 10 ( 24) 278 ( 8.8)1 Pireatellp and Pioltdency 2 ( 0.3) 4 ( 0.9) 278 ( 5.1)) 2 ( 0.4) 4 ( 0.9) 279 ( 5.8)t 1 ( 0.4) INNb Ffra ( ***) 0 ( 0.0) ( «4) 4 ( 4.8) .11,4) 2 ( 0.6) 10 ( 7.3) 2 ( 0.2) 4 ( 1.1) 282 (11.8)1 White State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Extreme rural State Nation Other State Nation AmRommin 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 caii:ion -- the nature of the sampk. does not allow accuratr determination of the variability of this estimated mean proficiency. *1" Sample size is msufficient to permit a rehable estimate (fewcr than 62 students). 100 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE Ab (continued) Teachers' Reports or4 the Ammmt of Time Students 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 Hour or More - TOTAL Peroentage and Proficiency 4 ( 0.5) 245 ( 2.7) ( 0.3) es.) 6 ( 2.4) ( 41I1* 5 ( 1.1) 4*1(44*) 1 ( OS) 5 ( 1.2) ( 3 ( 0.6) 4** ( *") 0 ( 0.3) ( II) 5 ( 0.7) I" ( Ill) 1 ( 0.3) I" ( "I) 4 ( 0.6) "I ( I") 1 ( 0.4) "I ( I") Permeate and Proficiency 43 ( 1.4) 269 ( 1.0) 43 ( 44) 256 ( 2.3) 45 ( 4.3) 248 ( 4.0) 49 ( 6.3) 240 ( 2.8) 46 ( 3.4) 264 ( 2.2) 43 ( 52) 249 ( 3.1) 44 ( 2.2) 273 ( 2.1) 44 ( 5.4) 265 ( 2.8) 41 ( 2.0) 277 ( 1,3) ( 4.7) 265 ( 2.5) 44 ( 1.7) 270 ( 1.2) 44 ( 4.4) 257 ( 2.9) 43 ( 1.9) 269 ( 1.4) 41 ( 4.4) 255 ( 2.3) Percentage and Proficiency 43 ( 1.5) 273 ( 1.1) 43 ( 4.3) 266 ( 2.6) 45 ( 4.5) 255 ( 3.5) 40 ( 6.1) 246 ( 3.7) 40 ( 32) 261 ( 22) 44 ( 5.8) 258 ( 2.7) 42 ( 2.1) 278 ( 1.6) 43 ( 5.8) 270 ( 3.6) 45 ( 2.1) 281 ( 1.6) 44 ( 4.1) 277 ( 3.0) 43 ( 1.7) 275 ( 1.4) 43 ( 4.3) 268 ( 2.9) 43 ( 1.9) 272 ( 1.3) 43 ( 4.7) 264 ( 2.8) Percentage and Proficiency ( 1.1) 285 ( 3.8) ( 1.9) 272 ( 5.7)1 3 ( 1.4) 8 ( 2.0) I" ( I") 9 ( 3.1) 7 ( 1.6) 7 ( 2,1) I" ( I") 9 ( 1.3) 295 ( $.2) 11 ( 2.3) 287 ( 6.1)1 7 ( 1.2) 285 ( 5.1) 9 ( 1.9) 273 ( 7.3)1 9 ( 1.2) 285 ( 3.8) 11 ( 2.0) 272 ( 5.7)1 Percentage and Proficiency 2 1 0.3) 4 ( 0.9) 278 ( 5,1)1 1 ( 0.6) ***) 1 ( 0.4) 3 ( 1.0) 41-4111 ( *It ) 4 ( 1.0) ( ***) 5 ( 1.3) «h.) 2 ( 0.5) 5 ( 1.3) 279 ( 7.7)1 2 ( 0.4) 4 ( 0.9) State Nation PARENTS EDUCATION HS non-graduate State Nation HS graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, 11,e 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 101 Idaho TABLE A7 I Students' Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT 1 None 15 Minutes 30 Minutes 45 Minutes An Hour or More TOTAL Percentage and Proficiency Percentage and Proaciency Percentage and Proficiency Percentage and Profidancy Percentage and Proficiency State 14 ( 0.8) 29 ( 1.1) 28 ( 1.1) 14 ( 0.8) 15 ( 0.7) 272 ( 1.9) 274 ( 1.1) 271 ( 1.3) 271 ( 1.9) 269 ( 1.7) Nation ( 0.8) 31 ( 2.0) 32 ( 1.2) 16 ( 1.0) 12 ( 1.4) 251 ( 2.8) 204 ( 1.9) 263 ( 1.9) 206 ( 1.9) 258 ( 3.1) RACE/ETHNICITY White State 14 ( 0.9) 29 ( 1.2) 28 ( 1.1) 14 ( 0.9) 14 ( 0.7) 274 ( 2.0) 276 ( 1.3) 273 ( 1.3) 273 ( 2.0) 273 ( 1.9) Nation 10 ( 1.0) 33 ( 2.4) 32 ( 1.3) 15 ( OA) 11 ( 1.3) 258 ( 3.4) 270 ( 1.9) 270 ( 2.1) 277 ( 2.2) 268 ( 3.3) Hispanic State 12 ( 2.4) 24 ( 3.6) 414 Mr ) Nation 12 ( 0 ( 1.8)) 27 ( 246 ( 3.0) 3.6) 30 ( 248 ( 2.6) 3.4) 17 ( 241 ( 2.1) 4.3) 14 ( 1.7) 441 American Indian State 12 ( 3.1) "4) 4, 14 ( 42) «4) 30 ( 7.1) 0** ( ) ( ) Nation 13 ( 5.3) 30 (10.0) ***) 27 ( 6.7) 24 (142) ft* ( 111 1 ( 6 ( 6.4) TYPE OF COMMUNITY Extreme nye! State 12 ( 1.0) 31 ( 1.4) 23 ( 1.4) 16 ( 1.2) 17 ( 1.0) 271 ( 3.0) 272 ( 4.8) 265 ( 1.5) 268 ( 3.1) 29 ( 2.4) Nation 36 ( 260 ( 4.6) 3.5)' 311 2551 2.3) 5.1)1 18 ( 3.8) 7 ( 2.7) Other State 15 ( 1.1) 28 ( 1.4) 29 ( 1.4) 13 ( 1.0) 14 ( 0.8) 271 ( 2.3) 274 ( 1.6) 273 ( 1.6) 271 ( 2.5) 269 ( 2.3) Nation 9 ( 1.0) 30 ( 1.8) 32 ( 15 ( 1.1) 13 ( 1.1) 250 ( 3.8) 263 ( 2.3) 264 ( 2.3) 267 ( 2.1) 258 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r 102 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A7 I Students' Reports on the Amount of Time They (continued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes ... An Hour or More TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 14 ( 0.8) 29 ( 1.1) 28 ( 1.1) 14 ( 0.8) 15 ( 0.7) 272 ( 1.9) 274 ( 1.1) 271 ( 1.3) 271 ( 1.9) 269 ( 1.7) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 16 ( 1.0) 12 ( 1.1) 261 ( 2.8) 284 ( 1.9) 263 ( 1.9) 266 ( 1.9) 258 ( 3.1) PARENTS' EDUCATION non-graduate State 13 ( *44 2.7) .41 27 ( 1040 ( 2.9) 31 ( 3.4) 13 ( ( 2.7) 15 ( *** 3.5) ft* ) Nation 17 ( 40-4,4 3.0) 26 ( 246 ( 3.3) 4.0) 34 ( 248 ( 4.4) 2.6) 12 ( 2.5) «iv) 10 ( 41* ( 22) ) HS graduate State 15 ( 19) 28 ( 2.1) 26 ( 2.4) 17 ( 2.1) 14 ( 1.5) 2$8 ( 4.1) 267 ( 2.5) 262 ( 2.3) 262 ( 4.2) 255 ( 2.9) Nation 10 ( 1.7) 33 ( 22) 31 ( 1.9) 16 ( 1.4) 11 ( 1.5) 246 ( 4.2) 259 ( 3.2) 254 ( 2.4) 256 ( 2.8) 244 ( 3.4) Some college State 16 ( 1.8) 30 ( 2.2) 26 ( 1.9) 14 ( 2.0) 13 ( 2.0) 275 ( 2.6) 277 ( 2.2) 275 ( 2.9) 269 ( 3.2) 276 ( 3.2) Nation 9 ( 12) 30 ( 2.7) 36 ( 2.1) 14 ( 1.8) 11 ( 1.5) 266 ( 3.0) 266 ( 2.6) 274 ( 3.5) 4-4', ( College graduate State 13 ( 1.3) 29 ( 1.4) 29 ( 1.4) 13 ( 1,1) 16 ( 1.2) 282 ( 2.7) 280 ( 1.9) 278 ( 1.7) 281 ( 2.7) 277 ( 2.1) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Male State 19 ( 1.2) 30 ( 1,4) 26 ( 1.6) 13 ( 1.2) 12 ( 1.0) 273 ( 2.4) 275 ( 1.5) 273 ( 1.6) 273 ( 2.8) 268 ( 2,4) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 266 ( 2.4) 26$ ( 3.0) 258 ( 4.1) Rune!. State 9 ( 1.1) 28 ( 1,7) 30 ( 1.3) 15 ( 1.3) 17 ( 1.2) 270 ( 3.5) 272 ( 1.6) 269 ( 1.8) 270 ( 2.3) 270 ( 2.3) Nation 7 0,9) 28 ( 2.0) 35 ( 1.7) 17 ( 1,0) 13 ( 1.3) 246 ( 41) 263 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 103 Idaho TABLE A8 I Teachers' Reports on the Emphasis Given To 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHFMATICS 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 Percentage and Prof Mency Percentage and Proficiency Percentage and Proficiency State 48 ( 1.8) 11 ( 0.7) 10 ( 1.1) 271 ( 1.1) 292 ( 2.7) 266 ( 2.5) Nation 49 ( 3.8) 15 ( 2.1) 17 ( 3.0) 260 ( 1.8) 287 ( 3.4) 250 ( 5.6) RACE/ETHNICITY While State 48 ( 1.6) 12 ( 0.9) 10 ( 12) 273 ( 1.1) 293 t 2.9) 269 ( 2.6) Nation 48 ( 3.7) 16 ( 2.4) 14 ( 3.4) 267 ( 2.2) 289 ( 3.5) 259 ( 6.9)1 Hispanic State 57 ( 5.3) 253 ( 4.1) 6 ( 1.8) ...) 11 ( 2.8) ...) Nation 47 ( 8.7) 248 ( 4.6) 8 ( 2.2) .4. ...) 23( 4.1) American Indian State 47 ( 7.7) - ( *4* 3 ( 2.3) 4" ( 4") 9 ( 4.7) ...) Nation 84 (18.5) Itit ( 1'4 6 ( 6.9) 444 ( 444) ( 8.7) ...) TYPE OF COMMUNITY Extreme rural State 61 ( 4.9) 7 ( 1.0) 8 ( 2.6) 269 ( 1.9) 281 ( 4,0) 261 ( 7.4)i Nation 53 (12 4) 257 ( 7.1)i ( 3.6) **if ( 6 ( 4.9)) Other State 42 ( 2.2) 12 ( 1.1) 10 ( 1.2) 271 ( 1.8) 291 ( 3.2) 266 ( 3.5) Nation 52 f 4.1) 16 ( 2.7) S6 ( 3 9) 260 ( 2.3) 286 ( 3.6) 253 ( 7.1)1 Percentage Percentage Percentage and and and Proficiency Proficiency Proficiency 44 t 12) 14 ( 0.7) .14 ( 1.5) 276 ( 2.1) 269 ( 2.2) 268 ( 1.7) *.e3 ( 4.0) 28 ( 3.8) 21 ( 3.3) 272 ( 4.0) 260 ( 3.2) 264 ( 5.4) 4,2 ( 1.2) 279 ( 2.3) 36 ( 4.7) 277 ( 4.3) 30 ( 4.2).) 34 ( 5.8) 255 ( 4.4)1 47 ( 8.8) ) 13 (15.5) ) 40 ( 3.9) 270 ( 3.3) 32 (11.7) 2651 9.1 )1 41 ( 1.8) 277 ( 2.6) 34 ( 5.3) 270 ( 4.6) 14 ( 0.8) 270 ( 2.2) 27 ( 4.4) 265 ( 3.3) 9 ( 2.8) ...) 27 6.8) 14 ( 7.8) ( .4. ) 16 (19.7) ...) 7 ( 1.1) 268 ( 7.2) 9 ( 6.1) 4 ..) 15 ( 1.0) 269 ( 2.3) 28 ( 4.6) 260 ( 3.9) 34 ( 1.6) 270 ( 1.7) 22 ( 3.4) 273 ( 5.8) 34 ( 4.4) 41. ***) 16 ( 5.5) 44 ( 9,0) 0*, ( *01 8 (10.4) 44. ...) 