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DOCUMENT RESUME ED 330 566 SE 052 076 TITLE The State of Mathematics Achievement in Minnesota: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathcatics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS *Minnesota; National Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In Minnesota, 2,584 students in 97 public so;lools were assessed. This report describes the mathematics proficiency of Minnesota eighth-graders, compares their overall performance to students in the Central region of the United States and the nation (using data from the NAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/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, Minnesota students had an average proficiency of 276 compared to 261 nationwide. Many fewer students (Minnesota-20%; U.S.-12%) appear to have acquired reasoning and problem solving skil.s. (JJN/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS tit) VIZ ,, obi 4 -4 The STATE of Mathe a"cs AleW in MINNESOTA The Trial State Assessment at Grade Eight MSAiLlei U S DEPARTMENT Of EDUCATtON CtM r .11 E Ow. at,ong, Reaearrn and ,,,L,fo.ernent I OUC IONAI. NE SOURCES INFORMATION CE NTER ERICt ;$ Ooc.ment r,as Dee° ,epfncluc.Pti IS rec ev(k<1 trom IMP verson or orgornrrafron ryflritrrisj r Monne < hinvps nave twen made to .mprove. ,eproducl.on c.b..amy _ Po,IS ot re*, or op, S stated tr,7S Ark kr mon, C1C, r+01 ^1..t eSiratrIN. <..preSPnt ottrc <al ci P (705,1 1 pl.,11tr y Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD. the National Assessment of Educational Progress (NAFP) is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1969, assessments have been conducted periodically in reading, mathematics, science, writing, history/geography. and other fields. By making objective information on student performance available to policymakers at the national, state, and local levels. NAEP is an integral part of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics. the U.S. Department of Education. The Commissioner of Education Statistics is responsible. by law, for carrying out the NAEP project through competitive award.s to qualified organizations. NAEP rt_ports directly to the Commissioner, who is also responsible for providing continuing reviews, including validation studies and solicitation of public comment, on NAEP's conduct and usefulness. In 1988. Congress created the National Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The board is resisible for set:A:ling the subject areas to he 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; designing the assessment methodology; developing guidelines and standards for data analysis and for reporting and disseminating results; developing standards and procedures for interstate. regional. and national comparisons; improving the form and use of the National Assessment; and ensuring that all items selected for use in the National Assessment are free from racial, cultural, gender. or regional bias. The National Assessment Governing 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 Education Sacramento. California David P. Battini High School History Teacher Cairo.Durham High School Cairo, New York Parris C. Rattle Teacher Horace Mann Elementary School Miami, Florida Mary R. Blanton Attorney Cromweil, Porter. Blanton 15z. Blanton Salisbury. North Carolina Boyd W. Rochije Attorney Gaass. Bochlje Pella, Iowa Linda R. Bryant Teacher Greenway Middle School Teaeher Cone, Pittsburgh. Pennsylvania Honorabk Michael N. Castle Governor of Delaware Carve! State Office Building Wilmington, Delaware Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hartford, Connecticut Chester E. Finn, Jr. Professor of Education and Public Pohey Vanderbilt University Washington, D.C. Michael S. Glade Wyoming State Board of Educatiim Saratoga, Wyoming t llristine Johnson Principal Abraham Lincoln High School Denver. Colorado John Lindley Principal South Colby Elementary School Port Orefr,u, Washington Carl J. Moser Director of Schools Pre Lutheran Church Missouri Synod International Center St. Louis, Missouri Mark D. Muskk President Southein Regional Education Board Atlanta. Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith, Arkansas Matthew W. Prophet, Jr. Superintendent Portland Oregon School District Portland. Oregon Honorabk William T. Randall Commissioner of Education State Department of Education Denver, Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington. D.C. Howrable Richard W. Riley Attorney Nelson. Mullins, Riley and Scarborough Columbia, South Carolina Thomas Topuzes Attorney Law Offices of Frank Rogozienski Coronado, California Herbert J. Walberg Professor of Education University of Illinois Chicago, Illinois Assistant Secretary for Educational Research and Improvement (Fs-Officio) 1.7.S. Department of Education Washington, DC. Rny Truby Executive Director, NAGB Washington, D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of M thematics Achievement in MINNESOTA The Trial State Assessment at Grade Eight THE NATION'S REPORT CARO Report No: 21-ST-02 June 1 9g1 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bmno V. Mdnno Acting Assistant Sectetary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Library of Cccgress, Catalog Card Number: 91-61478 ISBN: 0-88685-14-9 The work upon which this publication is based was performed for the National Center for Education Statistics, Office of Educational Research and Improvement, by Educational Testing Service. Educational Testing Service is an equal opportunity/affirmative action employer. Educational Testing Service, ETS, and ars registered trademarks of Educational Testing Servio Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION 7 Overview of the 1990 Trial State Assessnient 8 This Report 9 Guidelines for Analysis 12 Profile of Minnesota 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Minnesota Public Schools? 17 Chapta 1. Students' Mathematics Performance 18 I Awe ls of Mathematics Proficiency 19 Content Area Performance 19 Chapter 2. Mathematics Performance by Subpopulations 24 Race / Ethnicity 24 Type of Community 27 Parents' Education Level 19 Gender Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT III PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics' 39 Cuniculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Delivered' 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used" 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Lighth-Grade Mathematics? 67 Educational Backgound 68 Summaly 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX si DATA APPENDIX 97 iv THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota ME NATION'S REPORT CARO EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Hucational Progress (NAFP), which included -- for the first time in the projeci's history -- a provision authorizing voluntary state-by-state :1essments on a tria1 basis, in addition to continuing its primary mission, the national inents that NALP has conducted since its inception. As a result of the leslation, the 1990 NALP progfam included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each of 37 states, the District of Columbia. and two territories in February 1990. The sample was carefully designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the progam. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. THE 1990 NAEP TRIAL STATE ASSESSMENT 1 Minnesota In Minnesota, 97 public schools participated in the assessment. The weighted school participation rate was 93 percent, which means that all of the eighth-grade students in this sample of schools were representative of 93 percent of the eighth-grade public-school students in Minnesota. 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 S 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 activitits and/or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 0 percent and 3 percent of the population, respectively. In total, 2,584 eighth-grade Minnesota public-school students were assessed. The weighted student participation rate was 95 percent. This means that the sample of students who took part in the assessment was representative of 95 percent of the eligible eighth-grade public-school student population in Minnesota. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from Minnesota on the NAEP mathematics scale is 276. 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, NAM) 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 NAM' scale. 2 THE 1990 NAEP TRIAL STATE ASSTSSMENT Minnesota In Minnesota, 99 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving wifn whole numben (level 200). However, many fewer students in Minnesota (20 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 Minnesota performed higher than students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Thal State Assessment permits reporting on the performance of various subpopulations of the Minnesota eighth-grade student population defined by raceiethnicity, type of community, parents' education level, and gender. In Minnesota: White students had higher average mathematics proficiency than did Black. Hispanic, or Asian students. Further, a geater percentage of White students than Black or Hispanic students and about thc same percentage of White as Asian students attained level 300. The results by type of community indicate that the average mathematics performance of the Minnesota students attending schools in advantaged urban areas was about the same as that of students attending schools in extreme rural areas and areas classified as "other". In Minnesota, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 30 points higher than that of students whose parents did not graduate fwm high school. The results by gender show that there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in Minnesota. In addition, there was no difference between the percentages of males and females in Minnesota who attained level 300, Compared to the national results, females in Minnesota performed higher than females across the country; males in Minnesota performed higher than males across the countr. 1, 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 3 Minnesota A Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information about student achievement. Some of the salient results for the public-school students in Minnesota are as follows: About half of the students in Minnesota (52 percent) were in schools where mathematics was identified as a special priority. This is about the same percentage as that for the nation (63 percent). In Minnesota, 80 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in Minnesota were taking eighth-grade mathematics (54 percent) than were taking a course in pre-algebra or algebra (42 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 Minnesota spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 10 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions Students whose teachers placed 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. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota In Minnesota, 12 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed. while 23 percent of the students were taught by teachers who got only some or nooe of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Minnesota, 20 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. In Minnesota, 44 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (76 percent) had teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in Minnesota 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 Minnesota (15 percent) watched one hour or less of television each day; 7 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. 4 A THE 1990 NAEP TRIAL STATE ASSESSMENT 5 Minnesorq THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Louisiana Arkansas Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Minnesota This repc t describes the performance of the eighth-grade public-school students in Minnesota and consists of three sections: This Introduction provides background information about the Trial State Assessment and this report. It also provides a profile of the eighth-grade public-school students in Minnesota, Part One describes the mathematics performance of the eighth-grade public-school students in Minnesota, the Central region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Minnesota, the Central region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survey instrument for the eighth grade and shall conduct a demonstration of the instrument in 1990 in States which wish to participate, with the purpose of determining whether such an assessment yields valid, reliable State representative data. (Section 406 (i)(2)(C)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(i))) As a result of the legislation, the 1990 NAFP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 14 8 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patterned after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that auth.)rized the Trial State Assessment, the federal government arranged for the National Science Foundation and the U.S. Department of Education to issue a special grant to the Council of Chief State School Officers in mid-1987 to develop the objectives. The development process included careful attention to the standards developed by the National Council of Teachers of Mathematics,' the formal mathematics objectives of states and of a sampling of local districts, and the opinions of practitioners at the state and local levels as to what content should be assessed. There was an extensive review by mathematics educators, scholars, states' mathematics supervisors, the National Center for Education Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-grade public-school students in Minnesota, in the Central 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 Minnesota 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. lise of the regional and national results from the 1990 national NAEP program was necessary because the voluntary nature of the Trial State Assessment Program did not guarantee representative nat.nal or regional results, since not every state participated in the program. National Council of Teachers of Mathernancs, Curricuhim and Evaluation Standardv pr School Mathematics (Reston, VA: National Council of Teaclrrs of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 9 Minnesota RACE/ETIENICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Pmcedural 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 Minnesota. 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 ittend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The repo:ting of results by each type of community was also subject to a minimum student samplc 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 gaduated college. The response indicating the higher level of education was selected for reporting. 10 l'HE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota GENDER Results are reported .-.,eparately for males and females. REGION The United States has been divided into four regions: Northeast, Southeast, Central, and West. States included in each region are shown in Figure 1. All SO states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type, Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. FIGURF 1 I Regions of the Country THE NATION'S REPORT CARD NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Alabama Illinois Alaska Delaware Arkansas Indiana Arizona District of Columbia Florida Iowa California Maine Gaorgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana New Jersey North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohio Oklahoma Rhode Island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT 11 Minnesota Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those goups 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 significa.nt), 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 goup 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 p-oups, the confidence interval included zero, and thus no difference could be assumed between the goups. When three or more groups are being compared, a Bonferroni procedure is also used, The statistical tests and Bonferroni procedure are discussed in geater detail in the Procedural Appendix. S 12 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota 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 algebra or pre-algebra is giver. 