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DOCUMENT RESUME ED 330 584 SE 052 094 TITLE The State of Mathematics Achievement in Wyoming: Tile Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. ETS-21-ST-02; ISBN-0-88685-14-9 Jun 91 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) REPORT NO PUB DATE NOTE EDRS PRICE DESCRIPTORS IDENTIFIERS ABSTRACT Progress (NAEP) MF01/PC06 Plus Postage. Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Hatnematics Tests; National Programs; Problem Solvf.,,g; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing National Assessment'of Educational Progress; *Numeracy; State Mathematics Assessments; Trial State Assessm9nt (NAEF); *Wyoming In 1990, the National Assessment of Educational 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 Wyoming, 2,701 students in 6 public schools were assessed. This report describes the mathematics proficiency of Wyoming 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), P resents the average proficiency separately for the five content areas, and summarizes the performance of subpopulatiohs.,(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, Wyoming students had an average proficiency of 272 compared to 261 nationwide. Many.fewer students (Wyoming-15%; U.S.-I2%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Ah e e t in WYOMING The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD MST COPY AVAILABLE , U S DEPARTMENT OF EDUCATION Office of EckKat.orlo Ramiro and rmprovment F UCATIONAL RESOURCES INFORMATION CE NTE R IERICI TN% docrnent has peen reproduced aS rece,..0 trpm the oerson or organuatron orgmatmg ,t - Sknor changes nave Peen made to rmoroye reproducton quatrty Ponds ot rm.,* Or OpnrOnS Stated In thiS (IOC ment do not necesSertty represent Ottrcrel OE RI pos.lion or pohcy Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Education:1i Research and improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD. the National Assessment of Educational Pi-ogress tNAFP), is the only nationally representative and continuing osessment of what America's students know and can do in various subject areas. Since 1969, assessments have been conducted pcnodically in reading. mathematics. science. writing. history/geography. and ofher fields. By making objective intOrmation on student performance available to policymakers at the national. state. and local levels. NAEP is an integral part of our nation's evaluation of the condition and progress of education. Only information relaPW to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statbtics, the 11.S. Department of FAlucation. The Commissioner of Education Statistics is responsiWe. hy law, for canying, out the NAEP pmject thmugh competitive awards to qualified organizations. NAEP reports directly to the (.7ommissioner. who is also responsible lOr pnwidingcontinuing reviews, including validation studies and wlicitation of public comment. on NAEP's conduct and usefulness. In 19/48, Congress created the National Assessment Governing Board (NAGS) to formulate policy guidelines fOr NAEP. The board is responsible for selecting the subject areas to be assessed. which may include adding to those specified by Congress: identifying appropriate achievement goals for each age and grade; developing assessment objectives: developing test specifications: &signing the assessment methodology; developing guidelines and standards for data analysis and for reporting and disseminating results; developing standards and procedures for interstate. regional. and national comparisons: improving the form and use of the National Assessment; and ensuring that all iwms selected for use in the National Assessment are free from racial. cultural. gender. or regional bias. The National Assessment Governing Board Richard A. Boyd. Chairman Executive Director Martha Holden Jennings Foundation Cleveland. Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.O.C.E.S. Saratoga Springs. New York Franck Alexander Associate Superintendent California Department of Educatkm Sacramento. California David P. Baffin! High School History Teacher Cairo-Durham High School Cairo. New York Parris C. Battle Teacher Horace Mann Elementi. Miami. Florida Mary R. Blanton Attorney Cromwell, Porter, Blanton & Blanton Salisbury. North Carohmi Boyd W. Boehlje Attorney Gaass. Klyn. & Bochhc Pella, Iowa Linda FL Bryant Teacher Greenway Middle School Teacher Center Piusburgh. fiLmnsylvania Honorable Michael N. Castle Governor of Delaware Carve! State Office Building Wilmington. Dclawarc Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislatiw Office Building Hartford, Connecticut Chester E. Finn. Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.C. Michael S. Glode Wyonfing State Roan! of Education Saratoga. Wyoming Christine Johmson Principal Abraham Lincoln High School Denver. Colorado John Lindley Principal South Colby Elementary School Port Orchard. Washington Carl J. Maser Dnector of Schook The Lutheran Church - Missiniri Synod hnernational Center St, Louis, Missoun Mark D. Muskk President Southern Regional Education Board Atlanta, Georgia Honorabk Carolyn Pollan Arkinsas House of Representatives Fort Smith. Arkansas Matthew W. Prophet. Jr. Superintendent Portland Oregon School District Portland, Oregon Honorable William T. Randall C(mmissioncr of Educatim State Department of Education Denver. Colorado Dorothy K. Rich President Home and School Institute Special Pri)jects Office Washington. Honorabk Richard W. Riley Attorney Nelson, Mullins. Riley and Scarborough Columbia. South Carolina Thomas Topuzes Attorney Law (Nikes of Frank Rogozienski onado, California Herbert J. Walberg Professor of Educatkm University of Illinois Chicago. Illinois Assistant Sccr.:tary for Educational Research and improvement (Ex-Off:dot '.S. Department of Education Washrigton. Roy Truby N:otivc Director, NAGB Washington, D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The SU= of Mathema'cs Achievement ht WYOMING The Trial State Assessment at Grade Eight Report No: 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education 4 U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports arc available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Congress, Catalog Card Numirer: 91-61478 ISBN: 0-88685-14-9 The work upon which this publication is based was pmfornted for the Naticral Center for Education Statistics. Office of Educational Research and Improvement, by Educational Testing Service. Educational Thsting Service is an equal opportunity/affirmative action auployer. Educational Tastins Service, EFS, and are registernd trademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of Wyoming 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed IS PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Wyoming Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 Levels of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Euhpopulations 24 Race/Ethnicity 24 Type of Communit) 27 Parents' Education Lel .4 29 Gender 31 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT lii PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathetnatks? 39 Cuniculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Delivered' .49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used' 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics? 67 Educational Background Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDU RAL APPEN DIX 81 DATA APPENDIX 97 iv THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming THE NATION'S REPORT CARO EXECUTIVE SUMMARY in 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessmmts on a trial basis, in addition to continuing its primary mission, the national assessIlViltf that NAEP has conducted since its inception. As a result of the legislation, the 199G NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to repusent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50.percent of tbe sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT 1 Wyoming In Wyoming, 69 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-gradc students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in Wyoming. 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 8 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment bemuse they were categorized as LEP or had an IEP represented 0 percent and 4 percent of the population, respectively. In total, 2,701 eighth-grade Wyoming 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 Wyoming. Students' Mathematics performance The average proficiency of eighth-grade public-school students from Wyoming on the NAEP mathematics scale is 272. This proficiency is higher than that of students across the nation (261). Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail. NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming In Wyoming, 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 Wyoming (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). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in Wyoming 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 subpopulatious of the Wyoming eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In Wyoming: White students had higher average mathematics proficiency than did Hispanic oi American Indian students. Further, a water 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 Wyoming students attending schools in areas classified as "other" was lower than that of students attending schools in extreme rural areas. In Wyoming, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 24 points higher than that of students whose parents did not graduate from high school. The results by gender show that eighth-grade males in Wyoming had a higher average mathematics pioficiency than did eighth-grade females in Wyoming. In addition, a greater percentage of males than females in Wyoming attained level 300. Compared to the national results, females in Wyoming performed higher than females across the coui.try; males in Wyoming performed higher than males across the country. THE 1990 NAEP TRIAL. STATE ASSESSMENT 3 Wyoming 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 idormation, 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 Wyoming are as follows: Less than half of the students in Wyoming (43 percent) were in schools where mathematics was identified as a special priority. This is a smaller percentage than that for the nation (63 percent). In Wyoming, 72 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 Wyoming were taking eighth-grade mathematics (48 percent) as were taking a course in pre-algebra or algebra (47 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 Wyoming spent 15 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. 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 had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. 11 4 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming In Wyoming, 32 percent of the eighth-grade students had mathematics teachers who reported getting a11 of the resources they needed, while 16 percent of the students were taught by teachers who got only some or none of the resources they needed. Aeross the nation, these figures were 13 percent and 31 percent, respectively. In Wyoming, 18 percent of the students neves used a calculator to work problems in class, while 52 percent almost always did. In Wyoming, 30 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About half of the students (46 percent) had teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in Wyoming who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of these materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. Some of the eighth-grade public-school students in Wyoming (18 percent) watched one hour or less of television each day; 7 percent watched six hours or more. Average mathematics proficiency was highest fos students who spent one hour or less watching television and lowest for students who watched television six hours or more each day. THE 1990 NAEP TRIAL STATE ASSESSMENT S If Wyoming ME NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Proigess (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 n n Nor Virn Islands Idiaa th Dakota gi THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Wyoming This report describes the perfomiance of the eighth-grade public-school students in Wyoming and consists of three sections: This Introduction provides background information about the Trial State Assessment at I this report. It also provides a profile of the eighth-grade public-school students in Wyoming. Part One describes the mathematics performance of the eighth-grade public-school students ii Wyoming, the West region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Wyoming, the West region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's historv -- 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 (1)(2)(C)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(1))) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's stiff 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 monitoiing indicated a high degree of quality and uniformity across sessions. 1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming The Trial State Assessment war based on a set of mathematics objectives newly developed for the program and patterned after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National Science I ,undation and the U.S. Department of Education to issue a special grant to the Council of Chief State Schoul 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 Mathvatics,' 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 extenkve 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 refmed by NAEP's Item Development Panel, reviewul 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 Wyoming, 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. Definitions of the subpopulations referred to in this report are presented below. The results for Wyoming are based only on the students included In the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nationally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAEP program was necessary because the voluntary naiure 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, Currkulum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics. 1989). 1 5 THE 1990 NAEP TRIAL STATE ASSESSMENT 9 Wyoming RACE/ETIENICITY Results art presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according tO the faowing mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria &scribed 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 Wyoming 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 group live in metropolitan statistical areas and attend schools where a high proportion of the students' parents are on welfare or are not regularly employed. Extreme Rural: Students in this group live 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 worke-s. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for repotting. i 6 10 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming GENDER Results are reported separately for males and females. REGION The United States has been divided into four regions: Northeast, Southeast, Central, and West. States included in each region are shown in Figure I. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, reeonal comparisons for Virginia will be to the Southeast. FIGURE I I Regions of the Country NORTHEAST SOUTHEAST CENTRAL WEST - Connecticut Alabama Illinois Alaska Dalawars Arkansas Indiana Arizona District of Columbia Florida Iowa California Maine Giorgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louana Minnesota Idaho New Hampshire Mississippi Missouri Montana *ow Jamey North Carolina Nebraska Nevada Maw York South Carolina North Dakota Naw Mexico Pennsylvania Tennessee Ohio Oklahoma Rhoda island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming PA, THE 1990 NAEP TRIAL STATE ASSESSMENT 11 Wyoming Guideli"es for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual backga-ound questions. It does not include an analysis of the relationships among comtinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken thto account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard =ors 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 goups are being compared, a Bonferroni procedure is also use41. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendix. 18 12 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either olgebra 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 of the groups the 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 stieistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT 13 Wyoming Profile of Wyoming EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in Wyoming, the West region, and the nation. This profile is based on data collected from the students and schools participating in the Trial State Assessment. TABLE 1 I Profile of Wyoming Eighth-Crade I Public-School Students PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Wyoming Wait Nation DEMOGRAPHIC SUBGROUPS Parconts. Pan:inter Piwcantago Race/EthnIcIty White 86 ( 0.8) 63 ( 1.9) 70 ( 0.5) Black 1 ( 0.2) 7 ( 2.0) 16 ( 0.3) Hispanic 9 ( 0.6) 21 ( 1.5) 10 ( 0.4) Asian 1 ( 0.2) 4 ( 1.3) 2 ( 0.5) American Indian 3 ( 0.4) 4 ( 2.3) 2 ( 0.7) Typo ot Community Advantaged urban o ( 0.0) 14 ( 8.5) 10 ( 3.3) Disadvantaged urban 0 ( 0.0) 19 ( 7.5) 10 ( 2.8) Extreme rural 27 ( 0.8) 10 ( 3.8) 10 ( 3.0) Other 73 ( 0.8) 58 (10.1) 70 ( 4.4) Parants` Education Did not finish high school 5 ( 0.4) 10 ( 1.3) 10 ( 0.8) Graduated high school 23 ( 1.0) 19 ( 2.5) 25 ( 1.2) Some education after high school 23 ( 0.8) 16 ( 1.2) 17 ( 0.9) Graduated college 43 ( 1.0) 42 ( 4.0) 39 ( 1.9) Gender Male 51 ( 0.8) 55 ( 2.1) 51 ( 1.1) Female 49 ( 0.8) 45 ( 2.1) 49 ( 1.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percene 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 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 "1 don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Wyoming schools and students sampled for the 1990 Trial State Assessment. In Wyoming, 69 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in Wyoming. TABLE 2 I Profile of the Population Assessed in Wyoming EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution Weighted school participation rate after substitution Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number of participating schools 100% 100% 69 es 59 EIGHTH-GRADE PUSLIC-SCHOW. STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students selected to participate in the assessment Number of students withdrawn from the assessment Percentage of students who were ot Limited English Proficiency Percentage of students excluded from the assessment due to Limited English Proficiency Percentage of students who had an individualized Education Plan Percentage of students excluded from the assessment due to Individualized Education Plan status Number of students to be assessed Number of students assessed 90% 3,058 126 4% 0% 8% 4% 2,824 2,101 In Wyoming, the Trial State Assessment was based on all eligible schools. There was no sampling of schools. 