37 ( 4.4) 267 ( 2.0) 16 ( 7.9) 33 ( 1.7) 268 ( 2.2) 24 ( 4.3) 265 ( 5.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that for each population of interest, the value for the entire population is within t 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 amurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 it 104 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE AS I Teachers' Reports on the Emphasis Given to (continued) 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Numbers and Operations nurement Geometry Heavy Emphasis -..1 Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage and Proticiem Percentage and Prcaciency Percentage and Preedency Percentage aid Pro !Weeny Percentage and Pratidenay Percentage aid Proeciency State 48 ( 1.8) 11 ( 0-7) 10 ( 1.1) 41 ( 1.2) 14 ( 0.7) 34 ( 1.5) 271 ( 1.1) 292 ( 2.7) 206 ( 2.5) 276 ( 2.1) 266 ( 2.2) 266 ( 1.7) Nation 49 ( 3.8) 15 ( 2.1) 17 ( 3.0) 33 ( 4.0) 2$ ( 3.5) 21 ( 3.3) 260 ( 1.8) 287 ( 3.4) 250 ( 5.6) 272 ( 4.0) 250 ( 3.2) 264 ( 5.4) PARENTS EDUCATION HE non-graduate State 52 ( 255 ( 5.6) 4.1) ( 2.2) *IN ) 34 ( INN ( 5.0) 10 ( 3.1) ( 441 Nation 60 ( 6.9) 251 ( :AA) 7 ( 2.3) 22 ( 5.3) h.) *44 IIM14) 32 ( 63) .44.) HS graduate State 53 ( 2.0) 11 ( 2.2) 35 ( 16 ( 2.0) 33 ( 2.8) 264 ( 2.2) ( ( 7.2)1 269 ( 4.2) 268 ( 5.1) 261 ( 3,3) Nation 55 ( 4.8) 11 ( 2.8) 17 ( 3.9) 27 ( 5.0) 27 ( 4.5) 24 ( 5.1) 269 ( 2.9) ( INN ) 251 ( 8.1)! 253 ( 4.7)1 255 ( 4.2) 246 ( 4.8)1 Same college State 50 ( 2.8) ( 2.0) 42 ( 2.1) 13 ; 1.9) 321 22) 276 ( 1.9) 268 ( 5.5)I 275 ( 2.9) 270 ( 4.1) 270 ( 2.8) Nation 47 ( 4.4) 17 ( 3.3) 12 ( 2.7) 39 ( 5.5) 27 ( 5.0) 23 ( 4.1) 265 ( 2.6) 284 ( 4.1)1 ( 279 ( 4.5) 262 ( 4.8)1 270 ( 4.7) College graduate State 44 ( 2.3) 13 ( 1.2) 10 ( 1.5) 45 ( 1.9) 13 ( 1.5) 34 ( 2.1) 276 ( 1.5) 298 ( 3.9) 273 ( 4.4) 285 ( 3.0) 274 ( 3.8) 275 ( 2.0) 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 48 ( 2.2) 10 ( 0.9) 10 ( 1.4) 40 ( 1.9) 13 ( 1.1) 35 ( 2.0) 272 ( 1.3) 293 ( 2.7) 272 ( 4.0) 280 ( 2.6) 272 ( 2.3) 270 ( 2.4) Nation 48 ( 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) 206 ( 6.8) Female State 48 ( 1.9) 12 ( 1.0) 10 ( 1.5) 42 1.7) 14 ( 1.1) 33 ( 2.0) 269 ( 1.8) 290 ( 3.6) 260 ( 3.3) 273 ( 23) 267 ( 2.9) 265 ( 2.0) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 280 ( 2.0) 286 ( 3.3) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 263 ( 5.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimad mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 t THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Idaho TABLE A8 I Teachers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT -, Analysis, Statistics, and Probability Algebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentaga end Proficiency 9 ( 0.8) 273 ( 3.3) 14 ( 2.2) 269 ( 4.3) 9 ( 0.9) 276 ( 35) 14 ( 2.4) 276 ( 4.1) 1 ( 1.1) *** (***) 3 ( 4.2) *. ***) ( 1.7) *14 ( *IN 5 ( 5.4) 8 ( 0.9) 272 ( 3.5) 15 ( 2.9) 287 ( 4.7) Percentage end Proficiency 70 ( 1.3) 273 ( 1.1) 53 ( 4.4) 261 ( 2.9) 70 ( 1.4) 276 ( 1.1) 53 ( 5.0) 271 ( 3.1) 68 ( 4.3) 241 ( 5.4) 56 ( 6.3) 248 ( 4.4) ( 82 (29.1) 71 ( 3.3) 269 ( 2.2) 65 (16.9) 254 ( 6.7)i 70 ( 1.8) 273 ( 1.6) 53 ( 5.2) 260 ( 3.4) Percentege and Proficiency Se ( 1.5) 28/ ( 0.9) 48 ( 3.6) 275 ( 2.5) 58 ( 1.6) 282 ( 1.0) 48 ( 4.2) 281 ( 3.0) 39 ( 5.1) ( 46 ( 5.9) 257 ( 4.0)1 45 ( 8.4) 16 (213) 01,11. 51 ( 4.9) 275 ( 1.9) 33 ( 8.1) 58 ( 2.0) 282 ( 1.1) 47 ( 4_3) 276 ( 2.8) Percentage and Pronclency 13 ( 0.9) 243 ( 2.4) 20 ( 3.0) 243 ( 3.0) 12 ( 0.9) 245 ( 2.4) 18 ( 2.8) 251 ( 3.3) 22 ( 3.2) ( *41 I) 18 ( 4.2) *44. **It) 14 ( 6.5) .44 87 13 ( 2.1) 248 ( 3.3) 42 (16.0) ( 5.9)1 13 ( 1.0) 242 ( 2.7) 17 ( 3.3) 245 ( 4.4)1 State Nation RACE/ETHNICITY White State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY 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 ei.rors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis- category is not include& ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 106 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TAB1,E AS 1 Teachers' Reports on the Emphasis Given To (continued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No _ Emphasis TOTAL Percentage and Proficiency Percerdage and Proficiency Percentage and Proficiency Percentage and Proficiency State 9 ( 70 ( 1.3) 56( 1.5) 13 ( 0.9) 273 ( 3.3) 273 ( 1.1) 261 ( 0.9) 243 ( 2.4) Nation 14 ( 2.2) 53 ( 4.4) 46 ( 3.0) 20 ( 3,0) 269 ( 4.3) 261 ( 2.9) 275 ( 2.5) 243 ( 3.0) PARENTS' EDUCATION HS non-graduate State 79 ( 3.9) 43 ( 5.3) 253 ( 4.5) 281 ( 4.9) Nation 53 ( 240 ( 7.7) 6.2) 29 ( 8.9) ii**) HS graduate State *.. 65 ( 262 ( 3.0) 2.0) 48 ( 271 ( 2.8) 2.1) 14 ( 236 ( 2.1) 3.8) Nation 17 ( 3.7) 54 ( 5,4) 44 ( 4.8) 23 ( 3,9) 261 ( 6.0)1 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Some college State 72 ( 2.6) 59 ( 2.3) 278 ( 2.0) 281 ( 2,4) ( Nation 13 ( 2.5) 57 ( 5.8) 48 ( 4.8) 17 ( 3.1) ( 270 ( 3.-1 278 ( 3.0) ( ***) College graduate State 9 , 1,3) 69 ( 1,8) 62 ( 2,0) 10 ( 1.2) 282 ( SA) 283 ( 1.8) 288 ( 1.6) 250 ( 2.7) Nation 15 ( 2.4) 53 ( 4,4) SO ( 3,9) 18 ( 2,4) 282 ( 4.5) 275 ( 3.8) 288 ( 3.0) 249 ( 4.0) GENDER Male State 8 ( 0,9) 71 ( 1.5) 54 ( 2.0) 14 ( 1.2) 272 ( 4.1) 274 ( 1.6) 280 ( 1.3) 242 ( 2.2) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.6) 275 ( 5.8) 260 ( 3.5) 276 ( 3.2) 243 ( 3.0) Fomale State 9 ( 1.3) 69 ( 1,7) 58 ( 1.8) 11 ( 1.0) 274 ( 3.7) 271 ( 1.2) 282 ( 1.5) 244 ( 4.3) Nation 16 ( 2.4) 53 ( 4.5) ( 3.6) 18 ( 2.9) 263 ( 4.4) 262 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire populathm is within .1 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. f. 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 Idaho TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL I Get All the Resources I I Get Most of the I Oct Some or None of STATE ASSESSMENT Nesd Resources I Need the Resources I Need TOTAL Percentile ow' PrclicieneY Pereentage and Proficiency Percentage and Proficiency State $ ( 1.7) 52 ( 1.9) 40 ( 1.1) 271 ( 2.6)1 272 ( 1.3) 271 ( 1.0) Nation 13 ( 2.4) 50 ( 4.0) 31 ( 4.2) 265 ( 4.2) 205 ( 2.0) 261 ( 2.9) RACE/ETHNICITY White State 8 ( 1.9) 52 ( 2.2) 41 ( 1.2) 274 ( 2.1)1 275 ( 1.3) 273 ( 1.1) Nation 11 ( 2.5) 58 ( 4.6) 30 ( 4.8) 275 ( 3.5)1 270 ( 2.3) 287 ( 3.3) Hispanic State 10 ( 2.5)*) 58 ( 248 ( 4.6) 3.4) Nation 23 ( 7.6) 44 ( 4.9) 34 ( 7.7) 248 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 American Indian State ( 3.4) 42 ( 9.4) Vi Nation *** ( ***) 72 (26.8) 22 (20.7) TYPE OF COMMUNITY Extreme rural State 12 ( 5.9) 57 ( 4.8) 31 ( 4.0) 275 ( 4.9)1 268 ( 1.2) 264 ( 1.9) Nation 2 ( 2.R) 54 (10.4) 43 (10.3) ( 260 ( 6.9)1 257 ( 5.0)1 Other State 7 ( 1.2) 50 ( 1.9) 44 ( 1.4) 270 ( 2.7) 273 ( 1.7) 272 ( 1.1) Nation 11 ( 2.9) 58 ( 5.4) 31 ( 5.6) 265 ( 3.9)1 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "'It Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TAB! A9 I Teachers' Reports on the Availability of (continued) Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL I Get All the Resources I I Get Most of tho I Gt Some or None of STATE ASSESSMENT Need Resources I Need the Resources I Need TOTAL Percentage and Proficiency Percentage and Pronclancy Percentage and Profichincy State ( 1.1) 52 ( 1.9) 40 ( 1.1) 271 ( 2.6)t 272 ( 1.3) 271 ( 1.0) Nation 13 ( 2.4) 58 ( 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 261 ( 2.9) PARENTS EDUCATION HS non-graduate State 48 ( 5.4) 43 ( 4.9) ( .") 