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 that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STA' E ASSESSMENT 13 Minnesota Profile of Minnesota EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in Minnesota, the Central region, and the nation. This profile is based on data collected from the students and schools participating in the Trial State Assessment. TABLE 1 I Profile of Minnesota Eighth-Grade I Public-School Students PERCENTAGE OF STUDENTS - WOO NAV TRIAL STATE ASSESSMENT Minnesota Central Nation - DEMOGRAPHIC SUBGROUPS 1 Race/Ethnicity White Black Hispamc Asian American Indian Type of Community Advantaged urban Disadvantaged urban Extreme rural Other Parents' Education Did not finish high school Graduated high school Some education after high school Graduated college Gender Male Female Percentap Porcentage Percentage 90 ( 0.9) 79 ( 2.6) 70 ( 0.5) 2 ( 0.5) 13 ( 3.2) 16 ( 0.3) 3 ( 0.4) 5 ( 1.0) 10 ( 0.4) 3 ( 0.4) 1 ( 0.4) 2 ( 0.5) 2 ( 0.5) 1 ( 0.4) 2 ( 0.7) 24 ( 3.3) 3 ( 3.1) 10 ( 3.3) 0 ( 0.0) 10 ( 4.3) 10 ( 2.8) 29 ( 4.6) 8 ( 6.0) 10 ( 3.0) 47 ( 5.3) 79 ( 7.7) 70 ( 4.4) 4 ( 0.3) 7 ( 0.9) 10 ( 0.8) 27 ( 1.0) 33 ( 2.1) 25 ( 1.2) 22 ( 0.8) 19 ( 0.9) 17 ( 0.9) 42 ( 1-2) 35 ( 1.8) 39 ( 1.9) 50 ( 1.0) 50 ( 1.4) 51 ( 1.1) 50 ( 1.0) 50 ( 1.4) 49 ( 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. The percergages for Race/Ethnicity may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 :20 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota SCHOOLS AND STUDENIS ASSESSED Table 2 provides a profile summarizing participation data for Minnesota schools and students sampled for the 1990 Trial State Assessment. In Minnesota, 97 public schools participated in the assessment. The weighted school participation rate was 93 percent, which means that all of the eighth-grade students in this sample of schools were representative of 93 percent of the eighth-grade public-school students in Minnesota. TABLE 2 j Profile of the Population Assessed in Minnesota 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 108 3 94 5 3 97 EIGHTH-GRADE PUBLIC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students selected to part!cipate in the assessment Number of students withdrawn from the assessment Percentage of students who were of Limited English Proficiency Percentage of students excluded from the assessment due to Limited English Proficiency Percentage of students who had an Individualized Education Plan Percentage of students excluded from the assessment due to Individualized Education Plan status Number of students to be assessed Number of students assessed 95% 2,907 105 1% 0% 8% 3°Ai 2,715 2,584 TH E 1990 NAEP TRIAL STATE ASSESSMENT 15 Minnesota !n 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 because they were categorized as LEP or had an IEP represented 0 percent and 3 percent of the population, respectively. In total, 2,584 eighth-grade Minnesota public-school students were assessed. The weighted student participation rate was 95 percent. This means that the sample of students who took part in the assessment was representative of 95 percent of the eligible eighth-grade public-school student population in Minnesota. 16 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Minnesota 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 scaie, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficiency of eighth-wade public-school students in Minnesota. Chapter 1 compares the overall mathematics performance of the students in Minnesota to students in the Central 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. 4. LI THE 1990 NAEP TRIAL STATE ASSESSMENT 17 Minnesota CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from Minnesota on the NAEP mathematics scale is 276. This proficiency is higher than that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency NALP Mathematics Scale 200 225 250 275 300 500 n.- Average Proficiency 1-1,04 Minnesota Central Nation 216 265 261 ( ( ( 0.9) 2.8) 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 7±- 2 standard errors of the esnmated mean (95 percent confidence interval, denoted by P44). 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 moans that with about 95 percvnt certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 18 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the result! from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at thc 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 =practical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are Oven in Figure 3. It is important to note that the definitions of these levels are based solely on student performance on the 1990 mathematics assessment. The levels arc not judgmental standards of what ought to bc achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In Minnesota, 99 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 Minnesota (20 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 Minnesota, Central region, and national results for each content area. Students in Minnesota performed higher than students in the nation in all of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Minnesota FIGURE 3 I Levels of Mathematics Proficiency THE NATION'S REPORT Nip CARD I 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-step word problems and seleCt the greatest four-diglt 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 siudents can recognize translations of word problems to numerical sentences and extend simple pattern sequences. LEVEL 250 I Simple Multiplicative Reasoning and Two-Step Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to other elementary two-step word problems. In these basic problem-solving situations, they can identify missing or extraneous information and have some knowledge of when to use computational estimation. They have a rudimentary understanding of such concepts as whole number place value, "even," "factor," and "multiple." in measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple prnblems. 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 Minnesota FIGURE 3 I Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasoning and Problem Solving involving Fractions, Docimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations Students at this level are able to represent, interpret, and perform simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, and recognize the equivalence between common fractions and decimals, including pictorial representations. They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expressions, including those with exponents and negative integers. In measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions 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. LEVEL 350 Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability Students at this level have extended their knowledge of nurntier and algebraic understanding to include some properties of exponents. They can recognize scientific notation on a calculator and make the transition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles to solve problems. They can find the circumferences of circles and the surface areas of solid figures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirPct measurement. These students alSo can apply their knowledge of the properties of geometric figures )Ive problems, such as determining the slope of a line. in data analysis, these students can compute means from frequency tables and determine the probability of a simple event. In algebra, they can identify an equation describing a linear relation provided in a table and solve literal equations and a system of two linear equations. They are developing an understanding of linear functions and their graphs, as well as functional notation, including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. THE 3990 NAEP TRIAL STATE ASSESSMENT 21 Minnesota FIGURE 4 I Levels of Eighth-Grade Public-School Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation 1-4.4 1.01"'""rni 1-1041 1-4.0.04 Hal 0-1,0 PM 20 40 so 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within i 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by P+1), If the confidence intervals for the populations da not overlap, there is a statistically significant difference between the populations. 22 THE 1990 NAEP TRIAL STATE ASSESSM ENI Percantage 0 ( 0.1) ( 0.2) ( 0.2) 20 ( 1,1) 12 ( 2.5) 12 ( 1.2) 82 ( 1.0) 70 ( 3.2) 64 ( 1.6) 99 ( 0.3) 90 ( 0.9) 97 ( 0.7) Minnesota 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 0 200 225 250 275 300 Average Prolicleicy 279 ( 1.0) 270 ( 2.7) 266 ( 1.4) 272 ( 1.1) 263 ( 3.4) 256 ( 1.7) 273 ( 1.1) 262 ( 3.1) 259 ( 1.4) 279 ( 0.9) 265 ( 3.2) 262 ( 1.8) 274 ( 0.9) 263 ( 2.1) 260 ( 1.3) 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 14-4). If the confidence intervals for the populations do not overlap, there is a statisucally sigrnficant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT 23 CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY' The Trial State Assessment results can be compared according to the different racialjethnic groups when the number of students in a raciaLethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Black, Hispanic, and Asian students from Minnesota are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black, Hispanic, or Asian students. Figure 7 presents mathematics perfbrmance by proficiency levels. The figure shows that a geater percentage of White students than Black or Hispanic students and about the same percentage of White as Asian students attained level 300. 24 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota FIGURE 6 I Average Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity NAEP Mathematics Scale 200 225 250 275 300 500 Tie NOWT CMO Average Proficiency 1111,004 0-001 1formsw4 Minnesota Wtilte -VS ( Black 2* 4.9$ Hispanic ( 3:7) Asian IN ( 44) Central White 272 ( 2.6) Black 231 3.6)f Hispanic 14" ( a") Asian ( ***) Nation White IN ( 1.5) Black 2 ( 2.8) Hispanic 243 ( 2A) Asian 200 ( 5.6)1 The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within t 2 standard errors of the estimated mean (95 percent confidence interval, denoted byI-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 0") THE 1990 NAEP TRIAL STATE ASSESSMENT 25 Minnesota FIGURE 7 I Levels of Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian LEVEL 250 State White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian LEVEL 200 Stat. White Black Hispanic Asian Region White Black Hispanic Asian Nation White Black Hispanic Asian 1-0-00mq 111141 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-+4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. t Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 22 ( 1.2) 6 ( 2.8)1 3 ( 2.5) 13 ( 5.7) 15 ( 1.5) 2 ( 1.3) 3 ( 1.1) 31 ( 6.2)1 85 ( 0.9) 34 ( 7.4)1 37 ( 5.8) 71 ( 5.8) 75 ( 3.1 ) 23 ( 4,7)1 :us ) puot **) 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) SO ( 5.6)1 100 ( 0.2) 87 ( 6.5)1 92 ( 3.3) $118 ( 1.9) 100 ( 0.4) 91 ( 4.4)i mut ) '4" ea ( 0.4) 1118 ( 3.1) 93 ( 1.6) 97 ( 2.5)1 Minnesota TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, extreme mai areas, and arms classified as "other". (These are the "type of community" groups in Minnesota with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Minnesota students attending schools in advantaged urban areas was about the same as that of students attending schools in extreme rural areas and areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community wwwAr NAEP Mathematics Scale 200 225 250 275 300 SOO WC INONT CAM Average Proficiency Minnesota tr Advantaged urban 277 1.7) til Extreme rural 1.45) 144 Other 271 ( 1.3) Central Advantaged urban .molg ( *el Extreme rural w 1--1004 Other 1111 ( 3.4) Nation Advantaged urban 211 ( 3AI 1-4144.04 Extreme rural 201 ( Other 2111 ( 1.6) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted 'by 1-4-1). 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 re:,able estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 27 Minnesota FIGURE 9 LEVEL 300 State Adv. urban Ext. rural Other Region My. urban Ext. rural Other Nation Mv. urban Ext. rural Other LEVEL 250 State Adv. urban Ext. rural Other Region Adv. urban Ext. rural Other Nation Mv, urban Ext. rural Other LEVEL 200 state Adv. urban Ext. rural Other Region Mv. urban Ext. rural Other Nation Mv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community 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 1-44). If the coi-.fidence 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 student.$). Percentage 22 ( 2.3) 18 ( 2.1) 23 ( 1.9) *) 13 ( 2.9) 4.8)) ( 2.3)1 12 ( 1.2) 82 ( 1.8) 84 ( 1.9) 85 ( 1.7) .** ) pm* * ) 73 ( 4.2) 83 ( 4.6)1 58 ( 6.2)1 $4 ( 2.3) 90 ( 0.6) 100 ( 0.3) 100 ( 0.2) *Am ) RI* ) 90 ( 0.9) 100 ( 0.0) 97 ( 2.8)1 97 ( 1.0) 100 25 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics pmficiency (see Figures 10 and 11). In Minnesota, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 30 points higber 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 Minnesota (42 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 4 percent for Minnesota and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School i Mathematics Proficiency by Parents' Education Minnosota HS non-graduate HS graduate Some college College graduate Cntral HS non-graduate HS graduate Some college College graduate Nation HS non-graduate HS graduate Some college College graduate The standard errors are presented m 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 14-9. If the confidence intervals for the populations do not overlap, there is a statistically significant difTerence between the populations. *** Sample size is insufficient to permit a reliable esumate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Minnesota r-v NATION'S IOW FIGURE 11 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. Region HS non-grad. HS graduate SOO* COltege College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad, HS graduate Some college College WV. 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. 5 ( 2.8) ( 1.7) 25 ( 2.0) 30 ( 1.7) PIXCX ( ***) ( 3.9) 14 ( 3.4) 17 ( 3.7) 1 ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.9) 59 ( 6.7) 72 ( 2.1) 92 ( 1.5) 99 ( 1.4) ROM ( Ad) 96 ( 4.1) 75 ( 5.1) 79 ( 3.9) 37 ( 4.6) 56 ( 2,7) 71 ( 2.6) 75 ( 2.0) 97 ( 2.3) 99 ( 0.5) 100 ( 0.0) 100 ( 0,3) nom ( .) ( 1.2) 100 ( 0.0) 99 ( 0.9) 96 ( 1.9) ( 0.8) 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, *** Sample size is msufficient to permit a reliable estimate (fewer than 62 students). 100 g.) 30 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 ( 0.7) SO ( 0.7) Minnesota GENDER As shown in Figure 12, there appears to be no difference in the average mathematics proficiency of eighth-grade males and females attending public schools in Minnesota. Compared to the national results, females in Minnesota performed higher than females across the country; males in Minnesota performed higher than males across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender Minnesota Male Female Central Nate Female Nation Male Female The nandard 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 corfidence 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. As shown in Figure 13, the= was no difference between the percentages of males and females in Minnesota who attained level 200. The percentage of females in Minnesota who attained level 200 was greater than the percentage of females in the nation who attained level 200. Also, the percentage of males in Minnesota who attained level 200 was greater than the percentage of males in the nation who attained level 200. THE 1940 NAEP TRIAL STATE ASSESSMENT 31 Minnesota FIGURE 13 I Levels of Eighth-Grade Public-School I Mathematics Proficiency by Gender LEVEL 300 State Male Female Region Male Female Nation Male Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female 20 40 ea 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-0-4). 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 22 ( 1.5) 19 ( 1.2) 14 ( 4.8) ( 2.3) 14 ( 1.7) 10 ( 1.3) 811 ( 1.3) 92 ( 1.3) ( 3.3) 71 ( 4.0) 64 ( 2.0) 54 ( 1.8) 91) ( 0.4) 99 ( 0.3) 99 ( 0.6) 011 ( 1.2) 97 ( 0.9) 97 ( 0.8) Minnesota In addition, there was no difference between the percentages of males and females L.1 Minnesota who attained level 300. The percentage of females in Minnesota who attained level 300 was geater than the percentage of females in the nation who attained level 300. Also, the percentage of males in Minnesota who attained level 300 was greater than the percentage of males in the nation who attained level 300. CONTENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Minnesota TABLE 3 I Eighth-Grade Public-School Mathematics I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1910 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Massursat" 1 "saw" Data Analysis, Statistics' ana Probability "IbraFixoctkomand TOTAL PraNciancy Pnaliciancy Prattolancy Prods:lam Prodloisncy State 279 ( 1.0) 272 ( 1.1) 273 ( 1.1) 279 ( 0.9) 274 0.9) Region 270 ( 2/) 263 ( 3.4) 262 ( 3.1) 265 ( 3.2) 263 2.1) Nation 208 ( 1.4) 2W ( 1.7) 259 ( 1.4) 262 ( 1.8) 240 1.3) RACE/ETItNICITY 11111 its State 262 ( 1.0) 275 ( 1.1) 275 ( 1.0) 282 ( 0.8) 278 ( 0.0) Region 276 ( 2.9) 271 ( 3.7) 268 ( 3.0) 273 ( 3.1) 289 ( 2.3) Nation 273 ( 1.6) 267 ( 2.0) 267 ( 1.5) 272 ( 1.8) 268 ( 1.4) Slack State 242 ( 4.6)1 233 ( 7.8)1 235 ( 5.7)1 245 ( 5.8)1 240 ( 6.0)1 Region 241 ( OS)! 223 ( 3.5)1 231 ( 4.2)1 225 ( 7.0)1 231 ( 1.9)1 Nation 244 ( 3.1) 227 ( 3.6) 234 ( 2.8) 231 ( 3.8) 237 ( 2.7) Hispanic State Region 245 ( ( 4.7) ...) 228 ( ( 4.7) ...) 241 ( ( 3.6) ...) 240 ( ( 4.5) ...) 239 ( ( 4.2) ***) Nation 248 ( 2.7) 238 ( 3.4) 243 ( 3.2) 239 ( 3.4) 243 ( 3.1) Asian State Region 271 ( ( 5.0) 252 ( ( 6.3) ...) 267 ( 4.9) 261 ( ( 52) 270 ( ( 82) Nation 285 ( 5.9)1 278 ( 6.3)1 275 ( 5.9)1 282 ( 6.9)1 278 ( 6.7)1 TYPE Of COMMUNITY Advantagad urban State Region 280 ( ( 1.9) "") 272 ( ( 2.1) ...) 273 ( 1.8) 282 (( 1.8) ...) Nation 283 ( 3.2)! 281 ( 3.2)1 277 ( 5.2)1 285 ( 4.8)1 277 ( 4.8)1 Extrema rural State Region 280 ( ( 2.1) ...) ( ...) 273 ( ( 2.1) ...) 