21 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming In each school, a random sample of students was selected to participate in the assessmeat. As estimated by the sample, 1 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP) while 8 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 permitled to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 0 percent and 4 percent of the population, respectively. In total, 2,701 eighth-grade Wyoming public-school students were assessed. Tht; 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 Wyoming. 16 THE 1990 NAEP TRIAL STAI E ASSESSMENT Wyoming NE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Wyoming 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 Wyoming. Chapter 1 compares the overall mathematics performance of the students in Wyoming to students in the West region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 summarizes the students' overall mathematics performance for subpopulations defined by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 17 Wyoming CHAPTER 1 Students' Mathematics Performance As shown in Fig= 2, the average proficiency of eighth-grade public-school students from Wyoming on the NAEP 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 I Mathematics Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by )-1-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 24 18 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provide5 a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To defme 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 Wyoming, 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 Wyoming (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 Wyoming, West region, and national results for each content area. Students in Wyoming performed higher than students in the nation in all of these five content areas. 5 THE 1990 NAEP TRIAL STATE ASSESSMENT 19 MEP., Wyoming FIGURE 3 I Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-Step word problems and select the greatest tour-cligit number In a list. In measurement, these students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they are able to read Simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to 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 tnese basic problem-solving situations, they can identity 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 c zystem when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate art Initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch 0 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 Wyoming FIGURE 3 I Levels of Mathematics Proficiency (continual) I LEVEL 300 Reasoning and Problem Solving involving Fractions, Decimals, Percents, Momentary Geometric Properties, and Simple A14 bralc Manipulations Students at this level are able to represent, interpred, and perform simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, arr recognize the equivalence between common fractions and decimals, including pictorial representations. They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to Interpret expressions, including those with exponents and negative Integers. In measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, Identifying the solution to open 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. . SMIMINIMEM.1. LEVEL 350 Reasoning and Problem Solving involving Gametic 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 .:Ircumferences 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 of a line. In data analysis, these students can compute means frc.t 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 ot two linear equations. They are developing an understanding of linear functions and their graphs, as well as function3I notation, including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. 27 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 Wyoming FIGURE 4 I Levels of Eighth-Grade Public-School 1 Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation 0 20 40 60 80 0 ( 0.1) 0 ( 0.4) 0 ( 0.2) 15 ( 0.7) 12 ( 2.4) 12 ( 1.2) SO ( 1.0) 03 ( 2.8) 54 ( 1.6) 100 ( 0.1) 97 ( 1.0) 97 ( 0.7) 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. S 22 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming FIGURE 5 I Eighth-Grade Public-School Mathematics Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation NE NATION'S REPORT CARD 101P",11 DATA 'ANALYSIS, ST4TISTICS, AND PROBABILITY 1-0.4 9-4.4 ALGEBRA AND FUNCTIONS 1.,"400,01 PINS I44 romiA, OVIrminow Average Proficiency 275 ( 0.7) 264 ( 2.6) 268 ( 1.4) 270 ( 0.9) 258 ( 3.0) 2S8 ( 1.7) 270 ( 0.6) 260 ( 2.6) 259 ( 1.4) 274 ( 0.7) 262 ( 3.6) 262 ( 1.8) 270 ( 0.7) 259 ( 2.4) 260 ( 1.3) 0 200 225 250 275 300 500 Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-4-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 I) THE 1990 NAEP TRIAL STATE ASSESSMENT 23 Wyoming 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 Assesament results can be compared according to the different racial/ethnic groups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics perfonnance results for White, Hispanic, and American Indian students from Wyoming 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. 3 0 24 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming FIGURE 6 I Average Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity Po Pool Wyoming White Hispanic American Indian WItSt White Hispanic American Indian Nation White Hispanic American Indian The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 31 THE 1990 NAEP TRIAL STATE ASSESSMENT 25 Wyoming NE NPZION1 REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARD 1 Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Hispanic Amer. Indian Region White Hispanic Amer. Indian Nation White Hispanic Amer. Indian LEVEL 250 State White Hispanic Amer. Indian Region White Hispanic Amer. Indian Nation White Hispanic Amer. Indian LEVEL 200 Stat. White Hispanic Amer. Indian Region White Hispanic Amer. Indian Nation wh t e Hispanic Amer. Indian sloolose Parcentage 1$ ( 0.8) 5 ( 1.6) 3 ( 2.4) 16 ( 3.2) 3 ( 1.6) mor ***) 15 ( 1.5) 3 ( .1) 1 ( 2.3)1 tri ( 1.0) 57 ( 4.8) OS ( 5.8) 74 ( 3.3) 41 ( 5.4) .*) 74 ( 1.8) 41 ( 4.5) 45 (18.0)1 100 ( 0.1) 96 ( 1.3) 100 ( 0.8) 99 ( 0.8) tPI 93 ( 2.0) mug 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 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 32 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 09 ( 0.4) .3 ( 1.6) 97 ( 6.7)1 Wyoming TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in areas dusified as "other" and extreme rural areas. (These are the "type of community" groups in Wyoming with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Wyoming students attending schools in areas classified as "other" was lower than that of students attending schools in extreme rural areas. FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community AMP flattionaties Scale 200 225 250 275 300 500 Average Proficiency Wyoming Extreme rural Other 273 ( !..) West 11.411111001111111 Extreme rural 243 ( 7.3$ Other ( 3.6) P-1,004 Nation Extreme rural 21111 ( 4.1)1 P-4104 14,4 Other 211 1.8) 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-t). 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. 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 Wyoming NATION'S FIGURE 9 Levels of Eighth-Grade Public-School REPORT Mathematics Proficiency by Type of CARD Community LEVEL 300 stab 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 Other Region Ext. rural Other Nation Ext. rural Othe, 17 ( 1.7) 15 ( 0.9) ( 4.8)1 10 ( 1.8) ( 2.3)1 12 ( 1.2) 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within * 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-4.4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 100 ( 0.2) 100 ( 0.2) 96 ( 1.3)1 96 ( 1.7) 97 ( 2.8)1 97 ( 1.0) 100 34 28 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In Wyoming, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 24 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, about the same percentage of students in Wyoming (43 percent) and in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 5 percent for Wyoming and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School Mathematics Proficiency by Parents' Education MEP Mathematics Scale 0 200 225 250 275 300 500 Average istenciency Wyoming) i-164 HS non-graduste 2113( 241 t44 HS graduate an Some college Int( ea) College graduate Mb( te) Vint HS non-graduate 24$ ( 4.4) t-t-t HS graduate am C 2.2) Some college in ( 3.0) 1-- College graduate V31 3.3) Nation 144 HS non-graduate 243( 2.0) pot HS graduate 214( 1.5) P44 Some college ( 1.1) PM College graduate 234( 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 H-i). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 3 5 THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Wyoming ME MATIONS REPO& mop FIGURE II I Levels of Eighth-Grade Public-School CARD Mathematics Proficiency by Parents' Education LEVEL 300 State HS non-grad. HS graduate Some college College grad. Raglan HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. ROISan HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. 0 20 40 80 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 100 30 THE 1990 NAEP TRIAL STATE ASSESSMENT 2 ( 1.7) 6 ( 1.3) 14 ( 1.6) 23 ( 1.5) 2 ( 2.3) 2 ( 1.3) 15 ( 2.8) 21 ( 3S) 1 ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.9) 63 ( 5.1) 70 ( 1.8) 1110 ( 1.7) 00 ( 1.1) 44 ( 98) 51 ( 4.4) 75 ( 4.1) 76 ( 3.6) 37 ( 4.6) 56 ( 2.7) 71 ( 2.6) 78 ( 2.0) 100 1 0.0) SO ( 0.4) 100 ( 0.1) 100 ( 0.0) ( 3.2) ( 1.6) ( 0.7) ( 0.7) ( 1.9) ( 0.8) ( 0.7) ( 0.7) Wyoming GENDER As shown in Figure 12, eighth-grade males in Wyoming had a higher average mathematics proficiency than did eighth-grade females in Wyoming. Compared to the national results, females in Wyoming performed higher than females across the country; males in Wyoming performed higher than males across the country. FIGURE 12 I Average Eighth-Grade Public-School i Mathematics Proficiency by Gender NAEP Mathematic* Scale 200 225 250 275 300 SOO hPel PM ,Allnmmos a Average Pro Weary Wyoming Male 224 ( 011) Female 1170 ( 0.3) Wost Male t 3.5) Female VA ( 2.48) Nation Male 1.3) Female 2 ( 1.3) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by t-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in Wyoming who attained level 200. The percentage of females in Wyoming who attained level 200 was greater than the percentage of females in the nation who attained level 200. Also, the percentage of males in Wyoming who attained ievel 200 was greater than the percentage of males in the nation who attained level 200. 3 e..1 THE 1990 NAEP TRIAL STATE ASSESSMENT 31 Wyoming FIGURE 13 I Levels of Eighth-Grade Public-School I Mathematics Proficiency by Gender LEVEL 300 State Male Female Region Male Female Nat ;on Male Female LEVEL 250 flita4 Male Female Region Male Female Nation Male Female LEVEL 200 Stat 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 i-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 82 ( 1.3) 78 ( 1.5) GS ( 4.1) 81 ( 3.2) 84 ( 2.0) 84 ( 1.8) 100 ( 0.2) 100 ( 02) 97 ( 1.2) ( 1.0) 97 ( 0.9) 97 ( 0.8) Wyoming In addition, a greater percentage of males than females in Wyoming attained level 300. The percentage of females in Wyoming who attained level 300 was similar to the percentage of females in the nation who attained level 300. Also, the percentage of males in Wyoming 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. 3 5) THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Oilmmailo Wyoming TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1080 NAEP TRIAL STATE ASSESSMENT _ MUITINWS and Operations , sstratnent Ma Geometry Data Anair as. and Statistic% Probability Algebra and Functions TOTAL. Proficiency Mildew Profidency Proltdancy State 275 ( 0.7) 270 ( 0.9) 270 ( 0.8) 274 ( 0.7) 270 ( 0.7) Region 264 ( 2.8) 256 ( 3.0) 280 ( 2.8) 282 ( 34) 25a ( 2.4) Nation 206 ( 1.4) 258 ( 1.7) 259 ( 1.4) 262 ( 1.8) 280 ( 1.3) RACE/ETHNICITY Wt. State 277 ( 0.8) 273 ( 0.9) 272 ( 0.8) 276 ( 0.7) 273 ( 0.8) Region 271 ( 32) 287 ( 3.9) 287 ( 3.0) 272 ( 4.4) 267 ( 2.8) Nation 273 ( 1.6) 287 ( 2.0) 287 ( 1.5) 272 ( 1.8) 268 ( 1.4) Hispanic State 257 ( 2.7) 251 ( 3.6) 254 ( 2.3) 257 ( 2.9) 250 ( 2.8) Region 248 ( 3.5) 239 ( 4.2) 245 ( 4.4) 240 ( 4.7) 243 ( 4.0) Nation 248 ( 2.7) 23$ ( 3.4) 243 ( 3.2) 239 ( 3.4) 2.43 ( 3.1) American Indian State Region 262 ( 3.1) Vi 248 ( *tn. 4.1) 258 ( ( 3.3) 44.) 260 ( 4.0) 252 ( 4.4) Nation 249 ( 7.8)1 247 ( 8.8)1 24$ ( 8.6)1 242 ( 5.2)1 242 ( 4.9)i TYPE OF COMMUNITY Extrma rural State 278 ( 1.4) 274 ( 1.8) 274 ( 1.4) 278 ( 1.5) 273 ( 1.5) Region 254 ( 8.6)1 254 ( 4.6)i 252 ( 9.4)1 253 ( 8.8)1 251 ( 8.5)1 Nation 25$ ( 4.3)1 254 ( 4.2)1 253 ( 4.5)1 257 ( 5.0)1 256 ( 4.8)1 Othar State 276 ( 1.0) 271 ( 1.3) 270 ( 0.7) 274 ( 0.9) 271 ( 1.1) Region 262 ( 3.5) 255 ( 4.2) 258 ( 3.4) 259 ( 4.2) 258 ( 3.5) Nation 286 ( 1.9) 257 ( 2.4) 259 ( 1.7) 281 ( 2.2) 281 ( 1.7) The standard errors of the estimated statistics appear m parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability uf this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE 3 Eighth-Gradt. .,iic-School Mathematics (continued) I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measurement ..- Geometry a Analysi Dat s " Statistics, and Probability Algebra and Finctions TOTAL Pnadency Pralkaancy Praidency Pralickm PosIkkocir State 275 ( 270 ( 0.9) 270 0.8) 274 0.7) 270 ( 1).?) Region 284 ( 2.8) 2. ( 3.0) 200 2.8) 262 3.6) 259 ( 2A) Nation 288 ( 1.4) 253 ( 12) 259 1.4) 282 1.8) 280 ( 1.3) PARENTS' EDUCATION IIS non-graduate State 280 ( 2.8) 253 ( 4.3) 258 ( 22) 25i ( 3.0) 254 ( 3.1) Region 248 ( 4.2) 242 ( 6.2) 248 ( 4.9) ( 6.2) 245 ( 6.1) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) ( 3.1) 242 ( 3.0) 14S graduate State 266 ( 1.3) 257 ( 1.8) 282 ( 1.5) 203 ( 1.8) 260 ( Region 254 ( 2.5) 245 ( 3.0) 251 ( 3.8) 249 ( 3.2) 250 ( 2.4 Nation 259 ( 1.6) 243 ( 2.1) 252 ( 1.8) 253 ( 22) 253 ( 2.0 Some ;mhos State 278 ( 1.1) 275 ( 13) 274 ( 1.2) 280 ( 1.3) 273 ( Region 272 ( 2.7) 268 ( 5.3) 264 ( 32) 271 ( 4.9) 264 ( 3.2 Nation 270 ( 1.5) 264 ( 2.7) 202 ( 2.0) 209 ( 2.4) 263 ( 2.2 Cones. graduate State 283 ( 1.0) 280 ( 1.2) 277 ( 1.0) 262 ( 0.9) 279 ( 1.4) Region 275 ( 2.7) 271 ( 3.0) 271 ( 2.3) 270 ( 4.3) 272 ( 22) Nation 27$ ( 1.8) 272 ( 2.0) 270 ( 1.5) 276 ( 2.2) 273 ( 1.7) GENDER Mate State 277 ( 0.8) 275 ( 1.1) 273 ( 0.7) 2n ( 1.0) 280 ( 1.0 Region 264 ( 3.8) 283 ( 3.5) 201 ( 3.4) 264 ( 4.1) 200 ( 3.3) Nation 208 ( 2.0) 202 ( 2.3) 200 ( 12) 282 ( 2,1) 200 ( 1.0) Rommel* State 272 ( 0.9) 285 ( 1.3) 263 ( 1.0) 270 ( 0.9) 270 ( 1.0) Region 263 ( 21) 252 ( 2.6) 259 ( 2.9) ( 4.0) 259 ( 2.8) Nation 200 ( 1.4) 2$3 ( 1.0) 258 ( 1.5) 261 ( 14) 260 ( IA) The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent cenainty that, for each population of interest, the value for the entire population is within ± 2 standard esors of the estimate for the sample. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Wyoming 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 particip ,r1 the 1990 Trial State Assessment, their mathematics teachers, and the prin:ipals or othci administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information on student achievement. It is important to note that the 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. 4 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 37 Wyoming Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an enormous impact on fui. -e academic achievmment. 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. 43 38 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are chanfOg the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.' This chapter focuses on curricular and instructional content issues in Wyoming public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: Less than half of the eighth-grade students in Wyoming (43 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curbs 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, 19). Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Education (Washington. DC: National Academy Press, 1989). 4 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Wyoming In Wyoming, 72 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Many of the students in Wyoming (87 percent) were taught mathematics by teachers who teach only one subject. More than half (66 percent) of the students in Wyoming 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 Wyoming Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation Percentage of elghth-grade students in public schools that identified mathematics as receiving special emphasis In school-wide goals and objectives, Instruction, In-service training. etc. Percentage of eighth-grade public-school students who are offered a cotes* in algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who teach only mathematics Percentage of eighth-grade students in public schools WhO are assigned to a mathematics class try their ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics instruction per week Percentage Pimento. Percentage 43( 0.8) 61 ( 8.8) 83 ( 5.9) 72 ( 0.7) 92 ( 4.7) 78 ( 4.6) 87 ( 1.6) 98 ( 1.6) 91 ( 3.3) 66 ( 1.7) 64 , 82) 63 ( 4.0) 21 ( tO) 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. 4 5 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming CURRICULUM COVERAGE To place students' mathematics proficiency in a cuniculum-related context, it is necessary to examine the extent to which eighth graders in Wyoming are taking mathematics courses. Based on their responses, shown in Table 5: About the same percentage of students in Wyoming were taking eighth-grade mathematics (48 percent) as were taking a course in pre-algebra or algebra (47 percent). Amass the nation, 62 percent were eighth-grade mathematics and 34 percent were taking a course in p bra or algebra. Students in Wyoming who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 1 Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - _ 1980 KAEP TRIAL STATE ASSESSMENT Wyoming West Nation Percentage and Proficiency Percentage angi Proficiency Percentage and Proficiency What kind of mathematics class are you taking this year? Eighth-graft mathematics 48 ( 1.0) 63 ( 2.7) 62 ( 2.1) 266 ( 0.9) 252 2.4) 251 ( 1.4) Pre-algebra 31 ( 0.9) 15 ( 2.7) 19 ( 1.9) 270 ( 1.1) 266 ( 3.6) 272 ( 2.4) Algebra 16 ( 0.8) 17 ( 1.8) 1S ( 1.2) 303 ( 1.2) 299 ( 4.5) 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Wyoming Further, from Table AS in the Data Appendix:4 About the same percentage of females (48 percent) and males (46 percent) in Wyoming were enrolled in pre-algebra or algebra courses. In Wyoming, 48 percent of White students, 43 percent of Hispanic students, and 31 percent of American Indian students were enrolled in pre-algebra or algebra courses. Similarly, 46 percent of students attending schools in areas classified as "other" and 28 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 their teachers, the greatest percentage of eighth-grade students in public schools in Wyoming spent 15 minutes doing mathematics homework each day; according to the students, the greatest percentage spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes daily. Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix): In Wyoming, 3 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 Wyoming and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. 4 For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations -- race ethnicity, type of community, parents' education level, and gender. 