252 ( 3.8) Nation 8 ( IP" ( 2.6) ***) 54 ( 244 ( 5.7) 2.7) 38 ( 243 ( 6.3) 3.5)1 HS graduate State 53 ( 3.1) 39 ( 2.5) ( 261 ( 1.9) 262 ( 2.4) Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.9) 253 ( 4.8)1 258 ( 1.9) 256 ( 2.8) Soma college State 8 ( 2.1) 49 ( 3.1) 42 ( 2.6) 277 ( 1.6) 272 ( 1.7) Nation 13 ( 3.3) 62 ( 4.3) 25 ( 4.1) 269 ( 2.5) 267 ( 3.8) College graduate State 7 ( 1.6) 52 ( 2.7) 41 ( 2.1) 276 ( 3.6)1 281 ( 1.6) 278 ( 1.4) Nation 15 ( 2.9) 56 ( 4.9) 30 ( 5.1) 276 ( 5.4)1 276 ( 2.2) 273 ( 3.7) GENDER Mate State 8 ( 2.0) 4P ( 2.4) 43 ( 1.5) 270 ( 4.1)i 273 ( 1.7) 272 ( 1.5) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4.0) 264 ( 5.0); 265 ( 2.6) 264 ( 3.3) Female State 7 ( 1.7) 55 ( 2.0) 38 ( 1.5) 271 ( 2.8)1 271 ( 1.3) 269 ( 1.1) Nation 13 ( 2.4) 55 ( 4,4) 32 ( 4.7) 266 ( 3.9) 264 ( 2.0) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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 is insufficient to permit a reliable estimate (fewer than 62 students). _a THE 1990 NAEP TRIAL STATE ASSESSMENT 109 Idaho TABLE Al Cta I Teachers' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TR!Al. STATE ASSESSMENT At Least Onc a Week Less Than Once a Week Now TOTAL and PectIdency Pereentaf. and Proildency Percentage and Prelideney State 55 ( 22) 33 ( 2.3) 12 ( 0.8) 272 ( 1.0) 271 ( 1.2) 272 ( 2.9) Nation 50 ( 4.4) 43 ( 4.1) 8 ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 6.4)I RACE/ETHNICITY White State 54 ( 2.3) 33 ( 2.4) 12 ( 0.6) 274 ( 1.0) 273 ( 1.0) 274 ( 2.8) Nation 49 ( 4.6) 43 ( 4.5) 8 ( 2.3) 265 ( 2.7) 271 ( 22) 285 ( 4.9)1 Hispanic State 59 ( 4.2) 32 ( 4.7) 9 ( 2.7) 248 ( 3.2) v.* 04114 ) 044 ( *IN) Nation 84 ( 246 ( 7 2) 2.5) 32 ( 247 ( 6.9) 8.3)! 4 ( 1.4) .4.4) American Indian State 67 ( 9.2) *41 26 ( 7.3) 8 ( MP* 4.4) 1141 Nation 18 (24.3) 80 (272) 2 ( 3.7) *** ( '1") TYPE OF COMMUNITY Extreme rural State 56 ( 4.91 33 ( 54) 11 ( 1.7) 269 ( 1.2) 268 ( 3.5)1 261 ( 3.6) Nation 35 (14.6) 56 (17.1) 9 ( 9.6) 255 ( 5.5)! 258 ( 5.9)1 Other State 55 ( 2.2) 32 ( 22) 13 ( 1.0) 271 ( 1.4) 273 ( 1.3) 275 ( 3.6) Nation 50 ( 4.4) 44 ( 4.5) 8 ( 1.8) 260 ( 2.4) 284 ( 2.8) 277 ( 8.3)t 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). 110 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE Al Oa I Teachers' Reports on the Frequency of &nail (continued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIEN& 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Wirek LOU Than Once a Week Now TOTAL Percentage and Preficiency pow**, and Proncloney Percentage and ProecianCY State 55 ( 2.2) 33 ( 2.3) 12 ( 0.8) 212 ( 1.0) 271 ( 1.2) 272 ( 2.9) Nation 50 ( 4.4) 43 ( 4.1) 8 ( 2.0) 200 ( 2.2) 204 ( 2.3) 277 ( 5.4)1 PARENTS EDUCATION NS non-graduate State 52 ( 5.1) 37 ( 5.3) 11 ( 3.4) 248 ( 34) Nation 60 ( 6.4) 39 ( 6.5) 1 ( 1.4) 244 ( 3.2) 244 ( 3.2)1 sI4* HS graduate State 55 ( 3.7) 34 ( 3.8) 10 ( 19) 282 ( 1.9) 263 ( 2.5) Nation 49 ( 4.8) 45 ( 5.1) 6 ( 2.5) 252 ( 2.8) 257 ( 2.7) Some college State 53 ( 2.9) 32 ( 2.8) 15 ( 1.9) 275 ( 1.9) 275 ( 2.0) 272 ( 2.8) Nation 51 ( 5.2) 42 ( 5.1) ( 2.3) 266 ( 3.1) 268 ( 32) fl^C, ) College graduate State 56 ( 2.6) 33 ( 2.7) 1 1 ( 1.1) 280 ( 1.4) 218 ( 1.7) 284 ( 3.9) Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 216 ( 3.0) 285 C 4.9)1 GENDER Male State 53 2.6) 33 ( 2,5) 14 ( 1.0) 273 ( 1.5) 273 ( 1.7) 271 ( 3.5) Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 265 ( 3.1) 278 ( 5.33! Female State 57 i 2.3) 33 ( 2.5) 10 ( 1.1) 271 ( 1.1) 269 ( 1.8) 273 ( 3.1) Nation 50 ( 4.7) 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 8.81t The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for ew:h population of interest, the value for the enure population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL. STATE ASSESSMENT 111 Idaho TABLE AlOb 1 Teachers' Reports on the Use of Mathematical Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Neva TOTAL Percentage and Prone:fancy 20 ( 1.2) 274 ( 1.5) 22 ( 3.7) 254 ( 3.2) 20 ( 1.21 276 ( 1.6) 17 ( 4.0) 201 ( 3.8)I 17 ( 3.1) 39 ( 7.5) 247 ( 3.8) 15 ( 5.1) ( 0.1 78 (34.8) ( 25 ( 5.9) 268 ( 4.1)1 27 (14.9) 0011 ( 001 18 2.2) 277 ( 2.4) 19 ( 43) 253 ( 3.9)! Parentage and Proectency 64 ( 1.1) 270 ( 0.8) 69 ( 3.9) 263 ( 1.9) 63 ( 1.3) 273 ( 0.8) 72 ( 4.2) 269 ( 2.1) 72 ( 2.9) 247 ( 3.1) 55 ( 7.3) 245 ( 3.8)t 66 ( 6.3) 44. 22 (34.8) ( 4.1 62 ( 5.1) 287 ( 1.3) 65 (14.6) 262 ( 2.8)I 86 ( 1.9) 271 ( 1.1) 72 ( 5.0) 263 ( 22) Percentage and Proectency 10 ( 0.8) 276 ( 2.0) 9 ( 2.6) 282 ( 5.9)! 17 ( 0.8) 27$ ( 2.0) 10 ( 2.7) 286 ( 6.2)1 11 ( 2.9) Mr* ( ( 2.6) ( '41 20 ( 5$) 0 ( 0.0) ( et.) 13 ( 1,8) 272 ( 3.2) 000 ( 15 ( 1.1) 276 ( 3.0) 9 ( 3.3) 281 ( 1.1)1 State Nation RACE/ETHNIC1TY White State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Extreme nrai State Nation Other State Nation 0 AIL The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I -1 112 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A lOb f Teachers' Reports on the Use of Mathematical ("mtinued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a we* Loss Than Ono a Wes* Now III1Mr TOTAL Percentage and Proficiency Posoentope and Profidency Porconlogo Prondoncy State 20 ( 1.2) 64 ( 1.1) 16 ( 0.8) 274 ( 1.5) 270 ( 0.8) 276 ( 2.0) Nation 22 ( 3.7) 89 ( 3.9) 9 ( 2.6) 254 ( 32) 263 ( 1.9) 282 ( 5.9)1 PARENTS' EDUCATION KS non-gradust State 20 ( 3.6) 72 ( 4.2) 8 ( 2.5) 441 44) 250 ( 3.2) Nation 2$ ( 5.6) 66 ( 7.2) 9 ( 6.5) 01P, ( 0.41 243 ( 2.2) KS graduato State 22 ( 2.4) ( 2.7) 14 ( 1.8) 266 ( 2.7) 260 ( 1.6) Nation 23 ( 4.8) 70 ( 5.3) 246 ( 4.0)1 255 ( 2.2) Some college State 21 ( 1.9) 63 ( 2.4) 16 ( 2.1) 277 ( 2.7) 274 ( 1.6) 274 ( 3.0) Nation 18 ( 4.0) 73 ( 4.3) 9 ( 2.4) 261 ( 4.4)1 269 ( 2.3) Canoga grackiat. State 20 ( 1.6) 61 ( 1.9) 20 ( 1.7) 280 ( 2.1) 279 ( 1.1) 284 ( 2.9) Nation 20 ( 3.9) 69 ( 3.7) 11 ( 2$) 266 ( 3.5)1 274 ( 22) 297 ( 42)1 GENDER Male State 21 ( 13) 64 ( 1.4) 15 ( 1.2) 277 ( 2.1) 270 ( 1.1) 278 ( 2.9) Nation 22 ( 4.1) 691 4.1) ( 2.0) 255 ( 4.1) 265 ( 2.1) 287 ( 7.2)1 Female State 19 ( 1.5) 63 ( 1.6) 18 ( 1.3) 270 ( 1.6) 270 ( 1.2) 275 ( 2.0) 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 b. 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). 1 : S THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Idaho TABLE Al la I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Weak or Less TOTAL Percentage and Proficiency Percentage and Prandency Pareenta9a and Proftdency State 75 ( 1.9) 22 ( 1.8) 274 ( 0.8) 268 ( 1.9) 111,1 Nation 62 ( 3.4) 31 ( 3.1) 7 ( 1.8) 267 ( 1.8) 254 ( 2.9) 260 ( 5.1)1 RACE/ETHNICITY White State 75 ( 2.1) 22 ( 2.0) 3 ( 0.5) 276 ( 0.8) 270 ( 1.9) ( ".) Nation 64 ( 3.7) 28 ( 3.2) 8 ( 2.3) 272 ( 1.9) 264 ( 3.4) 264 ( 5.4)1 Hispanic State 77 ( 4.1) 19 ( 3.5) 3 ( 1.8) 251 ( 2.4) 944 ( *** ( ".) Nation 61 ( 251 ( 6.8) 3.1) 32 ( 240 ( 5.3) 4.3)1 8 ( i-4 2.3) *el Amorican Indian State 68 ( 8.0) 26 ( 7.2) 7 ( 4.5) *HI ( *411 ( "") Nation 15 (25.9) 83 (28.3) 2 ( :>.0) ( ( 4) TYPE OF COMMUNITY Extreme nye! State 89 ( 1.9) 11 ( 1.8) 0.4) 269 ( 1.5) 264 ( 3.8) titit 1-t Nation 50 (10.6) 40 (10.0) 1 0 7.3) 268 ( 4.0)1 247 ( 7.6)1 Other State 69 ( 2.1) 27 ( 2.0) 4 ( 0.6) 276 ( 1.1) 268 ( 2.2) ( ) Nation 63 ( 3.9) 31 ( 3.6) 6 ( 1.9) 267 ( 2.3) 2551 3.1) 257 ( 5.8)t The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent mrtainty 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). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE Al la I Teachers' Reports on the Frequency of (continued) 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 Less TOTAL Percentage and Proficiency 75 ( 1,9) 274 ( 0.5) 62 ( 3.4) 267 ( 1.8) 72 ( 4.6) 254 ( 2.6) 67 ( 5.5) 245 ( 3.2) 72 ( 3.1) 264 ( 1.7) 61 ( 4.4) 257 ( 2.5) 74 ( 2.8) 277 ( 1.4) 68 ( 4.2) 272 ( 2.7) 77 ( 2.4) 282 ( 1.2) . 61 ( 4.0) 281 ( 2.2) 73 ( 2.6) 275 ( 1.1) SO ( 3.7) 269 ( 2.1) 76 ( 1.6) 273 ( 1.0) 65 ( 3.6) 296 ( 1.8) Percentage and Proaciency 22 ( 1.8) 266 ( 1.9) 31 ( 3.1) 254 ( 2.9) 22 ( 4.4) 27 ( 5.2) ( .41 23 ( 2.5) 260 ( 2.5) 34 ( 3.7) 250 ( 2.9) 22 ( 2.8) 270 ( 3.4) 26 ( 3.7) 258 ( 5.2) 22 ( 2.4) 276 ( 2.6) 31 ( 3.9) 265 ( 3.1) 24 ( 2.4) 2r-9 ( 2.3) 33 ( 3.4) 256 ( 3.6) 21 ( 1.5) 266 ( 2.0) 28 ( 3.3) 253 ( 2.5) Peeverdage and Proficiency 3 ( 0.5) 111141. ( 7 ( 1.11) 260 ( 5.1)1 6 ( 2.6) ( S ( 2.1) O.* ( 5 ( 1.7) 044 ( 041 ( 0.9) eV. ( 1111 6 ( 1.9) ,-*** ***) ( "4) ( 3.1) ( 3 ( alp ( ***) ( 1.9) 261 ( 6.7)1 3 ( 0.7) ***/ ***) State Nation PARENTS EDUCATION HS non-graduate State Nation 115 graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statistics appear in 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 115 Idaho TABLE Al lb I Teachers' Reports on the Frequency of i Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Lust Several Times STATE ASSESSMENT a Week About Once a Week Less than Weekly TOTAL Peseentage and Proficiency Percentage and Proedency Percentage and Proficiency State 29 ( 2.0) 34 ( 1.2) 36 ( 2.0) 26$ ( 1.6) 270 ( 1.1) 27$ ( 12) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 260 ( 2.3) 274 ( 2.7) RACE/ETHNICITY White State 29 ( 2.2) 33 ( 1.3) 38 ( 2.2) 268 ( 1.6) 273 ( 1.0) 280 ( 1.2) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Hixpanic State 24 ( 42) 39 ( 4.3) 37 ( 4.0) *el 243 ( 4.3) Nation 41 ( 7.7) 26 ( 5.3) 33 ( 7$) 242 ( 32)1 244 ( 5.1)1 257 ( 2.3)1 American Indian State 26 ( 6 1) 41 ( 8.7) *44) 33 ( 5.9) 1HHI Nation 10 (18.6) 76 (36.2) 13 (18.5) *1- ROY ) TYPE OF COMMUNITY Extreme rural State 31 ( 5.4) 39 ( 4.0) 30 ( 3.7) 267 ( 3.6'1 267 ( 1.9) 270 ( 1.8) Nation 27 (14.3i 49 (12.7) 24 (10.1) 258 ( 6.7)1 111. Other State 25 ( 1.4) 33 ( 1.8) 42 ( 2.0) 283 ( 2.1) 271 ( 1.4) 279 ( 1.4) Nation .30 ( 4.4) 35 ( 4.3) 36 ( 4.2) 256 ( 3.3) 259 ( 2.8) 272 ( 2.9) The standard errors of the estima:ed 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). 4 I's '1 -A. A 116 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE Al lb I Teachers' Reports on the Frequency of (continued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week About Once a leek Less than Weekly TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Ptak:homy State 20 ( 2.0) 34 ( 1.2) 38 ( 2.0) 265 ( 1.6) 270 ( 1.1) 278 ( 1.2) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 260 ( 2.3) 274 ( 2.7) PARENTS EDUCATION KS non-graduate State 37 ( 4.9) 29 ( 4.5) 247 ( 3.3) Nation 35 ( 239 ( 6.0) 33) 29 ( 6.3)*) 36 ( 250 ( 6.9) 4.5)1 KS graduate State 32 ( 3.3) 33 ( 2.7) 35 ( 3.1) 256 ( 3.0) 262 ( 2.7) 268 ( 2.2) Nation 35 ( 5.3) 36 ( 43) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 263 ( 3.4) Some college State 29 ( 2.8) 32 ( 1.9) 39 ( 2.8) 269 ( 2.3) 273 ( 2.1) 280 ( 2.0) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 266 ( 4.2) 278 ( 2.6) College graduate State 26 ( 2.3) 34 ( 2.1) 39 ( 2.5) 275 ( 2.2) 278 ( 1.7) 285 ( 1.8) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Male State 31 ( 2.5) 33 ( 1.5) 38 ( 2.6) 266 ( 1.9) 270 ( 1.2) 281 ( 1.9) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 261 ( 2.8) 275 ( 3.2) Female State 27 ( 1.9) 34 ( 1.4) 40 ( 2.0) 264 ( 1.8) 270 ( 1.8) 276 ( 1.1) Nation 34 ( 4.1) o2 ( 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). TH E 1990 NAEP TRIAL STATE ASSESSMENT 117 Idaho TABLE Al2 Students' Reports on the Frequency of Small i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATCS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week New TOTAL Mervimedge and Pro Wain Percenbge and Proficiency Percergage and Proficiency State 29 ( 1.0) 29 ( 1.0) 41 ( 1.1) 271 ( 1.2) 274 ( 1.2) 271 ( 1.1) Nation 26 ( 2.5) 28 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 261 ( 1.6) RACE/ETHNICITY W1Hte State 29 ( 1.0) 30 ( 1.1) 42 ( 12) 274 ( 12) 276 ( 1.2) 273 ( 1.0) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 268 ( 3.1) 272 ( 1.9) 270 ( 1.7) Hispanic State 37 ( 4.6) 38 ( 4.8) ( 249 ( 3.4) Nation 37 ( 52) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) American Indian State 36 ( *re ( 6.5) 35 ( 0411, 5.6)- 29 ( 6.1) Nation 31 ( 5.1)) 35 ( 4" ( 5.5) 4") 33 ( 5.0) TYPE OF COMMUNITY Extreme nwal State 33 ( 2.6) 27 ( 1.8) 40 ( 3.1) 271 ( 1.3) 270 ( 1.7) 267 ( 2.2) Nation 34 (10.8) 27 ( 3.8) 39 (11.6) 249 ( 5.2)1 264 ( 3.5)i 256 ( 6.2)l Other State 29 ( 1.2) 30 ( 1.4) 41 ( 1.7) 270 ( 1.8) 274 ( 1.6) 273 ( 1.5) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 264 ( 2.1) 262 ( 22) 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 populavon is within 1 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 rehable estimate (fewer than 62 students). I THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE Al2 I Students' Reports on the Frequency of Small (continued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Len Than Once a Week Never TOTAL Percentage and PrOktdenCy Parcentaga and Praikdandy Parcentage and Prolkdancy State 29 ( 1.0) 29 ( 1.0) 41 ( 1.1) 271 ( 1.2) 274 ( 1.2) 271 ( 1.1) Nation 28 ( 2.5) 25 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 201 ( 1.6) PARENTS' EDUCATION HS non-graduate State 22 ( 3.6) 45 ( 4.7) ( *4* ( 441 255 ( 3.6) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4.5) 242 ( 3.4,1 244 ( 3.0) 242 ( 2.7) HS graduate State 30 ( 2.5) 29 ( 2.7) 41 ( 2.2) 261 ( 22) 262 ( 1.8) 262 ( 2.6) Nation 28 ( 3,0) 28 ( 1.8) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some college State 27 ( 2$) 29 ( 2.9) 43 ( 3.0) 276 ( 22) 277 ( 2.1) 272 ( 1.6) Nation 27 ( 3.9) 27 ( 2.4) 46 ( 3.8) 265 ( 3.6) 288 ( 3.3) 766 ( 2.1) College graduate State 30 ( 1.6) 30 ( 1.9) 40 ( 1.8) 279 ( 1.4) 281 ( 1.9) 279 ( 1.4) Nation 28 ( 3.0) 28 ( 1.9) 44 ( 3.6) 270 ( 2.7) 278 ( 2.8) 275 ( 2.2) GENDER Male State 29 ( 1.6) 27 ( 1.3) 44 ( 1.6) 272 ( 1.6) 273 ( 2.0) 273 ( 1.4) Nation 31 ( 2.9) 28 ( 1.7) 41 ( 2.9) 259 ( 3.3) 268 ( 2.6) 262 ( 1.8) Female State 30 ( 1.6) 32 ( 1.6) 38 ( 1.9) 270 ( 1.5) 274 ( 1.4) 268 ( 1.6) Nation 26 ( 2.4) 27 ( 1.8) 47 ( 3.2) 257 ( 2.8) 266 ( 1.7) 260 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Idaho TABLE A 13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week - Lees Than Once a Week Never TOTAL and Preadenc4 Pereettage end Proadency Ponnelese and Prgliciancy State 21 ( 1.3) 34 ( 1.1) 45 ( 06) 269 ( 1.8) 274 ( 1.1) 271 ( 1.1) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.6) 209 ( 1.5) 259 ( 1.0) RACE/ETHNICITY White State 20 ( 1.4) 35 ( 1.3) 45 ( 1.1) 272 ( 1.7) 276 ( 1.1) 274 ( 1.1) Nation 27 ( 1.9) 33 ( 1.6) 40 ( 2.5) 206 ( 2.0) 275 ( 1.0) 268 ( 1.8) Hispanic State 28 ( 3.5) 26( 3-3) .44(444) 40 ( 249 ( 3.7) 4.2) Nation 38 ( 4.2) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) American Indian State 19 ( 6.7) ..44) 36 ( 044 ( 6.4) 441 46 ( 444 ( 7.5) *1111) Nation 35 ( 3.4) 37 ( 4+4 ( 8.2) .44) 28 ( 8.8) TYPE OF COMMUNITY Octreme rural State 24 ( 3.0) 37 ( 1.6) 39 ( 2.7) 266 ( 3.7) 272 ( 1.0) 268 ( 1.7) Nation *41. 