278 ( ( 1.7) .4.) .4. ( ...) Nation 258 ( 4.3)1 254 ( 4.2)1 253 ( 4.5)1 257 ( 5.0)I 256 ( 44)1 Other' State 282 ( 1,4) 275 ( 1.7) 276 ( 1.6) 282 ( 1.7) 277 ( 1.3) Region 273 ( .3.5) 266 ( 4.3) 264 ( 3.7) 267 ( 4.1) 265 ( 2.8) Nation 288 ( 1.9) 257 ( 2A) 259 ( 1.7) 261 ( 2.2) 261 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE 3 I Eighth-Grade Public-School Mathematics (continued) I Content Area Performance by Subpopuiations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Nuatdael add Operations Meaurement Geometry Ana Data lysis, Statistics, and Probability and Functions TOTAL Proaciency Proficiency Proncioncy !Widow/ Preadincy State 279 ( 1.0) 272 ( 1.1) 273 ( 1.1) 279 ( 0.9) 274 ( 0.9) Region 270 ( 2.7) 263 ( 3.4) 262 ( 3.1) 265 ( 3.2) 263 ( 2.1) Nation 266 ( 1.4) 258 ( 1.7) 256 ( 1.4) 202 ( 1.8) 200 ( 1.3) PARENTS' EDUCATION NS nort-graduate State Region 258 ( 251 ( 3.9) .44) 257 ( Mk* ( 4.0) Man 253 ( 4.0) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) 240 ( 3.1) 242 ( 3.0) HS graduate State 268 ( 1.8) 258 ( 2.0) 262 ( 1.8) 267 ( 1.5) 262 ( 1.4) Region 289 ( 2.5) 258 ( 3.8) 257 ( 9.4) 200 ( 3.2) 250 ( 3.4) Nation 259 ( 1.8) 248 ( 2.1) 252 ( 1.6) 253 ( 22) 253 ( 2.0) Some college State 285 ( 1.4) 284 ( 1.8) 278 ( 1.3) 266 ( 1.3) 280 ( 1.3) Region 275 ( 32) 270 ( 5.7) 264 ( 4.9) 273 ( 4.7) 266 ( 3.7) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 2621 2.2) College graduate State 288 ( 1.4) 281 ( 1.3) 281 ( 1.2) 269 ( 1.2) 263 ( 1$) Region 277 ( 4.2) 270 ( 4.4) 270 ( 4.3) 273 ( 4.5) 271 ( 3-1) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 276 ( 2.2) 273 ( 1.7) GENDER Male State 279 ( 1.2) 278 ( 1.3) 273 ( 1.4) 279 ( 1.2) 272 ( 1.2) Region 271 ( 3.9) .287 ( 4.8) 264 ( 3.7) 265 ( 3.4) 263 ( 2.2) Nation 266 ( 2.0) 262 ( 2.3) 260 ( 1.7) 2e2 ( 2.1) 260( 1.8) Female State 279 ( 1.2) 268 ( 1.4) 272 ( 1.2) 279 ( 1.2) 275 ( 1.1) Region 270 ( 2.7) 259 ( 3.4) 200 ( 3.1) 26$ ( 4.0) 262 ( 2.8) Nation 266 ( 1.4) 253 ( 1.6) 258 ( 1.5) 281 ( 1.9) 260 ( 1.4) The standard errors of the estimated statistics appear in parentheses. It can be said with a certainty that, for each population of interest, the value for the entire population is within ± 2 of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate students). bout 95 percent standard errors (fewer than 62 ft I THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Minnesota 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, teacher 'students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information on student 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, fir results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. THE 1990 NAEP TRIAL STATF: ASSESSMENT 37 Minnesota 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 stratesOes 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 future academic achievement. Yet, as shown in Chapters 3 and 7, large proportions of students report having spent much more time each day watching television than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instnictional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 4 3 38 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.' This chapter focuses on curricular and instructional content issues in Minnesota public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffmg. Some of the salient results are as follows: About half of the eighth-grade students in Minnesota (52 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curtis McKnight, ci al., The Underachieving Curriculum. Assessing U.S. School Mathematks from an International Perspective, A Nati(' -al Report on the Second International Mathematics Study (Champaign, Stipes Publishing Company, 1987). Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 19 Minnesota In Minnesota, 80 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Many of the students in Minnesota (84 percent) were taught mathematics by teachers who teach only one subject. a More than half (63 percent) of the students in Minnesota were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was equally prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in I Minnesota Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation _ Percentage of eighth-grade students in public schools that identified mathematics as recelvklg special emphasis in school-wide goals and objectives, instruction, In-service training, etc. Percentage of eighth-grade public-school students who are offered a course in algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachees who teach only mathematics Percentage of eighth-grade students in public schools who are assigned to a mathematics dan by their abNity in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics Instruction per week Percentage Parcente90 Penentage 52 ( 4.5) 70 (13.8) 83 ( 6.9) 80 ( 4.1) 89 (15.4) 76 ( 4.6) 84 ( 3.1) $7 ( 7.8) 91 ( 3.3) 63 ( 4.0) 00 ( 5.7) 63 ( 4.0) 42 ( 4.0) 25 ( 8.6) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in Minnesota are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in Minnesota were taking eighth-grade mathematics (54 percent) than were taking a course in pre-algebra or algebra (42 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pm-algebra or algebra. Students in Minnesota who were enrolled in pre-algebra or algebra courses exhibited higher average mathtmatics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pm-algebra and algebra courses may be the more able students who have already mastered the general eiegh-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Mkinesota Central Nation _ Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency What kind of mathematics class are you taking this year? Eighth-grade mathematics 54 ( 3.0) si 4.8) 62 ( 2.1) 266 ( 1.3) 255 ( 3.1) 251 ( 1.4) Pre-aigebra 25 ( 2.4) 22 ( 4.3) 19 ( 1.9) 281 ( 1.1) 276 ( 3.1)1 272 ( 2.4) Algebra 17 ( 1.4) 15 ( 2.8) 15 ( 1.2) 303 ( 1.6) 289 ( 5.4) 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Minnesota Further, from Table A5 in the Data Appendix:4 About the same percentage of females (42 percent) and males (42 percent) in Minnesota were enrolled in pre-algebra or algebea courses. In Minnesota, 43 percent of White students, 29 percent of Black students, 30 percemt of Hispanic students, and 46 percent of Asian students were enrolled in pre-algebra or algebra courses. Similarly, 41 percent of students attending schools in advantaged urban areas, 40 percent in schools in extreme rural areas, and 41 percent in schools in areas classified as "other" were enrolled in pre-algebra or algebra courses. MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in Minnesota spent either 15 or 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes daily. Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix): In Minr,esota, 2 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 2 percent of the students in Minnesota 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 7 42 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota The itsults by race/ethnicity show that 2 percent of White students, 1 percent of Black students, 1 percent of Hispanic students, and 8 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 2 percent of White students, 2 percent of Black students, 6 percent of Hispanic students, and 6 percent of Asian students spent no time doing mathematics homework. In addition, 1 percent of students attending schools in advantaged urban areas, 1 percent in schools in extreme rural areas, and 4 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In cnmparison, 2 percent of students attending schools in advantaged urban areas, 0 percent in schools in extreme rural areas, and 2 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 10 NAEP TRIAL STATE ASSESSMENT Mktnesota Central Nation Percents,. and Pro lidera* 2 ( 0.5) Percentage and Prollicloncy 1 ( 0.8) *IS ( Mel Percentage and Pr*: fancy ( 0.3) 4.1 About how much time do students spend on mathematics homework each day? None 15 minutes 48 ( 3.4) 34 ( 7.1) 43 ( 4.2) 273 ( 1.5) 255 ( 4.1) 250 ( 2.3) 30 minutes 42 ( 3.3) 48 ( 9.8) 43 ( 43) 278 ( 1.8) 272 ( 3.5) 203 ( 2.6) 45 minutes 7 ( 1.6) 13 ( 6.0) 10 ( 1.9) 290 ( 4.0)I 261 (12.5)I 272 ( 5.7)1 An hour or more 2 ( 1.1) 6 ( 2.3) 4 ( 0.9) 287 ( 8.3)! ( 44) 276 ( 5.1)1 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 valt, for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Minnesota 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 _ . 1900 NAEP TRIAL STATE ASSESSMENT Minnesota Centre! Nation , Porto Idw and lreackagy Peewits. Mid Pnifisieney Percentage Wel Proliamey About how much time do you usually spend ach day on mathematics homework? None 10 ( 271 ( 0.7) 2.4) 7 (1.4) 441 ( 251 ( 0.5) 2.5) 15 minutes 33 ( 1.3) 34 ( 4.8) 31 ( 2.0) 278 ( 1.2) 2e0 ( 3.8) 264 ( 1.9) 30 minutes 30 ( 1.0) 32 ( 2.3) 32 ( 1.2) 278 ( 1.3) 264 ( 3.8) 263 ( 1.9) 45 minutes 15 ( 1.0) 15 ( 1.2) 18 ( 1.0) 278 ( 1.8) 285(4.0) 288 ( 1.9) An hoar or more 12 ( 1.0) 12 ( 3.4) 12 ( 1.1) 214 ( 1.8) 262 ( 8.2)1 25$ ( 3.1) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). And, according to the students (Table 7 and Table A7 in the Data Appendix): In Minnesota, 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, 12 percent of the students in Minnesota and 12 percent of students in the nation spent an hour or more each day on mathematics homework. The results by race/ethnicity show that 11 percent of White students, 14 percent of Black students, 15 percent of Hispanic students, and 22 percent of Asian students spent an hour or more on mathematics homework each day. In comparison, 10 percent of White students, 10 percent of Black students, 7 percent of Hispanic students, and 4 percent of Asian students spent no time doing mathematics homework. 4 :4 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota In addition, 11 percent of students attending schools in advantaged urban areas, 14 percent in schools in extreme rural areas, and 10 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 9 percent of students attending schools in advantaged urban areas, 9 percent in schools in extreme rural areas, and 11 percent in schools in areas classified as "other" spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement.' Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless 4. of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of leachers of Mathematics, 1989). 50 THE 1990 NAEP TRIAL STATE ASSESSMENT 45 Minnesota The responses of the assessed students' teachers to the topic emphasis questions for each content area were combined to create a new variable. For each question in a particular content area, a value of 3 was given to "heavy emphasis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations 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 Minnesota TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT 1 Minnesota I Central Nation Teacher "emphasis" categories by content areas Percentage and Pattie:henry Percentage and Proficiency Percentage end Proficiency Numbers and Operations Heavy emphasis 36 ( 3.3) S4 ( 7,2) 4$ ( 3..) 275 ( 1.8) 264 ( 4.3) 200 ( 1i) Little or no emphasis 13 ( 1,7) 13 ( 4.5) 15 ( 2.1) 301 ( 22) 285 ( 6.5)1 287 ( 3.4) Measurement Heavy emphasis 12 ( 2.2) 15 ( 5.7) 17 ( 3.0) 208 ( 4.1) 247 (12.5)1 250 ( $.8) Little or no emphasis 47 ( 3.8) 42 ( 9.7) 33 ( 4.0) 277 ( 1.8) 270 ( 7.7)1 272 ( 4.0) Geometry Heavy emphasis 19 ( 3.0) 26 ( 7.0) 2$ ( 3.8) 270 ( 2.5) 261 ( 7.9)I 260 ( 3.2) Little or no emphasis 27 ( 275 ( 2.9) 2,1) 3.5 ( 261 ( 7.2) 9.0)1 21 264 ( 3.3) ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 8 ( 1.8) 12 ( 2.5) 14 ( 2.2) 287 ( 3.3)1 262 ( 7.5) 269 ( 4.3) Little or no emphasis 89 ( 2.6) 57 ( 8.8) 53 ( 4.4) 279 ( 1.3) 264 ( 5.6)1 261 ( 2.9) Algebra and Functions Heavy emphasis 50 ( 32) 50 ( 7.6) 48 ( 3.8) 285 ( 13) 273 ( 3.6) 275 ( 2.5) Little or no emphasis 8 ( 1.3) 19 ( 3.9) 20 ( 3.0) 248 ( 3.4) 242 ( 5.5)1 243 ( 3.0) The standard errors of the estimated stausucs 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. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 Mbutesota SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: About half of the eighth-grade students in Minnesota (52 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Minnesota, 80 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. A greater percentage of students in Minnesota were taking eighth-grade mathematics (54 percent) than were taking a course in pre-algebra or algebra (42 percent). Across the nation, 62 percent were taking eighth-pude 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 Minnesota spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. In Mimiesota, 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, 12 percent of the students in Minnesota 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 STATE. ASSESSMENT Minnesota CHAPTER 4 yazo -22-3 IR 11111111111111111111111111 11111111111111 RI 11111111111111111111a111111 111M101111111114111111 11111111L1111.11111/111111 EV AMMO.. oinessourramos lena air MOM 211111111,411Nou JOU. 11111111IM 41111.8111111111111111111 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 Ftudents, selecting and tailoring methods for students with different styles of learning or for those who come from different cultural backgrounds is an important aspect of teaching.° An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. ° National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematks (Reston, VA: National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Minnesota From Table 9 and Table A9 in the Data Appendix: In Minnesota, 12 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 23 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Minnesota, 13 percent of students attending schools in advantaged urban areas, 16 percent in schools in extreme rural areas, and 10 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in Minnesota, 9 percent of students attending schools in advantaged urban areas, 23 percent in schools in extreme rural areas, and 26 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had higher mathematics achievement levels than those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1S00 NAEP TRIM_ STATE ASSESSMENT Minnesota Central 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 ad the resources I need. I get most of the resources I need. I get some or none of the ources I need Percentage and Proficiency Percentage Percentage and and Proficiency Proaciency 12 ( 281 ( 2.1) 2.8) 8 ( .0* ( 2.4) 13 ( 265 ( 2.4) 42) 65 ( 3.7) 45 ( 7.8) 56 ( 4.0) 276 ( 12) 271 ( 2.2)1 265 ( 2.0) 23 ( 3.8) 47 ( 7.3) 31 ( 4.2) 273 ( 1.9) 259 ( 3.5) 261 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors er the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r J 50 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' 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: Less than half of the students in Minnesota (43 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics pmblems in small groups (7 percent). The largest percentage of the students (72 percent) used objects like nilers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (9 percent). In Minnesota, 73 percent of the students were assigned problems from a mathematics textbook almost every day; 4 percent worked textbook problems about once a week or less. Less than half of the students (39 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (29 percent). 7 Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Curriadum. Eighty-second Yearbook of the National Society for the Study of Education (Chicago, I L: University of Chicago Press, 1983). G THE 1990 NAEP TRIAL STATE ASSESSMENT 51 Minnesota TABLE 10 I Teachers' Reports on Patterns of Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1900 NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation A Percentage end Percents. Ind Penisniese and About how often do students work problems in small groups? Preidency Pralicioncy Proficiency At least once a week 43 ( 3.0) 50 ( 7.8) 50 ( 4A) 279 ( 111) 258 ( 4.1) 280 ( 2.2) Less than once a week 50 ( 3.1) 43 ( 8.6) 43 ( 4.1) 273 ( t4) 2138 ( 4.0)1 284 ( 2.3) Never 7 ( 12) ( 4.3) 8 ( 2.0) 279 ( 3.6)1 ***) 277 ( 5.4$ About how often do students use objects Percentage Percentage Percentage like rulers, counting blocks, Or geometric and and solids? Proficiency Proficiency PranameY At least once a week 19 ( 3.3) 15 ( 5.1) 22 ( 3.7) 271 ( 2.1) 255 ( 4.9)1 254 ( 32) Less than once a wopak 72 ( 3.4) 81 ( 8.0) 89 ( 3.9) 276 ( 0.9) 284 ( 3.3) 263 ( 1.9) Now 9 ( 1.8) 290 ( 4S) 4 ( 2.3) 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 Minnesota TABLE 11 I Teachers' Reports on Materials for I Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT klinnoseta Central Nation Percentage Percentage Percentage About how often do students do problems and Mid end from textbooks? Prelioirstay Prelkienay Madam Almost every day 73 ( 3.9) 82 ( 5.8) 82 ( 3.4) 279 ( 1.2) 269 ( 3-11) 267 ( 1.8) Several tknes a week 23 ( 3.9) 32 ( 4.2) 31 ( 3.1) 271 ( 1.8) 252 ( 53) 254 ( 2.9) Alma once a week or less 4 ( 1.3) 250 ( 6.1)I ( 2.7) .4* ( 41 7 ( 1.8) 200 ( 5.1)1 About how often do students do problems Percentage Percentage Percentage on worksheets? and and end Proficiency Prelidoncy Prolkimmy At least several times a week 39 ( 15) 38 ( 83) 34 ( 3.5) 271 ( 15) 252 ( 5.5)1 256 ( 2.3) About once a week 32 ( 3.5) 23 ( 4.8) 33 ( 3.4) 275 ( 1.9) 261 ( 8.1) 2e0 ( 2.3) Lass Man %resift 29 ( 3.8) 39 ( 7.0) 32 ( 3.5) 284 ( 2.2) 278 ( 4.1) 274 ( 2.7) The standard errors of the estimated statistics appear in psrentheses. lt can be said with about 95 percent certainty that, for each population of' interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). The next section presents the students' responses to a corresponding set of questions, as well as the relationship of their responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. THE 1990 NAEP TRIAL STATE ASSESSMENT 53 Minnesota COLLABORATING IN SMALL GROUPS In Minnesota, 45 percent of the students reported never working mathematics problems in small groups (see Table 12); 26 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 I Students' Reports on the Frequency of Small 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 ttAEP TRIAL STATE ASSESSMENT Minnesota Central Nation Percentage and Proficiency Percentage and Proficiency Percentage and Prnficiency How often do you work in small groups in your mathematics class? At toast once a weak 26 ( 2.0) 23 ( 4.6) 23 ( 2.5) 277 ( 1.7) 206 ( 8.5) 258 ( 2.7) Less than once a week 28 ( 1.7) 32 ( 3.3) 2$ ( 1.4) 279 ( 12) 206 ( 3.0) 267 ( 2.0) Nem 45 ( 2.3) 45 ( 8.3) 44( 2.9) 273 ( 1.3) 264 ( 3.4) 261 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standarderrors of the estimate for the sample. Examining the subpopulations (Table Al2 in tbf Data Appendix): In Minnesota, 19 percent of students attending schools in advantaged urban areas, 26 percent in schools in extreme rural areas, and 27 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 26 percent of White students, 39 percent of Black students, 28 percent of Hispanic students, and 25 percent of Asian students worked mathematics problems in small groups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (25 percent and 28 percent, respectively). 