4' 42 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming The results by race/ethnicity show that 1 percent of White students, 2 percent of Hispanic students, and 0 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 3 percent of White students, 2 percent of Hispanic students, and 18 percent of American Indian students spent no time doing mathematics homework. In addition, 2 percent of students attending schools in areas clacsified as "other" and 0 percent in schools in extreme rural areas spent an hour or more on mathematics homework daily. In comparison, 4 percent of students attending schools in areas classified as "other" and 2 percent in schools in exlreme 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 ASSESSMENT Wyomhig Wos4 Nation Percentage end Pr:dolma Percentage and Prallotenry Percentage and Proltdancy About how much time do students spend on mathematics hoework each day? 3 ( 257 ( 0.2) 2.4) ( ( 0.3) +4.1 1 ( 0.3) k,k) 15 minutes 47 ( 1.0) 42 ( 6.7) 43 ( 4.2) 269 ( 0.9) 258 ( 4.2) 258 ( 2.3) 30 inInulos 38 ( 1.0) 43 ( 6.2) 43 ( 4.3) 274 ( 0.9) 284 ( 4.7) 266 ( 2.8) 45 minutas 12 ( 0.6) 9 ( 2.3) 10 ( 1.9) 283 ( 2.3) 270 ( 8.5)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. 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). c` THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Wyoming TABLE 7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY NM NAEP TRIAL STATE ASSESSMENT Wyoming West Nation , About how much time do you usually spend each day on mathematics homework? Percentage and Preficiency Percentage end Proficiency Percentage end Proficiency None 10 ( 0.5) 12 ( 1.7) 9 0.8) 267 ( 2.1) 254 ( 4.2) 251 ( 2.8) 15 miciutes 29 ( 1.0) 31 ( 4.5) 31 ( 2.0) 274 ( 1.0) 263 ( 3.8) 264 ( 1.9) 30 miracles 31 ( 0.9) 28 ( 1.7) 32 ( 1.2) 275 ( 1.0) 261 ( 2.9) 283 ( 1.9) 45 miracles 16 ( 0.7) 15 ( 1.6) 18 ( 1.0) 270 ( 1.4) 267 ( 4.2) 208 ( 1.9) An hour or mor 14 ( 0.7) 14 ( 4.7) 12 ( 1.1) 267 ( 1.9) 261 ( 4.3) 258 ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. And, according to the students (Table 7 and Table A7 in the Data Appendix): In Wyoming, relatively few of the students (10 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 14 percent of the students in Wyoming 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 13 percent of White students, 17 percent of Hispanic students, and 10 percent of American Indian students spent an hour or more on mathematics homework each day. ln comparison, 10 percent of White students, 11 percent of Hispanic students, and 15 percent of American Indian students spent no time doing mathematics homework. 4 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming In addition, 14 percent of students attending schools in areas classified as "other" and 13 percent in schools in extreme rural areas spent an hour or more on mathematics homework daily. In comparison, 10 percent of students attending schools in arias classified as "other" and 9 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. Curricalum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 45 Wyoming s 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 emphaais" 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 had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. 46 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP I RIM. STATE ASSESSMENT Wyoming West Nation - Perventap and Prandenay Paraentsse and Prandial* Partantaga and Madam* Teacher "emphasis" categories by content areas Numbers and Operations Heavy ampitasis 42 ( 12) 42 ( 7.4) 49 ( 3.8) 274 ( 0.9) 257 ( 3.8) 280 ( 1.6) Little or no emphasis 19 ( 1.5) 13 ( 2.1) 15 ( 2.1) 281 ( 1.8) 291 ( 8.8) 287 ( 3.4) Measurement Heavy emphasis ( 0.4) 11 ( 2.8) 17 ( 3.0) 26$ ( 3.7) 251 ( 7.7)1 250 ( 5.6) Little or no emphasis 51 ( 1.7) 36 ( 5.3) 33 ( 4.0) 272 ( 1.6) 275 ( 8.3) 272 ( 4.0) Geometry Heavy emphasis 15 ( 0.9) 24 ( 6.3) 28 ( 3.8) 274 ( 1.5) 260 ( 2.8)1 260 ( 3-2) Little or no emphasis 35 ( 12) 16 ( 4.5) 21 ( 3.3) 27'2 ( 14) 277 (11.4)1 264 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 6 ( 0.7) 14 ( 3.7) 14 ( 2.2) 278 ( 2.6) 264 (10.6)1 269 ( 4.3) Little or no emphasis 75 ( 1.9) 54 ( 8.3) 53 ( 4.4) 274 ( 0.9) 262 ( 4.9) 261 ( 2.9) Algebra and Functions Heavy emphasis 48 ( 1.3) 43 ( 5.6) 46 ( 3.6) 282 ( 1.3) 277 ( 52) 275 ( 2.5) Little or no emphasis 13 ( 0.6) 23 ( 5.1) 20 ( 3.0) 247 ( 2.1) 243 ( 4.2)1 243 ( 3.0) . The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. 1 Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 52 THE 1990 NAEP TRIAL-STATE ASSESSMENT 47 Wyoming SUMMARY Although many types of mathematics learning can take place outside of the school environment, there art some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curticulum coverage, mathematics homework, and instructional emphasis has revealed the following: Less than half of the eighth-grade students in Wyoming (43 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Wyoming, 72 percest 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 Wyoming were taking eighth-grade mathematics (48 percent) as were taking a course in pre-algebra or algebra (47 percent). Across the nation, 62 percent were taking eighth-grade mathemfttics 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 Wyoming spent IS 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 IS or 30 minutes doing mathematics homework each day, while students repotted either 15 or 30 minutes dally. In Wyoming, relatively few of the students (10 percent) reported that they spent no time each day on mathematics homework, compared to 9 percent for the nation. Moreover, 14 percent of the students in Wyoming and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations had lower proficiency in this content area than students whose teachers placed little or no emphasis on Numbers and Operations. 48 THE 1990 NAEP TRIAL I.-TATE ASSESSMENT 0=01.1, Wyonting CHAPTER 4 NOM all1111111. II 111111111111111111M 111111 111111111111111111111111111 1111111l11111.11111111 1111119111t u 111111111011 OM .11111I.111111 M.71111111111111Will11111 15115 Iian Ar,sage 111111111111 'SWIM Alias 1111111alls How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning or for those who come from different cultural backgrounds is an important aspect of teaching.' An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. 6 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics' (Reston, VA: National Council of Teachers of Mathematics, 1991). r Ai THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Wyoming From Table 9 and Table A9 in the Data Appendix: In Wyoming, 32 percent of the vighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 16 percent of the students were taught by teachers who got only some or now of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Wyoming, 38 percent of students attending schools in areas classified as "other" and 27 percent in schools in extreme rural areas had mathematics teachers who got all the resources they needed. By comparison, in Wyoming, 12 percent of students attending schools in areas classified as "other" and 18 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 similoir to those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 011.1.01. IMO NAEP TRIAL STATE ASSESSMENT Wyoming West Nation Which of the following statements is true about how well supplied you are by your school system with the Instructional materials and other resources you need to teach your class? I get all the resources I need. I got most of the resources I need. I get some or none of the resources I need. Percentage Percentage Percentage and and and Proficiency Prolicienoy Proficiency 32 ( 0.9) 15 ( 52) 13 ( 2.4) 272 ( 1.0) 2e1( 5.9)1 265 ( 4.2) 53 ( 1.3) 62 ( 3.8) 58 ( 4.0) 273 ( 0.9) 206 ( 4.1) 265 ( 2.0) 16 ( 0.6) 23 ( 6.1) 31 ( 4.2) 272 ( 1.4) 257 ( 3.7)I 261 ( 2.9) The standard errors of t." 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 variabili f this estimated mean proficiency. rr 50 ME 1990 NAEP TRIAL STATE ASSESSMENT Wyoming PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielde4 many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: About three-quarters of the students in Wyoming (70 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics problems in small groups (7 percent). The largest percentage of the students (60 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (8 percent). In Wyoming, 71 percent of the students were assigned problems from a mathematics textbook almost every day; 10 percent worked textbook problems about once a week or less. About one-quarter of the students (27 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (31 percent). Thomas Romberg, "A Common Curricti1um for Mathematics," Individual Differences and the Common Curriculum Eighty-second Yearbook of the National Society for the Study of Education (Chicago, II,: University of Chicago Press, 1983). 5G THE 1990 NAEP TRIAL STATE ASSESSMENT SI Wyoming TABLE 10 1 Teachers' Reports on Patterns of Mathematics I Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1900 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation About how often do students work problems in small groups? At least once a week Less than once a week Never About how often do students use objects like rulers, counting blocks, or geometric solids? AI est once a week LOSS than onc a week Now Percentage and Proficiency 70 ( 1.4) 274 ( 0.7) 23 ( 1.3) 270 ( 1.6) 7 ( 0.5) 264 ( 2.5) Percentage and Pro &Amoy 32 ( 2.1) 268 ( 1.2) 80 ( 1.7) 274 ( 0.9) 8 ( 0.9) 280 ( 2.3) Percentage Percentage and end Proficiency Pro ficloncY 57 ( 8.9) 262 ( 4.2)1 39 ( 7.6) 266 ( 4.5) 3 ( 2.2) 44,4 50 ( 4.4) ( 2.2) 43 ( 4.1) 204 ( 2.3) 8 ( 2.0) 277 ( 54)1 Percentage Percentage and and Proticiency Proficiency 34 ( 8.2) 256 ( 4.9)1 57 ( 6.4) 265 ( 4.0) 114. do.**) 22 ( 3.7) 254 ( 3.2) 69 ( 3.9) 263 ( 1.9) 9 ( 2.6) 282 ( 5.9)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 52 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE 11 I Teachers' Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation Percentage and Proficiency Percentagen and Preackeicy Percentage and Pie/Waxy About how often do students do problems from textbooks? Muni every day 71 ( 0.03) 55 ( 8.0) 62 ( 3.4) 274 ( 0.8) 270 ( 3.3) 267 ( 1.8) Several times a week 20 ( at) 38 ( 5.1) 31 ( 3.1) 270 ( 1.3) 258 ( 5.2) 254 ( 22) About once a week or less 10 ( 0.4) 9 ( 4.9) 7 ( 1.8) 288( 1.3) 4144 ( 280 ( 5.1)1 About how often do students do problems on worksheets? Percentage and Percentage and Percentage and Prone:fancy Prolkiency Proficiency At least several times a week 27 ( 1.0) 25 ( 5.2) 34 ( 3.8) 270 ( 1.2) 258 ( 4.3)1 258 ( 2.3) About once a week 42 ( 1.6) 34 ( 4.6) 33 ( 3.4) 274 ( 0.7) 258 ( 4.1) 280 ( 2.3) Less than wesidy 31 ( 1.7) 41 ( 5.6) 32 ( 3.6) 272 ( 1.3) 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 witldri 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 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 Wyoming COLLABORATING IN SMALL GROUPS In Wyoming, 24 petcent of the students reported never working mathematics problems in small groups (see Table 12); 44 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 Students' Reports on the Frequency of Small i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFIC.ENCY MO NAEP TRIAL STATE ASSESSMENT Wyoming West Nation Percentage and Prodding,/ Percentage and Proliciency Percentage and Proficiency How often do you work in small groups ln your mathematics class? At least once a mirk 44 ( 1.3) 35 ( 4.8) 28 ( 2.5) 274 ( 0.9) 258 ( 4.2) 266 ( 2.7) Less than once a week 32 ( 0.8) 29 ( 2.8) 28 ( 1.4) 275 ( 0.8) 271 ( 3.1) 267 ( 2.0) Never 24 ( 1.0) 36 ( 4.8) 44 ( 2.9) 266 ( 1.4) 258 ( 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 subpelulations (Table Al2 in the Data Appendix): In Wyoming, 40 percent of students attending schools in areas classified as "other" and 56 percent in schools in extreme rund areas worked in small groups at least once a week. Further, 44 percent of White students, 42 percent of Hispanic students, and 43 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 (44 percent and 43 percent, respectively). 5!) THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: Less than half of the students in Wyoming (37 percent) never used mathematical objects; 27 percent used these objects at least once a week. Mathematical objects were used at least once a week by 23 percent of students attending schools in areas classified as "other" and 36 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 (29 percent and 25 percent, respectively). In addition, 27 percent of White students, 29 percent of Hispanic students, and II percent of American Indian students used mathematical objects at least once a week. TABLE 13 Students' Reports on the Use of Mathematics 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROP ENCY MO NAEP TRIAL STATE ASSESSMENT %Wyoming West Nation 41.1MMOWM/11MINMIM 111, How often do you work with objects like rulers, counting blocks, or geometric solids in your Mathematics class? Percentage and Proficiency Percentage and ProilckIncy Percentage and Pronciency At least once a week 27 ( 12) 38 ( 3.5) 28 ( 1.8) 270 ( 1.2) 260 ( 4.0) 258 ( 2.8) Loss than once a week 35 ( 1.0) 28 ( 1.8) 31 ( 1.2) 274 ( 0.9) 269 ( 2.7) 269 ( 1.5) Neves 37 ( 1.01 36 ( 3.3) 41 ( 2.2) 272 ( 1.0) 258 ( 2.8) 259 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. C THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Wyoming MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in Wyoming who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table A 14 in the Data Appendix): About three-quarters of the students in Wyoming (79 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 79 percent of students attending schools in areas classified as "other" and 78 percent in schools in extreme rural areas. TABLE 14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation ] How often do you do mathematics problems from textbooks in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage end Proficiency Almost every day 79 ( 0.8) 71 ( 3.5) 74 ( 1.9) 274 ( 0.6) 267 ( 2.4) 287 ( 1.2) Several times a week 40 ( 0.6) 45 ( 1.5) 14 ( 0.8) 287 ( 12) 251 ( 2.4) 252 ( 1.7) About once a week or less 10 ( 0.5) 14 ( 3.1) 12 ( 1,8) 285 ( 1.1) 242 (11,2)1 242 ( 4,5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, 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. Sb TH1i 1990 NAEP TRIAL STATE ASSESSMENT Wyoming And, for the fiequency of worksheet usage (Table 15 and Table Al5 in the Data Appendix): About one-quarter of the students in Wyoming (29 percent) used worksheets at least several times a week, compared to 38 percent in the nation. Worksheets were used at least several fines a week by 28 percent of students attending schools in areas classified as "other" and 29 percent in schools in extreme rural areas. TABLE 15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation How often do you do mathematics problems on worksheets in your mathematics class? Percentage mid Pro !Money Percentage and Predefine,/ Percentage and Prolidency At least several times a week 29 ( 0.9) 35 ( 4.0) 38 ( 2.4) 267 ( 1.1) 250 ( 4.2) 283 ( 2.2) About once a week 27 ( 0.9) 23 ( 2.6) 25 ( 12) 270 ( 1.0) 262 ( 2.1) 261 ( 1.4) Less than weekly 44 ( 1.1) 41 ( 4.1) 37 ( 2.5) 277 ( 0.9) 270 ( 3.4) 272 ( 1.9) The standard errors of the estimated statistics appear in parentheses. it can be s id with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. THE 1990 NAEP TRIAL STATE ASSESSMENT 57 Percentage Percentage Percentage Students Teachers Students Teachers Students Teadiars Percentage percentage Percentage Students Teachers Students Teachers Students Teachers 44 ( 1.3) 70 ( 1.4) 35 ( 4.8) 57 ( 8.9) 28 ( 2.5) 50 ( 4.4) 32 ( 0.8) 23 ( 1.3) 29 ( 2.6) 39 ( 7.6) 2$ ( 1.4) 43 ( 4.1) 24 ( 1.0) 7 ( 0.5) 36 ( 4.8) 3 ( 2,2) 44 ( 2.9) 8 ( 2.0) 27 ( 1.2) 32 ( 2.1) 36 ( 3.5) 34 ( 82) 23 ( 1.8) 22 ( 3.7) 35 ( 1.0) 60 ( 1.7) 28 ( 1.8) 57 ( 6.4) 31 ( 12) 69 ( 3.0) 37 ( 1.0) 8 ( 0.9) 36 ( 3.3) 8 ( 3.0) 41 ( 2.2) 9 ( 2.8) Wyoming TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS _ . 1990 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation , Patterns of classroom instruction Percentage of students who work mathematics problems in ansaN croups At least once a week Less than once a week Never Percentage of students vAio use objects like rulers, counting blocks, or geometric solids At least once a week Less than once a week Never Materials for mathematics innruction Percentage of students wt., use a mathematics textbook Almost every day Several times a week About once a week or less Percentage of students *ha use a mathematics worksheet At least several tIrtleS a week About once a week Less than weekly 79 ( 0.8) 71 ( 0.6) 71 ( 3.5) 55 ( 6.0) 74 ( 1.9) 62 ( 3.4) 10 ( 0.6) 20 ( 0.7) 16 ( 1.5) 38 ( 5.1) 14 ( 0.8) 31 ( 3,1) 10 ( 0.5) 10 ( 0.4) 14 ( 3.1) 9 ( 4.9) 12 ( 1.8) 7 ( 1.8) 29 ( 0.9) 27 ( 1.0) 35 ( 4.0) 25 ( 5.2) 38 ( 2.4) 34 ( 3.8) 27 ( OS) 42 ( 1.6) 23 ( 2.6) 34 ( 4.6) 25 ( 1.2) 33 ( 3.4) 44 ( 1.1) 31 ( 1.7) 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 t 2 standard errors of the estimate for the sample. 3 58 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery practices and resources. It appears that mathematics textbooks and worksheets continue to play a major role in mathematics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathanaties teachers: About three-quarters of the students in Wyoming (70 percent) worked mathematics problems in small groups at least once a week; relatively few never worked in small groups (7 percent). The largest percentage of the students (60 percent) used objects like mlers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (8 percent). In Wyoming, 71 percent of the students were assigned problems from a mathematics textbook almost every day; 10 percent worked textbook problems about once a week or less. About one-quarter of the students (27 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (31 percent). And, according to the students: In Wyoming, 24 percent of the students never worked mathematics problems in small groups; 44 percent of the students worked mathematics problems in small groups at least once a week. Less than half of the students in Wyoming (37 percent) never used mathematical objects; 27 percent used these objects at least once a week. About three-quarters of the students in Wyoming (79 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent 'of students in the nation. About one-quarter of the students in Wyoming (29 percent) used worksheets at least several times a week, compared to 38 percent in the nation. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT $9 Wyoming CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers -- have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks.' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. National Assessment of Educational Progress, 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 Wyoming Table 17 provides a profile of Wyoming eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 49 percent of the students in Wyoming had teachers who allowed calculators to be used for tests. A greater percentage of students in Wyoming than in the nation had teachers who permitted unrestricted use of calculators (36 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of Wyoming Policies on I Calculator Use PERCENTAGE OF STUDENTS _ 1900 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation Percentage of eighth-grade students In public schools whose teachers permit the unrestricted use of calculators Percentage of eighth-grade students in public schools whose teachers permit the use of calculator* for tests Percentage of eighth-grade students in public Schools whose teachers report that students have access to calculators owned by the school .40.=1, Percentage Percentage Percentage 36 ( 1.3) 20 ( 4.9) la ( 3.4) 49 ( 1.8) 48 ( 8.8) 33 ( 4.5) 73 ( 1$) 72 ( 7.4) 58 ( 46) The standard errors of the estimated statistics appear in parentheses. It can be said with abo.it 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. 6 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Wyoming ME AVAILABILITY OF CALCULATORS In Wyoming, most students or their families (99 percent) owned calculators (Table 18); however, fewer students (52 percent) had teachers who explained the use of calculators to them. From Table A 1 8 in the Data Appendix: In Wyoming, 51 percent of White students, 55 percent of Hispanic students, and 58 percent of American Indian students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (51 percent and 53 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 1990 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation Percentage and Proficiency 99 ( 02) 272 ( 0.6) 1 ( 02) Percentage and Proficiency Percentage and Proficiency 96 ( 0.6) 283 ( 2.6) 4 ( 0.6) Percentage and Proficiency Percentage and Proficiency 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( 3.8) Percentage and Proficiency Do you or your family own a calculator? Yes No Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes 52 ( 1.0) 59 ( 3.4) 49 ( 2.3) 288 ( 0.9) 260 ( 2.7) 258 ( 1.7) No 48 ( 1.0) 41 ( 3.4) 51 ( 2.3) 276 ( 0.8) 265 ( 3.0) 266 ( 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. *I" Sample size is insufficient to permit a reliable esumate (fewer than 62 students). 62 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming THE USE OF CALCULATORS As previowly noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment, study. were asked how frequently (never, sometimes, almost always) they used calculat, .s for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In Wyoming, 18 percent of the students never used a calculator to work problems in class, while 52 percent almost always did. Some of the students (13 percent) never used a calculator to work problems at home, compared to 36 percent who almost always used one. About one-quarter of the students (27 percent) never used a calculator to take quizzes or tests, while 26 percent almost always did. TABLE 19 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 Wyoming West Nation _ Percentage and Proficiency Percentage and Profidency Percentage and Pronclonicy How often do you use a calculator for the following tasks? Worting problems In class Almost always 52 ( 1.0) 53 ( 2.1) 48 ( 1.5) 269 ( 0.8) 255 ( 2.6) 254 ( 1S) Never 13 ( 0.8) 14 ( 2.4) 23 ( 1.9) 282 ( 1.3) 265 ( 3.0) 272 ( 1.4) Doing problems at home Almost always 36 ( 0.9) 29 ( 1.7) ( 1.3) 271 ( 0.9) 263 ( 3.3) ,t31 ( 1.8) Never 13 ( 0.6) 19 ( 1.6) 19 ( 0.9) 278 ( 1.7) 258 ( 3.7) 263 ( 1.6) Taking quizzes or tests Almost always 26 ( 0.9) 25 ( 1.6) 27 ( 1.4) 270 ( 1.2) 259 ( 3.9) 253 ( 2.4) Never 27 ( 0.9) 22 ( 3.0) 30 ( 2.0) 281 ( 1.0) 270 ( 3.3) 274 ( 1.3) The standard errors of the estimated statisncs appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t. 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. 68 THE 1990 NAEP TRIAL STATE ASSESSMENT 63 Wyoming WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not 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 sect;ons were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections were categorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items an d. did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming The data presented in Table 20 and Table A20 in the Data Appendix are highliAted below: fthout the same percentage of students in Wyoming were in the High group as were in the Other group. A smaller percentage of males than females were in the High gmup. In addition, 52 percent of White students, 48 percent of Hispanic students, and 39 percent of American Indian students were in the High group. TABLE 20 f Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Wyoming I Wind Nation "Calcu1ator-use" group Nigh Paroontaga and Roadway 51 ( 1.1) 277 ( 0.3) 49 ( 1.1) 268 ( 1.0) Poroontop ilantaitaga and and Proadany Wolk:km 36 ( 2.6) 273 ( 2.7) 62 ( 2.6) 253 ( 2.6) 42 ( 1.3) 272 ( 1.6) 56 ( 1.3) 255 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 Wyoming SUMMARY Given the prevalence of inevensive 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 =ate 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, 49 percent of the students in Wyoming had teachers who allowed calculators to be used for tests. A greater percentage of students in Wyoming than in the nation had teachers who permitted unrestricted use of calculators (36 percent and 18 percent, respectively). In Wyoming, most students or their families (99 percent) owned calculators; however, fewer students (52 percent) had teachers who explained the use of calculators to them. In Wyoming, 18 percent of the students never used a calculator to work problems in class, while 52 percent almost always did. Some of the students (13 percent) never used a calculator to work problems at home, compared to 36 percent who almost always used one. About one-quarter of the students (27 percent) never used a calculator to take quizzes or tests, while 26 percent almost always did. LI 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming 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.9 Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In Wyoming, 30 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About half of the students (46 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. ' Almost all of the students (91 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. vau,..;1.?.! Council of Teachers of Mathematics. Professional Standards for the Teaching of Mathematics Reston, VA: National Council of Teachers of Mathematics, 1991). 72 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 Wyoming TABLE 21 I Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 1860 NAEP TRIAL. STATE ASSESSMENT Wyoming West Nation Percentage of students whose mathematics teachers reported having the following degrees Percentage Percentage Percentage Bachelor's degree 10 ( 0.9) 68 ( 5.2) 56 ( 4.2) Master's or specialist's degree 30 ( 0.9) 32 ( 5.2) 42 ( 4.2) Doctorate or professional degree 0 f 0.0) 0 ( 0.0) 2 ( 1.4) Percentage of students whose mathematics teachers have the following types of teaching certificates that are recognized by Wyoming No regular certification 1 ( 0.4) 6 ( 2.4) 4 ( 1.2) Regular certification but less than the highest available 53 ( 1.3) 20 ( 3.3) 29 ( 4.3) Highest certiftcation available (permanent or long-term) 46 ( 1.3) 74 ( 3.3) 66 ( 4.3) Percentage of students whose mathematics teachers have the to/lowing types of teaching certificates that are recognized by Wyoming Mathematics (middle school or secondary) 91 ( 0.7) 881 3.0) 84 ( 21) Education (elementary or middle school) 9 ( 0.6) 9 ( 2.8) 12 ( 2.6) Other 1 ( 0.3) 2 ( 1.3) 4 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject arca. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. f t) 68 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In Wyoming, 61 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in Wyoming (20 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and i Graduate Fields of Study PERCENTAGE OF STUDENTS _ WOO NAEP TRIAL STATE ASSESSMENT Wyoming West Nation What was your undergraduate major? Percentage Percentage Percentage Mathematics 61 ( 0.9) 3t ( 5.9) 43 ( 3.9) Education 29 ( 0.7) 34 ( 6.6) 35 ( 3.8) Other 11 ( 0.7) 36 ( 6.6) 22 ( 3.3) What was your graduate major? Percentage Percentage Percentage Mathematics 20 ( 0.9) 19 ( 4.7) 22 ( 3.4) Education 28 ( 1.3) 36 ( 4.5) 38 ( 3.5) Other or no graduate level study 52 ( 1.3) 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 1. 2 standard errors of the estimate for the sample. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT 69 Wyoming Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In Wyoming, 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. Moss the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-sexvice training. Some of the students in Wyoming (20 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 uaining. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS 1000 NAEP TRIAL STATE ASSESSMENT Wyoming Winn Nation During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? None Ono to 15 hours IS hours or more Partantsge Parcentsgs Pmentage 20 ( 1.1) 11 ( 3.0) 11 ( 2.1) 45 ( 1.4) 45 ( 7.0) 51 ( 4.1) 36 ( 1.3) 44 ( SS) 39 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement." Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and tentories 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 Wyoming, 30 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About half of the students (46 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In Wyoming, 61 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in Wyoming (20 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. '° Archie E. Lapointe. Nancy A. Mead, and Gary W. Phillips, A World of Differences An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). Ina VS. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematks Achievement NA EP's 1990 Assessmen 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 Wyoming In Wyoming, 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 Wyoming (20 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. 7 "i 72 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming CHAPTER 7 The Conditions Beyond School that Facilitate Mathematics Learning and Teaching Because students spend much more time out of school each day than they do in school, it is reasonable to expect that out.of.school factors greatly influence students' attitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, encouragement, and participation in student learning experiences are powerful influences. Together, teachers and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment and mathematics proficiency, students participating in the Trial State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education. 7S THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Wyoming AMOUNT OF READING MATERIALS IN ME HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students participating in the Trial State Assessment were asked about the availability of 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 1 Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT Wyoming West Nation Does your family have, or receive on a regular basis, any of the following items: more than 25 books, an encyclopedia, newspapers, magavnes? Zero to two types Three types Four types PlIfellaillge and Proficiency Percentage and Prolidency Percentage and Proficiency 14 ( 0.7) 24 ( 1.6) 21 ( 1.0) 200 ( 1.7) 245 ( 4.1) 244 ( 2.0) 32 ( 0.9) 31 ( 1.4) 30 ( 1.0) 270 ( 1.0) 258 ( 2.4) 258 ( 1.7) 54 ( 0.7) 45 ( 1.9) 48 ( 1.3) 276 ( 0.8) 273 ( 3.2) 272 ( 1.5) .4111111M 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 Wyoming reveal that: 74 Students in Wyoming 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. 7 I) THE 1990 NAEP TRIAL STATE ASSESSMENT t Wyoming A smaller percentage of Hispanic and American Indian students l'ad 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 rural areas had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Wyoming West Nation How much television do you usually watch each day? and Proficiency Pen:adage and Proficiency Pementage and Proficiency One hour or loss 18 ( 1.0) 14 ( 1.8) 12 ( 0.8) 281 ( 1.2) 289 ( 3.8) 289 ( 2.2) Two hours 26 ( 0.9) 20 ( 1.6) 21 ( 0.9) 275 ( 1.1) 265 ( 3.6) 268 ( 1.8) Three hours 25 ( 0.9) 20 ( 1.2) 22 ( 0.8) 273 ( 1.1) 202 ( 32) ats ( 1.7) Four to nye hours 24 ( 0.8) 29 ( 1.7) 28 ( 1.1) 266 ( 1.1) 263 ( 2.9) 280 ( 1.7) Six hours or more ( 0.6) 16 ( 2.0) 16 ( 1.0) 2.53 ( 2.2) 246 ( 2.6) 245 ( 1.7) The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 756 Wyoming From Table 25 and Table A25 in the Data Appendix: In Wyoming, average mathematics proficiency was highest for students who spent one hour or less watching television and lowest for students who watched television six hours or more each day. Some of the eighth-grade public-school students in Wyoming (18 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, about the same percentage of males and females watched one hour or less per day. In addition, 7 percent of White students, 11 percent of Hispanic students, and 14 percent of American Indian students watched six hours or more of television each day. In comparison, 18 percent of White students, 13 percent of Hispanic students, and 13 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 Wyoming, average mathematics proficiency was highest for students who did not miss any days of school and lowest for students who missed three or more days of school. Less than half of the students in Wyoming (42 percent) did not miss any school days in the month prior to the assessment, while 23 percent missed three days or more. In addition, 22 percent of White students, 31 percent of Hispanic students, and 29 percent of American Indian students missed three or more days of school. Ei 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming Similarly, 25 percent of students attending schools in areas classified as "other" and 17 percent in schools in extreme rural artas missed three or more days of school. TABLE 26 I Students' Reports OD the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO *UP TRIAL STATI. ,,!...:4-,0191ENT Wyoming West Nation How many days of school did you miss last month? One or two days Three days or more Percentage and Proficiency 42 ( 0.9) 276 ( 0.8) 35 ( 0.8) 272 ( 1.0) 23 ( 0.8) 264 ( 1.3) Percentage Percentage and and Proficiency Proficiency 43 ( 2.7) 286 ( 3.5) 30 ( 1.4) ( 3.0) 27 ( 1.8) 2S0 ( 3.1) 45 ( 1.1) 265 ( 1.8) 32 ( 0.9) 266 ( 1.5) 23 ( 1.1) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 77 11111111MIIIMIIIIMIMMIM11111111- Wyoming STUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers uf Mathematics, 1..arning mathematics should require students not only to master essential skills and concepts 'out also to develop confidence in their mathematical abilities and to value mathematics as a discipline.' 2 Students were asked if they agreed or disagreed with five statements designed to elicit their perceptions of mathrsmatics. 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 Ls 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 nnthematics. For each of the five statements, students who responded "strongly agree" were given a value of 1 (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's respons, s were averaged over the five statements. The students were then assigned a perception index according to whether they tended to strongly agree with the statements (an index of 1), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statements (an index of 3). Table 27 provides the data for the students' attitudes toward matherr.itics as defined by their perception index. The following results were observed for Wyoming: 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 (30 percent) were in the "strongly agree" category (perception index of 1). This compares to 27 percent across the nation. About one-quarter of the students in Wyoming (22 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). 12 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 78 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE 27 1 Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIM. STATE ASSESSMENT Pententege end Preddaticv Portiontage and Pre *ism Pardentepo and Praikdency Student "perception index" groups Strongly agree 30 ( 0.8) 27 ( 1.9) 27 ( 1.3) ("perception index" of 1) 281 ( 0.4) 273 ( 3,9) 271 1.8) Aire. 48 ( 1.0) 48 ( 1.5) 441 ( 1.0) ("perception index" of 2) 272 ( 0.9) 282 ( 24) 202 ( 1.7) Undcidad, disagree, strongly disagree 22 ( 0.7) 25 ( 2.1) 24 ( 1.2) ("perception index" of 3) 200 ( 1.4) 249 ( 2.9) 231 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. The data related to out-of-school factors show that: Students in Wyoming who had four types of reading materials (an encyclopedia, newspapers, magaimes, 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 Wyoming Some of the eighth-grade public-school students in Wyoming (18 percent) watched one hour or less of television each day; 7 percent watched six hours or more. Average mathematics proficiency was highest for students who spent one hour or less watching television and lowest for students who watched television six hours or more each day. Less than half of the students in Wyoming (42 percent) did not miss any school days in the month prior to the assessment, while 23 percent missed three days or more. Average mathematics proficiency was highest for students who did not miss any days of school and lowest for students who missed three or more days of school. About one-quarter of the students (30 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. 80 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon which the assessment was based, and the procedurer used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State Schori Officers, and the items were developed through a similar process managed by Educational Testing Seriice. The development of the Trial State Assessment Program benefitted from the involvement of hundreds of representatives from State Education Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, providf!d important suggestions on all aspects of the program. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spi:v1 matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 coOtive mathematics items were developed for the assessment, including 35 open-ended items. The first step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks, Each block was designed to be completed in 15 minutes. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT 81 Wyoming The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complet 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 introduction to this report.' The assessment framework cJnsisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statigics, and Probability; and Algebra and Functions (see Figure A I). The three mathematical ability arras assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known plpulation proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on students' performance on the set of mathematics items they received. IRT provides a common scale on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This common scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) aad their overall performance in the assessment. I National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). 