37 ( 262 ( 4.7) 4.7)1 43 ( 251 ( 5.0) 5.2)I Other State 20 ( 1.3) 34 ( 1.6) 47 ( 1.4) 269 ( 2.5) 274 ( 1.6) 272 ( 1,5) 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 certamty 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). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Mao TABLE A 13 I Students' Reports on the Use of Mathematics (continued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Lust Once a Week Less Than Once a Week Never TOTAL and Proficiency Percentage and Pleat:honey Panetta. and Proficiency State 21 ( 1.3) 34 ( 1.1) 45 ( 0.9) 269 ( t$) 274 ( 1.1) 271 ( 1.1) Nation 28 ( 1.8) 31 ( 12) 41 ( 2.2) 258 ( 2.6) 269 ( t5) 258 ( 1.6) PARENTS' kLaUCATION HS non-graduate State 21 ( ...., ( 3.4) .41 29 ( ..... ( 3.7) .44) 49 ( 249 ( 5.0) 3.4) Nation 27 ( 4.2) 26 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 15) 240 ( 2.3) HS graduate State 20 ( 2.6) 35 ( 2$) 44 ( 2.7) 262 ( 3.0) 265 ( 2.2) 259 ( 23) Nation 27 ( 2.7) 34 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) S01114, college State 21 ( 2.2) 35 ( 2.6) 44 ( 2.6) 274 ( 3.0) 277 ( 1.8) 273 ( 1.8) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.6) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) College graduate State 21 ( 1.5) 33 ( 1.4) 48 ( 1.6) 274 ( 22) 280 ( 1.6) 281 ( 1.4) Nation 30 ( 2.5) 32 ( 2.0) 3$ ( 2.6) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Mate State 23 ( 1.8) 34 ( 1.6) 44 ( 1.5) 270 ( 2.4) 275 ( 1.5) 272 ( 1.3) Nation 32 ( 2.0) 30 ( 1$) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 19 ( 1.4) 35 ( 1.4) 46 ( 1.7) 266 ( 2.0) 273 ( 1.4) 270 ( 1.4) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 268 ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 c THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Idaho TABLE A14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 KAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Less TOTAL Percentage and Ptoliciency and Prolideney Pereenfil9, and Proficiency State 83 ( 0.9) 11 ( 0.6) 8 ( 274 ( 0.7) 263 ( 1.8) 247 ( 3.6) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 44) RACE/ETHNIC1TY white State 85 ( 0.9) 10 ( 0.8) 5 ( 0.7) 276 ( 0.7) 268 ( 1.8) 253 ( 3.7) Nation 78 ( 2.5) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 2.2) 252 ( 5.1)1 Hispanic State 71 ( 3.4) 19 ( 3.1) 10 ( 2.0) 253 ( 3.0) Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) American Indian State 78 ( 6.0) 19 ( 62)) 5 ( 3.4) Nation 61 ( .** 4.4) 22 ( 3.6) .41 17 ( 4.0) TYPE OF COMMUNITY Extreme rural State 87 ( 1.5) 8 ( 1.0) 5 ( 1.2) 271 ( 1.2) 259 ( 3.0) 252 ( 4.8)1 Nation 68 (11,3) 263 ( 4.2)1 15 ( 0..46 3.6) 17 ( $.2) ...) Other State 83 ( 1.1) 11 ( 0.8) 5 ( 0.6) 275 ( 0.9) 264 ( 2.3) 245 ( 4.7) Nation 75 ( 2.2) 14 ( 1.0) 10 ( 1.9) 267 ( 1.6) 252 ( 2.6) 239 ( 4.3)1 The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 7 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A14 I Students' Reports on the Frequency of (cmtinued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Less - TOTAL State Nation PARENTS' EDUCATION liS non-graduate State 78 ( 4.1) 257 ( 22) Nation 64 ( 3.4) 245 ( 2.3) NS graduate State 84 ( 1.9) Nation 71 { 3.6) and Proficiency 63 ( 0.9) 274 ( 0.7) 74 ( 1.9) 267 ( 1.2) Some college State 84 ( 1.7) 277 ( 1.2) Nation 80 ( 2.0) 270 ( 1.9) College graduate State 85 ( 1.1) 281 ( 1.0) Nation 77 ( 2.7) 279 ( 1.6) GENDER Male State 80 ( 1.2) 276 ( 0.9) Nation 72 ( 2.4) 268 ( 1.6) Female State 87 ( 12) 272 ( 0.8) Nation 76 ( 1.8) 285 ( 1.3) PercOntage and Proficiency 11 ( 0.6) 263 ( 1.8) 14 ( 0.8) 252 ( 1.7) *** ) 18 ( 2.0) Percentage and PrOficiency ( 0.6) 247 ( 3.6) 12 ( 1.8) 242 ( 4.5) ( GO* ) 18 ( 3.1) 04r* ( 10 ( ( 1.8) .41 6 ( 0411,1 1 ) 0411,1 16 ( 1.8) 13 ( 2.8) 249 ( 3.2) 239 ( 3.4)i 12 ( 1.7) 284 ( 3.5) 11 ( ....- ( 1.2) 11 9 ( 1.7) 0-** ) 10 ( 0.8) ( 0.7) 272 ( 2.0) 411 *el 13 ( 0.9) 1 0 ( 2.3) 260 ( 2.8) 257 ( 6.4)1 13 ( 0.7) 7 ( 0.9) 285 ( 2.1) 248 ( 4.9) 16 ( 1.2) 12 ( 2.1) 252 ( 25) 242 ( 6.1) 9 ( 1.0) 260 ( 3.0) *** 13 ( 1.0) 11 ( 1.6) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 45 percent certainty that, for each population of interest, the value for the entire population is within :t 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Idaho TABLE A15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Lust Several Times a Week About Once a Wet* Lau Than Weekly TOTAL Percentage and Proficiency Penentage and Proficiency Penalties and Proficiency State 27 ( 1.7) 219 ( 1.0) 47 ( 1.5) 263 ( 1.4) 270 ( 1.3) 278 ( 1.1) Nation 38 ( 2.4) 25 ( 1.2) 37 ( 253 ( 2,2) 231 ( 1.4) 272 ( 1.9) RACE/ETHNICITY White State 26 ( 1.8) 26 ( 1.0) 48 ( 1.6) 266 ( 1.4) 272 ( 1.3) 280 ( 1.0) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 282 ( 2.5) 269 ( 1.5) 277 ( 2.0) Hispanic State 33 ( 4.8) 29 ( 4.4) 38 ( 5.0) 239 ( 3.5) .1#11 256 ( 3.4) Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 238 ( 3.9) 247 ( 3.3) 243 ( 3.3) American Indian State 20 ( 5.8) 41 ( 8.8) ( Nation 41 ( 42) 30 (11.3) 28 (12.5) ( `") TYPE OF COMMUNITY Extreme rural State 27 ( 4.5) 28 ( 2.2) 46 ( 3.3) 266 ( 3.5)1 267 ( 1,3) 271 ( 1.6) Nation 42 (10.1 30 ( 4.4) 28 ( 7.5) 249 ( 4.0)1 256 ( 3.4)i 267 ( 7.3)1 Other State 24 ( 1.4) 26 ( 1.2) 50 ( 1.5) 260 ( 1.7) 270 ( 1.8) 279 ( 1.4) Nation 36 ( 2.9) 26 ( 1.2) 38 ( 2.9) 252 ( 3.0) 281 ( 2.1) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. I" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A15 I Students' Reports on the Frequency of ("mtinued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL At Least Several limes STATE ASSESSMENT a Wm* About Once a Wink Lass Than Woo My TOTAL and Proddancy Parootdago and Proildonty Partentapt area Prolisionoy State 27 ( 1.7) 20 ( 1.0) 47 ( 13) 2031 1.4) 270( 1-3) 276 ( 1.1) Nation 3' ( 2.4) 25 ( 1.2) $7 ( 24) 253 ( 2.2) 2.1 ( 1.4) 272 ( 1.9) PARENTS' EDUCATION NS non-graduate State 34 ( 4.9) .44.) 31 ( 253 ( 3.8) 3.3) 36 ( 4.3) ( gni Nation at ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.6) KS giltduate State 27 ( 2.9) 29 ( 1.9) 45 ( 2.6) 255 ( 2.8) 282 ( 2.3) 206 ( 2.1) Nation 40 ( 3.2) 29 ( 2.2) 32 ( 3.6) 247 ( 2.7) 258 ( 2$) 202 ( 2.2) Soma college State 28 ( 2.2) 23 ( 2.0) 50 ( 2.5) 269 ( 2.4) 271 ( 2.7) 279 ( 1.7) Nation 34 ( 3.4) 28 ( 2.2) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) College graduate State 25 ( 2.1) 26 ( 1.4) 49 ( 1.9) 270 ( 2.0) 277 ( 1.9) 285 ( 1.3) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 273 ( 2$) 285 ( 2.3) GENDER Male State 29 ( 2.3) 27 ( 1.5) 44 ( 1.9) 282 ( 1.9) 272 ( 1$) 280 ( 1$) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 280 ( 2.3) 274 ( 2.4) Female State 24 ( 1.6) 24 ( 1.3) 52 ( 1.7) 284 ( 1.7) 266 ( 1.7) 278 ( 1.1) Nation 37 ( 2$) 25 ( 1.5) 3$ ( 2.6) 253 ( 2.1) 259 ( 1.8) 289 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 :3 o THE 1990 NAEP TRIAL STATE ASSESSMENT 125 Idaho TABLE AlS Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Own a Calcsiator Teacher Explains Calculator Use Yes No Yes No TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 98 ( 0.3) ( 0.3) 42 ( 1.1) 56 ( 1.1) 272 ( 0.7) ( 265 (0.9) 274 ( 