54 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota USING MATHEMATICAL OBJECTS Students west asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A13 in the Data Appendix summarize these data: Less than half of the students in Minnesota (39 percent) never used mathematical objects; 23 percent used these objects at least once a week. Mathematical objects were used at least once a week by 21 percent of students attending schools in advantaged urban areas, 29 percent in schools in extreme rural arms, and 20 percent in schools in areas classified as "other". Males were as likely as females to use mathematical objects in their mathematics classes at least once a week (26 percent and 20 percent, respectively). In addition, 23 percent of White students, 28 percent of Black students, 22 percent of Hispanic students, and 27 percent of Asian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Minnesota 1 Central Nation How often do you work with objects like rulers, counting blocks, or geometric solids In your mathematics class? At least once a wed( Less than once a week Never Percentage Pervontage and and Proficiency !roadway 23 ( 2.1) 23 ( 2.9) Percentage and ringielaney 28 ( 1.8) 270 ( 1.5) 260 ( 3.5) 258 ( 2,6) 38 ( 1.5) 36 ( 2.5) 31 ( 1.2) 280 ( 1.1) 272 ( 2.9) 269 ( 1.5) 39 ( 22) 41 ( 4.6) 41 ( 2.2) 275 ( 1.3) 262 ( 2.8) 259 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certairty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. f; THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Minnesota MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in Minnesota who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning Regarding the frequency of textbook usage (Table 14 and Table A 14 in the Data Appendix): Many of the students in Minnesota (81 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 81 percent of students attending schools in advantaged urban areas, 81 percent in schools in extreme rural areas, and 84 percent in schools in areas classified as "other". TABLE 14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MO NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation How often do you do mathematics problems from textbooks Ifr your mathematics class? Percentage and Proficiency Porcentage and Proficiency Isercontage and Proficiency Almost every day 81 ( 1.5) 74 ( 4.7) 74 ( 1.9) 279 ( 0.9) 271 ( 2.2) 287 ( 12) Several times a wiook 12 ( 1.2) 15 ( 1.8) 14 ( 0.8) 2SS ( 1.8) 250 ( 4.2) 252 ( 1.7) About once a week or less 7 ( 12) 11 ( 4.3) 12 ( 1.8) 257 ( 4.4) 250 ( 4.7)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. 56 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota And, for the frequency of worksheet usage (Table 15 and Table Al 5 in the Data Appendix); Less than half of the students in Minnesota (33 percent) used worksheets at least several times a week, compared to 38 percent in the nation. Worksheets were used at least several times a week by 35 percent of students attending schools in advantaged urban areas, 33 percent in schools in extreme nwal areas, and 33 percent in schools in areas classified as othert% TABLE 15 I Students' Reports on the Frequency of 1 Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1880 MAEP TRIAL STATE ASSE5SIMENT Illnnesot& Central nation Percentage and Infoficiency Percentage and Proildatcy Percentage anti Proficiency How often do you do mathematics problems on worksheets in your mathematics class? At least several times a week 33 ( 2.2) 38 ( CO) 38 ( 2.4) 269 ( 1.5) 257 ( 4.9) 253 ( 2.2) About once a week 29 ( 1.6) 23 ( 2.3) 25 ( 1.2) 275 ( 1.3) 204 ( 2.8) 281 ( 1.4) Less than wieldy 37 ( 2.4) 40 ( 5.8) 37 ( 2.5) 282 ( 1.5) 273 ( 4.0) 272 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certaMty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. 62 THE 1990 NAEP TRIAL STATE ASSESSMENT 57 Minnesota TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instrucfion PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT masata Central Nation-,-. Patterns of classroom Instruction Percentele Students Teachers PeTcentege Shades* Teachets Porcudefe Students Teaches Percentage of students who work mathematics problems in small groups At least once a week 26 ( 2.0) 43 ( 3.0) 23 ( 4.8) 50 ( 7.8) 28 ( 2.5) SO ( 4.4) Less than once a week 28 ( 1.7) 50 ( 11) 32 ( 3.3) 43 ( 8.8) 28 ( 1.4) 43 ( 4.1) Never 45 ( 2.3) 7 ( 1.9) 45 ( 6.3) 7 ( 4.3) 44 ( 2.9) 6 ( 2.0) Percentage of students who use objects like rulers, counting blocks, or geometric solids At least once a week 23 ( 2.1) 19 ( 3.3) 23 ( 2.9) 15 ( 5.1) 28 ( 1.8) 22 ( 3.7) Less then once a week 30 ( 15) 72 ( 3.4) Se ( 2.5) 81 ( 6.0) ( 1.2) SO ( 3.9) Never 39 ( 2.2) 9 ( 1.8) 41 ( 4.6) 4 ( 2.3) 41 ( 22) 0 ( 2.8) Admeria Is for mathematics Percentage Percentege Percentage inttruction Students Teachers Students Teacher" Students Teachers Pemntage of students who us* a mathematics textbook Almost every day 31 ( 1.5) 73 ( 3.9) 74 ( 4.7) 82 ( 5.8) 74 ( 1.9) 62 ( 3.4) Several times a week 12 ( 1.2) 23 ( 3,9) 15 ( 1.8) 32 ( 4.2) 14 ( 04) 31 ( 3.1) About once a week or less 7 ( 1.2) 4 ( 1.3) 11 ( 4.3) ( 2.7) 12 ( 1,8) 7 ( 1.8) Percentage of students who use a mathematics worksheet At least several times a week 33 ( 2,2) 39 ( 3.5) 36 ( 8.0) 38 ( 8.3) 3$ ( 2.4) 34 ( 3.8) About once a week 29 ( 1.6) 32 ( 3$) 23 ( 2.3) 23 ( 4.8) 25 ( 1.2) 13 ( 34) Less than weekly 37 ( 24) 29 ( 3.6) 40 ( 5.6) 39 ( 7.0) 37 ( 2.5) 32 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 58 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery pradiees and resources. It appears that mathematics textbooks and worksheets continue to play a major role in math matics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachers: Less than half of the students in Minnesota (43 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 (72 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (9 percent). In Minnesota, 73 percent of the students were assigned problems from a mathematics textbook almost every day; 4 percent worked textbook problems about once a week or less. "Less than half of the students (39 percent) did problems from worksheets at least several times a week; about one-quarter did worksheet problems less than weekly (29 percent). And, according to the students: In Minnesota, 45 percent of the students never worked mathematics problems in small groups; 26 percent of the students worked mathematics problems in small groups at least once a week. Less than half of the students in Minnesota (39 percent) never used mathematical objects; 23 percent used these objects at least once a week. Many of the students in Minnesota (81 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of students in the nation. Less than half of the students in Minnesota (33 percent) used worksheets at least several times a week, compared to 38 percent in the nation. THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Minnesota 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.8 The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. National Assessment of Educational Progress, Mathematics Objectives. 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curriculwn and Evaluation Standards jor School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota Table 17 provides a profile of Minnesota eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 47 percent of the students in Minnesota had teachers who allowed calculators to be used for tests. A greater percentage of students in Minnesota than in the nation had teachers who permitted unrestricted use of calculators (31 percent and 18 percent, respectively). 1 ABLE 17 I Teachers' Reports of Minnesota Policies on Calculator Use PERCENTAGE OF STUDENTS MO NAEP TRIAL. STATE ASSESSMENT Mkomoota Percentage of elghth-grade students in public schools whose teachers permit the unrestricted um of calculators Percentage of eighth-grade stueePts in public schools whose teachers permit the use of calculator* for teats Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned by the school Percentage Pommel,' Percentage 31 ( 3.1) 27 ( 8.1) 18 ( 3.4) 47 ( 3.9) 44 ( 7.9) 33 ( 4.5) 58 ( 4.4) 55 ( 8.2) 58 ( 4.8) 41. The standard errors of the estimated stitilliCs appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Minnesota THE AVAILABILITY OF CALCULATORS In Minnesota, most students or their families (99 percent) owned calculators (Table 18); however, fewer students (51 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In Minnesota, 50 percent of White students, 67 percent of Black students, 58 percent of Hispanic students, and 48 percent of Asian students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (48 percent and 54 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 _ MO NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation Do you of your family own a calculator? Percentage and Proficiency 99 ( 0.2) 276 ( 0.8) 1 ( 0.2) v. ( Percentage and Profidency Percentage and Proficierwy 98 ( 0.6) 266 ( 2.5) 2 ( 0.6) ( ".) Percentage and Proficiency Percentage and Proficiency 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( 3.8) Percentage and Proficiency Yes No Does your mathematics teacher explain how to use a calculator for mathematics problems? Yrs 51 ( 2.1) 56 ( 4,9) 49 ( 2.3) 274 ( 1.3) 263 ( 3.0) 258 ( 1,7) No 49 ( 2.1) 44 ( 4.9) 51 ( 2.3) 278 ( 1.1) 269 ( 3.4) 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, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota THE USE OF CALCULATORS As previously noted, calculators can free students from tedious computations and allow them to concentrate instead on problem solving and other important skills and content. As part of the Trial State Assessment, stue-ms were asked how frequently (never, sometimes, almost always) they used calL.. ars for working problems in class, doing problems at home, and taking quizzes or tests. As repotted in Table 19: In Minnesota, 20 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. Some of the students (15 percent) never used a calculator to work problems at home, compared to 29 percent who almost always used one. Less than half of the students (31 percent) never used a calculator to take quizzes or tests, while 21 percent almost always did. TABLE 19 Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1960 NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation Percentage and Predictor"; Pareentege and Madam/ Portents. and Prolldenry How often do you use a calculator for the following tasks? Working problems In class Almost always 45 ( 1.5) 51 ( 3.8) 46 ( 1.5) 26a ( 1.2) 260 ( 2.8) 254 ( 14) Never 20 ( 1.6) 18 ( 3,6) 23 ( 1.9) 285 ( 1.2) 270 ( 4.111 272 ( 1.4) Doing problems at home Almost always 29 ( 1.3) 36 ( 22) 30 ( 1.3) 275 ( 1.3) 266 ( 2.8) 261 ( 1.8) Never 15 ( 0.8) 16 ( 2.1) 19 ( 02) 277 ( 1.7) 283 ( 3.3) 263 ( 14) Taking quizzes or tests Almost always 21 ( 1.5) 22 ( 4,5) 27 ( 1.4) 272 ( 2.1) 200 ( 4.0) 253 ( 2.4) Never 31 ( 1.6) 22 ( 4.8) 30 ( 2.0) 236 ( 1.2) 271 ( 3.4)1 274 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 7i 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 63 Minnesota 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 aculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the coffect 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 and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. G 64 THE 1990 NAEP TRIAL STkTE ASSESSMENT Minnesota The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: About the same percentage of students in Minnesota were in the High group as were in the Other group. A smaller percentage of males than females were in the High group. In addition, SO percent of White students, 40 percent of Black students, 40 percent of Hispanic students, and 45 percent of Asian students were in the High group. TABLE 20 I Students' Knowledge of Using Czkulators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1AINI NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation Perandage and Proficiency Piemonte AN aid Proficiency Pareettiles and Pnificiency "Calculator-use" group High 50 ( 1.0) 45 ( 1.8) 42 ( 1.3) 252 ( 1.0) 272 ( SA) 272 ( 1.8) Other 50 ( 1.0) 54 ( 1.$) 55 ( 1.31 ( 1.2) 2f10 ( 2.7) 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. 7 ( ) THE 1990 NAEP TRIAL STATE ASSESSMENT 65 Minnesota SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instructional time to teaching students how to perform routine calculations by hand. Using calculators to replace this time-consuming process would create more instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 47 percent of the students in Minnesota had teachers who allowed calculators to be used for tests. A greater percentage of students in Minnesota than in the nation had teachers who permitted unrestricted use of calculators (31 percent and 18 percent, respectively). In Minnesota, most students or their families (99 percent) owned calculators; however, fewer students (51 percent) had teachers who explained the use of calculators to them. In Minnesota, 20 percent of the students never used a calculator to work problems in class, while 45 percent almost always did. Some of the students (15 percent) never used a calculator to work problems at home, compared to 29 percent who almost always used one. Less than half of the students (31 percent) never used a calculator to take quizzes or tests, while 21 percent almost always did. 71 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota 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 ofeducating and certifying teachers.9 Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In Minnesota, 44 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 '..r students across the nation. About three-quarters of the students (76 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. Almost all of the students (98 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the 'leaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 67 Minnesota TABLE 21 I Profile of Eightb-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation , Percentage Percentage Percentage Percentage of students whose mathematics teachers reported having the Mowing degrees Bachelor's degree 56 ( 3.4) 4 ( 0.1) 56 ( 4,2) Master's or specialist's degree 44 ( 3.4) 4 ( SA) 42 ( 4.2) Doctorate or professional degree ( 0.0) 4 ( 2.7) 2 ( 1.4) Percentage et students whose mathematics teachers have the Mowing types of teaching certificates that are recognized by Minnesota No regular certification 2 ( 1.0) 4 ( 2.7) 4 ( 1.2) Regular certification but less than the highest available 22 ( 3.5) 25 ( 7.3) 29 ( 4$) Highest certification available (permanent Of long-term) 76 ( SS) TI ( 7.3) 90(4.3) Percentage of students *lose mathematics teachers have the bellowing types of teaching certificates that are recognized by Minnesota Mathematics (middle school or secondary) 90 ( 0.9) 77 ( 4.5) ( 2.2) Education (elementary or middle school) 1 ( 0.4) 17 ( 7.5) 12 ( 2.6) Other 2 ( 0.6) ( 4.6) 4 ( 1.5) The standard errors of the estimated statipiCE appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds more specifically, their undergraduate and graduate majors and their in-service training. 7 3 68 i e.F. 1990 NAEP TRIAL STATE ASSESSMENT Minnesota Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In Minnesota, 88 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. Less than half of the eighth-grade public-school students in Minnesota (40 percent) were taught mathetaatics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and I Graduate Fields of Study PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSENIMENT Minnesota Central Nation What was your undergraduate major? Mathematics Education Other What was your graduate major? Mathematics Education Other or no graduat Wei study Perapetage Pareenta. Pewees. 