82 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming FIGURE AI I Content Areas Assessed INumbers and Operations ThIS content area focuses on students' understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-world situations, as well as cOmputational and estimation situations. Understanding numerical relationships as expressed in ratios, proportions, and percents is emphasized. Students' abilities in estimation, mental computation, use of calculators, generalization of numerical patterns, and verification of results are also included. IMeasurement 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 for the eighth-grade Trial State Assessment. Proficiency in this concept area requires both manipulative facility and conceptual understanding: it involves the ability to use algebra as a means of representation and algebraic processing as a problem-soivinii tool. Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. THE 1990 NAEP TRIAL STATE ASSESSMENT 83 Wyoming FIGURE A2 f Mathematical Abilities The following three categoi-les of mathematical abilities are not to be construed ss hierarchical. For example, problem solving involves interactions between conceptual knowledge an, ocedural skills, but what is considered complex problem solving at one grade level may be ct.,isidered conceptual understanding or procedural knowledge at another. Conceptual understanding Students demonstrate conceptual understanding in mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts: can use and interrelate models, diagrams, and varied representations of concepts: can identify and apply principles; know and can apply facts and definitions: can compare, contrast, and integrate related concepts and principles: can recognize, Interpret, and apply the signs, symbols, and terms used to represent concepts: and can interpret the assumptions and relations Involving concepts in mathematical settings. Such understandings are essential to performing procedures in a meaningful way and applying them in problern-SOlving situations. 1 Procedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to select and apply appropriate procedures correctly, verify and Justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors inherent in problem settings. Procedural knowledge includes the various numerical algorithms In mathematics that have been created as tools to meet specific needs in an efficient manner. it also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncomputational skills such as rounding and ordering. Problem Solving In problem solving, students are required to use their reasoning and analytic abilities wtoln they encounter new situations. Problem solving Includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, data, models, and rbievant mathematics: generate, extend, and modify procedures: use reasoning (i.e., spatial, inductive, deductive, statistical, and proportional): and judge the reasonableness and correctness of solutions. r 84 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming 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 'four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defmed, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics items fr.= the 1990 assessment that discriminated well between adjacent levels. The criteria fc . selecting these "benchmark" items were as follows: To define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To defme 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. 90 THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Wyoming Once these empirically selected sets of questions bad been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students performing at each level. Each of the four proficiency levels was deemed by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of studentsat or above each of the four proficiency levels who correctly answered each question.2 Questionnaires for Teachers and Schools As part of the Trial State Assessment, questionnaires were given to the mathematics teachers of assessed students and to the principal or other administrator in each participating school. A Policy Analysis and Use Panel drafted a set of policy issues and guidelines and made recommendations concerning the design of these questionnaires. For the 1990 assessment, the teacher and school questionnaires focused on six educational areas: curriculum, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent an mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and :.he use of various instructional approaches. Because of the nature of the sampling fo , the Trial State Assessment, the responses to the mathematics teacher questionnai c do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 91. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT Level 200: Simple MOM, Reasoning end Problem Solving with Whole 1 Numbers Wyoming FIGURE A3 I Example Items for Mathematics Proficiency Levels ZE:7 LE:7 Sinis ow bib NY e0 Tee Coif %Om blk 7 . IA* WI dim iwit ism al de ism sir oat deo denim hie *I UM it env sem Dee fdis me es vie die bit of Imei sews. vele bas we bee Me fame Deb la At 0 TM lei vie tbo sees kik MI Wawa *evil ells 0 Tbs via girder bib 0 let win EXAMPLE 2 a 0 NOT PICKID AT FAAAWAY ?ADO leis Dip Cfle t C101ftesom=11 L. few ow hew of arse wow piglet as Thwwityl SI dD SO 0 70 0 se 0 00 0 I deal blow. Grade 4 Overall Percentege Count 73% Percentage Correct for Anchor Levels: 21/0 EA2 85 91 100 Grade 4 Overall Perm/nage Correct :.1: Percentage Correct for Mch.;* )1s: NO &IQ 2Q2 75 91 100 Grade $ Overall Percentage Owed: 119% Percentage Correct for Manor Levels: MIQ 21/2 112 78 87 98 100 Simple Multiplicative Reasoning and Ttro-Step Problem Solving I Wyoming FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) ILevel 250: EXAMPLE 7. What is the value of n + $ when a 3 I Answer EXAMPLE 2 V* calk siave flows A* mast a gawp ahm. Os dm deck Wow, t ante Fs* 9iimersIs tes fos is %ha Labs) sick pm el dos dodo pie Ida vb mot We soilic Did vow vs. chi csicastasee se Liss *mks* Vss ON. EXAMPLE 3 6. UMW* is peaking bowel& low bosom Dock loax Was Ihwebolls, hos 24 bids. WINck cumber wimate. will kelp km find cot hew away boar die will mod; CD 24 CD 24 + 4. it) 24 + w CD 14 xe go 0 (D I don't know. 98 Grade 8 Overall Pimento& Comet 75% Pementage Correct for Mawr Lave* ME Alt MG 0212 28 89 05 98 Grade 9 Overall Pementege Comet: 73% Percents& Correct for Many Lowly 2100 3011 21 55 92 92 Grads II Meng Percentage Wrect 77% Percentage Correct for Anchor Levels: EN MO SS 210 37 71 96 100 r-)t ME 19 90 NAEP TRIAL sum ASSESSMENT wonting FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Laval 300: EXAMPLE I Reasoning and Probium Sohling Waving Radom Ducimals, 1 Pares" Elementary Ommitdc Properties, end Ong* Algaluale Manipulations 4 Weak of de %bale. Awe the Si Biwa' the thew Inas& via distils It at EXAMPLE 2 babe neehraa ttat clas talk sw 1$ foe fail **011*****a * am.3 awed $ babes Ka* U tk* sew Ws etad. Woe Slime 10401 min rionomed bye ask soda isat ears Oak* WM elf rei yea wee the olealuer ea ail mood& 40 Vas 0 N. BEST COPY AVAILABLE ME 1990 NAEP TRIAL STA113 ASSESSMENT Grads 8 Overall Psnamtage am* 00% Percentage Correct for Mahar Leak: /02 212 100 33 49 77 90 Grads 12 Overall Peraudags Coma 75% Percordags Como for Mchot Lows: SO CO AS 46 79 95 Grade 8 Ovine Parosntage Ocaredt 59% Pan:~ Caveat for Packs Lass* 2E/ 2111 2110 17 48 88 99 89 Wyoming FIGURE A3 I Example Items for Mathematics Proficiency Levels (conthused) Level 350: Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations, and Begkmkig Statistics and Probability EXAMPLE 1 00 WOO If-11We to the Whorls puma of dot-figuo*. a It 0 5 t 2 1 U. if dti = of &Apra Is coottowod. bow tow dots w Is * the 1011th 430 100 CD 101 1101/ 00 300 CID 201 EXAMPLE 2 IT. EtAtio bow Tao fototi your awe to lowstiso U. Mower Grade 8 await Percentage comet 34% Peroentage Comet for Anchor Levels: 204 221 5151 13 19 53 88 Grade 12 OnoniN Percentage Correct QS Poventige correct tor Moho( Levels: 2iXt 221 21Q 22 48 90 Grade 8 Ovaralf Percentage Correct 15% Percentage Correct for Anchor Levels: 212Q 210 Zit IN 1 4 28 74 Grade 12 Overall Percentage Comet: 27% Percentege Correct tor Anchor Limos: 222 2111 XII Zig 3 22 74 90 'ME 1990 NAEP TRIAL srAm AMESSMENT Wyoming SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematic!, teachers or from a sample of schools, it is consistent with NAETs goal of providing information about the educational context and performance. of 5tudents. 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 pacentage 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, NAEP's total group and subgroup proficiency estimates are subject to a second source of uncertainty, in addition to sampling error. As previously noted, each student who participated Fn the Trial State Assessment was administered a subset of questions from the total set or questions. If each student had been administered a different, but equally amropriate, set of the assessment questions -- or the entire set of questions -- somewhat ,.lifferent 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. 96 THE 1990 NAEP TRIAL SI ATE ASSESSMENT 91 Wyoming In addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a background question in a certain way or the proportion of students in certain racial/ethnic groups) reflect only sampling error. NAEP uses a methodology called the jackknife procedure to estimate these standard errors. Drawing Inferences from the Results One of the goals of the Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inferences about the population. The use of confidence titervals, 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-mde 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. ry 4 92 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defmed by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defmed by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As an example, one might be interested in answering the question: Do students who reported spending 45 minutes or more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If ihe mean for the gyoup who reported spending 45 minutes or more on mathematics homewc rk 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 betwren the two gyoups 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 a-dement 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 degyee of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty called the standard error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the manner in which the standard error for an individual group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups ± 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zer0, 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 statistk ally significant (different) at the .05 level. S THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Wyoming 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 enors 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 thi:, difference is ,/ 2.02 + 2,12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard cr ors 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 intei val, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should e.onclude that there is insufficient evidence to claim a difference in average mathematics p oficiency between the population of eighth-grade females and males in public scaools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above weir 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 groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the woups. 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 ditference in the population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. 3 The procedure described above (especially the estimation of the standard error of the difference) is, in a strict sense, only appropriate when the statistics being compared come from independent samples. For certain comparisons in the report. the groups were not independent In those cases, a different (atid more appropriate) .gstimate of the standard error of the difference was used. C' 94 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming The procedures described in this section, and the certainty ascribed to interv als (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 compariwn 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 mote detailed description of the use of the Bonferroni wocedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol "!". In such Cases, the standard errors -- and any confidence intervals or significance tests involving these standard errors -- should be interpreted cautiously. Further details conceming procedures for identifying such standard errors are discussed in the Trial State Assessment technicalreport. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defmed by race/ethnicity and type of school community, as well as by gender and parents' education level. NAEP collects data fol five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantagal Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and/or background variable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probability of .8 or greater. 10 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 Wyoming The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-gade public-school population in the state or tenitory, divided by the standard deviation of the proficiency in the total population. If the true difference between subgruLp and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical report. Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage . Description oi Text in Report p = 0 None 0 < p 5 40 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 89 Many 89 < p < p = 100 100 Almost all All , 96 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming 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. 102 THE 1990 NAEP TRIAL STATE ASSESSMENT 97 Wyoming TABLE AS I Students' Reports on the Mathematics Claw They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Eighth-grade Mathematics Pre-isigebra Algebra ] TOTAL Parasols. and Panonts. and Random Parasols. and Pralldency State 48 ( 1.0) 31 ( 0.9) 16 ( 0.8) 266(0.9) 270 ( 1.1) 303 ( 1.2) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1-2) 251 ( 1.4) 272 ( 2.4) 298 ( 2.4) RACE/ETHNICITY Mho State 4$ ( 1.1) 31 ( 1.0) 17 ( ' .8) 268 ( 0.9) 272 ( 1.1) 304 ( 1.3) Nation 59 ( 2.5) 21 ( 2.4) 17 ( 1.5) 259 ( 1.6) 277 ( 2.2) 300 ( 2.3) Hispanic State 48 ( 3.5) 31 ( 3.4) 12 ( 2.3) 249 ( 2.8) 257 ( 3.4) m yen Nation 75 ( 4.4) 240 ( 2.4) 13 ( 3.9) ( 1.5) *re ( American Indian State 63 ( 4.7) 25 ( 4.9) 6 ( 1.6) 252 ( 3.8) Nation 84 ( 5.7) ( 72) 5 ( 2.7) ( ***) TYPE Of COMMUNITY Extreme rural State 88 ( 2.7) 16 ( 1.7) 13 ( 1.7) 271 ( 1.6) 275 ( 2.5) 304 ( 1.8) Nation 74 ( 4.5) 14 ( 5.0) 7 ( 2.2) 249 ( 3.1)1 Mier State SO ( 1.1) 2$ ( 0.9) 18 ( 1.0) 264 ( 0.9) 272 ( 1.4) 304 ( 1.5) Nation 81 ( 2.2) 20 ( 2.1) 16 ( 1.4) 251 ( 2.0) 272 ( 2.8) 284 ( 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 t 2 standard errors of the estimate for the sample. The percentages may not total WO 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. **1 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 98 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE AS I Students' Reports on the Mathematics Class (continued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Eilldh-9rade Mathematics Pra-algabra Algebra TOTAL Parantage and ProOkiency Percentage and Predictency Percentage and Prodicienstt State 445 ( 1.0) 31 ( 0.9) 16 ( OA) 266 ( 0.9) 270 ( 1.1) 303 ( 1.2) Nation 82 ( 2.1) 19 ( 1.9) 15 ( 12) 251 ( 14) 272 ( 2.4) 296 ( 24) PARENTS' EDUCATION HS non-graduate State 58 ( 43) 28 ( 4.4) 5 ( 1 .7 ) 257 ( 2.8) Mal Nation 77 ( 241 ( 37) 2.1) 13 ( *** 3.4) 3 ( ( 1.1) HS graduate State 55 ( 2.5) 32 ( 2.3) 8 ( 12) 260 ( 1.3) 261 ( 1.5) Nation 70 ( 2.6) 18 ( 2.4) 8 ( 1.1) 249 ( 1.9) 266 ( 35) 277 ( 5.2) Some college State 46 ( 2.1) 24 1.9) 17 ( 1.3) 270 ( 1.4) 274 ( 1.9) 300 ( 2.3) Nation 60 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 276 ( 2.8) 295 ( 32) Collage graduate State 43 ( IS) 30 ( 1.5) 23 ( 12) 271 ( 1.4) 275 ( 1.3) 307 ( 1.4) Nation 53 ( 21) 2/ ( 2.3) 24 ( 1.7) 259 ( 1.61 278 ( 2.8) 303 ( 2.3) GENDER Mete State 48 ( 1.3) 30 ( 1.2) 17 ( 1.1) 268 ( 0.9) 272 ( 1.5) 307 ( 1.6) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 12) 252 ( 1.6) 275 ( 2.9) 299 ( 2.5) Female State 48 ( 1.4) 32 ( 1.3) 16 ( 0.8) 263 ( 12) 288 ( 1.2) 297 ( 1.7) Nation 81 ( 2.6) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages ma not total 100 percent because a small number of students reported taking other mathematics courses. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Wyoming TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19100 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes An How or More TOTAL Perestiage and Prondenty 3 ( 0.2) 257 ( 2.4) 1 ( 0.3) 4MIN *4,1 3 ( 0.2) *.b.) ( 0.3) ( 0.8) 18 ( 4.2) 2 ( 0.3) 4 ( 0.3) 441.0. 011.41 .4* Percentage and Proficiency 47 ( 1.0) 269 ( 0.9) 43 ( 4.2) 256 ( 2.3) 48 ( 1.2) 271 ( 1.0) 39 ( 4.5) 266 ( 2.2) 41 ( 3.41 252 ( 3.4) 48 ( 7.8) 245 ( 3.0)1 74 (31.9) 44.* 50 ( 3.3) 274 ( 1.5) 68 (14.9) 253 ( 5.4)1 45 ( 1.3) 268 ( 1.3) 37 ( 4.3) 256 ( 3.1) Percentage and Proficiency 36 ( 1.0) 274 ( 0.9) 43 ( 4.3) 266 ( 2.6) 38( 1.1) 278 ( 1.0) 45 ( 5.1) 270 ( 2.7) 41 ( 3.1) 255 ( 3.4) 34 ( 8.8) 251 ( 42)1 24 ( 4.4) Of* ( *44) 22 (281) 38 ( 3.0) 279 ( 1.6) 14 (10.9) ( did 35 ( 1.3) 275 ( 1.2) 49 ( 5.1) 265 ( 2.5) Percetdage and Proficiency 12 ( 0.8) 233 ( 2.3) 10 ( 1.9) 272 ( 5.7)1 11 ( 0.9) 284 ( 2.8) 11 ( 2.4) 277 ( 7.8)I 13 ( 1.9) «hi 13 ( 2.9) 5 ( 2.8) 0 ( 0.0) 10 ( 3.7) 8 ( 5.6) .. 13 ( 0.9) 281 ( 1.7) 10 ( 2.4) 276 ( 6.6p Percentage and Proficiency 2 ( 0.3) fp.* 4 ( 0.9) 278 ( 5.1)1 1 ( 0.3) ( 441 4 ( 0.9) 279 ( 5.8)1 2 ( 0.8) *44 ( *41 7 ( 2 ) Mit ( iii ( 0.0) "it'..) 4 ( 4.8) **-0 1 0 ( 7.3) *4* 2 4 ( 1.1) 282 (11.6)1 state Nation PACE/ETHNICITY White State Nation Hispanic Ctate 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 ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A6 (continued) Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE Oc STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Wades An Hour Or More TOTAL Pavan's,' and Proficiency Percentage and Pro Odra Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 3 ( 257 ( 0.2) 2.4) 47 ( 269 ( 1.0) 0.9) 36 ( 274 ( 1.0) 0.9) 12 ( 283 ( 0.8) 2.3) 2 ( 0.3) *v.) Nation 43 ( 4.2) 43 ( 4.3) 10 ( 1.9) 4 ( 0.9) ( ***) 256 ( 2.3) 206 ( 2.6) 272 ( 5.7)1 278 ( 5.1)1 PARENTS' EDUCATION HS non-graduate State 3 ( 1.8) 50 ( 4.5) 34 ( 4.0) 12 ( 2.2) ( ***) 258 ( 3.7) ( .") Nation ( ( 0.8) 4.1 49 ( 240 ( 8.3) 2.8) 40 ( 246 ( 6.1) 3.7) 6 ( 1.7) 4 ( ( 1.3) "") HS graduate State 3 ( 0.5) 51 ( 2.6) 36 ( 2.5) 9 ( 1.2) 1 ( 0.0) ( ***) 283 ( 1.4) 261 ( 2.4) ( Nation 1 ( *** ( 0.5) 43 ( 249 ( 5.2) 3.1) 44 ( 258 ( 5.8) 2.7') 3 ( *** ( 1.0) **) Some college State 2 ( 0.6) ***) 46 ( 272 ( 1.8) 1.4) 35 ( 280 ( 2.3) 1.6) 16 ( 285 ( 1.6) 3.2) ( "") Nation 44 ( 5.4) ( 5.8) 7 ( 2.1) ( ***) 285 ( 2.6) 270 ( 3.6) ( "") College graduate State 4 ( 0.3) 48 ( 1.7) 37 ( 1.5) 12 ( 1.3) 2 ( 0.6) 276 ( 1.5) 285 ( 1.3) 290 ( 2.6) ( ***) Nation 0 ( 0.3) 40 ( 4.7) 44 ( 4.1) 11 ( 2.3) ( ".) 