0.9) Nation 97 ( 0,4) 3 ( 0.4) 49 ( 2.3) 51 ( 2.3) 263 ( 1.3) 234 ( 3.8) 258 ( 1.7) 266 ( 1.5) RACE/ETHNICITY White State 99 ( 0.3) ( 0.3) 42 ( 1.3) 58 ( 1.3) 274 ( 0.7) 414r1 270 ( 1.0) 277 ( 0.8) Nation 98 ( 0.3) 48 ( 2.6) 54 ( 2.6) 270 ( 1.5) 266 ( 1.8) 273 ( 1.8) Hispanic State 97 ( 1.3) 3 ( 1.3) 45 ( 3.6) 55 ( 3.6) 249 ( 2.5) ' 245 ( 3.7) 252 ( 3.5) Nation 92 ( 246 ( 12) 2.7) 8 ( 12) **) 63 243 ( 4.3) ( 3.4) 37 ( 246 ( 4.3) 2.9) American Indian State 95 ( 3.3) 5 ( 3.3) 42 ( 7 S) 58 ( 7.5) 255 ( 4.4) *** ( ( Nation 71 (16.7) 29 (16.7) ( *** m) ( TYPE OF COMMUNITY Extreme rural State 96 ( 0.4) 2 45 ( 2.3) 55 ( 2.3) 269 ( 1.1) 4." ( 267 ( 1.1) 270 ( 1.5) Nation 96 ( 1.3) 4 ( 1.3) 42 ( 8.7) 58 1 8.7) 257 ( 3.9)I 251 ( 4.8)1 261 ( 4.4)1 Other State 98 ( 0.4) 2 ( 0.4) 42 ( 1.4) 58 ( 1.4) 272 ( 1.0) 268 ( 12) 275 ( 1.3) Nation 97 ( 0.5) 3 ( 0,5) 50 ( 2.7) 50 ( 2.7) 263 ( 1.7) 233 ( 5.4) 258 ( 2.1) 266 ( 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. t Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 126 THE 1090 NAE2 TRIAL STATE ASSESSMENT Idaho TABLE Al8 (continued) Studente 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 Owr a Calculator Teacher Explains Calculator Use Yes No Yes No TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 99 ( 0.3) ( 0.3) 42 ( 1.1) 56 ( 1.1) 272 ( 0.7) Mr* 4-1,11 288 ( 0.9) 274 ( 0.9) Nation 97 ( 0.4) 3 ( 0.4) 49 ( 2.3) 51 ( 2.3) 263 ( 1.3) 234 ( 3.8) 2$8 ( 1.7) 266 ( 1.5) PARENTS EDUCATION HS non-graduate slate 94 ( 2.3) 6 ( 2.3) 43 ( 4.0) 57 ( 4.0) 252 ( 2.2) *** ( 246 ( 4.1) 256 ( 2.6) Nation 92 ( 1.6) 53 ( 4.8) 47 ( 4.8) tIS graduate 243 ( 2.0) ( ***) 242 ( 2.9) 243 ( 2.5) State 98 ( 262 ( 0.7) 1.4) 2 ( *** ( 0.7)*) 46 ( 258 ( 2.4) 1.9) 54 ( 285 ( 2.4) 1.8) Nation 97 ( 0.6) 54 ( 3.0) 46 ( 3.0) 255 ( 1.5) 252 ( 1.9) 258 ( 2.0) Some college State 98 ( 0.4) 2 ( 0,4) 44 ( 2.3) 56 ( 2.3) 275 ( 1.2) ( "") 273 ( 1.4) 276 ( 1.7) Nation 96 ( 0.9) 4 ( 0.9) 48 ( 3.2) 52 ( 3.2) 268 ( 1.8) ( 295 ( 2.4) 268 ( 2.2) College graduate State 100 ( 0.1) 0 ( 0.1) 39 ( 1.7) 61 ( 1.7) 279 ( 1.0) * ( '") 276 ( .5) 281 ( 1.1) Nation 99 ( 0.2) 1 ( 02) 46 ( 2.6) 54 ( 2.6) 275 ( 1.6) ( .") 268 ( 2.2) 280 ( 1.9) GENDER Male State 98 ( 0.4) ( 04) 42 ( 1.6) 58 ( 1.6) 273 ( 0.9) ( 4") 266 ( 1.2) 276 ( 1.0) Nation 97 ( 0.5) 51 ( 2.6) 49 ( 2.6) 284 ( 1.7) 256 ( 2.1) 269 ( 2.1) Female State 99 ( 0.3) 1 ( 0.3) 42 ( 1.4) 58 ( 1.4) 270 ( 0.8) ( 268 ( 1.2) 272 ( 1.1) Nation 97 ( 0.5) 3 ( 0.5) 47 ( 2.5) 53 ( 2.5) 262 ( 1.3) ( "") 258 ( 1.7) 263 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estima.e for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 17'2 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 Idaho TABLE A19 i Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11100 NAEP TRIAL STATE ASSESSMENT Worldng Problems In Pass _ Doing Prtib Isms at Home Taking Quizzes or Trots Almost Always Never , Almost Always _ I Never .. Almost Always Never TOTAL, Percentage and PrOffOkInCy Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 43 ( 1.1) 27 ( 1.2) 26 ( 1.0) 10 ( 0.9) 19 ( 0.9) 38 ( 1.2) 260( 1.0) 279 ( 1.3) 272 ( 1.3) 273 ( 1.8) 269 ( 1.5) 280 ( 1.1) Netion 46 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) RACE/ETHNIC1TY Whits State 43 ( 1.2) 28 ( 1.2) 26 ( 1.2) 16 ( 0.9) 19 ( 1.0) 40( 1.2) 268 ( 1.1) 281 ( 1.2) 274 ( 1.31 277 ( 1,7) 271 ( 1.0) 282 ( 1.0) Nation 46 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 25 ( 1.0) 32 ( 2.3) 262 ( 1.7) 278 ( 1.3) 270 ( 1.7) 269 ( 2.3) 263 ( 2.6) 270 ( 1.2) Hispanic State 46 ( 248 ( 5.1) 3.7) 21 ( 3.6) 23 ( *** ( 4.4) ***) 18 ( 3.0) 23 ( 2.9) 29 ( *** 4.2) Nation 51 ( 2,9) 16 ( 3$) 26 ( 3.2) 21 ( 2.1) 26 ( 2.7) 22 ( 3.1) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1) 237 ( 3.2) 256 ( 4.2) American Indian State 44 ( 7.0) 17 ( 5.2) ..**) 30 ( 6.0) 17 ( 4.5) *44) 27 ( ( 6.3) *41 21 ( 4441 ( 6.0) 14.) Nation 33 ( 9.15) ***) 23 ( opit. 4.9) ***) 15 ( 0.4p 4.9) 32 (10,1) 20 ( 8.2) 21 ( 7.8) TYPE OF COMMUNITY Extreme rural State 43 ( 2.6) 26 ( 3.2) 26 ( 1.8) 14 ( 0.9) 19 ( 2.2) 38 ( 2.5) 263 ( 1.3) 276 ( 2.2) 269 ( 2.0) 270 ( 2.6) 265 ( 2.0) 278 ( 1.3) Nation 46 ( 7.4) 29 ( 6.5) 20 ( 2$) 23 ( 3.9) 24 ( 6.6) 37 ( 8.3) 246 ( 4.3)1 268 ( 6.1)1 263 ( 4.4)1 270 ( 4.0)f Other State 44 ( 1.5) 26 ( 1.6) 26 ( 1.4) 16 ( 1.2) 20 ( 1.1) 37 ( 1.8) 267 ( 1.3) 280 ( 2.1) 272 ( 1.7) 274 ( 2.2) 270 ( 2.0) 80( 1.6) Nation 46 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1.8) 29 ( 2.1) 254 ( 2.1) 272 ( 1.8) 263 ( 2.3) 263 ( 2.8) 253 ( 2.7) 275 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 7 3 128 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A19 I Students' Reports on the Use of a Calculator (continued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL. STATE ASSESSMENT Working Pr Oki*" in Class Doing Problems at Home - Taking Quizzes or Tests Almost Always Never Almost Always Never Almost Always Never TOTAL. Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage end Proficiency Percentage and Proficiency Percentage and Proficiency State 43 ( 1.1) 27 ( 1.2) 26 ( 1.0) 16 ( 0.9) 19 ( 0.9) 38 ( 1.2) 266 ( 1.0) 279 ( 1.3) 272 ( 1.3) 273 ( 1.8) 269 ( 1.5) 280 ( 1.1) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.8) 203 ( 1.8) 253 ( 2.4) 274 ( 1.3) PARENTS' EDUCATION HS non-graduate State 37 ( 247 ( 4.1) 3.8) 25 I, 3.7) .44(444) 24 ( 4.8) .4.) 17 ( 3.5) *44(4*4) 18 ( *44 ( 2.3) NI) 38 ( 2.3 ( 4.6) 3.7) Nation 54 ( 3.3) 19 ( 3.3) 26 ( 3.1) 22 ( 2.6) 32 ( 3.6) 24 ( 3.2) 240 ( 2.3) 244 ( 3.8) 244 ( 4.2) 237 ( 2.3) 251 ( 4.6) HS giaduate State 48 ( 2.7) 25 ( 2.0) 27 ( 2.3) 14 ( 1.4) 19 ( 1.7) 35 ( 2.0) 257 ( 2,0) 266 ( 2.7) 264 ( 2,9) 262 ( 3.8) 260 ( 3.0) 268 ( 2.3) Nation 52 ( 2.5) 20 ( 2.4) 29( 1,9) 18 ( 1,5) 26 ( 1.8) 27 ( 2,2) 249 ( 1.4) 265 ( 2.7) 250 ( 2.4) 256 ( 2.4) 246 ( 2.8) 265 ( 2.0) Some college State 42 ( 2.4) 29( 1.8) 22 ( 1.9) 17 ( 1.6) 19 ( 2.1) 41 ( 2.4) 270 ( 1.6) 281 ( 1.8) 273 ( 2.7) 274 ( 2.8) 272 ( 3.0) 282 ( 1.5) Nation 46 ( 2.8) 26 ( 2.8) 23 ( 2.0) 20 ( 1.9) 26 ( 2.4) 35 ( 2.5) 258 ( 2.1) 272 ( 2.5) 267 ( 3.0) 268 ( 3.2) 255 ( 3.6) 275 ( 2.0) College graduate State 43 ( 1.4) 29( 1$) 28 ( 1.4) 18 ( 1.1) 19 ( 1.2) 40 ( 1.6) 274 ( 1.3) 287 ( 1.7) 278 ( 2.0) 282 ( 2.3) 278 ( 2.4) 288 ( 13) Nation 45 ( 1.9) 25 ( 2.4) 33 ( 2.0) 16 ( 14) 26 ( 1.6) 33 ( 2.7) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 268 ( 2.6) 285 ( 2.0) GENDER Male State 45 ( 1.7) 28 ( 1.4) 25 ( 1.3) 19 ( 1.4) 17 ( 1.4) 38 ( ° 5) 268 ( 1.2) 282 ( 1.7) 273 ( 1.7) 275 ( 2.2) 271 ( 2.0) 283 ( 4) Nation 50 ( 1,7) 20 ( 2,0) 29 ( 1.6) 19 ( 1.3) 27 ( 1.5) 26 ( 2.1) 255 ( 1.9) 275 ( 2.2) 284 ( 2.8) 263 ( 2.5) 256 ( 3.0) 277 ( 1.9) Female State 42 ( 1.7) 27 ( 1.5) 27 ( 13) 13 ( 0.8) 21 ( 1.4) 39 ( 1,9) 265 ( 1.2) 277 ( 1.3) 270 ( 1.3) 271 ( 2.9) 268 ( 2.2) 277 ( 1.3) Nation ( 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 9S 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. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 19C0 NAEP TRIAL STATE ASSESSMENT 129 Idaho TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL "Cabal "Calculator-use" STATE ASSESSMENT High later-Use" Group Other Crow , TOTAL Petventamt Pro &Nona Pettentege and Prat:Macy State ( 1.3) 52 ( 1.3) 276 ( 0.8) ( 13) Nation 42 1.3) 56 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACE/ETHNICITY White State 48 ( 1.3) 52 ( 1.3) 278 ( 0.9) 268 ( 1.3) Nation 44 ( 1.4) 56 ( 1.4) 277 ( 1.7) 283 ( 1.7) Hispanic State 53 ( 3,4) 47 ( 3.4) 250 ( 3.8) 248 ( 4.0) Nation 36 ( 4.2) 64 ( 42) 254 ( 4.8) 23$ ( 3.0) American Indian State 27 4.6 ( 7.1) ( 73 ( ( 7.1) *MI ) Nation 29 (12.0) ( 1141 71 (12.0) 44.) TYPE OF COMMUNITY Extreme rural State 51 ( 2.0) 49 ( 2,0) 273 ( 1.6) 282 ( 1.5) Nation 39 ( 5.6) 81 ( 5.6) 269 ( 4,4)1 248 ( 4.3)1 Other State 45 ( 1.5) 55 ( 1.5) 276 ( 1.3) 287 ( 1.7) Nation 42 ( 1.4) 58 ( 1,4) 271 ( 1,9) 255 ( 2.0) The standard errors of the estimated Statistics appear in parentheses. It Carl 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 vanability of this emanated mean proficiency. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND' AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT lator-U" Group High "Calcu se Other "Calculator-Use" Group TOTAL Percentage and Proficiency Percentage and Preaclency State 48 ( 1.3) 52 ( 1.3) 278 ( 0.9) 288 ( 1.3) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) PARENTS' EDUCATION KS non-graduate State 41 ( 4.6) 59 ( 4.6) 250 ( 3.2) Nation 34 ( 3.3) 66 ( 3.3) 248 ( 4.4) 242 ( 2.4) HS graduate State 45 ( 2.9) 55 ( 2.9) 264 ( 2.3) 257 ( 2.3) Nat:on 40 ( 22) 60 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some college State 50 ( 2.4) 50 ( 2.4) 282 ( 1.8) 269 ( 2.4) Nation 48 ( 2.2) 52 ( 2.2) 277 ( 2.6) 258 ( 2.5) College graduate State 49 ( 1,8) 51 ( 4.8) 282 ( 1,3) 274 ( 1.9) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER Male State 45 ( 1.7) 56 ( 1.7) 277 ( 1.3) 268 ( 1.7) Nation 39( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 51 ( 1.8) 49 ( 1.8) 274 ( 1.2) 264 (. 1.5) Nation 45 ( 1.8) 55 ( 1.8) 269 ( 1.7) 254 ( 1.3) The standard errors of the estimated statist= appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within s 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). -.. C.) THE 1990 NAEP TRIAL STATE ASSESSMENT 131 Idedro TABLE A24 I Students' Reports on rypes of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Thee Twos Four Types - TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 16 ( 0.9) 32 ( 0.9) 53 ( 12) 258 ( 1.9) 270 ( 1.2) 2-7 ( 0.8) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) ( 1.5) RACE/ETHNICITY White State 14 ( 0.9) 31 ( 1.1) 55 ( 12) 263 ( 2.0) 272 ( 1.2) 278 ( 0.8) Nation 16 ( 1.1) 29 ( 1.3) 50 ( 1.5) 251 ( 22) 268 ( 1.5) 278 ( 1.7) Hispanic State 38 ( 4.3) 242 ( 3.2) 34 ( 4.4) 444, 28 ( 3.3) .41 Nation 44 ( 3.0) 30 ( 2.4) 26 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) Ainerican Indian State Nation ,Hh.) 29(11.1) ***) 40 ( 4.9) *** ( "HI **V ( ***) 31 ( 92) * ( **) TYPE OF COMMUNITY Extreme rural State 17 ( 1.4) 31 ( 1.6) 52 ( 2.0) 255 ( 2.2) 268 ( 1.5) 274 ( 1.5) Nation 33 ( 3.2) 50 ( 5.1) 253 ( 4.3)1 263 ( 5.6)1 Other State 15 ( 1.1) 33 ( 1.2) 52 ( 15) 259 ( 2.8) 270 ( 1.7) 277 ( 1.1) Nation 22 ( 1$) 30 ( 1.3) 48 ( 15) 244 ( 2.6) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure 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). " 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A24 I Students' Reports on Types of Reading (wntinued) i Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 MAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Typos - Four Typos _ TOTAL peroentage and Pro lidenay 18 ( 0.9) Ilarastdaga and Madam 32 ( 0.9) Peraintnta and Prolkdancy 53 ( 12) state 258 ( 1.9) 270 ( 12) 277 ( 0.11) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) PABENTS' EDUCATION NS non-graduate State ( 230 ( 3.9) 2.7) 32 ( iv* 4.9) 21 ( 3.5) Nation ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 246 ( 3.3) NS graduate State 22 ( 2.2) 33 ( 2.4) 45 ( 1.6) 255 ( 3.1) 262 ( 2.0) 265 ( 2.1) Nation 28 ( 2.2) 33 ( 1.9) 40 ( 1.7) 246 ( 2.2) 253 ( 2.7) 260 ( 2.1) Sem college State 15 ( 1.6) 33 ( 2.2) 52 ( 2.8) 268 ( 2.8) 272 ( 1.9) 278 ( 1.7) Nation 17 ( 1.5) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduate State ( 1.0) 30 ( 1.6) 63 ( 1.7) 269 ( 3.0) 278 ( 2.1) 281 ( 1.0) Nation 10 ( 0.8) 28 ( 1.8) 82 ( 2.0) 254 ( 2.8) '7^ 2.5) 280 ( 1.8) GENDER Male State 16 ( 1.3) 32 ( 1.3) 51 ( 1.5) 261 ( 2.4) 271 ( 1.8) 278 ( 1.2) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Female State 15 ( 1.0) 31 ( 1.4) 54 ( 1.7) 255 ( 2.5) 288 ( 1.4) 276 ( 1.1) Nation 22 ( 1.2) 28 ( 1.4) 49 ( 1.9) 244 ( 2.2) 258 1 1.9) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 133 Idaho TABLE A25 I Students' Reports on the Amount of Time Spent 1 Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One Hour or Less - Two Hours Three Hours Four to Five Hours _ Six Hours or More TOTAL Percentage and Proficiency 19 ( 0.9) 278 ( 1.1) 12 ( 0.8) 269 ( 2.2) 19 ( 1.1) 281 ( 1.3) 13 ( 1.0) 276 ( 2.5) ( ) 14 ( 2.4) *** *4,-1 20 ( 62) ( 13 ( 5.0) *** 18 ( 1.1) 277 ( 1.5) ( 3.3) . 19 ( 1.1) 278 ( 1.5) 12 ( 1.0) 268 ( 2.6) Percentage and Proficiency 20 ( 1.1) 276 ( 1.3) 21 ( 0.9) 268 ( 1.8) 26 ( 12) 278 ( 1.3) 23 ( 1.2) 275 ( 2.2) 20 ( 2.5) 245 ( 3.2) ( 17 ( 8.4) **. 24 ( 1.7) 272 ( 1.5) 19 ( 2.6) 4*-* t-* 27 ( 1.3) 277 ( 1.7) 21 ( 1.0) 269 ( 2.3) Percentage and Proficiency 24 ( 0.8) 272 ( 1.2) 22 ( 0.8) 265 ( 1.7) 25 ( 0.9) 274 ( 1.3) 24 ( 1.1) 272 ( 1.9) 25 ( 3.1) 19 ( 2.1) 242 ( 5.8) 21 ( 5.3) 21 (10.5) *44 ) 25 ( 1.4) 268 ( 1.8) 23 ( 2.0) 24 ( 1.1) 273 ( 1.5) 23 ( 1.2) 265( 2.1) Percentage and Proficiency 24 ( 1.0) 266 ( 1.$) 28 ( 1.1) 260 ( 1.7) 23 ( 1.1) 268 ( 1.5) 27 ( 1.4) 267 ( 1.7) 28 ( 3.5) 31 ( 3.1) 247 ( 3.5) 27 ( 6.3) .01 28 ( 5.7) 25 ( 2.2) 267 ( 2.1) 26 ( 2.7) 256 ( 3.6)1 23 ( 1.1) 265 ( 2.0) 27 ( 1.2) 259 ( 2.2) Percentage and Proildency 7 ( 0.6) 258 ( 2.7) 16 ( 1.0) 245 ( 1.7) 6 ( 0.6) 259 ( 2.5) 12 ( 1.2) 253 ( 2.6) 12 ( 2.7) «61 17 ( 1.7) 236 ( 3.8) 10 ( 4.9) 22 ( 8.4) ( 0.7) 251 ( 3.1) 19 ( 3.8) 7 ( 0.7) 256 ( 3.9) 17 ( 1.4) 248 ( 2.5) State Nation RACE/ETHNICITY White State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY 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 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). 1 d 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A25 I Students' Reports on the Amount of Thne Spent (continued) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _.. MO NAEP TRIAL STATE ASSESSMENT One Hour or Lass - Hours Two Throe Hours Four to Flys Hours Six Hours or More TOTAL Porasidaga and Pralkiency Percertrawas and Prang:Wm Peratatage and *Wien Parentage and Madam Payola. and Pro Nohow State 19 ( 0.9) 2e ( 1.1) 24 ( 0.6) 24 ( 1.0) 7 0.4) 278 ( 1.1) 276 ( 1.3) 272 ( 12) 206 ( 14) 268 (2.7) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0-6) 26 ( 1.1) 18 1.0) 289 ( 2.2) 208 ( 1.8) 265 ( 1.7) 260 ( 1.7) 245 ( 1.7) PARENTS' EDUCATION HS non-graduat State 13 ( 2.6) 17 ( IP** ( 3.0) 25 ( ( 3.5) .41 33 ( 11411. ( 3.8) *el 11 ( 2.3) ( Nation 12 ( 22) 20 ( ( 3.1) 441 21 ( 25) 28 ( 244 ( 2.9) 3.2) 20 ( 2.4) HS graduate State 16 262 ( 1.7) ( 3.3) 22 ( 264 ( 1.8) 2.8) 24 ( 264 ( 2.1) 2.6) 29 ( 260 ( 2.5) 2.4) 9 ( 1.5) .40) Nation 8 ( 1.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 19 ( 1.8) 249 ( 4.7) 257 ( 2.6) 259 ( 3.2) 253 ( 2.5) 248 ( 3.0) Some college State 17 279 ( 22) ( 3.2) 26 ( 279 ( 2.6) 2.4) 23 ( 274 ( 2.1) 2,7) 27 ( 271 ( 2.3) 2.4) .44 ( 1.4) .4.11 Nation 10 ( 1.4) 44.) 