111 ( 2.0) 9 ( 1.6) 4 ( 1.6) ST ( 7.1) 29 ( 8.4) 14 ( 5.4) 43 ( 3.9) 35 ( 3.3) 22 ( 3.3) Percentage Percentage Percentage 40 ( 3.8) 23 ( 3.0) 37 ( 3.1) 34 ( 9.1) 34 ( 6.2) 32 ( 8.5) 22 ( 3.4) 36 ( 34) 40( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Minnesota Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In Minnesota, 34 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 Minnesota (11 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, I I percent of the students had mathematics teachers who spent no time on similar in-service training. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS 1900 KAEP TRIAL STATE ASSESSMENT Minnesota Central Nation During the last year, how much time in total have you spent on in-service eOucation in mathematics or the teaching of mathematics? None One to 15 hours 115 hours or more Percentage Percentage Percentage 11 ( 2$) ( 1.3) 11 ( 2.1) 55 ( 3.5) 71 ( 5.4) 51 ( 4.1) 34 ( 3.4) 26 ( 5.0) 39 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 1940 NAEP TRIAL STATE ASSESSMENT Minnesota SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement.'° Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher quAlifications and practices may point to areas worth further exploration. 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 Minnesota, 44 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (76 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In Minnesota, 88 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. Less than half of the eighth-fgade public-school students in Minnesota (40 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. Lapomte, Nancy A. Mead, and Gary W. Phillips, A World of Differences An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). Ina V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of ,fathematks Achievement NA EP's 1990 Assessment of the Nation and the Thal Assessment of the States (Prinmton, NJ: Nutional Assessment of Educational Progress, Educational Testing Service, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 71 Minnesota In Minnesota, 34 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 aad teachers who spent at least that much time on similar types of in-service training. Some of the students in Minnesota (11 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 0°1 72 THE 1990 NAEP TRIAL STATE ASSESSMENT 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 rolc in the education of their children. Family expectations, encouragement, and participation in student learning experiences arc 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. '7 S THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Minnesota AMOUNT OF READING MATERIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students 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 Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 11190 NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation r Does your family have, or receive on a regular basis, any of the following items: .more than 25 books, an encyclopedia, newspapers, magazines? Zero to two types Pm PAW Fotr typos Ihralfltife and Proficiency Percentage and Prolkiency Percentage mei PreSciency 12 ( 0.7) 19 ( 2.1) 21 ( 1.0) 258 ( 1.9) 250 ( 3.4) 244 ( 2.0) 31 ( 0.7) 31 ( 2.2) 30 ( 1.0) 274 ( 13) 285 ( 3.8) 258 ( 1.7) 57 ( 1.0) 50 ( 1.8) 48 ( 1,3) 281 ( 0.9) 272 ( 2.1) 272 ( 1$) The standard errors of the esumated statistics appear in parentheses, It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The data for Minnesota reveal that: Students in Minnesota who had all four of these types of materials in the home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. 74 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota A smaller percentage of Black and Asian students and about the same percentage of Hispanic students had all four types of these reading materials in their homes as did White students. About the same percentage of students attending schools in advantaged urban areas as in extreme rural areas and areas classified as "other" had all four types of these reading materials in their homes. HOURS OF TELEVISION WATCHED PER DAY Excessive television watching is generally seen as detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 1 Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 19.0 NAEP TRIAL STATE ASSESSMENT Minnesota Central Nation 11, How much television do you usually watch each day? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency One hour or less 15 ( 0.8) 11 ( 1.6) 12 ( 0.8) 281 ( 1.7) 270 ( 3.5) 269 ( 2.2) Two hours 27 ( 0.8) 22 ( 1.7) 21 ( 0.9) 281 ( 1.5) 274 ( 3.2) 268 ( 1.8) Tire* ha" 26 ( 0.9) 25 ( 2.4) 22 ( 0.8) 277 ( 1.1) 271 ( 4,0) 265 ( 1.7) Four to five hors 25 ( 0.7) 27 ( 3.0) 28 ( 1.1) 271 ( 1.4) 261 ( 2.9) 260 ( 1.7) Six hours or more 7 ( 0.5) 14 ( 1.6) 16 ( 1.0) 260 ( 2.3) 247 ( 3.4) 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 prors of the estimate for the sample. r r-t) THE 1990 NAEP TRIAL STATE ASSESSMENT 75 Minnesota From Table 25 and Table A25 in the Data Appendix: In Minnesota, average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Some of the eighth-grade public-school students in Minnesota (15 percent) watched one hour or less of television each day; 7 percent watched six hours or more. A greater percentage of males than females tended to watch six or more hours of television daily. However, a smaller percentage of males than females watched one hour or less per day. In addition, 6 percent of White students, 20 percent of Black students, 10 percent of Hispanic students, and 14 percent of Asi,an students watched six hours or more of television each day. In comparison, 15 percent of White students, 3 percent of Black students, 16 percent of Hispanic students, and 12 percent of Asian students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix: In Minnesota, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in Minnesota (44 percent) did not miss any school days in the month prior to the assessment, while 20 percent missed three days or more. In addition, 20 percent of White students, 33 percent of Black students, 29 percent of Hispanic students, and 11 percent of Asian students missed three or more days of school. S 1 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota Similarly, 22 percent of students attenditg, schools in advantaged urban areas, 19 percent in schools in extreme rural areas, and 19 percent in schools in areas classified as "other" missed three or more days of school. TABLE 26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY OM NAEP TRIAL II A '':. VISESSMENT Atkin's*: la How many days of school did you miss last month? One or two days Three days or more Panmdase and Pro Odeon 44 ( 1.0) 280 ( 1.0) 38 ( 1.0) 276 ( 1.3) 20 ( 0.9) 265 ( 1.4) Poivonlass Paroardap wed and Proficiency Proficiency 47 ( 1.7) 286 ( 2.5) ( 2.0) 271 ( 3.4) 23 ( 2.0) 252 ( 3.3) 45 ( 1.1) 285 ( 1.8) 32 ( 0.9) 246 ( 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. L.' THE 1990 NAEP TRIAL STATE ASSESSMENT 77 Minnesota 'TUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not only to master essential skills and concepts but also to develop confidence in their mathematical abilities and to value mathematics as a discipline." Students were aued if they agreed or disagreed with five statements designed to elicit their perceptions of mathematics. These included statements about: Personal experience with mathematics, including students' enjoyment of mathematics and level of confidence in their mathematics abilities: I like mathematics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevance to future work and life requirements: Almost all people use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for solving everyday problems. A student "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly agree" were given a value of I (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "unoecided," "disagree," or "strongly disagree" were given value of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception index according to whether they tended to strongly agree with the.statements (an index of I), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statements `san indl..x of 3). Table 27 provides the data for the students' attitudes toward mathematics as defined by their perception index. The following results were observed for Miunesota: Average mathematics proficiency was highest for students wh.1 were in the "strongly agree" category and lowest for students who were in the "undecided, disagee, strongly disagTee" category. About one-quarter of the students (26 percent) were in the "strongly agree" category (perception index of l). This compares to 27 percent across the nation. About one-quarter of the students in Minnesota (23 percent), compared to 24 percent across the nation, were in the "undecided, disagyee, or strongly disagree" category (perception index of 3). " National Council of Teachers of Mathematics, Currkulum and Evaluation Standards for Sclwol Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). (,(.3 3 78 THE 1990 NAEP TRIAL STATE ASSESFMENT Minnesota TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Minnesota Centrai Nation Student "perception index" groups Percentage and Prelicienqf Penentaga and Prodeleacar Pereadage and Prellakmay Strongly agree 28 ( 1.3) 25 ( 1.0) 271 1.3) (' perceptIon index" of 1) 289 ( 1.3) 272 3.5) 271 ( 1.9) Aare* 51 ( 1.3) 50 ( 1.8) 49 ( 1.0) ("perception index" of 2) 276 ( 1.1) 267 ( 3.1) 2112 ( 1.7) Undooldotl, clisagreo, strongly tilsagrso 23 ( 1.2) 2$ ( 2.2) 24 ( 1.2) ("perception Index" of 3) 263 ( 1.3) 258 ( 2.3) 251 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. SUMMARY Some out-of-school factors cannot be changed, but others can be altered in a positive way to influence a student's learning and motivation. Partnerships among students, parents, teachers, and the larger community can affect the educational environment in the home, resulting in more out-of-school reading and an increased value placed on educational achievement, among other desirable outcomes. The data related to out-of-school factors show that: Students in Minnesota who had four types of reading matnials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students wl.;) had zero to two types. THE 1990 NAEP TRIAL STATE ASSESSMENT 79 Minnesota Some of the eighth-grade public-school students in Minnesota (15 percent) watched one hour or less of television each day; 7 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Less than half of the students in Minnesota (44 percent) did not miss any school days in the month prior to the assessment, while 20 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. About one-quarter of the students (26 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" categorj and lowest for students who were in the "undecided, disagree, strongly disagree" category. 80 THE 1990 NAEP TRIAL STAIL ASSESSMENT Minnesota ME 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 desigy, the mathematics framework and objectives upon which the assessment was based, and the procedures used to analyze the trsults. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Et:...,i-ational Testing Service. The development of the Trial State Assessment Program benetitted from the involvement of hundreds of representative from State Education Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the program. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathemaiics items wem developed for the assessment, including 35 open-ended items. The first step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. THE 1990 NAEP TRIAL STATE ASSESSMENT 81 Minnesota The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment 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. Assemment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consPisus process, as described in the introduction to this report.' The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure Al). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (I RT) 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 subpcpulations, even when all students do not answer the same set of questions. This common scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) and their overall performance in the assessment. National Assessment of Priueational Progress, Mathematics Objectives 1990 Asse.ssment (Princeton, NJ: EAucational Testing Service. 1988). -/ 0 82 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota FIGURE Al I Content Areas Assessed THE NNW'S REPORT CARD 111, Numbers 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 ot calculators, generalization of numerical patterns, and verification of results are also included. Measurement This content area focuses on students' ability to describe real-world objects 'sing numbers. Students are asked to identify attribute% 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/welght, 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 siolls are important at all levels of schooling as well as in practical applications. Students need to be able to model and viStafIZe 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-solving tool. Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. 88 THE 1990 NAEP TRIAL STATE ASSESSMENT 83 Minnesota FIGURE A2 I Mathematical Abilities The following three categories of mathematical billtles are not to be coast i as hierarchical. For example, probiern solving Involves interactions between conceptual knowledge. procedural 'skills, but what is considered complex problem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. Conceptual Understanding Students demonstrate conceptual understanding in mathematics when they provide evidenGe that they can recognize, label, and generate examples and counterexamples of concepts; can use arid interrelate models, diagrams, and varied representations of concepts; can identify and apply principles; know and can aPPly facts and definitions; can compare, contrast, and integrate related concepts and principles; can recognize, interpret, and apply the signs, symbols, and terms used to represent concepts; and can interpret the assumptions and relations involving concepts in mathematical settings. Such understandings are essential to performing procedures in a meaningful way and applying them in problem-solvingsituations. 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 tha 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 noncomputationai skills such as rounding and ordering, LProblem Solving 1111.1.MIMIM.1111 In problem solving, students are required to usa their reasoning and analytic sbilit when they encounter new situations. Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, data, models, and relevant mathematics: generate, extend, and modify procedures: use reasoning (Le., spatial, inductive, deductive, statistical, and proportional): and judge the reasonableness and correctness of solutions. t3; 84 THE 1990 NAEP TRIAL. STATE ASSESSMENT Minnesota A scale ranging from 0 to 500 was created to report perfonnance for each content area. Each content-arm scale was based on the distribution of student perfomiance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In contrast, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics iter s from the 1990 assessment that discriminated well between adjacent levels. The critei a for selecting these "benchmark" items were as follows: 1 3 de :Inc performance at level 200, items were chosen that were answered cor-ectly by at least 65 percent of the students whose proficiency was at or eal 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 majoeity (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 Mgher than the percentage of students at the next lower level who answered it correctly. DO THE 1990 NAEP TRIAL STATE ASSESSMENT 85 Minnesota Once these empirically selected sets of questions had bevn identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.' 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-gade mathematics teachers consisted of two parts. The first requested information about the teacher, such as raceiethnicity and gender, as well as academic depees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and the use of various instructional approaches. Because of the nature of the sampling for the Trial State Assessment, the responses to the mathematics teacher questionnaire do not necessarily represent all eighth-pude mathematics teachers in a state or tenitory. Rather, they represent the teachers of the particular students being assessed. 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. n. I 86 THE 1V90 NAEP TRIAL STATE ASSESSMENT Minnesota FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE Cor 0 SAW 7. la& MO dow kw Wow a bbo swab ma owl slaw albums bah of bona w ion arm I the Ms owe box wiab sbo Mod a( balls dorm wimb boa WI bow dm fellow lo kV Ths boa v041 tho mode bob Tho boa owit tho lab 00 Ma boo wbb tho Mbar bolo 0 %a coo's wai. EXAMPLE 2 011 *UT MI= AT FARAWAY MAW 000016 UMW &woo* L. How awry boono of wooips woo Sang os Thwidayi CD SS O 60 O 70 0 so a) to CD I deal know. VIE 1990 MEP TRIAL STATE ASSESSMENT 9 2 Grads 4 Oman Paroardag CArrect 73% Percontag Correct for Anohor Lvela Mg MI 344 114 55 91 100 Grade 4 Ovarall Paroontaga Paroantaga Correct SG CIO 75 91 Grad. 8 Nara Percentage Percentage Caract VA 57 :yak,n. 80% for .ocr Levels: 2Q2 100 Correct: 89% for Anchor tavola: Si? 96 100 Sknple Mull !Okays Reasoning end Two-Step Problem Solving 1 Minnesota FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) ILin"! 