265 ( 2.5) 277 ( 3.0) 287 ( 6.1)1 GENDER Male State 47 ( 1.2) 36 ( 1.5) 12 ( 1.2) 2 ( 0.4) ( 272 ( 1.2) 276 ( 1.2) 287 ( 2.5) ( Nation 44 ( 4.4) 43 ( 4.3) 9 ( 1.9) 5 ( 1.3) 257 ( 2.9) 268 ( 2.9) 273 ( 7.3)1 279 ( 7.7)1 Femal State 3 ( 0.4) 48 ( 1.5) 36 ( 1.3) 11 ( 1.0) 1 ( 0 ) ( ***) 2% ( 1.2) 272 ( 1.3) 278 ( 2.4) MP* ( 1111, ) Nation 1 ( 0.4) 41 ( 4.4) 43 ( 4.7) 11 ( 2.0) 4 ( 0.9) .e. ( 255 ( 2.3) 284 ( 2.8) 272 ( 5.7)1 ( "C) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent cvrtainty that, for each population of interest, the %/Mile 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). 106 THE 1990 NAEP TRIAL STATE ASSESSMENT 101 Wyoming TABLE A7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 43 Minutes An Hour or More TOTAL, Percentage and Pradency Percentage and Pro Odom Percentage and Prolkieney Pereartage and Medway Percentage and Freedom State 10 ( 0.5) 29 ( tO) 31 ( 0.9) 16 ( 0.7) 14 ( 0.7) 267 ( 2.1) 274 ( 1.0) 275 ( 1.0) 270 ( 1.4) 207 ( 1.9) Nation 9 ( 0.6) 31 ( 2.0) 32 ( 1.2) 10 ( 1.0) 12 ( 1.1) 251 ( 2.8) 264 ( 1.9) 263 ( 1.9) 2.3 ( 1.9) 25$ ( 3.1) RACE/ETHNICITY White State 10 ( 0.5) 30 ( 1.1) 31 ( 0.9) 16 ( 0.7) ( 0.8) 270 ( 2.0) 277 ( 1.1) 277 ( 1.1) 274 ( 1.5) 270 ( 1.6) Nation 10 ( 1.0) 33 ( 2.4) 32 ( 1.3) 15 ( 0.9) 11 ( 1.3) 256 ( 3.4) 270 ( 1.9) 270 ( 2.1) 277 ( 2.2) 268 ( 3.3) HIspanIc State 11 ( 2.0) so,k eih.) 22 ( *** ( 2.5) *44) 31 ( 259 ( 3.6) 3.6) 19 ( 2.5) Nation 12 ( 1.8) 27 ( 3.0) 30 ( 2.8) 17 ( 2.1) 14 ( 1.7) 246 ( 3.6) 248 ( 3.4) 241 ( 4.3) American Indian State 15 ( 3.0) «H.) 30 ( 4.7) 31 ( 5.2) *44 ) Nation 13 ( ( 5.3) 30 (10.01 ***) 24 (14.2) ( ***) 6 ( 6.4) TYPE OF COMMUNITY Extran* rural State 9 ( 0.9) 29 ( 1.9) 32 ( 1.8) 17 ( 1.2) 13 ( 1.7) 278 ( 2.0) 280 ( 1.9) 275 ( 2.9) 264 ( 3.8) Nation 8 ( 2.3) 36 ( 4.6) 31 ( 2.9) 18 ( 3.8) 280 ( 3.5)1 255 ( 5.1)1 Mbar State 10 ( 0.8) 30 ( 1.3) 29 ( 1.2) 16 ( 0.9) 14 ( 0.9) 268 ( 2.7) 275 ( 1.2) 275 ( 1.2) 270 ( 1.7) 270 ( 2.2) Nation 9 ( 1.0) 30 ( 1.8) 32 ( 1.3) 15 ( 1.1) 13 ( 1.1) 250 ( 3.6) 263 ( 2.3) 284 ( 2.3) 207 ( 2.1) 25$ ( 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 stand:Ltd 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). 102 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A7 I Students' Reports on the Amount of Time They (continued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Nom 15 Minutes 30 Minutn 45 Minutes An Hour or Mors TOTAL Percentage and Praddincy Percentage and Proliclincy Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 10 1 0.5) 29 ( 1.0) 31 ( 0.9) 18 ( 0.7) 14 ( 0.7) 247 ( 2.1) 274 ( 1.0) 275 ( 1.0) 270 ( 1.4) 207 ( 1.9) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 18 ( 1.0) 12 ( 1.1) 251 ( 2.8) 264 ( 1.9) 283 ( 1.9) 286 ( 1.9) 258 ( 3.1) PARENTS EpticATION HS non-grsduato State 12 ( 2.5) 31 ( 3.7) 24 ( 3.5) 18 ( ( 2.9) .41 *** -*) Nation 17 ( 3.0) 26 ( 248 ( 3.3) 4.0) 34 ( 248 ( 4.4) 2.8) 12 ( 2.5) 1 0 ( 2.2) ***) HS grackiate State 11 ( 1.5) 29 ( 1.6) 31 ( 2.0) 16 ( 1.7) 13 ( 1.3) 259 ( 4.3) 287 ( 1.8) 263 ( 1.3) 282 ( 2.8) 253 ( 3.4) Nation 10 ( 1.7) 33 ( 22) 31 ( 1.9) 16 ( 1.4) 11 ( 1.5) 246 ( 4.2) 259 ( 3.2) 254 ( 2.4) 296 ( 2.8) 244 ( 3.4) Some college State 9 ( 1.3) 31 ( 1.8) 32 ( 1.9) 14 ( 1.4) 14 ( 1.7) 278 ( 1.5) 270 ( 1.9) 276 ( 2.8) 274 ( 2.2) Nation 9 ( *44 1.2) 30 ( 266 ( 2.7) 3.0) 36 ( 266 ( 2.1) 2.6) 14 ( 274 ( 1.8) 33) 11 ( *. 1.5) College graduate State 9 ( 0.8) 29 ( 1 4) 31 ( 1.4) 16 ( 1.1) 15 ( 1.0) 276 ( 3.1) 283 ( 1.5) 284 ( 1.4) 277 C 2.1) 276 ( 2.3) Nation ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Male State 11 ( 0.8) 32 ( 1.3) 30 ( 1.3) 15 ( 1.0) 12 ( 0.8) 267 ( 2.8) 278 ( 1.4) 277 ( 1.4) 272 ( 2.3) 270 ( 2,8) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 268 ( 2.4) 285 ( 3.0) 258 ( 4,1) Female State 9 ( 0.7) 27 ( 1.3) 31 ( 1.3) 17 ( 1.0) 16 ( 0.9) 266 ( 2.6) 271 ( 1.5) 272 ( 1.4) 269 ( 1.8) 265 ( 2.4) Nation 7 ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) ( 1.3) 246 ( 4.1) 263 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value ff,r the entire population is within 2 standard errors of the estimate for the sample. *** Sample size is insuilicient to permit a reliable estimate (fewer than 62 students). 1 THE 1990 NAEP TRIAL STATE ASSESSMENT 103 Wyoming TABLE A8 1 Teachers' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Numbers and Operationi Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Utile or No Emphasis TOTAL State Nation RACE/ETHNICITY Whitt State Nation Hispanic State Nation American Indian State Nation Percentage Penamitage Percentage Parcentaga Percentage Percentage and and aid and and end Prodclency Proficiency Proficiency Proficiency Proficiency Proficiency 42 274 49 260 42 278 46 267 40 254 47 246 48 84 TYPE OF COMMUNITY Extruna rural State 32 277 Nation 53 257 Other State 47 278 Nation 52 I 260 ( 1.2) 19 ( 7 ( 0.4) ( 0.9) 281 ( 1.8 260 ( 3.7) ( 3.8) 15 ( 2.1 17 ( 3.0) ( 1.6) 237 ( 3.4) 250 ( 5.6) ( 1.3) 19 ( 4.7) 7 ( 0.5) ( 1.2) 283 ( 1.9) 271 ( 4.5) ( 3.7) 1$ ( 2.4) 14 ( 3.4) ( 2.2) 289 ( 3.5) 259 ( 6.9)1 ( 3.7) ( 3.2) NI* ( *1111) *** ***) ( 8.7) 6 ( 2.2) ( 4.6) ( 5.4) ( MHO ) 12 ( 14* 4.5) 441 4 ( 2.6) *it*, (18.5) ( 441 8 (( 6.9) *44) 7 ( 8.7) ( 4.6) 20 ( 6.4) 11 ( 3.3) ( 24) 289 ( 7.8)1 *** ( "") (12.4) 6 ( 3.6) 6 ( 4.9) 7.1), ( 1.2) 14 ( 1.0) 7 ( 1.0) ( 1.0) 282 ( 2.7) 271 ( 5.2) ( 4.1) 16 ( 2.7) 16 ( 3.9) ( 2.3) 286 ( 3.6) 253 ( 7.1)1 51 ( 1.7) 15 272 1.o; 274 1.5 33 4.C) 26 3.8 272 ( 4.0) 260 ( 3.2) 50 ( 1.9) 15 ( 1.0) 276 ( 1.5) 275 ( 1.6) 36 ( 4.7) 27 ( 4.4) 277 ( 4.3) 265 ( 3.3) ST ( 3.5) 12 ( 21) 254 ( 5.7) 34 ( 5.6) 255 ( 4.4)! 55 ( 5.3) ***) 1 0 ( 3.4) 13 (15.5) 16 (19.7) Mt* 44111) 1.2 272 14 21 3.3 264 ( 5.4 34 ( 1.3) 275 ( 1.5) n ( 34) 273 ( Si) 38 ( 3.1) 25? ( 4.6) 16 ( 54) *44(4* 41 ( 0.4) *** ( imp) 6 (104) 44. ***) 38 ( 4.4) 25 ( 1.9) 29 ( 3.4) 276 ( 2.8) 274 ( 23) 277 ( 3.7) 32 (11.7) 9 ( 0.1) 16 ( 7.9) 2e5 9.1), 04* ( *IN.) SO ( 1.5) 14 ( 1.4) 35 ( 1.1) 275 ( 1.7) 273 ( 2.4) 272 ( 1.8) 34 ( 5.3) 2$ ( 4.6) 24 ( 4.3) 270 ( 4.6) 260 ( 3.9) 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 ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 CT 104 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A8 I Teachers' Reports on the Emphasis Given to (wntinued) i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Aumben and Op.rat1on Msaswams.tt Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis J I Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proency Pinatas* and Proficiency Percentage and Proficiency State 42 ( 1.2) 19 ( 1.5) 7 ( 0.4) 51 ( 1.7) 15 ( 0.9) 35 ( 1.2) 274 ( 0.9) 281 ( 1.8) 268 ( 3.7) 272 ( 1.8) 274 ( 1.5) 272 ( 1.4) Nation 49 ( 3.8) 15 ( 2.1) 17 ( 3.0) 33 ( 4.0) 28 ( 3.8) 21 ( 3.3) 280 ( 1.8) 287 ( 3.4) 250 ( 5.8) 272 ( 4.0) 260 ( 3.2) 264 ( 5.4) PARENTS EDUCATION KS non-graduate State 47 ( 5.0) 4.1*) 17 ( 3.6) 6 ( 2.1) .1.) 51 ( 5.1) 10 ( *44 ( 2.6) 441 36 ( 4.1) Nation 60 t 6.9) 251 3.4) (( 2.3) t* ) ( 25 ( 5.3) 20 ( (*44*44) 8.7) If S gransat State 43 ( 2.8) I S ( 2.5) 6 ( 1.4) 48 ( 3.0) 12 ( 1.8) 32 ( 2.0) 285 ( 2.4) 270 ( 3.0) iti 256 ( 3.1) 268 ( 4.3) 261 ( 3.0) Nation 55 ( 259 ( 4.8) 2.9) 11 ( 2.8) *4.) 1 ( 251 ( 3.9) 6.1)1 27 ( 253 ( 5.0) 4.7)1 27 ( 255 ( 4.5) 4.2) 24 ( 246 ( 5.1) 4.8)1 Sam college State ( 279 ( 1.8) 1.9) 21 ( 284 ( 2.1) 2.8) 8 ( 1.4) ..**) 52 ( 277 ( 2.9) 2.4) 16 ( 274 ( 2 1) 5.0) 37 ( 276 ( 2.1) 3.2) Nation 47 ( 265 ( 4.4) 2.6) 17 ( 284 ( 3.3) 4.1)4 12 ( 4.4 ( 2.7) **4 39 279 ( 5.5) 4.5) 27 ( 262 ( 5.0) 4.8)1 23 ( 270 ( 4.1) 4.7) College caliduat State 41 ( 1.4) 21 ( 1.7) ( 0.5) 51 ( 1.8) 16 ( 0.9) 35 ( 1.7) 281 ( 1.5) 282 ( 2.7) 273 ( 2.8) 284 ( 2.1) 280 ( 2.2) 281 ( 1.9) Nation 44 ( 4.1) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 269 ( 2.6) 298 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 6.4) GENDER Male State 40 ( 1.4) 19 ( 1.5) 8 ( 0.7) 51 1.7) 16 ( 1.0) 36 ( 1.5) 278 ( 1.3) 284 ( 2.3) 273 ( 4.3) 278 ( 2.1) 277 ( 2.2) 276 ( 1.7) 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) 283 ( 3.8) 266 ( 6.8) Female State 43 ( 1.5) 19 ( 1.9) 6 ( 0.5) 50 ( 2.1) 14 ( 1.1) 33 ( 1.4) 270 ( 1.4) 279 ( 2.0) 261 ( 5.6) 267 ( 2.3) 269 ( 1.8) 289 ( 1.8) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 260 ( 2.0) 286 ( 3.3) 241 ( 5.4) 268 ( 4.1) 256 ( 3.3) 263 ( 5.0) 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 percentages may not total 100 percent because the "Moderate emphasis" category is not included. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "' Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Wyoming TABLE A8 I Teachers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT Data I Alibi, Statistics, and Probability Algebra and Functions Heavy Emphasis Unto or No Emphasis Heavy Emphasis Little or No Emphasis MAL Percentage and Prolciancy Pententage and Madan Percentap and ProRdency Parcenitap and Proficiency State ( 0.7) 75 ( 1.9) 4$ ( 1.3) 13 ( OS) 278 ( 2.6) 274 ( 0.9) 282 ( 1.3) 247 ( 2.1) Nation 14 ( 2.2) 53 ( 4.4) 46 ( 3.6) 20 ( 3.0) 209 ( 4.3) 281 ( 2.9) 275 ( 2.5) 243 ( 3.0) RACE/ETHNICITY White State a ( 0.7) 75 ( 2.1) 49 ( 1.5) 12 ( 0.8) 280 ( 2.8) 276 ( 0.9) 284 ( 1.6) 251 ( 2.3) Nation 14 ( 2.4) 53 ( 5.0) 48 ( 4.2) 18 ( 2.8) 276 ( 4.1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) *aspen Ic State 8 ( 2.1) 60 ( 3.0) 46 ( 3.6) 17 ( 2.7) ( 200 ( 4.0) 264 ( 3.0) 4,4-1 Nation 15 ( 4.1) ( 6.3) 246 ( 4.4) 46 ( 5.9) 257 ( 4.0)! 18 ( 4.2) ( 41 American ;Mien State 5 ( 2.0) 73 ( 4.7) 30 ( 5.6) 33 ( 4.9) *In* ***) ( ***) *** ( Nation 3 ( 42) 82 (29.1) ** ( "#) 16 (21.5) ~) 67 (51.6) «. TYPE OF COMMUNITY Wrenn rural State 71 ( 6.3) 58 ( 5,9) 12 ( 0.9) filr - 282 ( 2.1) 281 ( 2.5) 247 ( 4.7) Nation 5 ( 5.4) 85 (16.9) 254 ( 6.7)1 33 ( $.1) **a ( 42 (16.0) 241 ( 5.9)1 Other State 7 ( 1.1) 74 ( 1.1) 49 ( 1.3) 10 ( 0.7) 283 ( 2.9) 273 ( 1.1) 283 ( 1.5) 247 ( 3.2) Nation 15 ( 2.9) 53 ( 5.2) 47 ( 4.3) 17 ( 3.3) 267 ( 4.7) 260 ( 3.4) 276 ( 2.8) 245 ( 4.4)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Interest, the value for the entire population is within 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 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 Wyoming TABLE A8 Teachers' Reports on 'the Emphasis Given To (amtinued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra and Functions Heavy Emphasis Uttie or No Emphasis Heavy Emphasis , Little Of No Emphasis TOTAL Percentage and loroaciency Percentage and ProeciencY Percentage and Pro Idiocy Percentage and Prot Money State 8 ( 0.7) 75 ( 1.9) 48 ( 1.3) 13 ( 0.6) 278 ( 2.6) 274 ( 0.9) 282 ( 1.3) 247 ( 2.1) Nation 14 ( 2.2) $3 ( 4.4) 48 ( 3.6) 20 ( 3.0) 249 ( 4.3) 261 (2.0) 275 ( 2.5) 243 ( 3.0) PARENTS' EDUCATION KS non-graduate State ( Ire* 2.5) ***) 75 ( 261 ( 42) 42) 37 ( 4.8) elm «rip) Nation 9 ( 3.0) 53 ( 240 ( 7.7) 6.2) 28 ( 5.2) .111, ***) 29 ( *4* ( 6.9) IIS graduate State 7 ( 1.2) 75 ( 2.0) 39 ( 2.8) 16 ( 1.8) 262 ( 22) 272 ( 2.7) 241 ( 3.0) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 261 ( 6.0)I 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Some college State 5 ( 2.0) 78 ( 281 ( 3.6) 1.5) 54 ( 280 ( 1.9) 1.6) 10 ( «yip 1.5) Nation 13 ( 2.5) 57 ( 5.8) 48 ( 4.8) 270 ( 3.7) 278 ( 3.0) *Int ( **4 Co Nage graduate State ( 0.8) 74 ( 1.8) 53 ( 1.8) 1 1 ( 0.8) 258 ( 3.5) 283 ( 1.2) 291 ( 1.7) 255 ( 4.1) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 32) 18 ( 2.4) 282 ( 4.5) 275 ( 3.8) 288 ( 3.0) 249 ( 4.0) GENDER Male State 6 ( 1.1) 76 ( 2.1) 48 ( 1.6) 13 ( 0.8) 284 ( 4.4) 279 ( 12) 282 ( 1.7) 245 2.8) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.8) 275 ( 5.8) 280 ( 3.5) 278 ( 3.2) 243 ( 3.0) Female State ( 0.6) 75 ( 2.1) 47 ( 1.6) 13 ( 0.9) 273 ( 4.0) 270 ( 1.2) 281 ( 1.5) 249 ( 3.5) Nation 16 ( 2.4) 53 ( 4S) 48 ( 3.6) 18 ( 2.9) 283 ( 4.4) 282 ( 24) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample siv. is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 107 Wyoming TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 MEP TRIAL I Get AU the Resources I 113et Most of the I Ost Some or None of STATE ASSESSMENT Need ROSOUIVIIS I Need the Resources I Need TOTAL Percentage aid Proadancy Pertientege Md Proficiency Percentage and Prodding/ State 32 ( 0.9) 53 ( 1.3) 16 ( 0.8) 272 ( 1.0) 273 ( 0.9) 272 ( 1.4) Nation 13 ( 24) 56 ( 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 261 ( 2.9) RACE/ETHNICITY Iflhitst State 33 ( 1.0) 52 ( 1.5) 15 ( 1.0) 274 ( 1.0) 276 ( 1.0) 275 ( 1.4) Nation 11 ( 2.5) 58 ( 4.6) 30 ( 4.6) 275 ( 3.5)1 270 ( 2.3) 267 ( 3.3) Hispanic State 22 ( Ir** 2.7) 55 ( 255 ( 3.3) 3.7) 23 ( 2.6) .**) Nation 23 ( 7.6) 44 ( 4.9) 34 ( 7.7) 246 ( 7.7)! 250 ( 2.9) 244 ( 3.0)! American Indian State NI* ( 47 ( am* ( 5.4) 19 ( 42) ( Mr* Nation *4* ( 7.4) 72 (28.8) 22 (202; TYPE OF COMMUNITY Extreme rural State 27 ( 2.3) 55 ( 4.2) 18 ( 3.2) 270 ( 2.3) 279 ( 1.8) 280 ( 2.0) Nation 2 ( 2.6, 54 (10.4) 43 (10.3) 280 ( 8.8)! 257 ( 5.0)! Other State 38 ( 1.1) 50 ( 1.2) 12 ( 0.7) 272 ( 1.0) 273 ( 1.1) 273 ( 2.4) Nation 11 ( 2.9) 58 ( 5.4) 31 ( 5.6) 265 ( 3.9)! 284 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). los THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE An I Teachers' Reports on the Availability of (continue°, Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1000 NAEP TRIAL I Oct AN the Resources I I Clid Most of the UNA Some or None of STATE ASSESSMENT Need Resources I Need the Resosccas I Need TOTAL Percentage and Preliolency Peoveatage and PnAlldency Percentage artd INvitolency State 32 ( 0.9) 53 ( 1.3) 16 ( 0.8) 272 ( 1.0) 273 ( 0.9) 272 ( 1.4) Nation 13 ( 2.4) SS ( 4.0) 31 ( 4,2) 215 ( 4.2) 265 ( 2.0) 261 ( 2.9) PARENTS' EDUCATIOA MS non-graduate State Ira* ( 54 ( 257 ( 3.8) 2.3) 19 ( ( 2.9) .41 Nation 8 ( 2.6) 54 ( 5.7) 38 ( 6.3) ( 244 ( 2.7) 243 ( 3.5)! HS graducla State 33 ( 2.3) 52 ( 3.0) 15 ( 1.7) 264 ( 2.0) 201 ( 1.4) 265 ( 2.5) Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.9) 253 ( 4.8)) 258 ( 1.9) 253 ( 2.8) Soma collegt State 31 ( 2.0) 53 ( 2.2) 16( 1.5) 276 ( 1.8) 277 ( 1.6) 276 ( 2.5) Nation 13 ( 3.3) 62 ( 4.3) 25 ( 4.1) ( tirtf ) 269 ( 2.5) 287 ( 3.8) College graduate State 32 ( 1.4) 53 ( 1.7) 15 ( 1.0) 279 ( 1.5) 282 ( 11) 280 ( 2.3) Nation 16 ( 2.9) 56 ( 4.9) 30 ( 5.1) 276 ( 5.4)1 276 ( 2.2) 273 ( 3.7) GENDER Male State 32 ( 1.1) 52 ( 1.6) 16 ( 1.2) 274 ( 1.2) 276 ( 1.1) 274 ( 1.8) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4.0) 264 ( 5.0)1 265 ( 2.6) 284 ( 3.3) Female State 32 ( 1.1) 53 ( 1.5) 18 ( 0.9) 270 ( 1.3) 270 ( 1.3) 270 ( 1.9) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 288 ( 3.9) 284 ( 2.0) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 Wyoming TABLE Al Oa I Teachers' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Lust Once a Week laSS Than Once a Week Never TOTAL. Penn MOW and Proficiency Percentage and Proficiency Peroentege and Profidency State 70 ( 14) 23 ( 1.3) 7 ( Oh) 274 ( 0.7) 270 ( 1.8) 284 ( 2.5) Nation 50 ( 4.4) 43 ( 4.1) 6 ( 2.0) 200 ( 2.2) 204 ( 2.3) 277 ( 5.4)1 RACE/ETHNICITY White State 71 ( 1.6) 23 ( 1.5) 6 ( 0.5) 277 ( 0.7) 272 ( 1.7) 268 ( 2.4) Nation 49 ( 4.6) 43 ( 4.5) 8 ( 2.3) 265 ( 2.7) 271 ( 2.2) 285 ( 4.9)1 Hispanic State 61 ( 3.2) 27 ( 2.1) 12 ( 2.0) 254 ( 2.5) No* ( Nation 64 ( 72) 246 ( 2.5) 32 ( 8.9) 247 ( 6.3)1 4 ( 1.4) elm ( ***) American Indian State 68 ( 5$) 22 ( 4.2) 10 ( 4.7) '41 *** ( Nation la (24.3) 80 (27.2) 2 ( 3.7) ( ***) **It ( 441 TYPE Of COMMUNITY Extreme rural State 78 ( 4.1) 22 ( 4.1) 0 ( 0.2) 276 ( 1.8) 278 ( 2.1) Nation 35 (14.6) 56 (17.1) 9 ( 9.8) 255 ( 5.5)! 256 ( 5.9)1 Other State 72 ( 1.1) 19 ( 0.9) ( 0.8) Nation 274 ( 0.7) 50 ( 4.4) 271 ( 2.1) 44 ( 4.5) 284 ( 2.9) e ( 1.8) 260 ( 2.4) 264 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 0 110 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE AI Oa I Teachers' Reports on the Frequency of Small (wntinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAEP TRIAL STATE ASSESSMENT At Wad Once a Week Lass Than Once a Week Never TOTAL Percentage and Proficiency Peoventage and Prolidency Percentage and Proficiency State 70 ( 1.4) 23 ( 1.3) 7 ( 0.5) 274 ( 0.7) 270 ( 1.6) 264 ( 2.5) Nation 50 ( 4.4) 43 ( 4.1) ( 2.0) 290 ( 2.2) 264 ( 2.3) 277 ( 5.4)! PARENTS' EDUCATION NS non-graduate State 63 ( 259 ( 3.9) 3.0) 29 ( 414 ( 3.3) 1,44) 3 ( 22) 444 ( open Nation 60 ( 6.4) 39 ( 6.5) 1 ( 1.4) gracluate 244 ( 3.2) 244 ( 32)! "") State 68 ( 2.9) 28 ( 2.9) 6 ( 1.4) 264 ( 1$) 261 ( 2.3) 414 ( 411 Nation 49 ( 4.8) 45 ( 5.1) 6 ( 2.5) 252 ( 2.8) 257 ( 2,7) ( Sono college State 69 ( 2.6) 23 ( 2.4) 8 ( 1.0) 278 ( 1.2) 278 ( 2.0) ( .") Nation 51 ( 5.2) 42 ( 5.1) 286 ( 3.1) 288 ( 32) ( Colter, graduate State 74 ( 1.6) 20 ( 1.5) 7 ( 0.7) 283 ( 1.1) 278 ( 2.1) ( "1 Nation 46 ( 52) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 276 ( 3.0) 285 ( 4.9)1 GENDER Mat State 71 ( 1.6) 22 ( 1$) 7 ( 0.6) 277 ( 0.9) 273 ( 1.9) 265 ( 2.7) Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 265 ( 3.1) 278 ( 5.3)1 F1111111. State 68 ( 11) 25 ( 1.5) ( 0.7) 271 ( 0.9) 267 ( 1.8) 262 ( 3.4) Nation 50 ( 4.7) 43 ( 4.7) ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.6)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 02 students). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT I II Wyoming TABLE AlOb I Teachers' Reports on the Use of Mathematical Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT At Lust Ono* a Ws4 tit Lass Than Owe a Week _ Never TOTAL Percentage and Proliciency Percentage and Pro& doing Percentage and Proficiency State 32 ( 2.1) GO ( 1.7) 6 ( 0.9) 268 ( 1.2) 274 ( 0.9) 280 ( 2.3) Nation 22 3.7) 69 ( 3.9) 0 ( 2.6) 254 ( 3.2) 283 (1.0) 262 ( 5.0)! RACEJEIHNICITY White State 32 ( 2.4) 00 ( 1.8) ( 1.0) 270 ( 1.2) 277 ( 0.9) 283 ( 2.7) Nation 17 ( 4.0) 72 ( 4.2) 10 ( 2.7) 261 ( 3.8)1 269 ( 2.1) 288 ( 6.2)i Hispanic State 26 ( 2.8) 85 255 ( 3.4) ( 3.2) 8 (. 2.3) ***) Nation 3S ( 7.5) 55 ( 7.3) ( 2.6) 247 ( 3.8) 245 ( 3.8)1 American Indian State 48 ( 4.7) 4141-0) 43 ( 5.4) ( *v. ( 2.9) **) Nation 78 (34.6) ( *441 22 (34.8) 0 ( *.- 0.0) ..**) TYPE OF COMMUNITY Extreme mil State 42 ( 8.6) 53 ( 4.9) 5 ( 2.8) 272 ( 1.8) 280 ( 2.0) Nation 27 (14.9) *** 85 202 (14.6) ( 2.8)1 8 ( 3.9) Other State 31 ( 1.2) 81 ( 1.4) ( 0.7) 267 ( 1.3) 274 ( 0.8) 284 ( 3.2) Nation if) ( 4.3) 72 ( 5.0) 9 ( 3.3) 253 ( 3.9)1 2e3 ( 2.2) 281 ( 7.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate dem 'nation of the variability of this estimated mean proficiency. *** Sample size is Insufficient to permit a rehab. estimate (fewer than 62 students). OW% 117 112 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE AlOb I Teachers' Reports on the Use of Mathematical (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a WM Lm Than Once a Week Never TOTAL Parcontage and Proddency Porosity' and Proficiency Percentage and ProNdency S.ate 32 ( 2.1) 00 ( 1.7) 8 ( 0.9) 268 ( 1.2) 274 ( 0.9) 280 ( 2.3) Nation 22 ( 3.7) 09 ( 3.9) 9 ( 2.6) 254 ( 3.2) 263 ( 1.9) 282 ( 5.9)1 PARENTS' EDUCATION HS non-graduat State 38 ( 4.3) 56 ( 257 ( 4.5) 3.9) ( .4* ( 2.1) Nation 25 ( 5.6) Me.) 06 ( 243 ( 7.2) 2.2) 9 ( es+ 6.5).) HS graduate State 35 ( 3.1) 59 ( 2.8) 261 ( 1.9) 265 ( 1.7) ( Nation 23 ( 246 ( 4.6) 4.0)1 ( 255 ( 5.3) 2.2) 7 ( 4..0* ( 2.8) Some college State 23 ( 3.6) 63 ( 2.9) 9 ( 1.7) 272 ( 1.8) 277 ( 1.6) Nation 18 ( 261 ( 4.0) 4.4)1 73 ( 269 ( 4.3) 2.3) 9 (2.4) 40 ( *-4.) College graduate State 31 ( 1.9) 81 ( 2.0) 8 ( 1.3) 276 ( 1.8) 282 ( 1.2) 290 ( 5.2) Nation 20 ( 3.9) 89 ( 3.7) 11 ( 2.5) 296 ( 3.5)1 274 ( 2.2) 297 ( 4.2)1 GENDER Male State 33 ( 2.2) 58 ( 1.8) 8 ( 1.1) 270 ( 1.3) 277 ( 1.2) 287 ( 2.6) Nation '22 ( 4.1) 69 ( 4.1) 8 ( 2.0) 255 ( 4.1) 285 ( 2.1) 287 ( 7.2)1 Female State 32 ( 2.4) 61 ( 2.1) 7 ( 1.0) 266 ( 1.8) 271 ( 1.0) 272 ( 4.2) Nation 21 ( 3.8) 68 ( 4.2) 10 ( 3.3) 254 ( 3.3) 262 ( 1.9) 278 ( 6.0)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 11E THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Wyoming TABLE AI Ia I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PinFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Less TOTAL Percentile and Madam Percentage and Prendiency State 71 ( 0.6) 20 ( 0.7) 274 ( 0.8) 270 ( 1.3) Nation 62 ( 3.4) 91 ( 3,1) 267 ( 14) 254 ( 2.9) RACE/ETHNICITY White State 70 ( 0.7) 20 ( 0.7) 276 ( 0,8) 273 ( 1.5) Nation 64 ( 3.7) 28 ( 3.2) 272 ( 1.9) 264 ( 3.4) Hispanic State 76 ( 3.2) 18 ( 2.8) 2$7 ( 2.8) Nation 61 ( 64) 32 ( 5.3) 251 ( 3,1) 240 ( 4.3)1 American Indian State 68 ( *44 5.1) 20 (- 3.6) Nation 15 (25.9) ***) $3 (28.3) ( *11 TYPE OF COMMUNITY Extreme rural State 63 ( 2.3) 34 ( 2.4) 277 ( 2.0) 277 ( 1.5) Nation 50 (10.8) 40 (10,0) 268 ( 4.0)1 247 ( 7.6)1 Other State 71 ( 0.9) 16 ( 1.0) 275 ( 0.9) 270 ( 2.1) Nation 63 ( 3.9) 31 ( 3.5) 267 ( 2.3) 255 ( 3.1) Percentage and Prolkdency 10 ( 0.4) 270 ( 1.3) ( 2.3) 204 ( 5.4)1 6 ( 1.4) we* ( *el 8 ( 2.3) ) 12 ( 31) *a. ( ) *44 ( *44 ) .4.01 14 ( 0.4) 268 ( 1.4) 6 ( 1.9) 257 ( 5.8)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency *** Sample size is insufficient to pernnt a reliable estimate (fewer than 62 students). 