25 ( 275 ( 2,4) 2.7) 23 ( 269 ( 2.6) 3.5) 28 ( 267 ( 2.2) 2.5) 14 242 ( 1.5) ( 3.4) College graduate State 22 ( 1.4) 29 ( 1.5) 25 ( 1,41 19 ( 1.5) 5 ( 0.8) 285 ( 1.6) 282 ( 1.7) 279 ( 1.6) 274 ( 2.4) 260 ( 42) Nation 17 ( 1A) 22 ( 23 ( 1.1) 25 ( 1.5) 12 ( 1.1) 282 ( 2.6) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 3.2) GENDER Male State 17 ( 1.1) 26 ( 1.4) 25 ( 1.3) 24 ( 1.5) 9 ( 0.9) 279 ( 2.1) 277 ( 1.7) 274 ( 1.8) 269 ( 2.1) 256 ( 3.8) Nation 11 ( 0.9) 22 ( 1,2) 22 ( 1,0) 28 ( 1.3) 17 ( 1.5) 269 ( 3.3) 267 ( 2.6) 267 ( 2.2) 262 ( 2.1) 248 ( 2.5) Female State 21 ( 1.5) 26 ( 1.6) 24 ( 1.4) 24 ( 1.4) 8 ( 0.7) 277 ( 1.8) 275 ( 1.6) 270 ( 1,6) 263 ( 1,8) 256 ( 4.6) Nation 14 ( 1,1) 20 ( 1.3) 23 ( 1.4) 28 ( 15) 15 ( 1.2) 269 ( 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Idaho TABLE A26 I Students' Reports on the Number of Days of 1 School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 101I0 NAEP TRIAL STATE ASSESSMENT Nona One or Two Days Throe Days or Moro TOTAL Percentage and Proficiency Pimento's and Proficiency Percentage and Proficiency State 43 ( 1.0) 38 ( 1.0) 21 ( 1.0) 273 ( 1.1) 273 ( 1.1) 267 ( 1.3) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 285 ( 1.8) 2.3 ( 1.5) 250 ( 1.9) RACE/ETHNICITY While State 43 ( 1.0) 36 ( 1.1) 21 ( 1.1) 275 ( 1.1) 275 ( 1.1) 269 ( 1.4) Nation 43 ( 1.2) 34 ( 1.2) 23 ( 1.2) 273 ( 1.8) 272 ( 1.7) 258 ( 2.1) Hispanic State 39 ( 3.7) 250 ( 4.3) 38 ( 4.0) 250 ( 3.7) 23 ( 3.4) es.. ( *Sri Nation 41 ( 3.3) 32 ( 22) 27 ( 2.8) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) American Indian State 35 ( 6.5) ". V") 39 ( 6.4) 26 ( 6.2) .4* Nation 23 ( 6.6) 04.41 39 ( 5.1) .4* **) ( e") TYPE OF COMMUNITY Extreme rural State 45 ( 1.8) 38 ( 1.8) 17 ( 1.4) 269 ( 1.5) 272 ( 1.5) 261 ( 1.5) Nation 43 ( 4.4) 32 ( 4.2) 25 ( 3.9) 257 ( 4.1)1 264 ( 6.8)1 Othar State 41 ( 1.3) 38 ( 1.1) 23 ( 1.1) 274 ( 1.5) 273 ( 1.6) 288 ( 1.8) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 288 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A26 I Students' Reports on the Number of Days of (continued) I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None One or Two Days Three Days or More TOTAL Percentage and Proficiency Percentage and Proficiency Peralatige mtd Proficiency State 43 ( 1.0) 36 ( 1.0) ( 1.0) 273( 1.1) 273 ( 1.1) 267 ( 1.3) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 206 ( 1$) 250 ( 1.9) PARENTS' EDUCATION HS non.graduate State 37 ( 258 ( 4.9) 4.1) 29 ( 41.4 ( 3.9) 34 ( ev- 4.8) Nation 36 ( 3.2) 28 ( 3.1) 33 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) NS graduate State 37 ( 2.5) 3$ ( 2.6) 25( 2.3) 265 ( 2.3) 262 ( 2.0) 257 ( 2.6) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.6) 249 ( 2.4) Some college State 42 ( 2.5) 3$ ( 2.3) 21 ( 1.9) 276 ( 1.9) 274 ( 1.7) 272 ( 2.7) Nation 40 ( 1.8) 37 ( 1.8) 23 ( 1.6) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) College graduate state 45 ( 1.7) 37 ( 1.6) 18 ( 1$) 279 ( 1.6) 2131 ( 1.8) 276 ( 2.1) Nation 51 ( 1.13) 33 ( 12) 16 ( 1.3) 215 ( 2.1) 2/7 ( 1.7) 265 ( 3.1) GENDER Mate State 48 ( 1.3) 33 ( 1.4) 21 ( 1.3) 273 ( 1.4) 274 ( 1.6) 269 ( 1.8) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 1.4) 266 ( 2.0) 267 ( 2.1) 250 ( 2.6) Femal State 39 ( 1.9) 39 ( 1$) 22 ( 1.3) 273 ( 1.4) 272 ( 1,4) 264 ( 1.9) Nation 43 ( 1.4) 32 ( 1.1) 25 ( 1.3) 284 ( 2.3) 266 ( 1.7) 250 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 137 Idaho TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT _ _ Sim* We. ASP.. - . Undecided, Disagree, Strongly Disagree TOTAL Percentage and Proficiency Percentage and Prolidency Percentage and Proficiency State 29 ( 0.9) 49 ( 1.0) 22 ( 1.1) 281 ( 1.1) 271 ( 0.8) 200 ( 1.5) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) RACE/ETHNICITY White State 30 ( 1.0) 49 ( 1.1) 21 ( 1.2) 283 ( 1.1) 274 ( 0.9) 263 ( 1.4) Nation 26 ( 1.6) 4$ ( 1.3) 26 ( 1.5) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Hispanic State 24 ( 0** ( 3.4) ***) 4$ ( 247 ( 3.9) 3.6) 28 ( *SI 3.5) ) Nation 24 1 2.5) 48 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 22) 236 ( 3.8) American Indian State 15 ( 4.9) 52 ( 7.6) ***) 33 ( 7.1) Nati CM 23 ( diht 7.4) 48 (14.9) .4* ( 29 ( *** 9.5) TYPE OF COMMUNITY Extreme nral State 30 ( 1.3) 51 ( 1.5) 19 ( 1.2) 277 ( 1.4) 269 ( 1.4) 256 ( 2.2) Nation 34 ( 2.8) 49( 2.2) 17 ( 1,4) 270 ( 3.9)1 252 ( 4.1)1 Othar State 29 ( 1.2) 49 ( 1.4) 23 ( 1.5) 282 ( 1.5) 272 ( 1.1) 2E0 ( 2.3) Nation 27 ( A) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 260 ( 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 mterest, 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). A 4' 1...3 13S THE 1990 NAEP TRIAL STATE ASSESSMENT Idaho TABLE A27 I Students' Perception of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1490 NPEP TRIAL STATE ASSESSMENT Strongly Agree _ ASP** Undecided, 'Nurse, Strongly Disagree TOTAL Percentage and Proficiency Percentage Ind Proficiency Percentage and Proficiency State 29 ( 0.9) 49 ( 1.0) 22 ( 1.1) 281 ( 1.1) 271 ( 0.8) 200 ( 1.5) Nation 27 ( 1.3) 49 ( tO) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) PARENTS' EDUCATION liS non-graduate State 25 ( 3.8) 50 ( 5.1) 25 ( 42) 252 ( 2.6) FR* ( IrOn Nation 20 ( 2.6) 50 ( 3.3) 30 ( 3.6) 243 ( 2.6) 238 ( 4.3) HS graduate State 23 ( 2.1) 49 ( 2.2) 28 ( 2.1) 268 ( 2.3) 263 ( 2.0) 255 ( 2.5) Nation 27 ( 2.1) 47 ( 2.3) 28 ( 2.0) 262 ( 2.7) 255 ( 2.3) 245 ( 2.4) Some college State 29 ( 1.9) 49 ( 2.0) 22 ( 2.0) 283 ( 1.8) 274 ( 1.6) 266 ( 2.3) Nation 28 ( 2.5) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 2$8 ( 32) College graduate State 33 ( 1.4) 49 ( 1.7) 18 ( 1.7) 288 ( 1.5) 279 ( 1.1) 266 ( 2.2) Nation 30 ( 2.3) 51 ( 1.6) 19 ( 1.8) 280 ( 2.4) 274 ( 22) 266 ( 2.5) GENDER Male State 30 ( 1.1) 1.4) 21 ( 1.5) 281 ( 1.3) 273 ( 1.2) 260 ( 1.9) Nation 28 ( 1.5) 48 ( 1.2) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Female State 28 ( 1.5) 48 ( 1.6) 23 ( 1.4) 281 ( 1.6) 270 ( 1.1) 259 ( 1.9) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 269 ( 2.1) 262 ( 1.8) 252 ( 1.9) The standard errc..rs of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the .,alue for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing Service (ETS), Westat, and National Computer Systems (NCS). The pi ogram benefitted from the contributions of hundreds of individuals at the state and local levels Goveznors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Finally, and most importantly, NAEP is grateful to the studeMs and school staff who participated in the Thal 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 Plannhig Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In particular, we note the significant contributions of Ramsay 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 Plannhig Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the US. 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 (NAGH) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scak 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 Mane% with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffler, 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 repeat John Mazzeo ovenaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koffier wrote the text for the report. Kent Ashworth was 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 tat and the analysts who checked the data. 1 US. GOVERNMENT PRINTING OFFICE ; 1991 0 - 298-275 QL 3 GIK. 131