250: EXAMPLE 1 1. What is the value of n + whez n a.. 3 Answer: EXAMPLE 2 The es* slows thews Ihe NO* el a serm d Irk Wee. On Ai Weis West, asks s tie* psalm Amen she dos la die al& Label aw1 iss al the chile ipapb with lie amen bar NW. Da Tv, ebe cabooses ea this Iterselese? 0 lb* 0 Hs EXAMPLE 3 6. Ilashkes I psalms bessIall Ws bons lad bee Web 6 baseballs. Obe hos 24 hak Which eassabse reeteeme iU help ha fled eel how we? hews aloe wit smog CD34 me 24 +4.0 024 +6-0 14 6 ee cp I deal bow. 138 Grade 8 Overall PINVINT11041 COM& 76% Percentage coma for Anchor Levels: 222 MN 202 MI) a ee 95 96 Grade 8 Overall Percentage Contact 73% Percentage Coma for Anchor Levels: 222 2111 MQ 21 119 92 92 Grade 8 Omit Pementag Correct 77% Percentage Correct for Anchor LavIs: 222 Mg 22/ 37 71 95 100 f? 3 ME 1990 NAM TRIAL STATE ASSIZE..4BM Minnesota FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) L Level 300: Reasoning and Problem Solving involving Fractions, Decimal% Percent% Elementary Geometric Properties, and Simple Alpbralc Manipulations EXAMPLE 1 IL Width el the fedeeriee show as mob et Aimee ths almsra usaaglo woe shs Vas it EXAMPLE 2 tV d sews dos a dos io bad*. e eat IS la loVuiriatia by a *de wail lead Jew V the seem ode i mak a 3.1 len Web weal be terremesod ei me)* mead hew dal Wes W#0 rod yea we abc aelehdeter ea dds 'wade? 0 Vie 0 Se Grade OveraN Percentage Correct OM Peroentege Corned for Moho( Levels: 2121 i22 33 40 77 90 Grade 12 Overall Percentage Correct: 75% Percentage Correct for Anchor Levels: 2411 210 222 --- 46 79 05 Grade 11 Overall Percentage Correct 50% Percentage Correct for Moho; Levels: ag, 2Q5/ 1,112 17 46 BB 90 BEST COPY AVAILABLE' Minnesota FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) 1 Level 350: Reasoning and Problem Solving involving Geometric Relationships, Algebraic Equations; and Beginning Statistics and Probability EXAMPLE Qwwitiono 16-17mint to th øi1a os sum do4-14ur.m 1 2 1 16. It &Ms dams al den-ligures ia eattnaood. bate may does wiI b 4i au 10474 figural CD 100 CID 101 CD 199 CD 200 CP 201 EXAMPLE 2 17. tipliin Mow you ;wind you, anon: ***gains 16. Mawr Grade 8 Overall Percentage Correct 34% Percentage Oxrect for Moho( Levels: Mg 22:1 gria 13 19 53 ea Grade 12 Overall Percentage Correct 49% Percentage Correct for Anchor 1.11V*11: 221 alg 292 222 --- 22 48 90 Grade 8 Overall Percentage Correct: 15% Percentage Correct for Anchor Levels: 2124 222 1 4 26 74 Grade 12 Overall Percentage Correct 27% Percentage Correct for Mchor Levels: ZSE 21§2 Ng MO 3 22 74 90 TIM 1990 NAB? TRIAL STA1E ASSESSMENT Minnesota 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, coursc offerings, and speciai 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. Ilaving the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAFP's goal of providing information about the educational context and performance of students. Estimating Variability The statistics xported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAFP) are subject to a certain degee of uncertainty, The uncertainty attributable to using samples of students is referred to as sampling error. like almost all estimates based on assessment measurc;, NAFP's total group and subgoup proficiency estimates are subject to a second source of .mcertainty, in addition to sampling error. As previously noted, each stucient who participraed in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropriate, set of the assessment questions or the entire set of questions -- somovhat different estimates oi' 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. n 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 Minnesota In addition to reporting estimates of avenge 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 methodolou called the jackknife procedure to estimate these standard errors. D-awing Inferences from the Results One of the goals of the Trial State As:essment 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 intepvals,bAscd on the standard errors, provides a way to make inferences about the population nans and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent ). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. S 7 92 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defined by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defined by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As an example, one might be interested in answering the question: Do students who reported spending 45 minutes or more doing mathematics homework each day exhibit higher average nulhematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is higher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in performance between the two groups in the population because of the uncertainty associated with the estimated average proficiency of the groups in the sample. Remember that the intent is to make ;, statement about the entire population, not about the particular sample that was assessed, The data from the sample are used to make inferences about the population as a whole. As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the populatiun 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 Jifference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard erroP 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 repreients an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between groups in the population. If the interval does not contain zero, the difference between groups is statistically significant (different) at the .05 level. THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Minnesota As an example, suppose that one welt interested in determining whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a partirular state's public schools. Suppose that the sample estimates of the meaal proficiencies and standard errors for females and males were as follows: Group Average Proficiency Standard Error Female 259 I.. 2.0 Male 255 2.1 The 4ifference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is Ni2.02 + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 (2.9) = 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a statistically significant difference in the population because of the magnitude of the standard errors. 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 appi opriate when the statistics being compared come from independent samples. For certain comparisons in the report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used. C 7 94 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significance is being performed. However, in each chapter of this report, many different groups are being compared (i.e., multiple sets of confidence intervals are being analyzed). When one considers sets of confidence intervals, statistical theory indicates that the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. lf 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 descri)-...: on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Er7ors 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 concerning procedures for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defmed by race/ethnicity and type of school community, as well as by gender and parents' education level. NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these 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. 1 o THE 199(1 NAEP TRIAL STATE ASSESSMENT 95 Minnesota The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or tenitory, dividal by the standard deviation of the proficiency in the total population. If the oue difference between subgroup and total group mean is .2 tot& group standard deviation units, then a sample size ef 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 temis 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 , Descripdon of Text in Report ... . ., p --:-- 0 None 0 < p .5_ 10 Relatively few 10 < p 5 20 Some 20 < p 5 30 About one-quarter 30 < p 5 44 Less than half 44 < p 5 55 About half 55 < p 5 69 More than half 69 < p 5 79 About three-quarters 79 < p 5 8g Many 89 < p < 100 Almost all p = 100 All . _i 96 THE 1990 NAEP TRIAL STATE ASSESSMENT 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 Minnesota TABLE AS 1 Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1 191113 NAEP TRIAL Eighth-grede STATE ASSESSMENT Mathematics Pre-Sigleri Algebra TOTAL Pactentapo and Pro Wow Ponmadage and fondialkanot Rintentaga and Prallohancy State 54 ( 3.0) 25 ( 24) 17 ( 1,4) 268( 1.3) 261 ( 1.1) 3C3 ( 1.6) Nation 621 2.1) 10( 14) 15 ( 1.2) 251 ( 14) 272 ( 2.4) 296 ( 2.4) NACE/ETHNICITY Milts State 53 ( 3.1) 25 ( 2.4) 18 ( 1.5) 269 ( 1.3) 262 ( 1.2) 308 ( 1.5) Nation 59 ( 2.5) 21 ( 2.4) 17 ( 1.5) 259 ( 1.6) 277 ( 2,2) 300 ( 2.3) Black State 71 ( 004 ( 6.2) 21 ( 4.4) .41 8 ( ( 3.2) ***) Nation 72 ( 4.7) 18 ( 3.0) 9 ( 22) 232 ( 3.4) 248 ( 6.4) ( ***) Hispanic State 65 ( 6.2) 23 ( 5 .5) ( 2.7) 01/ Me* Nation 75 ( 4.4) 13 ( 3.9) 6 ( 1.5) 240 ( 2.4) ( "*) Asian State 4,5 ( 6.1) 17 ( 3.4) 29 ( 4.7) ( Nation 32 ( 6.5) 21 ( 63) **..) 41 ( 7.4) TYPE OF COMMUNITY Advantaged urban State 58 ( 4.9) 27 ( 4.4) 13 ( 1.7) 267 ( 2.0) 286 ( 2.3)1 314 ( 3.7) Nation 55 ( 9.4) 22 ( 7.9) 21 ( 4.4) 269 ( 2.5)1 Extreme rural State 58 ( 6.8) 24 ( 4.9) 18 ( 3.2) 270 ( 2.0)1 280 ( 2.3)1 295 ( 45)1 Nation 74 ( 249 ( 4.5) 3.1)1 14 ( 5.0) .04.*) 7 ( 2.2) Other State 55 ( 5.0) 25 ( 4.2) 17 ( 2.3) 269 ( 23) 283 ( 1.7)1 308 ( 2.3) Nation 61 ( 2.2) 20 ( 2.1) 10 ( 1.4) 251 ( 2.0) 272 ( 2.8) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 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. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 98 THE 1990 NAEP TRIAL. STATE ASSESSMENT Minnesota TABLE AS I Students' Reports on the Mathematics Class (continued) They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pre-algebra TOTAL Pereentage anti Proficiency Peroentlles and Prelkiency Percents. and Proficiency State 54 ( 3.0) 25 ( 2.4) 17 ( 1.4) 2ee ( 1.3) 281 ( 1.1) 303 ( 1.6) Nation 62 ( 2.1) 19 ( 1.9) 16 ( 1.2) 251 ( 1.4) 272 ( 2.4) 293 ( 2.4) PARENTS' EDUCATION HS non-graduate State 70 ( 253 ( 5.2) 4.0) 17 ( 4 ( 42) **) 11 ( *iv ( 3.4) Nation 77 ( 3.7) 13 ( 3A) 3 ( 1.1) 241 ( 2.1) ra. trirl $43 gracluate State 64 ( 3.7) 29 ( 3.1, 9 ( 1.4) 259 ( 1.8) 275 ( 1.9) 288 ( 4.3) Nation 70 ( 2.6) 18 ( 2.4) $ ( 1.1) 249 ( 1.9) 266 ( 3$) 277 ( 5.2) Soma coliorga State 52 ( 3,5) 26 ( 2.7) 1: ( 2.2) 274 ( 1.7) 284 ( 2.0) 306 ( 2.3) Nation 80 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 276 ( 2.8) 295 ( 3.2) Co Nage graduate State 48 ( 3.n! 27 ( 2.9) 23 ( 2.0) 273 ( 284 ( 1.3) 310 ( 1.5) Nation 53 ( 2.7j 21 ( 2.3) 24 ( 1.7) 259 ( 1.5) 278 ( 2.8) 303 ( 2.3) GENDER Male State 54 ( 3.2) 24 ( 2.5) 18 ( 1.8) 266 ( 1.7) 281 ( 1.4) 305 ( 2.2) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.8) 275 ( 2.9) 299 ( 2.5) Female State 54 ( 3.2) 25 ( 2.5) 17 ( 1.6) 266 ( 1.4) 281 ( 1.4) 301 ( 2.1) Nation 61 ( 2.6) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear in i.,..rentheses. It can be said wnh about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages ray not total 100 percent because a small number of students reported taking other mathematics courses. *** Sample stze is insufficient to permit a reliable estimate (fewer than 62 students). 104 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Minnesota TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL STATE ASSESSMENT None 15 linen 30 Mkiutn 46 Minutes , An liar or Mors TOTAL Penntage and Praticisnty 2 ( 0.5) *44,) ( 0.3) *141 ( Van 2 ( 0.4) 1 ( 0.3) *44(4*4 ) 2 ( 1.8) ( ( 0.7) .44 ( *41 ( 3.1) .4* ( `44) ( 0.8) ( **4) 6 ( 3.0) *4-1 0 ( 0.0) 2 ( 0.7) 444 ( "*) ( 0.9) 0 ( 0.0) 2 ( 0.9) *IN ( *HP ) ( 04) 444 ( 414) Percentage and Praia Amy a ( 3.4) 273 ( 1.5) 43 ( 4,2) 251 ( 2.3) 46 ( 3.8) 27$ ( 14) 39 ( 4.5) 286 ( 2.2) 58 ( 6.9) *44(44*) 55 ( 7.8) 232 ( 3.1) 41 ( 7.6) 46 ( 7.8) 245 ( 3.0)1 30 ( 5.7) IP** ( 29 ( 7.8) 48 ( 5.2) 274 ( 3.1)1 61 (11.3) 273 ( 3.1)1 49 ( 8.5) 275 ( 2.5)1 68 (14.9) 253 ( 5.4)1 48 ( 4.5) 279 ( 1.9) 37 ( 4.3) 256 ( 3.1) State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extrema nral State Nation Other State Nation Peroseiage and Pre Many 42 ( $.3) 2.6) 276 1.6) 43 4.3 200 ) 42 ( 3,4) 278 ( 1.6) 45 ( 5.1) 270 ( 2.7) 34 ( 7.2) .641 40 ( 8.7) 24$ ( 5.3) 47 ( 7.1) .04* ( 441 34 ( 6.8) 251 ( 4.2)1 1144 ( 37 ( 8.8) 42 ( 4.7) 278 ( 2.8) 32 ( 8.8) 444 ( ***) 40 ( 8.0) 275 ( 3.8)1 14 (10.9) 4,4.) 44 ( 4.9) 277 ( 2.8) 48 ( 5.1) 265 ( 2.5) ihwasrata. and and libralkinagi Peak* lacY 7 ( 11) 2 ( 1.1) 290 ( 4.0$ 267 6.3)I 10 ( IA) 4 0.9) 272 ( 5.7)I 27$ 5.1)1 ( 1.6 2 (1.1) 292 ( 4,0)4 eel 11 ( 2.4) 4 ( 01) 277 ( 74)1 279 ( 5.9)4 7 ( 3.9) 1 ( 1.2) es.) 3 ( 1.2) 21 0.0 1141. IMO ) 44* ( (HI 2.6) ( 1.1) .44) INr 13 ( 2.9) 7 ( 2.1) 414 ( ( 4.3) ( 52) 44' ( 4441 10 ( 5.4) 24 (10.2) .44 ( -.* 3 ( 1.6) ( 0.9) "4 ( 444) 5 ( 3.4) 0 ( 0.0) mod, ( a** ( ( 4.2) 1 ( 1.1) ( 8 ( 5.8) 10 ( 7.3) *44(44*) +al 5 ( 1.3) 4 ( 2.7) *-4/4 41 ." ( 4") 10 ( 2.4) 4 ( 1.1) 276 ( 8.6)1 282 (11.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about cs 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 1 15 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A6 Teachers' Reports on the Amount of Time (cmtinued) Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT _ Vane 16 Minutes 30 Minutes 45 Minutes An Hour or More TOTAL State Nation PARENTS' EDUCATION aid Preaching 2 ( 0.5) ( *01 1 ( 0.3) ( ***) 6 3.1) 1 ( 0.8) «it 49) 1 ( 0.6) **it ( 0.5) ( 1 ( 0.6) 444 ( 444) 1 ( 0.9) "4 ( 4") 2 ( 0.7) ( 0.3) grfr, ( 1 ( 0.3) 2 ( 0.5) *** (*") 1 ( 0.4) *** ( * ) Perceniage and Proldency 46 ( 3.4) 273 ( 1.5) 43 ( 4.2) 250 ( 2.3) 45 ( 5.3) *el Aq ( 8.3) 240 ( 2.8) 50 ( 4.7) 263 ( 2.2) 43 ( 5.2) 249 ( 3.1) 44 ( 4.2) 281 ( 2.0) 44 ( 5.4) 265 ( 2.8) 45 ( 3$) 282 ( 1.7) 40 ( 4.7) 285 ( 2.5) 47 ( 3.8) 275 ( 1.8) 44 ( 4.4) 257 ( 2.9) 45 ( 3.5) 272 ( 1.7) 41 ( 4.4) 255 I 2.3) Perienteso and Proficiency 42 ( 3.3) 270 ( /11) 43 ( 4.3) 200 ( 2.6) 40 ( 54) 1141. NIP1 40 ( 6.1) 246 ( 3.7) 42 ( 4.7) 265 ( 1.9) 44 ( 5.8) 258 ( 2.7) 42 ( 3.8) 282 ( 2.1) 43 ( 5.8) 270 ( 3.6) 42 ( 3.1) 254 ( 2.2) 44 ( 4.1) 277 ( 3.0) 42 ( 35) 278 ( 2.1) 43 ( 4.3) 288 ( 2.9) 42 ( 3.3) 276 ( 1.8) 43 ( 4.7) 284 ( 2.8) Porcenialle and Proidensi 7 ( LS) 290 ( 4.0)I 10 ( 1.51) 272 ( 51), 6 ( 3.1) 6 ( 1.7) **4 ( "4) 4 ( 1.4) 9 ( 3.1) 11 ( 2.7) 7 ( 2.1) *** ( ***) 8 ( 1.8) 300 ( 3.9)1 11 ( 2.3) 207 ( 8.1)1 7 ( 1.6) 293 ( 5.1)1 9 ( 1.9) 273 ( 7.3)1 8 ( 1.8) 288 ( 5.0)1 11 ( 2.0) 272 ( 5.7)1 Paved.. and Prodding, 2 ( 1.1) 207 ( 03)f 2748 5a9.4 3 ( 2.4) gvn 4 ( 1.3) 2 ( 1.3) 3 ( 1.0) 04+ ( 3 ( 1.4) 4 ( 1.0) 444 ( 444) 3 ( 1.0) 5 ( 1.3) ( 5 ( 1.3) 279 ( 7.7)1 3 ( 1.2) 4,4) IM non-graduate State Nation NS graduate State Nation Some college State Nation College graduat State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statistics apoear in parentheses. It can be said with certainty that, for each population of interest, the value for the entire population is within ± of the estimate for the sample. ! Interpret with caution -- the nature of the sample does n determination of the variability of this estimated mean proficiency. *** Sample size is insulT reliable estimate (fewer than 62 students). about 95 percent 2 standard errors ot allow accurate icient to permit a THE 1990 NAEP TRIAL STATE ASSESSMENT 101 Minnesota TABLE A7 I Students' Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT None 16 Minutes - 30 Itkuttes 46 Minutes i An Hoar or 1 Mere TOTAL Percentege and Proficiency Percentene and Proficiency Peroentegs and Proliciency Percentage and Prelicioacy Percentage and Proficiency State 10 ( 0.7) S3 ( 1.3) 30 ( 1.0) 1.0) 12 ( 1.0) 271 ( 24) 278 ( 1.2) 276 ( 1.3) 276 1.6) 274 ( 1.8) Nation ( 0.3) 31 ( 2.0) 32 ( 1.2) 10 1.0) 12 ( 1.1) 251 ( 24) 254 ( 1.13) 263 ( 12) 266 ( 1.9) 256 ( 3.1) RACE/ETHNICITY *Hite State 10 ( 0.8) 34 ( 1.4) 30 ( 1.1) 15( 1.1) 11 ( 0.9) 273 ( 22) 230 ( 1.1) 279 ( 1.3) 278 ( 1.7) 279 ( 1.9) Nation 10 ( 1.0) 33 ( 2.4) 32 ( 1.3) 15 ( 0.11) 11 ( 1.3) sack 293 ( 3.4) 270 ( 1.9) 270 ( 2.1) 277 ( 2.2) 268 ( 9.9) State 10 ; 3.4) 22 ( 5.3) hi* ( «pi 13 ( 4.0) *Mt 14 ( 5.7) «NI ( ( ( ( Nation 26 ( 2.5) 33 ( 2.7) 18 ( 2.3) 18 ( 1.9) 241 ( 3.6) 237 ( 3.5) 240 ( 16) 232 ( 3.7) Hispanic State 7 ( 3.4) 32 ( 4.9) 31 ( 3.9) 10 ( 3.9) 15 ( 3.4) 1,44 -** ) Ir* MIN) *44 ( *Of ) Nation 12 ( 1.5) 27 ( 3.0) 30 ( 2.6) 17 ( 2.1) 44 ( 1.7) ( eee) 246 ( 3.6) 248 ( 3A) 241 ( 4.3) Asian State 4 ( 2.2) 20 ( 4.7) 30 ( 5.9) 22 ( 4.6) Nation 4 ( 2.0) ***) 22 ( 4.6) 31 ( 5.6) 18 ( 3.9) 25 ( 6.2) TYPE OF COMMUNITY Advantaged urban State 9 ( 1.6) «N.) 36 ( 2.6) 281 ( 2.4) 32 ( 1.8) 277 ( 3.2) 11 ( 1.7) Nation ( 41 (124) 27$ ( 3.0)1 31 ( 6.6) 230 ( 4.5)1 12 ( 3.3) eee ( ) 7 ( 3.4)-) Extreme nral State 9 ( 1.6) 31 ( 2.8) 28 ( 2.1) 18 ( 2.6) 14 ( 2.0) 278 ( 2.4)1 273 ( 2.8)1 274 ( 2.2) 271 ( 2.5)1 Nation 8 ( 2.3) *iv 41.11 38 ( 4.6; 260 ( 3.5)1 31 ( 2.9) 255 ( 5.1)! 