1 ; r .... a/ 114 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE Al la I Teachers' Reports on the Frequency of (cantinued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19410 NAEP TRIAL STATE ASSESSMENT _ Almost Every Day Several Times a We* - &mut Once a Week or Less TOTAL Percentage and Prolidency Paresilai and Prat:fancy Percentage mid Pro/Wow State 71 ( 0.6) 20 ( 0.7) 10 ( 0.4) 274 ( 01) 270 ( 1.3) 268 ( 1.3) Nation 02 ( 3.4) 31 ( 3.1) ( 1.8) 2ei ( 1.8) 254 ( 24) 260 ( 5.1)1 PARENTS EDUCATION NS non-graduate State 69 ( 4.4) 21 ( 3.5) 10 ( 2.4) 259 ( 3.2) 0** ( ) Nation 87 ( 245 ( 5.5) 3.2) 27 ( 444 ( 5.2) 041 .44 ( 2.1) «41 NS graduate State 69 ( 265 ( 1.9) 1.3) 19 ( 257 ( 1.6) 2.8) 12 ( 1.5) .44 ( el Nation 81 ( 257 ( 4.4) 2$) 34 ( 250 ( 3.7) 2.9) 6 ( 1.5) .44 ( «.4) Some college State 73 ( 2.1) 19 ( 1.9) 7 ( 0.7) 277 ( 1.3) 279 ( 2.3) Nation 68 ( 272 ( 42) 2.7) 26 ( 258 ( 3.7) 5 2; 8 ( «14 ( 14) College graduate State 71 ( 1.2) ( 1.1) 10 ( 0.7) 282 ( 1.3) 279 ( 1.8) 276 ( 1.9) Nation 61 ( 281 ( 4.0) 2.2) 31 ( 265 ( 3.9) 3.1) 8 ( «.4 3.1) ) GENDER Mal. State 70 ( 1.0) 21 ( 1.0) 9 ( 0.4) 276 ( 1.0) 275 ( 1.5) 270 ( 1.0) Nation 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2.1) 256 ( 3.6) 281 ( 6.7)1 Female State 71 ( 1.0) 18 ( 0.9) 10 ( 0.7) 272 ( 1.0) 264 ( 2.0) 265 ( 2.5) Nation 65 ( 3.6) 28 ( 3.3) ( 2.2) 266 ( 1.8) 253 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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. *0* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 12 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 115 Wyoming TABLE Al lb I Teachers' Reports on the Frequency of i Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Lust Several Times a Iffeek About Once a Week Less than Weeidy TOTAL Percentage and ProRciency Percentage and Proficiency Percentage and Proficiency State 27 ( 1.0) 42 ( 1.6) 31 ( 1.7) 270 ( 1.2) 274 ( 0.7) 272 ( 1.3) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 200 ( 2.3) 274 ( 2.7) RACE/ETHNICITY Whit. State 27 ( 1.0) 42 ( 1.8) 31 ( 1.9) 272 ( 1.3) 277 ( 0.7) 275 ( 1.3) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Hispanic State 24 ( 2.5) «Hi 46 ( 3.3) 257 ( 3.4) 33 ( 3.5) 251 ( 42) Nation 41 ( 1.7) 28 ( 5.3) r ( 7.5) 242 ( 32)I 244 ( 5.1)? 257 ( 2.3)I American Indian State 36 ( 5.7) 37 ( 5 1) 11-114 41-11-* ) *** ) Nation 10 (18.6) ( *v.) 76 (36.2) 13 (18.5) TYPE OF COMMUNITY Extreme rural State 27 ( 2.3) 43 ( 4.7) 30 ( 5.7) 273 ( 2.2) 278 ( 1.3) 279 i 30)1 Nation 27 (14.3) 49 (12.7) 24 (10.1) 258 ( 6.7)1 Other State 26 ( 0.9) 41 ( 1.3) 33 ( 1.1) 270 ( 1.7) 276 ( 0.8) 271 ( 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 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). 116 THE 2990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A I lb I Teachers' Reports on the Frequency of (continued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ,..MINNI.MMIMMIII.1111101 IWO NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Less than Weekly TOTAL Percentage and Medan Percentage and Proficiency Percentage and Proficiency State 27 ( 1.0) 42 ( 1.6) 31 ( 1.7) 270 ( 1.2) 274 ( 0.7) 272 ( 1,3) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 250 ( 2.3) 260 ( 2.3) 274 ( 2.7) PARENTS EDUCATION KS non...graduate State 28 ( 4.6) 34 ( 4.8) 38 (( 4.6) 0,1 Nation 35 ( 6.0) 29 ( 6.3) 36 ( 6.9) 239 ( 3,5) 250 ( 4.5)i HS graduate State 30 ( 2.6) 41 ( 2.8) 28 ( 2.9) 262 ( 1.8) 265 ( 1.9) 261 ( 2.5) Nation 35 ( 5.3) 36 ( 4.5) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 283 ( 3.4) Some college State 23 ( 1.5) 43 ( 22) 34 ( 2.9) 277 ( 2.1) 277 ( 1.8) 277 ( 1.9) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 266 ( 4.2) 278 ( 2.8) College graduate State 26 ( 1.5) 44 ( 1.7) 30 ( 1.8) 277 ( 1.8) 283 ( 1.2) 281 ( 1.7) Nation 3$ ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2,9) GENDER Mato State 26 ( 1.3) 42 ( 1.8) 32 ( 2.0) 274 ( 1.6) 278 ( 1.0) 274 ( 1.8) Nation 35 ( 4.1) 35 ( 3$) 31 ( 3,5) 257 ( 3.2) 2e1 ( 2.8) 27$ ( 3.2) Female State 28 ( 1,2) 43 ( 1.8) 30 ( 1.9) 266 ( 1.6) 271 ( 1.2) 271 1.6) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 117 Wyoming TABLE Al2 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT At Lout Ono a we* Lass Than Onco a weak Now TOTAL POreentalli and Proficiency Pannedage and Pr/Adana Ponnontaga and Pralkiency State 44 ( 1.3) 92 ( 04) 24 ( 1.0) 274 ( 0.9) 27$ ( 04) 246 ( 1.4) Nation 2$ ( 24) 26 ( 1.4) 44 ( 2.9) 25$ ( 2.7) 267 ( 2.0) 261 ( 1.6) RACE/ETHNICITY White State 44 ( 1.4) 32 ( 0.9) 23 ( 1.0) 277 ( 1.0) 276 ( 0.9) 26$ ( 1.3) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3$) 268 ( 3.1) 272 ( 1.9) 270 ( 1.7) Hispanic State 42 ( 3.0) 27 ( 3.1) 30 ( 3.9) 252 ( 3.2) 260 ( 3.2) 251 ( 3.9) Nation ( 5.2) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) American Indian State 43 ( tee* ( 5.1) *41 25 (. ( 4.9) 32 ( ( 4.4) *41 Nation ***) 35 ( 5.5) 33 ( 5.0) «Ai TYPE OF COMMUNITY Extreme rural State 56 ( 3.4) 31 ( 1.8) 12 ( 2.3) 276 ( 1.6) 279 ( 1.9) 267 ( 3.0) Nation 34 (10.8) 27 ( 3.8) 39 (11.6) 249 ( 5.2)! 264 ( 3.5) 256 ( 6.2)1 Other State 4.0 ( 1.4) 32 ( 1.0) 29( 1.1) 276 ( 1.2) 274 ( 1.0) 266 ( 1.7) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 264 ( 2.1) 202 ( 2.2) The standard errors of the estimated statstics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not 2110W accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 118 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE Al2 I Students' Reports on the Frequency of Small (continued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Lust Once a Weelt Lass Than Once a Weak Never .1NI5 TOTAL Pareente. and Prelicienty 44 ( 1.3) 274 ( 0.9) 28 ( 2.5) 25$ ( 2.7) Peroeniese and firolloiency 32 ( 0.8) 275 0.8) 28 ( I A) 287 (2.0) State Nation PARENTS EDUCATION ItS nen-graduat State 38 ( 3.9) 33 ( 3.8) Int* *4* ( Nation 29 ( 4.5) 29(3.0) 242 ( 3.4) 244 ( 3.0) HS graduate State 42 ( 2.1) 30 ( 2.0) 2as ( 1.7) 263 ( 1.8) Nation 28 ( 3.0) 28 ( 41.8) 251 ( 3.7) 261 ( 2.6) Some college State 44 ( 2.2) 32 ( 1.8) 279 ( 1.7) 270 ( 1.8) Nation 27 ( 3.9) 27 ( 2.4) 265 ( 3.6) 258(3.3) College graduate State 46 ( 1.6) 33 ( 1.3) 232 ( 1.3) 282 ( 1.3) Nation 28 ( 3.0) 28 ( 111) 270 ( 2.7) 278 ( 2.8) GENDER Male State 43 ( 1.8) 31 ( 1.1) 277 ( 1.4) 277 ( 1.1) Nation 31 ( 2.9) 2F, ( 1.7) 259 ( 3.3) 286 ( 2.6) Female State 44 ( 1.4) 32 ( 11) Nation 271 ( 1.2) 2e ( 2.4) 271 ( 1.2) 27 ( 1,8) 257 ( 2.8) 2es ( 1.7) and Proficiency 2 (.1 4 06 24 ( 1.1 44 ( 2.9 261 ( 1.6) 29 ( 4.2)-) 42 4.5) 242 ( 2.7) 28 ( 2.4) 258 ( 2.0) 43 ( 3.4) 252 ( 1.7) 24 ( 1.7) 271 ( 1.8) 48 ( 3.6) 266 ( f% 1) 21 ( 1.3) 278 ( 1.7) 44 ( 3.6) 275 ( 2.2) 25 ( 1.3) 267 ( 1.7) ( 2.9) 202 ( 1.8) 23 ( 1.3) 264 ( 1.7) 47 ( 3.2) 200 ( 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). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Wyoming TABLE A13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Prcackincy Percentage and Prollciency Percentage and Proltdency State 27 ( 1.2) 35 ( 1.0) 37 ( 1.0) 270 ( 1.2) 274 ( 0.9) 272 ( 1.0) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.8) 269 ( 15) 259 ( 1.6) RACE/ETNN CITY Witte State 27 ( 1.3) 36 ( 1.2) 37 ( 1.1) 273 ( 1.2) 276 ( 0.9) 275 ( 0.9) Nation 27 ( 1.9) 33 ( 1.6) 40 ( 2.5) 266 ( 2.6) 275 ( 1.8) 268 ( 1.8) HisPanic State 29 ( 3.4) 32 ( 2.9) 39 ( 3.6) 249 ( 3.9) 261 ( 3.0) 251 ( 4.4) Nation 38 ( 42) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) American Indian State 18 ( 3.9) 38 ( 4.6) 46 ( *** ( 5.3) ***) Nation 35 ( ( 3.4) ***) 37 ( *** ( 8.2) ***) *** ( ***) TYPE OF COMMUNITY Extrem nrat State 36 ( 3.9) 33 ( 2.9) 31 ( 2.2) 275 ( 2.3) 280 ( 1.9) 272 ( 1.8) Nation 21 ( 3.1) 37 ( 4.7) 43 ( 5.0) *** ( 4") 262 ( 4.7)1 251 ( 5.2)1 Other State 23 ( 1.3) 38 ( 1.3) .19 ( 1.4) 270 ( 1.4) 273 ( 1.2) 273 ( 1.4) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 256 ( 2.9) 270 ( 1.8) 260 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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). 5 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A 13 I Students' Reports on the Use of Mathematics (wntinued) i Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT At Least Once a Week Lees Than Once a Week NOW TOTAL Remota. and Residency Peeventege and Proficiency Pawning and Proficiency State 27 ( 1.2) 35 ( 1.0) 37 ( 1.0) 270 ( 1.2) 274 ( 0$) 272 ( 1.0) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 25$ ( 2.6) 200 ( 1.5) 25a ( 1.6) PARENTS EDUCATION 14$ non-graduat State 33 ( 3.6) ( ( Nation 27 ( 42) 21) ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) NS graduate State 29 ( 1.9) 34 ( 2.1) 37 ( 2.8) 262 ( 2.1) 264 ( 1.4) 262 ( 2.0) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some willow State 28 ( 2.4) 38 ( 2.3) 34 ( 1.9) 273 ( 1.9) 273 ( 1.6) 277 ( 1.8) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.6) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) Collage graduate State 28 ( 1.7) 35 ( 1.7) 39 ( 1.7) 260 ( 1.8) 261 ( 1.4) 281 ( 1.3) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.8) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Male State 29 ( 1.5) 35 ( 1.4) 35 ( 12) 271 ( 1.7) 278 ( 1.2) 274 ( 1.2) Nation 32 ( 2.0) 30 ( 14) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 200 ( 1.8) Female State 25 ( 1.6) 35 ( 1.5) 40 ( 1.6) 268 ( 1.8) 270 ( 1.0) 269 ( 1.2) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 268 ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 126 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Wyoming TABLE A14 I Students' Reports on the Frequency of I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MO NAEP TRIAL About Once a Walk or STATE ASSESSMENT Almost Evary Day Sawa Times a Mask Loss , TOTAL Pare Mitap and Praidatcy Parombio and Prelkiency Percentage and Proliciency State le ( 0.8) 10 ( 0.6) 10 ( 0.5) 274 ( 0.8) 267 ( 18) 266 ( 1.1) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 18) 287 ( 12) 252 ( 1.7) 242 ( 4.5) RACE/ETHNICITY IMita State 80 ( 0.8) 10 ( 0.8) 11 ( 0.5) 278 ( 0.7) 270 ( 2.0) 267 ( 12) Nation 78 ( 2.5) 13 ( 0.8) 11 ( 22) lilsoanle 274 ( 1.3) 258 ( 22) 252 ( 5.1)! State 78 ( 255 ( 2.9) 2.6) ( 441 9 ( MI* ( 1.6) *ea) Nation 81 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) American Indian State 72 ( 259 ( 4.9) 3.8) 13 ( ( 3.2) 15 ( *** 4.1) Nation el ( ow* ( 4.4) 41 22 ( 3.6) ***) 17 ( 4.0) 440) TYPE OF COMMUNITY Extreme rural State 78 ( 1.9) 18 ( 1.6) 8 ( 1.3) 277 ( 1.4) 275 ( 3.0) 4 *14 ) Nation 68 (11.3) 15 ( 3.8) 17 ( 8.2) 263 ( 4.2)! 414. ( Other State 79 ( 0.8) 7 ( 0.8) 14 ( 0.5) 275 ( 0.9) 263 ( 2.8) 265 ( 1.2) Nation 75 ( 2.2) 14 ( 1.0) 10 ( 1.9) 267 ( 1.8) 252 ( 2.6) 239 ( 4.3)I The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample stze is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A 14 I Students' Reports on the Frequency of (continued) i Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Walk About Ones . Weak or Loris TOTAL Porvantage Ind Pnaldway pairventapi and Pr:Adana Paraantage and Praftioncy State 79 ( 0.8) 10 ( 0.6) 10 ( 0.5) 274 ( 0.6) 267 ( 1.8) 255 ( 1.1) Nation 74 ( 1.9) /4 ( 0.8) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 4.5) PARENTS' EDUCATION KS non-graduate State 77 ( 259 ( 3.6) 2.8) 11 ( 04. ( 2.8) 44) ID** ( *41 Nation 84 ( 3.4) 18 ( 2.0) 245 ( 2.3) *Sir ( «ye ***) HS graduate State 76 ( 2.0) 12 ( 1.4) 13 ( 1,5) 284 ( 1.3) 259 ( 2.4) 258 ( 2.9) Nation 71 ( 3.0) 16 ( 1,8) 13 ( 2.8) 258 ( 1.6) 249 ( 3.2) 239 ( 3.4)1 Some collage State 83 ( 1.4) 10 ( 1.3) 3 ( 0.9) 277 ( 1.0) *** 0**) Mt* ( IP** ) Nation 80 ( 270 ( 2.0) 1.9) 11 ( 12) 9 ( 0*0 ( 1.7) 41 College graduate State 80 ( 12) 9 ( 1.0) 10 ( 0.8) 282 ( 0.9) 277 ( 2.8) 274 ( 2.1) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 260 ( 2.6) 257 ( 6.4)1 GENDER Make State 80 ( 1.0) 10 ( 0.8) 10 ( 0.6) 276 ( 0.7) 271 ( 2.1) 266 ( 1.5) Nation 72 ( 2.4) 16 ( 1.2) 12 ( 2.1) 288 ( 1.8) 252 ( 2.5) 242 ( Female State 79 ( 1.1) 10 ( 0.9) 11 ( 0.7) 271 ( 0.9) 263 ( 2.7) 263 ( 1.7) Nation 78 ( 1.8) 13 ( 1.0) 11 ( 1.6) 266 ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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. **0 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 128 THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Wyoming TABLE Al5 I Students' Reports on the Frequency of 1 Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL Al Least Several Times STATE ASSESSMENT a Week About Once a Week Loss Than Weekly TOTAL State Nation RACE/ETHNICITY White State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Extrema nral State Nation Other State Nation Pilaw Nap and kdancy 29 ( 0.9) 2e7 ( 1.1) 38 ( 2.4) 253 ( 2.2) 28 ( 1.0) 270 ( 1.1) 35 ( 2.9) 262 ( 2.5) 31 ( 2.7) 246 ( 3.7) 44 ( 4.1) 238 ( 3.9) 43 ( 5.8) 41 ( 4.2) ***) 29 ( 2.2) 272 ( 1.8) 42 (10.1) 249 ( 4.0)! 28 ( 1.1 ) 267 ( 1.4) 36 ( 2.9) 252 ( 3.0) Poroodage and Prolkdon Poroontops and Progicioncy 27 ( 0.9) 44 ( 1.1) 270 ( 14) 277 ( 25 ( 2.1 ( 1.2) 1.4) $7 ( 272 ( 24 1.9 28 ( 04) 44 ( 12) 272 ( 1.0) 280 ( 0.9) 24 ( 1.3) 41 ( 3.0) 266 ( 14) 277 ( 2.0) 22 ( 3.9) 40 ( 3.6) 257 ( 3.8) 258 ( 3.1) 25 ( 3.4) 32 ( 4.3) 247 ( 3.3) 248 ( 3.3) 19 ( 044 ( 3.4) 4,44) 30 (11.3) 28 (12.5) et. ( Inn 28 ( 1.9) 42 ( 2.6) 275 ( 1.7) 270 ( 2.1) 30 ( 4.4) 28 ( 7 4) 256 ( SA)! 207 ( 7.3)I 26 ( 1.1) 46 ( 1.:!) 270 ( 1.4) 278 ( 1.2) 26 ( 1.2) 38 ( 2.9) 261 ( 2.1) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE Als Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT At Lust Seurat Thus a Week About Once a Week Less Than Weekly TOTAL and Profidency Pwcenlage and Proficiency Pementacts and Proficiency State 29 ( 0.9) 27 ( 0.9) 44 ( 1.1) 267 ( j 270 ( 1.0) 277 ( 0.9) Nation 3$ ( .4.4) 25 ( 1.2) 37 ( 2.5) 253 ( 2.2) 261 ( 1A) 272 ( 1.9) PARENTS' EDUCATION KS non-graduate State 31 ( ( 4.0) 31 ( .44 ( 3.2) 38 ( 3.3) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) NS graduate State 32 ( 2.2; 28 ( 2.1) 40 ( 2.2) 260 ( 1.6) 260 ( 1.5) 267 ( 2.3) Nation 40 ( 3.2) 29 ( 2.2) 32 ( 3.6) 247 ( 2.7) 256 ( 2.5) 262 ( 2.2) Some coneys, State 23 ( 1.7) 2$ ( 2.0) 49 ( 2.1) 271 ( 1.7) 274 ( 1.8) 280 ( 1.3) Nation 34 ( 3.4) 26 ( 2.2) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) Codeine graduate State 29 ( 1.3) 26 ( 1.3) 45 ( 1.7) 275 ( 1.8) 279 ( IL) 285 ( 1.4) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 273 ( 2.5) 285 ( 2.3) GENDER Male State 28 ( 1.5) 28 ( 1.2) 44 ( 1.0) 269 ( 1.4) 273 ( 1.5) 279 ( 1.3) Nation aa ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 263 ( 2.3) 274 ( 2.4) Fouls State 30 ( 1.2) 27 ( 1.3) 43 ( 1.3) 264 ( 1.4) 267 ( 1.5) 275 ( 1.3) Nation 37 ( 2.5) 25 ( 1.5) 36 ( 2.6) 253 ( 2.1) 259 ( 1.8) 269 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 130 THE 1990 NABP TRIAL STATE ASSESSMENT 125 Wyoming TABLE A18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111110 NAEP TRIAL STATE ASSESSMENT . Own a Calculator Teacher Explains Calculator Use , Yes No . Yes No 1 TOTAL Parostaga and PM WOW 09 ( 0.2) 272 ( 0.8) 97 ( OA) 283 ( 1.3) 275 ( 0.8) 98 ( 0.3) 270 ( 1.5) 98 ( 1.0) 254 ( 2.3) 92 ( 1.2) 245 ( 2.7) 97 ( 1.8) 258 ( 2.8) 94 ( 3.1) ( *1.1 99 ( 0.5) 276 ( 1.1) 9e ( 1,3) 257 ( 3.0)1 99 ( 0.3) 273 ( 0.8) 97 ( 0.5) 203 ( 1.7) Portiontage and 1 ( 0.2) 3 *a 234 ( 3.8) I ( 0.2) trent ( tgrit) 2 ( 0.3) ( 1.2) ***) 3 ( 1.8) .Hfr .41 ( 3.1) ***) *440 ( ) 4 ( 1.3) ( 1 ( 0.3) 3 ( 0.5) 233 ( 5.4) Paraentaga and Pro lialancy 52 ( 1.0) 260 ( 0.9) 49 ( 2.3) 258 ( 1.7) 51 ( 12) 271 ( 0.9) 48 ( 2.8) 288 ( 1.8) 55 ( 2.8) 252 ( 2.7) 83 ( 43) 243 ( 3.4) 58 ( 5.8) 254 ( 3.5) 71 (161) HI* ( 53 ( 3.3) 273 ( 1.7) 42 ( $.7) 251 ( 4.8)1 47 ( 1.1) 268 ( 1.3) 50 ( 2.7) 25$ ( 2.1) Parcantap and Pra *dam 48 ( 1.0) 270 ( 0.11) 51 ( 2.3) 2011 ( 15) 49 ( 1.2) 279 ( 0.8) 54 ( 2.0) 273 ( 1.8) 45 ( 2.8) 258 ( 3.1) 37 ( 4.3) 245 ( 2.9) 42 ( 5.8) ( 114411) 29 (10.7) ( 47 ( 3.3) 279 ( 1.6) 58 ( 8.7) 261 ( 4.4)! 53 ( 1.1) 276 ( 1.0) 50 ( 2.7) 200 ( 2.0) State Nation RACE/ETHNICITY Mite State Nation Hispanic State Nation Meet& II Indian State Nation TYPE OF COMMUNITY Extrema rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! 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 stidents). .1 3 126 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE AIS (continued) Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Own a Calculator . Teacher lbcplaIns Calculator Use Yes _ No Yes No TOTAL Perventapt end Re Odium Pareartage and Proficiency Partise Nage and Pro adorn Pura Near and Pro Wank" State 99 ( 0.2) 0.2) 52 ( 1.0) 44 ( 272 ( 0.6) 268 ( 0.9) 276 0.6 Nation 97 ( OA) 3 ( 0.4) 49 ( 2.3) 51 24 203 ( 1.3) 234 ( 3.8) 258 ( 1.7) 200 ( 14) PARENTS' EDUCATION NS non-graduate State 95 ( 2.1) 5 ( 2.1) 51 ( 3.9) 49 ( 3.9) 257 ( 2.3) Mr* 1111 252 ( 2.9) 201 ( 3.0) Nation 92 ( 243 ( 1.6) 2.0) 8 ( 4** ( 1.6) 53 ( 242 ( 4.6) 2.9) 47 ( 243 ( 4.6) 2.5) NS graduate State 99 ( 263 ( 0.3) 1.2) ( ( 0.3) 441 53 ( 260 ( 2.4) 1.2) 47 ( ( 2.4) 1.9) Nation 97 ( 255 ( 0.6) 1.5) 3 ( 0.6) ***) 54 ( 252 ( 3.0) 1.9) 46 ( 258 ( 3.0) 2.0) Soma collo", State 99 ( 0.5) 51 ( 2.1) 49 ( 276 ( 0.9) ( ".) 271 ( 1.4) 281 ( 1.5) Nation 96 ( 0.9) 4 ( 0.9) 43 ( 3-2) 52 ( 32) 268 ( 1.8) ( ***) 265 ( 2.4) 268 ( 2.2) Collis,. gradual. State 09 ( 0.3) 1 ( 0.3) 51 ( 1.5) 49 ( 1.5) 281 ( 0.8) *** ( 277 ( 1.3) 254 ( 1.2) Nation 99 ( 02) 1 ( 02) 46 ( 2.6) 54 ( 2.6) 275 ( 1.6) ( ***) 268 ( 2.2) 280 ( 1.9) CIENDER Maio State 99 ( 275 ( 0.3) 0.6) 4-44 ( 0.3) 53 ( 270 ( 1.3) 1.2) 47 ( 280 ( 1.3) 1.1) Nation 97 ( 04) 3 ( 0.5) 51 ( 2.6) 48 ( 2.6) 284 ( 1.7) 258 ( 2.1) 268 ( 2.1) Female, State 99 ( 0.3) 1 ( 0.3) 51 ( 1.6) 48 ( 16) 270 ( 0.8) ( 267 ( 1.1) 272 ( 1.3) Nation 97 ( 0.5) 3 ( 0.5) 47 ( 24) 53 ( 24) 262 ( 1.3) "4. ( 4") 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 estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 Wyoming TABLE A19 I Students' Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 NAEP TRIAL STATE ASSESSMENT Wosidng Problems in Dins Doing Problems at Home Taking Quinn or Tests Almost Always aVer Almost Always NOM Almost Always Never TOTAL Percentage and Pro Selena Percentage and Proficiency Percentage and Proficiency Peeveniege and Proficiency Percentage end Proficiency Percentage and Proficiency State 52 ( 1.0) 18 ( 0.8) 38 ( 0.9) 13 ( 0.6) 26 ( 0.9) 27 ( 0.9) 289 ( 0.8) 232 ( 1.3) 271 ( 0.9) 276 ( 1.7) 270 ( 1.2) 281 ( 1.0) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 ( 1.4) 90 ( 2.0) 254 ( 1.5) 272 ( 1.4) 281 ( 1.8) 283 ( 1.8) 253 ( 2.4) 274 ( 1.3) RACE1ETHNIC1TY White State 52 ( 1.0) 16 ( 0.9) 35 ( 1.0) 12 ( 0.8) 2$ ( 1.0) 27 ( 1.0) 272 ( 0.8) 284 ( 14) 272 ( 1.0) 279 ( 1.8) 273( 1.3) 283( 1.1) Nation 46 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 25 ( 1.6) 32 ( 2.3) 262 ( 12) 278 ( 1,3) 270 ( 1.7) 269 ( 2.3) 263 ( 2.6) 279 ( 1.2) Hispanic State 50( 251 ( 4.3) 3.5) 16 ( 2.2) 40 ( 261 ( 2.8) 2.3) «Hi ( tift) 26 ( 3.2) .