1$ ( 3.8) ( 2.7) *4. Other State 11 ( 1.2) 34 ( 2.4) 31 ( 1.7) 14 ( 1.5) 10 ( 1.4) 276 ( 3.4) 280 ( 1.9) 278 ( 1.3) 278 ( 2.7) 279 ( 3.5) Nation 9 ( 1.0) 30 ( 16) 32 ( 1.3) 15 ( 1.1) 13 ( 1.1) 250 ( 3.3) 283 ( 2.3) 264 ( 2.3) 267 ( 2.1) 258 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 1 Interpret with caution - the nature of the sample does not allow accarate determination of the variability of this estimated mean proficiency. **6 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 102 1 7 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A7 Students' Reports on the Amount of Time They (mitinued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 NAEP TRIAL STATE ASSESSMENT None I 15 Minutes 30 Minutes 45 Minutes An Kew or Mere TOTAL Pementa. and Prailitisty Permits. and Prelideney Permits. and Prenaiony Percentage and tree:ken Poivaidage and Prolkiency State 10 ( 0.7) 33 ( 1.3) 30 ( 1.0) 15 ( 1.0) 12 ( 1.0) 271 ( 2.4) 278 ( 1.2) 276 ( 1.3) 278 ( 1.8) 274 ( 1.6) Nation ( 0.6) 31 ( 2.0) aa ( 12) le ( 1.0) 12 ( 1.1) 251 ( 21) 264 ( 1.9) 263 ( 1.9) 206 ( 1.9) 256 ( 3.1) PARENTS' EDUCATION NS nen-graduato State 11 044 ( 3.5) ( *01 30 ( 5.0) 23 ( 5.1) 14 ( 3.6) 22 ( 044. 5.5) Nation 17 ( 3.0) 26 ( 3.3) 34 ( 4.4) 12 ( 2.5) 10 ( 2.2) ( 2445 ( 4.0) 246 ( 2.6) *IN ( 641 ( NI graduate State 12 ( 1.1) 33 ( 2.1) 23 ( 1.9) 14 ( 1.5) 13 ( 1.5) 267 ( 3,6) 296 ( 2.0) 203 ( 2.4) 262 ( 2.9) 262 ( 3.3) Nation 10 ( 1.7) 33 ( 22) 31 ( 1.9) 16 ( 1.4) 11 ( 1.5) 24$ ( 4.2) 250 ( 32) 254 ( 2.4) 256 ( 2.8) 244 ( 3.4) Sane ceflege State 8 we. ( 12) 36 ( 285 ( 2.1) 1.9) 31 ( 282 ( 1.6) 2.2) 16 ( 282 ( 1.8) 2.5) ( ( 1.3) «64) Nation 9 ( 1.2) 30 ( 2.7) 36 ( 2.1) 14 ( 1.8) 11 ( 1.5) ( 266 ( 3.0) 266 ( 2.6) 274 ( 3.5)- 11-4-0 **111 While graduate State 9 ( 1.0) 33 ( 1.9) 32 ( 1.7) 15 ( 1.3) 12 ( 1.2) 278 ( 3.0) 285 ( 1.5) 285 ( 1.7) 286 ( 2.8) 286 ( 2.8) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER M. State 14 ( 1.2) 33 ( 1.5) 27 ( 1.4) 15 ( 1.1) 11 ( 1.2) 273 ( 2.2) 279 ( 1.8) 277 ( 1.7) 276 ( 2.5) 273 ( 2.6) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 256 ( 2.4) 265 ( 3.0) 255 ( 4.1) Female State ( 0.6) 34 ( 1.6) 33 ( 1.3) 15 ( 1.3) 12 ( 1.1) 266 ( 4.3) 277 ( 1.5) 276 ( 1.6) 275 ( 2.1) 276 ( 2.5) Nation 7 ( 0.9) 28 ( 2.0) 35( 1.7) 17 ( 1.0) 13 ( 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 populittion of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 103 Minnesota TABLE AS I Teachers' Reports on the Emphasis Given To 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 116.11M 1990 NAEP TRIAL STATE ASSESSMENT Numbers and Oplrations Measurement Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation RACE/ETHNICITY Percents. and Proficiency 36 ( 3.3) 275 ( 1.8) 49 ( 3.8) 26) ( 1.8) 36 ( 3.4) 276 ( 1.8) 48 ( 3.7) 267 ( 2.2) 29 ( 7.0) oN)* ( 54 ( 7.9) 2434 4.3) 48 ( 6.8) ( 47 ( 8.7) 246 ( 4.8) 27 ( 7.7) ***) 32 ( 0.8) ( ) 40 ( 6.2) 273 ( 3.2)1 28 (13.0) 45 ( 9.8) 277 ( 4.0)1 53 (12.4) 257 ( 7.1)1 32 ( 4.1) 280 ( 2.9) 52 ( 4.1) 260 ( 2.3) Poreentene and Proficiency 13 ( 1.7 901 ( 2.7 15 ( 2.1 237 ( 3.4) 13 ( 1.8) 902 ( 2.7) 18 ( 2.4) 2as ( 3.5) 14 ( 4.8) 11 ( 3.3) ( 4.1 5 ( 2.5) «H. ( 8 ( 2.2) 27 ( 5.2) 0* 41** ) 22 ( XS) 302 ( 5.3)1 16 ( 42) 5 ( 2.5) 6 ( 3.6) .1.4, 9 ( 1.5) 304 ( 5.3)1 16 ( 2.7) 286 ( 3.8) Perventage and Proficiency 12 2.2) 206 4.1 17 as 250 ( 5.8 ) 13 ( 2.3) 268 ( 4.3) 14 ( 3.4) 259 ( 8.9)1 8 ( 3.4) *gm *41 25 ( 7) 228 ( 2.6)1 11 ( 4.8) *4* ( 4.414) 23 ( 4.1) 11 ( 5.2) 441 23 ( 5.6) ',h.) 11 ( 4.2) 9 ( 7.0) **. ***) 14 ( 5.1) ( "e) 6 ( 4.9) 12 ( 3.5) 27a 7.2)1 16 ( 3.9) 253 ( 7.1)1 Tercentage and Treadway 47 ( 3.1 277 ( 1.3 33 ( 4!:#) 272 ( 4.0) 47 ( 3.7) 280 ( 1.7) 96 ( 4.71 277 ( 4.3) 34 ( 6.4) *11(141 23 4 5.7) 238 ( 8.1)i 52 ( 7.9) 34 (5.8) 255 ( 4.4)1 48 ( 8.9) 4.. 44 ( 8.9) 45 ( 4.2) 276 ( 3.5) 40 ( 8$) m 40 ( 9.4) 280 ( 4.6)1 32 (11.7) 265 ( 9.1)1 52 ( 5.6) 278 ( 2.8) 34 ( 5.3) 270 ( 4.6) Percentage end Proficiency 19 ( 3.0 270 ( 2.5 28 ( 3.8 260 ( 3.2 19 ( 3.1) 273 ( 2.4) 27 ( 4.4) 265 ( 3.3) 24 ( 6.5) *** 4441 93 ( 7.9) 242 ( asp 20 ( 6.9) *** 27 ( 0.5) *44) 19 ( 5.9) *** .41 34 ( 9.2) 25 ( 5.0) 276 ( 3.8)1 38 ( 9.4) 207 ( 4.9)1 23 ( 9.0) 270 ( 3.0)1 9 ( 61) *44 ( 11.4 *) 14 ( 3.8) 272 ( 4.2)1 28 ( 4.6) 260 ( 3.9) White State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extrema rural State Nation Other State Nation Perosnlais and Proficiency 27 2.9) 275 2.11 21 3.3) 264 ( 5.4) 27 ( 3.0) 277 ( 2.0) 22 ( 3.4) 273 ( 5.8) 17 ( 8.4) 24 ( 7.3) 233 ( 4.7)4 29 ( 6.5) *** ***) 16 ( 5.5) 32 ( 7.9) 14 4 6.8) (+0440*) 30 4 3.4) 275 ( 4.5) 13 ( 3.2) 04,-..) 21 ( 5.5) 272 ( 3.2)1 16 ( 7.9) ..** .00.) 29 ( 5.8) 278 4 3.41i 24 ( 4.3) 265 ( 5.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). () t 104 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE AS I Teachers' Reports on the Emphasis Given to ("'Itinued) 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL. STATE ASSESSMENT Numbers and Operations Measurement Geometry - - Heavy Emphasis , Little or No Emphasis Heavy Emphasis - Utile or No Emphasis Heavy Emphasis , Uttle or N.) Emphasis TOTAl. State Nation PARENTS' EDUCATION NS non.grackiate State Nation HI graduate State Nation Some cottage State Nation College graduate State Nation GENDER Male State Nation Female State Nation Percentage Percenfage Percentage Peon*. Pernotage Poraeillage and and aid and and and Prolliciency Praficiency Proficienay Prfaciancy Pripeciancy 2g 3:4 1771 12 288 4.1 49 ( 3.8 15 2.1 17 3.0 280 ( 1.8) 237 ( 3.4) 250 5.0 38 ( 8.5) 5 ( 2.4) 11 ( 4.0) ***) c.a.) so ( 63) 7 ( 2.3) 22 ( 5.3) 251 ( 3.4) ( *** ( ) 39 ( 4.3) 9 ( 1.9) 18 ( 3.3) 265 ( 3.2) *" ( ***) 248 ( 8.0)i 55 ( 4.8) 11 ( 2.8) 17 ( 3.9) 259 ( 23) ( ") 251 ( 6.1)1 36 ( 33) 12 ( 2.1) 8 ( 2.1) 282 ( 2.4) 296 ( 5.4) *** ( it") 47 ( 4.4) 17 ( 3.3) 12 ( 2.7) 265 ( 2.8) 284 ( 4.1)1 *** ( 32 ( 3.4) 18 1 2.1) 12 ( 2.5) 283 ( 2.2) 308 ( 3.0) 279 ( 5.0)I 44 ( 4.1) 19 ( 2.4) 16 ( 3.3) 289 ( 2.8) 298 ( 3.4) 264 ( 7.2)1 36 ( 3.5) 13 ( 2.0) 14 ( 2.8) 274 ( 2.4) 304 ( 33) 272 ( 42y 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 261 ( 2.5) 287 ( 4.4) 258 ( 0.7) 35 ( 3.5) 13 ( 1.7) 11 ( 1.9) 276 ( 2.2) 299 ( 3.0) 2e0 ( 6.1) 51 ( 3.9) 15 ( 2.4) 17 ( 32) 260 ( 2.0) 286 ( 3.3) 241 ( SA) ,ft. 47 ( 277 ( 1.8 191 2311 2r5 33 ( 272 ( 4.0 4.0 25 3.81 21 143 48 ( *44, ( 5.7) ***) 20 ( 51) 29 I 5.4) 25 5.31 32 ( «14 ( 8.3) 20 ( ibmt 48 ( 4.8) 21 ( 4.5) 25 ( 3.4) 262 ( 34.2) 261 ( 4.1 $ ( 3.1) 27 ( 5.0) 21 ( 4.5) 24 ( 5.1) 253 ( 4.7)4 255 ( 4.2) 248 ( 4.3)4 47 ( 3.8) 19 ( 3.4) 26 ( 3.3) 218 ( 23) 276 ( 2.5)4 279 ( 23) 30 ( 5.5) 27 ( 5.0) 23 ( 4.1) 279 ( 4.5) 262 ( 4.8)1 270 ( 4.7) 48 ( 3.7) 18 ( 23) 2$ ( 3.3) 287 ( 2.0) 277 ( 3.5) 286 ( 2.7) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 383 ( 3.8) 270 ( 3.8) 280 ( 84) 47 ( 3.7) 19 ( 3.0) 27 ( 23) 282 ( 2.4) 269 ( 3.7) 275 ( 2.7 32 ( 33) 29 ( 4.1) 20 ( 3.3) 275 ( 41) 263 ( 3.8? 266 ( ILO 47 ( 3.8) 20 ( 3.3) 27 ( 3,2 272 ( 2.1) 271 ( 2.5)4 275 ( 2.4 35 ( 4.3) 27 ( 3.9) 23 ( 3.5 268 ( 4.1) 256 ( 3.3) 263 ( 5.0 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. " Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Minnesota TABLE A8 I Teachers' Reports on the Emphasis Given To (mntinued) I Specific Mathematics Content Areas r ERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Analysis, Statistics, and Probability Algebra and Functions Heavy Empnasis Little or No Emphasis Heavy Emphasis _ Little or No Emphasis TOTAL Pooantage and Pralksidacy Percentage and Prilicioncy Pamintsige arid Proficiency Percoodip. and Pralkidney State ( 18) 69 ( 2.8) SO ( 3-2) ( 1.3) 207 ( 3.3)i 279 ( 1.3) 285 ( 1.5) 248 ( SA) Nation 14 ( 2.2) 53 ( 4.4) 4$ ( 3.8) 20 ( 3.0) 280 ( 4.3) 261 ( 2.9) 275 ( 2$) 243 ( 3.0) RACE/ETHNICITY Milts State 9 ( 1.8) 09 ( 2.7) 51 ( 3.2) 8 ( 1.3) 288 ( 3.1)1 282 ( 1.2) 287 ( 1.5) 252 ( 3.5) Nation 14 ( 2.4) 53 ( 5.0) 48 ( 4.2) 1$ ( 2.8) 270 ( 4.1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) Slack State ( 4.2) OS (11.0) 49 ( 8.2) 14 ( 7.6) ( ***) dire. ( 'imp) Nation 14 ( 3.4) 53 ( 82) 39 ( 7.1) 27 ( 6.9) 22.5 ( 43) 253 ( 6.3) 226 ( 2.2)1 Hispanic State 5 ( 2.9) 801 4.8) 35 ( SI) 23 ( 5.7) ( ( ear ) Nation 15 ( 4.1) 56 ( 6.3) 4$ ( 5.9) 18 ( 4.2) *** ( "") 246 ( 4.4) 257 ( 4.0)1 Asian State 4 ( 2.0) SO ( 7,$) 14 ( 4.9) ( "") *** IP**) ( ***) Nation 34 ( 8.7) *** ( "`) 35 ( 7.1) 0.*) 61 ( 8.1) ( "HI 9 ( 4.9) TYPE OF COMMUNITY Advantaged urban State 81 ( 5.4) 58 ( 3.9) 12 ( 3.4) ( ***) 281 ( 3.0) 288 ( 3.3) Nation 11 ( 6.6) 65 (19.4) 41 ( L9) 18 ( 5.3) 284 ( 7.4)1 298 ( 7.9)1 Extreme rout State 4..4) 83 ( 5.6) 278 ( 2.2) 37 ( 8.3) 280 ( 4.2)1 Nation BS (16.9) 42 (16.0) 254 ( 6.7)1 241 ( 5.9)1 Other State 11 ( 2.8) 8T( 5.0) 51 ( 4.7) 10 ( 2.1) 291 ( 7.1)1 281 ( 2.2) 286 ( 2$) 254 ( 4.0)1 Nation 15 ( 2.9) 53 ( 5.2) 47 ( 4.3) 17 ( 3.3) 267 ( 4.7) 260 ( 3.4) 276 ( 2.8) 24$ ( 4.4)1 4111=M111 The standard errors of the estimated statistics appear in parentheses, lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 ciandard 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. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 106 THE 1990 NAEP TRIAL STATE 1,ES:21SSMENT Minnesota TABLE A8 I Teachers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and ProbabilNy Algebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Parcantd0 and Pralkievay Poreantage and Profit:tang/ PoradINN and Praalency Parcsolage and kWh:Wm State 8 ( 1.8) 69 ( 2.6) 50 ( 3.2) ( 1.3) 207 ( 3.3)1 279 ( 1.3) 215 ( 1$) 249 ( 3.4) Nation 14 ( 2.2) 53 ( 4.4) 4e ( 3.8) 20 ( 3.0) 259 ( 4.3) 261 ( 2.9) 275 ( 2$) 243 ( 3.0) PARENTS EDUCATION fiS non-graduate State 5 ( Mit ( 3.5) 11441 72 ( 257 ( 5.8) 5.2) 36 ( *0* ( 5.0) *41 15 ( 4.3) ( roe) Nation 9 ( ( 3.0) 53 ( 240 ( 7.7) 6.2) 25 ( .. 5.2) 29 ( 8.9) .44,) HS graduate State S ( 2.5) 72 ( 3.2) 41 ( 4.0) 11 ( 2.0) *44 ( 441 267 ( 1.7) 272 ( 2.5) 243 ( 4.8) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 261 ( 6.0)1 247 ( 2.9) 265 ( 3.5) 239 ( 3.4) Sonia college State 7 ( 1.9) 72 ( 286 ( 3.0) 1.9) 53 ( 288 ( 3.8) 22) 8 ( 1.4) 1114") Nation 13 ( 2.5) .41 57 ( 270 ( 5.8) 3.7) 48 ( 278 ( 4.8) 3.0) 17 ( 3.1) Whigs graduate State 9 ( 2.2) 65 ( 3.4) 58 ( 3.2) 6 ( 1.3) 298 ( 4.8)1 289 ( 1.5) 292 ( 1.8) ( Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 18 ( 2.4) 282 ( 4.5) 275 ( 3.6) Via ( 3.0) 249 ( 4.0) GENDER Male State ( 1.9) 71 ( 2.6) 49 ( 3.1) 10 ( 1.6) 288 ( 4.1)1 278 ( 1.9) 284 ( 1.8) 246 ( 3.9) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.6) 275 ( 5.8) 2e0 35) 27$ ( 3.2) 243 ( 3.0) FIKMI111 State 8 ( 1.8) 65 ( 2.9) 52 3.5) 7 ( 1.3) 285 ( 4.3)1 279 ( 1.6) 295 ( 1.6) 248 ( 4.9) Nation 16 ( 2.4) 53 ( 45) 48 ( 3.6) 18 ( 2.9) 263 ( 4.4) 282 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within + 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 107 Minnesota TABLE A9 I Teachers' Reports oil the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAY TRIAL I Get AM the Resources I I Get Most of the I Get Same or Mom of STATE ASSESSMENT hood Resources I Need the Resources I Need Pmentase and Proliaistcy 12 ( 2,1) 281 ( 2.8) 13 ( 285 ( 42) Panagabor IM 69(3.7 27$ ( 12) 5$ ( 4.0) 285 ( 2.0) PereeNtese an6 Pnalliciancy 23 273 31 201 ( 3.01) ( 1.9) ( 4.2) ( 2.9) State Nation RACE/ETHNICITY State 12 ( 2.1) 135 ( 3.7) 23 ( 3.8) 263 ( 2.8) 278 ( 1.0) 277 ( 1.8) Nation 11 ( 2.5) 58 ( 4.8) 30 ( 4.5) 275 ( 3.5)1 270 ( 2.3) 207 ( 3.3) Mark State 1 ( IS* ( 1.8) 89 (167) 29 (10.4) .44) Nation 15 ( 4.2) 52 ( 8.8) 33 ( 7 2) ttlivente 241 ( 53)1 242 ( 2.4) 236 ( 4 .11) State 19 ( 5.9) ***) 59 ( 8.1) 21 ( 5.8) *4* 0.041 Nation 23 7.8) 44 ( 4.9) 34 ( 7.7) 248 ( 7.7)1 250 ( 2.9) 244 ( 3.0)! Asian State 14 ( 04* ( 5.0) 44) et* ( hal 32 ( 7.8) 11.414' Mgr) Nation 19 ( *fr. 8.8) 37 ( 7.7) 44 (12.7) ( *41 TYPE OF COP' /AUNITY Adventn..4 titan State 13 ( 4.1) 76 ( 4.7) 0 ( 3.7) 281 ( 8.1)1 277 ( 2.1) Nation 36 ( 9.2) 50 ( 8.9) 3 ( 3.1) lbdreme nrel 272 ( 8.5)1 26a ( 13)1 State 18 ( 4.7) 81 ( 5.4) 23 ( 8.3) 278 ( 4.2)1 275 ( 2.5)1 273 ( 2.7)1 Nation 2 ( ( 2.8) .41 54 (10.4) 200 ( 6.8)1 43 (10.3) 257 ( 5.0)4 Other State 10 ( 3.1) 84 ( 8.0) 26 ( OA) 250 ( 5.4)1 270 ( 14) 279 ( 2.7)1 Nation 11 ( 2.9) 56 ( 5.4) 31 ( 5.8) 265 ( 3.9)1 264 ( 21) 283 ( 4.2) The standard errors of the estimaied 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 ?stimate for the sample, ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this 7.itimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A9 I Teachers' Reports on the Availability of (continuee I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 MEP TRIAL I Got All the Resotrces I I Got Most of the I G( Some or None of STATE ASSESSMENT Need Resotrces 1 hood the Resources I Need TOTAL Percentage and Proficiency Portentage and Proficiency Percentage and Proficiency State 12 ( 2.1) 65 3.7) 23 ( 3.8) 281 ( 2.8) 278 ( 1.2) 273 ( 1.9) Nation 13 ( 2.4) 58 ( 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 261 ( 2.9) PARENTS EDUCATION HS non-graduate State 10 ( 3.0) 57 ( 6.7) 33 ( 7.0) Nation B ( 2.8) ...) 54 ( 244 ( 5.7) 2.7) 38 ( 243 ( 8.3) 3.5)1 HS graduate State io ( 2.2) 67 ( 4.7) 24 ( 4.7) 264 ( 1.8) 262 ( 2.9)1 Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.2) 253 ( 4.8)1 256 ( 1.9) 256 ( 2.8) Some college State 12 ( .44 ( 2.2) 65 ( 283 ( 4.1) 1.6) 23 ( 281 ( 4.3) 2.4)1 Nation 13 ( 'hp* 3.3) 62 ( 269 ( 4,3) 23) 25 ( 267 ( 4.1) 3.8) College gradmte State 14 ( 2.5) es 3.4) 21 ( 3.6) 288 ( 3.3) 284 ( 1.5) 284 ( 2.1) Nation 15 ( 2.9) 56 ( 4.9) 30 ( Si) 276 ( 5.4)1 276 ( 2.2) 273 ( 3,7) GENDER Male State 11 ( 1.9) 68 ( 3.7) 21 ( 3.6) 284 ( 3,7) 277 ( 1.4) 272 ( 3,0) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4,0) 264 ( 5.0)1 265 ( 2.6) 264 ( 3.3) Female State 13 ( 2.4) 62 ( 4.0) 25 ( 4.3) 279 ( 2.8) 275 ( 1.3) 274 ( 2.1) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 2r; ( 3.9) 264 ( 2.0) 257 ( 3.0) The standard errors of the esumated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! 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). 174 THE 1990 NAEP TRIAL STATE ASSESSMENT 109 ilinv Minnesota TABLE AlOa I Teachers' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Now TOTAL and Praidency poresodage and Proficiency Peroonfage and Proficiency State 43 ( 10) 50 ( 3.1) ( 1.9) 279 ( 1.8) 213 ( 1.4) 279 ( 3.8)1 Nation 50 ( 4.4) 43 ( 4.1) 8 ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 5.4)1 RACE/ETHNICITY White State 43 ( 3.0) 50 ( 3.2) 8 ( 1.9) 281 ( 1.8) 275 ( 1.2) 281 ( 3.6)1 Nation 49 t 4.6) 43 ( 4$) 8 ( 2.3) 265 ( 2.7) 271 ( 2.2) 285 ( 4.9)1 Black State 45 ( 6.6) ***) 49 ( 6.7) ( S ( 3.1) ) Nation 47 ( 8.1) 240 ( 3.4) 45 ( 7.0) 238 ( 4.0) 9 ( 4.1) ( ***) Hispanic State 43 ( 7.2) 56 ( 73) 2 ( 1.6) *** ( *44) Nation 64 ( 72) 32 ( 6.9) 4 ( 1.4) 246 ( 2.5) 247 ( 6.3)1 ( *1") Asian State 51 ( 7.2) 10 ( 4.7) *411 ( ViHt Nation 60 ( 6.2) *** ( ***) 37 ( 7.9) 4 ( 2.7) ( ***) TYPE OF COMMUNITY Advantaged titan State 38 ( 2.8) 5.S ( 4.7) 9 ( 3.3) 284 ( 5.0) 274 ( 2.4) ( ".) Nation 39 (22.9) 41 (17.9) 20 (12.2) 273 ( 6.0)1 ( *4") Extreme rural State 38 ( 8.2) 53 ( 8.3) 9 ( 5.0) 279 ( 3.8)! 271 ( 14)1 4HIN Nation 35 (14.6) 255 ( 5.5)! 50 (17.1) 258 ( 5.9)1 9 ( 9.6) 4.4" ( ***) Other 5tate 48 ( 5.3) 46 ( 4.8) ( 2.3) 280 ( 2.7) 277 ( 2.6) Nation 50 ( 4.4) 44 ( 4$) ( 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). 110 THE 1990 NAEP TRIAL ST1TE ASSESSMENT Minnesota TABLE AI Oa Teachers' Reports on the Frequency of Small (c°ntinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT - At Least Once a Week Less Than Once a Week Never emInmplow TOTAL Percentage and Proficiency Percentage and Preficiertcy Percentage and Proficiency State 43 ( 3.0) 50 ( 3.1) ( 1.9) 279 ( 14) 273 ( 1.4) 279 ( 34)1 Nation 50 ( 44) 43 ( 4.1) 8 ( 2.0) 200 ( 2.2) 264 ( 2.3) 277 ( 5,4)1 PARENTS' EDUCATION NS non-graduate State 39 ( 5.3) 54 ( 5.4) 7 ( 3.3) 4 Nation 60 ( 8.4) 36 ( as) 1 ( 1.4) 244 ( 3.2) 244 ( 3.2)1 NS graduate State 42 ( 3.9) 51 ( 4.3) 7 ( 2.0) 267 ( 2.1) 263 ( 2.3) 11.** Nation 49 ( 4.8) 45 ( 5.1) ( 2.5) 252 ( 2.8) 257 ( 2.7) Some cottage State 44 ( 285 ( 3.9) 1.9) 50 ( 279 ( 3.9) 1.7) .4* Nation 51 ( 266 ( 5.2) 3.1) 42 ( 268 ( 5.1) 3.2) 7 ( **, ( 2.3) *44. ) College graduate State 43 ( 3.1) 48 ( 3.2) 9 ( 22) 289 ( 2.3) 281 ( 1.8) 289 ( 3.7)1 Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 276 ( 3.0) 285 ( 4.9)1 GENDER Male State 44 ( 3.2) 48 ( 3.1) 8 ( 1.9) 280 ( 2.1) 273 ( 1.8) 279 ( 5.4)1 Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 201 ( 3.0) 265 ( 3.1) 278 1 5.3)1 Female State 41 ( 3.1) 52 ( 3.5) 7 ( 2.0) 278 ( 1.9) 273 ( 1.5) 278 ( 4.9)! 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 62 students). 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 111 Minnesota TABLE AlOb I Teachers' Reports on the Use of Mathematical Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never L_ TOTAL Percentage and Proaciency Percentage and Preticiency Percentage and Prcadency State 19 ( 3.3) 72 ( 3.4) 9 ( 1.8) 271 ( 2,1) 276 ( 0.9) 290 ( 41.;) Nation 22 ( 3.7) 3.9) 9 ( 2.6) 254 ( 32) 2.3 ( 1.9) 282 ( 5.9)) RACE/ETHNICITY White State 19 ( 3.4) 71 ( 3.5) 10 ( 1.9) 274 ( 1.9)1 278 ( 0.9) 292 ( 4.5) Nation 17 ( 4.0) 72 ( 4.2) 10 ( 2.7) 261 ( 3.8)1 269 ( 2.1) 288 ( 6.2)' Slack State 20 ( 9,3) 70 ( 1 0 4 ( 2.9) *4* ( Nation 22 ( 5.9) 70 ( 6.3) 8 ( 3.9) 233 ( 5.9)1 241 ( 2.9) Hispanic State 17 ( 5.4) Nation 39 ( 247 ( 7.5) 3,8) 55 245 ( 7.3) ( 3,8)1 ***) Asian State 16 ( Or* 5.5) .