**) 23 4-4.* ( 2.4) Nation 51 ( 2.9) 16 ( 3.5) 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 56 ( 5.4) eita) 25 ( *** 4.5) 25 ( 4.0) ) 18 ( 3.5) 21 ( ( 4.9) 26( 5.0) Nation 33 ( et. 9.6) 23 ( ( 4.9) .64) ( 32 (101) 20 ( «Hp 62) 21 ( 7.8) TYPE OF COMMUNITY Extreme rural State 44 ( 2.4) 20 ( 2.4) 33 ( 1.8) 14 ( 1.2) 21 ( 1.9) 33 ( 3.2) 271 ( 1.4) 284 ( 2.8) 273 ( 1.6) 279 ( 2.6) 273 ( 2.0) 284 ( 2.3) Nation 46 ( 246 ( 7.4) 4.3)1 29 ( 268 ( 95) 6.1)1 111414 *** 23 ( 263 ( 3.9) 4.4)1 24 ( 6.6) 41 37 ( 270 ( 8.3) 4.0)1 Other State 51 ( 1.2) 20 ( 0.9) 34 ( 1.2) 13 ( 0.9) 28 ( 1.2) 28 ( 1.1) 270 ( 1.1) 281 ( 1.4) 271 ( 1.3) 278 ( 2.3) 270 ( 1.4) 281 ( 1.3) Nation 48 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1.8) 29 ( 2.1) 254 ( 2.1) 272 ( 1.6) 263 ( 2.3) 263 ( 2.8) 253 ( 22) 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. 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). 133 128 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming 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 Waiting Problems Pass Doing Problems at Home Taking Quizzes or Teets Almost Always Never Almost Always Never Almost Always Never TOTAL Percentage and Proadan Percentage and Prolkiency Percentege aid Proficiency Percentage nd Proficiency State 52 ( 1.0) 18 ( 0.8) 38 ( 0.9) 13 ( 0.6) 269 ( 0.8) 282 ( 1.3) 271 ( 0.9) 27$ ( Nation 4$ ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( OA 254 ( 1.5) 272 ( 1.4) 281 ( 1.8) 283 ( 1.8 PARENTS EDUCATION NS non-graduate State 55 ( 255 ( 4.4) 2.7) 13 ( 2.6) 32 ( 3.9) *se ) ( It** 2.3) ..) Nation 54 ( 3.3) 19 ( 3.8) 20 ( 3.1) 22 ( 2.6) 240 ( 2.3) 4 ( 11111 244 ( 3.6) 244 ( 4.2) liS graduate State 53 ( 1.7) 18 ( 1.5) 36 ( 22) 14 ( 1.6) 261 ( 1.5) 271 ( 3.4) 262 ( 1.7) 269 ( 3.4) Nation 52 ( 2.5) 20 ( 2.4) 29 ( 1.9) 18 ( 1.5) 249 ( 1.4) 265 ( 2.7) 250 ( 2.4) 256 ( 2.4) Some college State 51 ( 2.2) 19 ( 2.0) 30 ( 1.9) 11 ( 1.3) 273 ( 1.4) 280 ( 2.8) 274 ( 1.9) 281 ( 2.6) Nation 48 ( 2.8) 26 ( 2.8) 2$ ( 2.0) 20 ( 1.9) 258 ( 2.1) 272 ( 2.5) 287 ( 3.0) 268 ( 3.2) College graduate State 51 ( 1.4) 19 ( 1.1) 37 ( 1.3) 12 ( 1.0) 277 ( 1.2) 292 ( 1.5) 277 ( 1.2) 286 ( 2.6) Nation 4.5 ( 1.9) 25 ( 2.4) 33 ( 2.0) 16 ( 1.4) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) GENDER Male State 54 ( 1.4) 16 ( 0.9) 34 ( 1.3) 14 ( 1.0) 272 ( 1.0) 286 ( 1.8) 274 ( 1.3) 278 ( 2.2) Nation 50 ( 1.7) 20 ( 2.0) 29 ( 1.6) 10 ( 1.3) 255 ( 1.9) 275 ( 22) 264 ( 2.8) 263 ( 2.5) Female State 49 ( 1.8) 19 ( 1.3) 37 ( 1.2) 11 ( 0.9) 266 ( 1.0) 278 ( 1.8) 288 ( 1.3) 274 ( 2.1) Nation 48 ( 2.0) ( 2.1) 32 ( 1.6) 18 ( 1.2) 252 ( 1.7) 289 ( 1.8) 25$ ( 1.7) 263 ( 2.1) Potent.. Percentap and and ProficiencY ProaceoncY 24 ( 0.9 27 ( 0.9 270 ( 1.2 281 ( 1.0 27 ( 1.4 30 ( 2.0 253 ( 2.4 274 ( 1.3 28 ( 4.0) 4** ( *41 32 ( 3.0) 237 ( 2.3) 28 ( 1.7) 201 ( 2.4) 26 ( 1.8) 248 ( 2.8) 25 ( 2.2) 274 ( 2.0) 26 ( 2.4) 255 ( 3.8) 25 ( 1.4) 279 ( 1.0) 20 ( 1.8) 268 ( 2.8) 23 ( 1.2) 272 ( 16) 27 ( 1.5) 256 ( 3.0) 29 ( 1.3) 208 ( 1.4) 27 ( 1.8) 251 ( 2.4) 22 ( 3.7) 24 ( 3.2) 251 ( 4.6) 22 ( 1.5) 272 ( 2.5) 27 ( 2.2) 265 ( 2.0) 31 ( 2.1) 280 ( 1.7) 35 ( 2.5) 275 ( 2.0) 28 ( 1.4) 289 ( 1.4) 33 ( 2.7) 285 ( 2.0) 25 ( 1.1) 285 ( 1.5) 26 ( 2.1) 277 ( 1.9) 28 ( 15) 277 ( 1.4) 33 ( 2.1) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 Wyoming TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 19 I 90 NAEP TRIAL "Calm "Calculator-Use STATE ASSESSMENT High lator-Usa" Chow Other Group , TOTAL Percentage and ProadanCY Percentage and Pr:we:fun State 51 ( 1.1) 49 ( 1.1) 277 ( 0.8) 266 ( 1.0) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACE/ETHNICITY Whit* State 52 ( 1.4) 43 ( 1.4) 279 ( 0.9) 269 ( 1.1) Nation 44 ( 1.4) 56 ( 1.4) itispanic 277 ( 13) 263 ( 1.7) State 43 ( 4.0) 52 ( 4.0) 260 ( 2.7) 248 ( 3.4) Nation 36 ( 4.2) 64 ( 4.2) 254 ( 4.6) 238 ( 3.0) American Indian State 39 ( 5.8) .44) Nation 29 (12.0) 71 (12.0) *** `") TYPE OF COMMUNITY Extrema nwal State 55 ( 2.0) 45 ( 2.0) 280 ( 2.0) 270 ( 1.8) Nation 39 ( 5.6) 61 ( 5.6) 269 ( 4.4)1 248 ( 4.3)1 Other State 49 ( 1.6) 51 ( 1.6) 278 ( 1.2) 267 ( 1.3) Nation 42 ( 1.4) 56 ( 1.4) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to' permit a reli tble estimate (fewer than 62 students). 135 130 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1fite NAV TRIAL STATE ASSESSMENT * H "Calculator-Use" Group Odier "Caladator-Use" Group TOTAL 'wattage and Prof Macy Percentage end Proficiency State 51 ( 1.1) 49 ( 1.1) 277 ( 0.8) 206 ( Nation 42 ( 13) 519 ( 1.3) 272 ( 255 ( 1.5) PARENTS' EDUCATION MS nod-graduate State 43 ( 5.7) $7 ( 5.7) 249 ( 2.9) Nation 34 ( 3.3) 66 ( 3.3) 248 ( 4.4) 242 ( 2.4) NS graduate State 47 ( 2.3) 53 ( 2.3) 266 ( 1.6) 259 ( 1.8) Nation 40 ( 2.2) 60 ( 2.2) 263 ( 2.0) 249 ( 1.8) Same codege State 53 ( 2.3) 47 ( 2.3) 280 ( 1.4) 273 ( 1.8) Nation 48 ( 22) 52 ( 2.2) 277 ( 2.6) 258 ( 2.5) College graduate State 58 ( 1.8) 44 ( 1.8) 284 ( 13) 275 ( 1.4) Nation 48 ( 2.0) 54 ( 2.0) 282 ( 2.1) 288( 1.9) GENDER Mate State Nation 48 ( 280 ( 39 ( 1.8) 1.1) 2.0) 52 ( 289 ( 81 ( 1.6) 1.4) 2.0) 274 ( 2.0) 255 ( 2.3) Female State 55 ( 273 ( 1.5) 1.2) 45 ( 294 ( 1$) 1.4) Nation 46 ( 1.8) 55 ( 1.8) 289 ( 1.7) 254 ( 1.3) The standard errors of the esUrnated 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 withm ± 2 standard errors of the estimate for the sample. a** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 Wye-4,in TABLE A24 I Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Zero to Two Typos Throe Types Four Types TOTAL Perentage and ProliciencP Percentage and Proficiency Percen18118 and Proldency StaLe Nation 14 ( 260 ( 21 ( 0.7) 1.7) 1.0) 32 ( 270 ( 30 ( 0.9) 1.0) 1.0) 54 ( 27:10 ( 0.7) 0.8) 1.3) 244 ( 2.0) 258 ( 1.7) 2i. ( 1.5) RACE/ETANICITY Whit. State 13 ( 0.7) 31 ( 0.9) 56 ( 0.8) 284 ( 1.4) 273 ( 1.2) 278 ( 0.8) Nation 18 ( 1.1) 29 ( 1.3) b6 ( 1.5) 251 ( 2.2) 268 ( 1.5) 276 ( 4.7) Hispanic State 24 ( 9) 3....) ( 251 ( 3.8) 2.9) 42 ( 261 ( 3.9) 3.3) Nati,. 44 ( 3.0) 30 ( 2.4) 26 ( 23) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) American Indian Sta,e 14 ( 3.1) ...) 51 ( 5.7) ...) Nation 29 (11.1) .44 ( ..) 31 ( iii 9.2) TYPE OF COMMUNITY Extreme nral State 12 ( 1.4) 32 ( 2.1) 55 ( 1.8) 263 ( 2.8) 274 ( 2.9) 279 ( 1.6) Nation 17 ( 4.0) 33 ( 3.2) 50 ( 5.1) ( 253 ( 4.3)1 263 ( 5.6)1 Other State 12 ( 0.8) 32 ( 1.2) 56 ( 0.9) 263 ( 2.0) 269 ( 1.2) 277 ( 1.1) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 1.5) 244 ( 2.8) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "1' Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A24 Students' Reports on Types of Reading (continued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 UAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Four Types _ Air TOTAL Percentage and Prondency Pon:entail* and Proilcianc:y Pemaintaga and Prolicioncy State 14 ( 0.7) 32 ( 0.9) 54 ( 0.7) 200 ( 1.7) 270 ( 1.0) 278 ( 0.8) Nation 21 ( 1.0) $0 ( 1.0) 46 ( 1.3) 244 ( 2.0) 256 ( 1.7) 272 ( 1.5) PARENTS EDUCATION NS non-graduate State 34 ( 4.3) 34 ( ( 3.9) 441 32 ( 3.9) Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3,4) 243 ( 3.3) 248 ( 3.3) HS graduate State 19 ( 1.7) 36 ( 2.1) 46 ( 1.8) 255 ( 2.1) 262 ( 1.8) 288 ( 1.6) Nation 26 ( 2.2) 33 ( 1.9) 40 ( 1.7) 246 ( 2.2) 253 ( 2.7) 260 ( 2.1) Some college State 12 ( 1.3) 32 ( 1.6) 55 ( 1.9) 274 ( 3.2) 276 ( 1.6) 277 ( 1.4) Nation 17 ( 1.5) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduate State 8 ( 0.8) 29 ( 1.4) 63 ( 1.3) 269 ( 3.4) 278 ( 1.6) 283 ( 0.9) Nation 10 ( 0.8) 28 ( 1.8) 62 ( 2.0) 254 ( 2.8) 269 ( :7'5) 280 ( 1.8) GENDER Male State 14 ( 1.0) 33 ( 1.1) 53 ( 1.1) 263 ( 2.2) 272 ( 1.3) 279 ( 1.0) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Female State 14 ( 0.9) 32 ( 1.3) 84 ( 1.4) 258 ( 2.2) 267 ( 1.3) 274 ( 1.1) Nation 22 ( 1.2) 29 ( 1.4) 49 ( 1.9) 244 ( 2.2) 258 ( 1.9) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSFSSMENT 133 Wyoming TABLE A2$ 1 Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1NO NAEP TRIAL STATE ASSESSMENT One Hour or Loss Two Ho rs _ Thr ee Hours Four to Five Hours Six Hours or Mara TOTAL 114110111010 and Preithancy Parcentage *Ma fancy iftraantage and Proficiency peraantags and Pre lkdancy State 16 ( 1.0) 0.9) 25 ( 0.9) 24 0.1) 261 ( 1.2) 275 1.1) 273 ( 1.1) 208 1.1) Nation 12 ( 0.8) 21 0.0) 22 ( 0.8) 28 1.1) 209 ( 2.2) 216 ( 1.6) 205 ( 12) 200 ( 1.7) RA0E/ETHNICITY Whits State 18 ( 1.0) 27 ( 1.0) 25 ( 1.0) 23 ( 1.0) 283 ( 1.2) 277 ( 1.1) 275 ( 1.1) 209 ( 1.2) Nation 13 ( 1.0) 23 ( 1.2) 24 ( 1.1) 27 ( 1.4) 276 ( 2.5) 275 ( 2.2) 272 ( 1.2) 267 ( 1.7) Hispanic State 13 ( 2.0)*) 23 ( 3.3) 24 ( 2.6) 00, 29 ( 251 ( 2,5) 4.4) Nation 14 ( 2.4) 20 ( 2.5) 19 ( 2.1) 31 ( 3.1) IFOr 24$ ( 3.2) 242 ( 5.6) 247 ( 3.5) American Indian State 13 ( 4.0) 24 ( 4.5) fen 22 ( 4.0) ( fly) 27 ( *** ( 4.6) Nation 43 ( ( 5.0) .41 17 ( 8.4) ***) 21 (10.5) .,11. (en 28 ( 5.7) ..**) TYPE Of COMMUNITY Extreme rural State 16 ( 2,5) 27 ( 1.5) 25 ( 2.1) 24 ( 1.8) 263 ( 2.1) 279 ( 2.4) 277 ( 2.4) 270 ( 2.3) Nation 14 ( 3.3) *et.) 19 ( 2.6) 23 ( 2.0) v. 26 ( 256 ( 2.7) 3.8)1 Other State 19 ( 1.0) 25 ( 1.2) 25( 1.1) 24 ( 1.2) 262 ( 1.5) 278 ( 1.4) 273 ( 1.4) 267 ( 1.3) Nation 12 ( 1.0) 21 ( 1.0) 23 ( 1.2) 27 ( 1.2) 266 ( 2.8) 269 ( 2.3) 265 ( 2.11 259 ( 2.2) Panuntivp and Pri 7 049 253 2.2) 16 tO) 245 1.7) ( 258 ( 2.5 12 ( 1.2 253 ( 2.6) ( *in 17 ( 1.1) 236 ( 5.11) 14 ( 3.6)) n ( SA) 0 ( 12) 1141. .19 ( 3.11) el 7 ( 0.7) 254 33) 17 ( 14) 246 ( 24) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 3 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A25 I Students' Reports on the Amount of Time Spent (contintted) i Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 19110 NAEP TRIAL One Hour or Four to Five Six Hours or STATE ASSESSMENT Less Two Hours Three Hours Hours More , TOTAL Percentage and Proficiency Pommies' and Proficiency Percentage and Proficiency Perceniage and Proficiency Percentage and Proltdency State 18 ( 1.0) 26 ( 0.9) 25 ( 0.9) 24 ( 0.8) 7 ( 0.6) 281 ( 1.2) 275 ( 1.1) 273 ( 1.1) 266 ( 1.1) 253 ( 2.2) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 281 1.1) 16 ( 1.0) 269 ( 2.2) 268 ( 1.8) 26$ ( 1.7) 260 ( 1.7) 245 ( 1.7) PARENTS' EDUCATION HS non-graduate State 12 ( 2.6) 19 ( 3.6) 17 ( .* 2.5)) 40 ( 258 ( 4.6) 3.1) 11 ( *** 3.0) ***) Nation lie graduate ( **At) 20 ( 3.1) 21 ( .04 ( 2.6) 441 28 ( 244 ( 2.9) 32) 20 ( ( 2.4) .44) State 13 ( 1.8) 22 ( 1.9) 27 ( 1.8) 29 ( 2.0) 9 ( 1.3) 268 ( 2.7) 269 ( 2.1) 265 ( 2.1) 257 ( 1.9) Nation 8 ( 1.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 19 ( 1.0) 249 ( 4.7) 257 ( 2.8) 259 ( 32) 253 ( 2.5) 248 ( 3.0) Some college State 16 ( 2.0) 28 ( 1.8) 26 ( 1.7) 22 ( 1.6) 8 ( 1.2) 282 ( 2.3) 278 ( 2.1) 277 ( 2.3) 273 ( 2.0) *441 Nation 10 ( 1.4) 25 ( 2.4) 23 ( 2.6) 28 ( 22) 14 ( 1.5) 275 ( 2.7) 269 ( 3.5) 267 ( 2.5) 242 ( 3.4) College graduate State 22 ( 1.3) 29 ( 1.5) 24 ( 1.3) 20 ( 1.2) 5 ( 0.7) 290 ( 1.5) 281 ( 1.8) 280 ( 1.4) 275 ( 1.4) Nation 17 ( 1.3) 22 ( 1.6) 23 ( 1.1) 25 ( 1.5) 12 ( 1.1) 282 ( 2.6) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 3.2) GENDER Male State 16 ( 1.1) 25 ( 1.3) 25 ( 1.3) 24 ( 1.0) 9 ( 0.8) 284 ( 2.2) 279 ( 1.6) 276 ( 1.5) 270 ( 1.6) 254 ( 2.5) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 28 ( 1.3) 17 ( 1.5) 269 ( 3.3) 267 ( 2.6) 287 ( 2.2) 262 ( 2.1) 248 ( 2$) Female State 19 ( 1.3) 27 ( 1.2) 24 ( 1.3) 24 ( 1.3) 6 ( 0.7) 279 ( 1.4) 272 ( 1.6) 270 ( 1.5) 263 ( 1.8) 250 ( 4.0) Nation 44 ( 1.1) 20 ( 1.3) 23 ( 1.4) 2$ ( 1.6) 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). 140 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Wyoming TABLE A26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT None One or Two Days Throe Days or Moro , TOTAL Penanta. and 14v liciancy Parandasa and Pridicioncy Islwasainta and Prolidancy State 42 ( 0.9) 35 ( 0.8) 23 ( 0.3) 276 ( 0.3) 272 ( 1.0) 264 ( 1.3) Nation 46 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 200 ( 1.5) 260 ( 1.9) RACE/ETHNICITY Whitt State 42 ( 1.1) 35 ( 1.0) 22 ( 0.8) 279 ( 0.8) 276 ( 1.1) 26$ ( 1.3) Nation 43 ( 12) 34 ( 1.2) 23 ( 1.2) 273 ( 1.6) 272 ( 1.7) 258 ( 2.1) Hispanic State 31 ( 3.1) 38 ( 3.7) 31 ( 3.3) 260 ( 3.2) 25.5 ( 3.4) 248 ( 3.6) Nation 41 ( 3.3) 32 ( 2.2) 27 ( 2.6) 246 ( 4.6) 250 ( 3.3) 235 ( 3.1) American Indian State 42 ( 5.1) 29 ( 3.9) **I) *44 ( 441 Nation 23 (( 6.6) ..**) 39 ( 5.1) ( eel 38 ( 52) rt. ( rtr) TYPE OF COMMUNITY Extramo rural State 48 ( 2.3) 34 ( 1.9) 17 ( 1.4) 277 ( 1.2) 277 ( 2.1) 270 ( 3.2) Nation 43 ( 4.4) 32 ( 4.2) 257 ( 4.1)1 264 ( 5.8)! Mt* ( *el R) Other State 40 ( 1.0) 35 ( 1.0) 25 ( 0.9) 277 ( 1,1) 273 ( 1.2) 265 ( 1.3) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 266 ( 1.9) 251 ( 2,4) Ap The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! 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). 141 136 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A26 I Students' Reports on the Number of Days of (c*ntinued) 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 Poramtage and Proficiency Piroants. ard Proficiency Percents.' aeW Pollicisney State 42 ( 0.9) 35 ( 0.8) 23 0.0) 276 ( 0.8) 272 ( 1.0) 264 1.3) Nation 45 ( 1.1) &? ( 0.9) 23 1.1) 265 ( 14) 286(14) 250 ( 1.9) PARENTS'JDUCATION HS non-graduate State 32 ( .4* ( 4.5) 37 ( 3.2) ( *4i 31 ghlk* ( 4.0) .41 Nation 36 ( 3.2) 26 ( 3.1) 38 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) HS graduate State 38 ( 1.8) 35 ( 14) 27 ( 2.0) 267 ( 2.1) 262 ( 1.8) 256 ( 2.3) Nation 43 ( 2.4) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.6) 249 ( 2.4) Soots college State 45 ( 2.0) 32 ( 2.5) 24 ( 2.1) 279 ( 1,5) 277 ( 1.9) 270 ( 2.4) Nation 40 ( 1.8) 37 ( 1.6) 23 ( 1.6) 270 ( 3.0) 271 ( 2,5) 253 ( 3.1) College graduate State 44 ( 1.5) 37 ( 1.5) 19( 1.1) 283 ( 1.4) 280 ( 1.2) 275 ( 1.9) Nation 51 ( 1.6) 33 ( 1.2) 18 ( 1.3) 275 ( 2.1) 277 ( 1.7) 265 ( 31) GENDER Mate State 45 ( 1.6) 34 ( 1.3) 21 ( 1.1) 279 ( 1.1) 273 ( 1.3) 268 ( 1.5) Nation 47 ( 1.5) 31 ( 1.4) 22 ( 1.4) 246 ( 2.0) 267 ( 2.1) 250 ( 2.6) Female State 39( 1.6) 36 ( 1.4) 25 ( 1.4) 273 ( 1.3) 271 ( 1.5) 262 ( 1.8) 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). 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 Wyoming TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1N0 NAEP TRIAL STATE ASSESSMENT Woo* dams Alava Undecided, Disagree, Sfrong ly Disagree TOTAL. Perm Cage and !redolency Perceseage and Preecleney Percentage and Prodolemy State 30 ( 0.8) 48 ( 1.0) 22 ( 0.7) 261 ( 0.8) 272 ( 0.9) 200 ( 1A) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 12) 271 ( 1.9) 282 ( 1.7) 251 ( 1.8) RACE/ETHNICITY Mite State 30 ( 1.0) 49( 1.1) 21 ( 0.9) 283 ( 1.0) 275 ( 0.9) 263 ( 1.3) Nation 26 ( 1.6) 48 ( 1.3) 26 ( 1$) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Hispanic State 24 ( .44 ( 32) 47 ( 254 ( 3$) 2.9) 29 245 ( 22) ( 42) Nation 24 ( 2.5) 48 ( 2.6) 28 ( 2.1) 257 ( 5.51 244 ( 2.2) 238 ( 3.8) American Indian State 31 ( 5.7) 43 ( 5.8) 26 44. ( 4.4) ( 441 Nation 23 ( 7.4) 4$ (14.9) .4. ( 44.) 29 ( 9,5) 441 TYPE OF COMMUNITY Extreme rural State 30 ( 1.3) 51 ( 1.7) 19 ( 1.4) 282 ( 1.6) 278 ( 1.6) 264 ( 2.8) Nation 34 ( 270 ( 2.8) 3.9)1 48 ( 252 ( 2.2) 4.1)t 17 444 ( 1.4) ( .44) Other State 31 ( 1.1) 47 ( 1.3) 22 ( 1.0) 282 ( 1.1) 273 ( 1.2) 200 ( 1.9) Nation 27 ( 1.4) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 22) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 138 THE 1990 NAEP TRIAL STATE ASSESSMENT Wyoming TABLE A27 I Students' Perceptions of Mathematics (continued) PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE AS5538MENT StragNIIYA9114. *PP Undecided, Disagree, Strongly Disagree TOTAL and Proliakeval Pireiciancv State 30 ( 0.8) 4$ 1.0) 261 ( 0.8) 272 OA) Nation 27 ( 1.3) 49 12) 24 12 271 ( 1.9) 262 ( 1.7) 251 PARENTS EDUCATIOI 1411 non-graduat State 21 ( 3.4) 48 ( 4.5) 33 ( 261 ( 3.6) ( Nation 50 ( 3.3) 30 ( 3.4 243 ( 2.6) 238 (43) NS graduate State 27 ( 1.9) 49 (2.1) .9 Nation 270 ( 27 ( 2.0) 2.1) 264 47 2.3 251 26 2.3 22 262 ( 21) 255 ( 2.3 245 2.4 Some college State 33 ( 2.2) 4$ ( 2.3) 20 281 ( 12) 276 ( 1.5) MS 2.4 Nation 28 ( 2.5) 47 ( 2.4) 25 12 274 ( 3.1) 267 ( 1.9) 253 32) Casege graduate State 33 ( 1.4) 49 ( 1.4) 18 ( 1.0) 290 ( 1.4) 279 ( 1.3) 268 ( 1.8) Nation 30 ( 2.3) 51 ( 1.8) 19 ( 1.8) 280 2.4) 274 ( 2.2) 208 ( 2.5) OENDR Mak, State 31 ( 1.3) 43 ( 1.5) 21 ( 1.3) 285 ( 1.3) 274 ( 1.2) 261 ( 1.8) Nation 28 ( 1.5) 45 ( 1.2) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Fensate State 29 ( 1.1) 49 ( 1.2) 23 ( 1.0) 277 ( 1.4) 271 ( 1.2) 258 ( 1.6) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 12) 269 ( 2.1) 262 ( 12) 252 t 12) 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). 144 THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment WM truly a collaborative effort amoog staff from State Education Ageacies, the National Center for Education Statistiek (NCES), Educatiosial Testing Service (ETS), Westat, and National Computer Systems (NCS). The program benefitted from the contrilutions of hundrech of individuals at the state and local kvels Governors, Chief State School Officers, State and District Test Direct" State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Fmally, and most importantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (CCSSO) for its considerable contrilutions to the program, especially ks management of the National Assessment Plannhig Project. That project resulted in the mathematics framework and objectives for the assessment and re:mm=1660ns about reporting the results of the program. In particular, we note the significant amtributions of Ramsay Selden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the U.S. Department of Edumtion. Emerson Elliott, NCES Acting Commissiooer, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen GOMA Maureen Tracy, and Raul Garza worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people from school districts, colleges and universities, and State Education Agencies worked tirelessly to help EFS staff develop the assessment and a framework for interpreting the results. Under the NAEP contract to ETS, Archie Lapointe served as the projeet direetor and Ina Mullis as the deputy director. Statistical and psychometric activitim were led by John Mazzeo, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Korner, 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 Monis 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 Thal State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based an 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 aeated the system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Fizzuti. 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 text and the analysts who checked the data. 145 U.& GOVERNMENT PRINTING OFFICE : 1291 0 -- 293-275 QL. 8 (BK. 40) 1 6