-**) 5 ( ( 3.2) *0.) Nation 52 ( 5.7) 6 ( 4.2) *.) TYPE OF COMMUNITY Advantaged whin State 9 ( 4.5) 84 ( 4.7) "`) 277 ( 2,0) Nation 23 (14A) 63 (11,5) 15 ( 9.3) 278 ( 5.6)1 Extreme rural State 38 ( 9.3) 54 ( 9.2) 8 ( 2.8) 270 ( 1.3)1 276 ( 1.9)) Nation 27 (14.9) 65 (14.6) 8 ( 3.9) 262 ( 2.8)1 Other Stat 15 ( 4.0) 73 ( 4.7) 11 ( 3.6) 272 ( 4.0)I 278 ( 1.6) 285 ( 52)1 Nation 19 ( 4.3) 72 ( 5.0) ( 3.3) 253 ( 3.9)1 263 ( 22) 281 ( 7,1)1 Im The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ' Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 , r 112 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE AlOb I Teachers' Reports on the Use of Mathematical (c°ntinued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Al Least Once a Week Less Than Once a Week Never _ TOTAL Peroentage mid Proficiency Percentage and Proficiency Percentate aid Praiidancy State 19 ( 3.3) 72 ( 3.4) 9 ( 1.6) 271 ( 2.1) 276 ( 0.9) 290 ( 4$) Nation 22 ( 3.7) 69 ( 3.9) 9 ( 2,6) 264 ( 3.2) 263 ( 1.9) 262 ( 5.9)1 PARENTS' EDUCATION HS non-graduate State 23 ( 5.1) 71 ( 5.2) 6 ( 2.7) . alt ( 044 Hrlt ) 4*-41 ) Nation 25 ( 5.6) irk, ( I4r11) 66 ( 243 ( 7.2) 2.2) 9 ( 8$) -e) HS graduate State 22 ( 4.5) 69 ( 4.5) 8 ( 1.9) 262 ( 3.0)1 265 ( 1.5) ( Nation 23 ( 4.8) 246 ( 4.0)1 70 ( 255 ( 5.3) 22) 7 ( 2.8) ,H.4) Some college State 18 ( 3.r) 280 ( 2.8)1 73 ( 281 ( 4.1) 1.5) .44 Nation 18 ( 4.0) 261 ( 4.4)i 73 ( 269 ( 4.3) 2.3) 9 ( 2.4)) College graduate State 16 ( 3.0) 73 ( 3.3) 11 '( 2.3) 281 ( 2.9)1 284 ( 1,3) 297 ( 4.5)1 Nat on 20 ( 3.9) 89 ( 3.7) 11 ( 2.5) 266 ( 3.5)1 274 ( 2.2) 297 ( 4.2)1 OENDER Male State 18 ( 3.2) 72 ( 3.4) 9 ( 1.8) 270 ( 3.1) 276 ( 1.2) 294 ( 4.7) Nation 22 ( 4.1) 69 ( 4.1) 8 ( 2.0) 255 ( 4.1) 265 ( 2,1) 287 ( 7.2)1 Female State 19 ( 3.6) 71 ( 3.7) 9 ( 2.0) 273 ( 2.5) 275 ( 1.3) 285 ( 4.6)1 Nation 21 ( 3.6) 69 ( 4.2) 10 ( 3.3) 254 ( 3.3) 262 ( 1.9) 278 ( 6.0)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each populauon of interest, the value for the entire population is within I 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficie.lcy. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Minnesota TABLE Alla I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY UM NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week - About Once a Wook or Less TOTAL Percentage and Proficiency Percentage and Proficiency Percentile and ProgicioncY State 73 ( 3.9) 29 ( 3.9) 4 ( 1.3) 279 ( 1.2) 271 ( 1.8) 259 ( 6.1)1 Nation 82 ( 3.4) 31 ( 3.1) 7 ( 1.8) 287 ( 1.8) 254 ( 2.9) 280 ( 5.1)1 RACE/ETHNICITY White State 73 ( 4.0) 23 ( 4.0) 4 ( 1 ) 281 ( 1.1) 273 ( 1$) 262 ( 5.6)1 Nation 84 ( 3.7) 28 ( 3.2) 8 ( 2.3) 272 ( 1.9) 284 ( 3.4) 264 ( 5.4)! Black State 84 (13.9) ...) 26 (11.7) Vi 10 ( 444 ( 63) 444) Nation 50 ( 7.7) 41 ( 7.9) 2 ( 1.4) 244 ( 4.0) 233 ( 3,9)1 "4 ( 4") Hispanic State ...) 24 ( 5.5) 14 ( 5.2) Nation 81 ( 8.8) 32 ( 5,3) 8 ( 2.3) 251 ( 3.1) 240 ( 4.3)1 4" ( 44) Asian State *Mir 24 ( 8.8) 2 ( 444 ( 2.3) 444) Nation 83 284 ( 8.9) ( 7.0)1 1 0 ( 31) ...) ( ( 5.1) 444) TYPE OF COMMUNITY Advantaged urban State 81 280 ( 5.6) ( 2.3) ...) 7 Nation 83 283 (15.9) ( 7.3)t 23 ( 52) 14 (14.6) . ) Extreme twat State 67 (10 3) 30 (10.5) 2 ( 2.5) 277 ( 2.4)1 271 ( 2,7)1 Nation 50 268 (10.6) ( 4.0)1 40 247 (10.0) ( 7,6)1 10 ( 7.3) .4.) Other State 73 ( 5.5) 23 ( 5.5) 4 ( 2.3) 282 ( 1.9) 278 ( 1.7)1 ) Nation 63 ( 3.9) 31 ( 3.5) 6 ( 1.9) 267 ( 2.3) 255 ( 3.1) 257 ( 5.8)1 The standard errors of the esOmated 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). 1 114 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE Al la I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1990 NAEP TRIAL Day Several Times Week About Once a Week or STATE ASSESSMENT Almost Every a Lass _ TOTAL Percentage awl Proficiency Pereentage and 'Drachm/ ParaNdapo and PrOdency State 73 ( 3,9) 23 ( 3.9) ( 1.3) 279 ( 1.2) 271 ( 1.6) 259 ( 0.1)1 Nation 62 ( 3.4) 31 ( 3.1) 7 ( 1.8) 267 ( 1.8) 254 ( 2.9) 200 ( PARENTS EDUCATION HS non-graduate State 62 ( 7.3) 34 ( 72) .44) 4 ( 2.7) ( del Nation 67 ( 5.5) 27 ( 5.2) ( 2.1) 245 ( 32) 4911 HS graduate State 71 ( 4.7) 24 ( 4.4) 5 ( 1.6) 269 ( 1.4) 258 ( 3.5)1 Nation 61 ( 4.4) 34 ( 3.7) 6 ( 1.5) 257 ( 2.5) 250 ( 2.9) Some college State 74 ( 284 ( 4.3) 1.3) 22 ( 280 ( 4.2) 2.1)1 4 ( .44 1.4) Nation 68 ( 4.2) 26 ( 3.7) 6 ( 1.9) 272 ( 2.7) 258 ( 52) College graduate State 75 ( 3.7) 21 ( 3.6) 4 ( 1.5) 288 ( 1.5) 280 ( 2,3) Nation 81 ( 4.0) 31 ( 3.9) ( 3.4) 281 ( .2.2) 285 ( 3.1) GENDER Male State 72 ( 3.9) 23 ( 3.8) 280 ( 1.3) 289 ( 2.1) ( ".) Nation 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2.1) 258 ( 3.8) 281 ( 8.7)1 Female State 73 ( 4.3) 23 ( 42) 3 ( 1.1) 278 ( 1.5) 272 ( 1.7)1 ( ***) Nation 65 ( 3.6) 28 ( 3.3) 268 ( 1.8) 253 ( 2.5) ...M1=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 enure population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 115 Minnesota TABLE Al lb I Teachers' Reports On the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT At Least Several Times a Week About Onca a Week Less than Weeidy TOTAL Peroaddp atd Prof/Ana Porountage And Prolickacy Pitramta. and Proitolency State 39 ( 33) 32 ( 3.5) 29 ( 3.6) 271 ( 1.5) 275 ( 1.9) 284 ( 2.2) Nation 34 ( 3.6) 33 ( 3.4) 32 ( 3.6) 256 ( 23) 260 ( 2.3) 274 ( 2.7) RACE/ETHNICITY Whit State 39 ( 3,5) 32 ( 3.6) 30 ( 3.7) 273 ( 1.5) 278 ( 1.7) 266 ( 2.2) Nation 32 ( 264 ( 4.1) 2.7) 33 ( 264 ( 35) 2.7) 35 279 ( 3.8) ( 2.9) Mack State 42 ( 79) 20 ( 4.5) 444 ( 441 Nation ( 7.5) 31 ( 7.6) 23 ( 6.3) 232 ( 3.1)1 243 ( 2.3)1 246 ( 7.0)1 Hispanic State 62 ( 7.6) 29 ( 6.6) 20 ( 7.2) ( Nation 41 ( 7.7) 26 ( 5,3) 3$ ( 7.61 242 ( 32)) 244 ( 5.1)1 257 ( 23)1 Asian State 35 ( 7.0) **4 ( ***) 22 .4* ( 5.3) ( Nation 37 ( 6.3) 35 ( 9.7) 27 (10.4) TYPE OF COMMUNITY Advantaged urban State 39 ( 6.5) 31 ( 4.5) 30 ( 5.3) 270 ( 4.5)1 275 ( 3.6) 288 ( 4,2)1 Nation 59 (1;,.9) 20 ( 6,0) 21 ( 8.2) 273 t Extrema rural State 32 ( 8.5) 45 ( 7.4) 23 ( 7.7) 269 ( 1,5)1 275 ( 2.4)1 283 ( 4,6)1 Nation 27 (14.3) 49 (12,7) 24 (10.1) re ( ) 258 ( 6.7)1 Other State 42 ( 5.4) 24 ( $.6) 34 ( 6.0) 275 ( 1$) 280 ( 4.1)! 283 ( 3.3)1 Nation 30 ( 4.4.) 3.5 ( 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 r 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE Al lb 1 Teachers' Reports on the Frequency of (continued) mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT At Least Sews] Times a Week About Once a West Less than WIdy TOTAL Percentage and ProRdency Percentage and Proecietioy Percentage and Pronclency State 39 ( 3.5) 32 ( 3.5) 29 ( 3.6) 271 ( 1.5) 275 ( 1.9) 264 ( 2.2) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 260 ( 2.3) 274 ( 2.7) PARENTS EDUCATION HS non-graduate State 48 ( 5.2) 19 ( 4.6) .44) Nation 35 ( 6.0) 29 ( 6.3) 36 ( 69) 239 ( 3.5) 250 ( 43)1 NS graduate State 45 ( 4.7) 30 ( 4.3) 25 ( 4.2) 262 ( 23) 263 ( 2.5) 272 ( 2.4) Nation 35 ( 5.3) 36 ( 4.5) 30 ( 4.6) 250 ( 3.8) 250 ( 2.7) 263 ( 3.4) Some college State 35 ( 4.0) 37 ( 4.6) 28 ( 3.4) 276 ( 2.3) 293 ( 1.9) 290 ( 2.5) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 266 ( 4,2) 278 ( 2.6) College graduate State 36 ( 3.6) 31 ( 3.4) 33 ( 3.9) 279 ( 1.9) 285 ( 2.3) 292 ( 2.4) Nation 35 ( 3.6) 32 ( 3.4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Male Esate 41 ( 3.6) 31 ( 3.5) 28 ( 3.4) 271 ( 2.0) 275 ( 2.3) 265 ( 2.4) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 261 ( 2.6) 275 ( 3.2) Female State 37 ( 3.6) 33 ( 3.7) 30 ( 3.9) 270 ( 1.8) 275 ( 2.2) 284 ( 2.5) 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. 6** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 117 Minnesota TABLE A 12 I Students' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Oncoa Weak 'Loss Than Once a Walk Now TOTAL State Nation RACEiETNNICITY White State Nation Mack State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extrema rural State Nation Other State Nation Ponandage Peroatitaga Percentage ind and and PraIdency Proldercy Prolicioncy 2e( 2.0) 28 ( 1.7) 45 ( 2.3) 277 ( 1.7) 279 ( 1.2) 273 ( 1.3) 28 ( 24) 28 ( 1.4) 44 ( 2.9) 25$ ( 2.7) 267 ( 2.0) 261 ( 1.6) 26 ( 1.9) 28 ( 1.9) 46 ( 2.4) 280 ( 1.9) 281 ( 1.2) 276 ( 1.1) 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 268 ( 3.1) 272 ( 1.9) 270 ( 1.7) 39 ( 53) 24 ( 5.0) 37 ( 7.0) 11-41, ) 11. ft* ( ) 4.441 28 ( 3.0) 24 ( 34) 48 ( 4.7) 234 ( 3.0) 245 ( 4.6) 234 ( 3.1) 23 ( 4.7) 29 ( 5.0) 43 ( 5.4) ( 4** ( 0+1 11. *** ) 37 ( 5.2) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) 25 ( 8.9) 27 ( 6.8) 4.8 ( 7.4) *IV ( GI ) Rt. *** ) ( ) 28 ( 6.4) 32 ( 4.0) 40 ( 6.2) 441 ( !WO ) 4* ( MI* ) 4*14 ( SIM ) 19 ( 2.7) 29 ( 2.9) 51 ( 3.5) 277 ( 44) 279 ( 2.2) 276 ( 1.8) 27 (13.9) 33 ( 44) 4° (13.4) 28e 5.4)1 279 ( 3.5)1 26 ( 3.9) 24 ( 3.9) SO ( 5.1) 281 ( 4.6) 278 ( 2.9)1 272 ( 1.8)1 34 (10.8! 27 1 3.8) 39 (11.6) 249 ( 52)1 264 ( 34)1 256 ( 6.2)4 27 ( 3.0) 31 ( 2.8) 42 ( 3.8) 278 ( 2.3) 283 ( 1.7) 277 ( 2.3) 27 1 2.6) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 254 ( 2.1) 262 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It c. be said with about 95 percent certamty that, for each population of interest, the value for the entire population is within -; 2 standard errors of the estimate for the sample, ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I 4 r , IS THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A 12 I Students' Reports on the Frequency of Small (continued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Weak Less Than Once a Week Never TOTAL Percentage mid PrOdckenty Parentage and Proficiency Percentage and Mildewy State 26 ( 2.0) 28 ( 1.7) 45 ( 2.3) 277 ( 1.7) 279 ( 1.2) 273 ( 1.3) Nation 2$ ( 2.5) 28 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 261 ( 1.6) PARENTS' EDUCATION HS non-graduate State 24 ( 04* ( 5.0) 111111 21 ( 3.9) 55 ( 6.3) ...) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4$) 242 ( 3.4) 244 ( 3.0) 242 ( 2.7) HS graduate State 25 ( 2.3) 26 ( 2$) 49 ( 3.0) 263 ( 2.6) 269 ( 2.1) 262 ( 22) Nation 28 ( 3.0) 2$ ( 1.8) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some college State 25 ( 2.7) 31 ( 2.51 44 ( 3.1) 285 ( 3.1) 285 ( 1.9) 280 ( 1$) Nation 27 ( 3.9) 27 ( 2.4) 48 ( 3.8) 265 ( 3.6) 268 ( 3.3) 266 ( 2.1) College graduate State 28 ( 2,3) 30 ( 2.0) 4.. ( 2.3) 287 ( 2.0) 285 ( 1.6) 283 ( 1.7) Nation 28 ( 3,0) 28 ( 1.8) 44 ( 3.6) 270 ( 2.7) 278 ( 2.8) 275 ( 2.2) GENDER Male State 28 ( 2.2) 29 ( 2.1) 43 ( 2.5) 277 ( 2,0) 280 ( 1.6) 274 ( 1.6) Nation 31 ( 2.9) 28 1.7) 41 ( 2.9) 259 ( 3.3) 268 ( 2.6) 282 ( 1.8) Female State 25 ( 2.0) 28 ( 1,9) 47 ( 2.6) 277 ( 2.2) 279 ( 1.6) 272 ( 1.5) Nation 26 ( 2.4) 27 ( 1.8) 47 ( 3.2) 257 ( 2.8) 266 ( 1.7) 260 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample, *** Sample We is insufficient to permit a reliable estimate (fewer than 62 students). 1 4. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Minnesota TABLE A13 I Students' Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a We* Never TOTAL Percentage and Proficiency Perventege and Proltdency Perteldip State 23 ( 2.1) 38 ( 14) 39 ( 22) 270 ( 1.5) 280 ( 1.1) 275 ( 1.3) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 256 ( 2.8) 209 ( 1.5) 259 ( 1.8) RACE/ETHNICITY Who State 23 ( 2.2) 39 ( 1.7) 38 ( 2.3) 273 ( 1.5) 282 ( 1.1) 278 ( 1.3) Nation 27 ( 1.9) 33 ( 1.8) 40 ( 2.5) 208 ( 2.8) 275 ( 1.6) 2e$ ( 1.8) Black State 28 ( 8.8) ( «al 29 ( 54) ..«*) 43 ( 11111 7.1) ***) Nation 27 ( 3.3) 27 ( 3.2) 48 ( 4.5) 234 ( 3.7) 24.8 ( 43) 232 ( 2.6) Hispanic State 22 ( 4.7) ( *al 38 ( 4.6) 42 ( 5.7) $4,41 38 ( 42) 23 ( 2.0) 40 ( 4.0) 241 ( 4.8) 253 ( 4.3) 240 ( 1.9) Asian State 27 (10.1) ( 25 ( *** 5.8) ( Nation 32 ( 3.7) *v.) 30 ( 3.2) 38 ( 4.04, 4.7) TYPE OF COMMUNITY Advantaged urban State 21 ( 3.4) 41 ( 2.4) :119 ( 3.8) 271 ( 3.8)1 260 ( 2.7) 2/8 ( 2.1) Nation 36 (10.3) 33 ( 4.8) 32 (11.1) 278 ( 6.1)1 264 ( 3.2)1 281 ( 5.9)3 Extreme rtral State 29 ( 5.6) ( 3.9) 31 ( 4.3) 289 ( 1.9)1 280 ( 1.8) 277 ( 2.8) Nation 37 ( 4.7) 43 ( 5.0) ilhb ( *YIP) 262 ( 4.7)1 251 ( 5.2)I Other State 20 ( 3.0) 37 ( 2.6) 43 ( 4.2) 278 ( 2.7) 282 ( 1.8) 27'6 ( 1.9) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 256 2.9) 270 ( 1.8) 260 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A 13 I Students' Reports on the Use of Mathematics ("mtinued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAV TRIAL STATE ASSESSMENT At Least Once a Week Loss Than Once a Wook New TOTAL Peivantage and Prolicioncy Percentage and Proficiency Rorcontace and Proficiency State 23 ( 2.1) 38 ( 1.5) 38 ( 2.2) 270 ( 1.5) 260 ( 1.1) 275 ( 1,3) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 25$ ( 2.8) 289 1.5) 259 ( 1.8) PARENTS EDUCATION HS non-graduate State 23 ( 4.1) 33 ( 5.6) 44 ( 4.7) ) Nation 27 ( 4.2) 26 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) HS graduate State 24 ( 3.2) 38 ( 2.2) 40 ( 2.9) 258 ( 3.0) 271 ( 1.8) 282 ( 1.7) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some college State 21 ( 2.0) 40 ( 2.4) 39 ( 2.9) 277 ( 3.0) 285 ( 1.3) 283 ( 2.2) Nation 29 ( 2.8) 36 ( 2.3) 35 ( 2.6) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) College graduate State 23 ( 2.4) 39 ( 1.9) 38 ( 2.8) 281 ( 1.9) 287 ( 1.8) 285 ( 1.7) Nation 30 ( 2$) 32 ( 2.0) 38 ( 2.6) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Male State 26 ( 2.3) 38 ( 1.7) 38 ( 2$) 271 ( 2.0) 280 ( 1.3) 276 ( 1.8) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 25$ ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 20 ( 2.4) 40 ( 2.1) 40 ( 2$) 269 ( 2,5) 280 ( 1.5) 274 ( 1.4) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 10) 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 msufficient to permit a reliable estimate (fewer than 62 students). 126 THE 2990 NAEP TRIAL STATE ASSESSMENT 221 Minnesota TABLE A14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 /MEP TRIAL STATE ASSESSMENT Almost Every Day Several Tknes a Week About Once a Week or Less TOTAL and Proficiency Percentage and PnatIciency Peramtage and Proficiency State 81 ( 1.5) 12 ( 1-2) 7 ( 1.2) 279 ( ('.9) 206 ( 1.8) 257 ( 4.4) Nation 74 ( 1-9) 14 ( 0.8) 12 ( 1.8) 267 ( 1.2) 252 1.7) 242 ( 4.5) RACE/ETHNICITY White State 82 ( 1.4) 12 ( 1.2) 6 ( 1.0) 281 ( 0.9) 268 ( 1.8) 264 ( 3.8) Nation 76 ( 2.5) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 2.2) 252 ( 5.1)1 Black State 76 (12.8) 3 ( 2.1) 21 (14.4) .4* 4Nri Nation 71 ( 2.8) 15 ( 1.7) 14 ( 32) 240 ( 2.9) 232 ( 3.1) 223 ( 6.1)1 Hispanic State 69 ( 5.8) Vi 12 ( ( 3.7) 18 ( frS Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 51) 224 ( 3.4) Asian State 73 ( 5.0) 9 ( 3.4) *4. ( ) ( ***) ( Nation 79 ( 289 ( 4.9) 5.0)1 13 ( *** ( 3.4) ***) 8 ( *** ( 2.6) ***) TYPE OF COMMUNITY Advantaged urban State 81 ( 3.4) 12 ( 2.5) 280 ( 1.6) Nation 73 (11.1) 13 ( 1.7) 14 (10.4) 286 1. 4.6)1 *4-Ir Extreme rural State 81 ( 3.8) 14 ( 3.0) 277 ( 1.9) 270 ( 2.8)1 Nation 68 (11.3) 15 ( 3.6) 17 ( 8.2) 263 ( 4.2)1 ( Other State 84 ( 1.4) 9 ( 1.5) 7 ( 2.0) 282 ( 1.5) 269 ( 2.8) 257 ( 5.2)1 Nation 75 ( 2.2) 14 ( 1.0) 10 ( 1.9) 207 ( 1,5) 252 ( 2.6) ( 4.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, *I's Sample Sin is insufficient to permit a reliable estimate (fewer than 62 students). 'I 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A14 I Students' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Win* or Loss TOTAL Poreordago and Pso Scion Percentage and ProMoney Peiventage and Modality State 81 ( 1.5) 12 ( 12) 7 ( 1.2) 279 ( 0.9) 200 ( 1.8) 257 ( 4.4) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 4.5) PARENTS' EDUCATION non-gracksate State 60 ( 3.7) 11 ( 2.7) 9 ( 3.0) 256 ( 3.6) ( *44 ( Nation 64 ( 245 ( 3.4) 2.3) 18 ( ow. 2.0) 18 ( *44 ( 3.1) .") HS graduate State 78 ( 267 ( 2.2) 1.5) 13 ( 257 ( 1.5) 2.7) 9 ( 1.4) Nation 71 ( 3.6) 16 ( 1.8) 13 ( 2.8) 25$ ( 1.6) 249 ( 3.2) 239 ( 3.4)1 Some cottage State 81 ( 2.2) 13 ( 1.9) 6 285 ( 1.3) 276 ( 3.8) ( Nation 80 ( 270 ( 2.0) 1.9) "* ( ) ***) Co liege graduate State 85 ( 1.7) 10 ( 1.3) 5.( 1.3) 287 ( 1.1 ) 275 ( 3.1) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 260 ( 2.8) 257 ( 6.4)1 GENDER Male State 79 ( 1.8) 13 ( 1.3) 8 ( 1.5) 280 ( 1.2) 265 ( 2.8) 258 ( 4.7) Nation 72 ( 2.4) 16 ( 1.2) 12 ( 2.1) 268 ( 1.6) 252 ( 2.5) 242 ( 6.1) Female State 84 ( 1.5) 11 ( 1.4) 5 ( 0.9) 278 ( 1.1) 267 ( 2.4) 255 ( 5.1) Nation 76 ( 1.8) 13 ( 1.0) 11 ( 1.6) 265 ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can bc 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 de.?rmination of the variability of this estimated mean proficiency. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Minnesota TABLE Al5 1 Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Least Several Times STATE ASSESSMENT Week About Once a Week Liss Than Weekly - TOTAL ond Proficiency and Proficiency Percentage and Proficiency State 33 ( 2.2) 29 ( 1.6) 37 ( 2.4) 269 ( 1$) 275 ( 1.3) 282 ( 1.5) Nation 38 ( 2.4) 25 1.2) 37 ( 2.5) 253 ( 2.2) 261 ( 1.4) 272 ( 1.9) RACE/ETHNICITY White State 32 ( 2.2) 30 ( 1.7) 38 ( 2.6) 273 ( 1.3) 277 ( 12) 284 ( 1.5) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 282 ( 2.5) 269 ( 1.5) 277 ( 2.0) Mack State 46 (11.2) 31 ( 7.9) 23 ( 8.8) 41,*4 .414 Nation 413 ( 3.8) 32 ( 2.7) 20) 3.1) 232 ( 4.3) 241 ( 2.9) 241 ( 4.4) Hispanic State 50 ( 5.8) 27 ( 5.5) 24 ( 5.1) ..*) Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 238 ( 3.9) 247 ( 3.3) 248 ( 3.3) Asian State 26 ( 5.2) 22 ( 5.8) 52 ( ***) ( 4- ) Nation 32 ( 5.1) *** ( e") 51 ( 5.9) ***) TYPE OF COMMUNITY Advantaged urban State 35 ( 3.8) 28 ( 2.4) 37 ( 3.9) 269 ( 3.6) 277 ( 2.7) 285 ( 2.8) Nation 50 t 9.0) 31 ( 9.3) 271 ( 3.3)1 ( 299 ( 5.3)1 Extreme nes! State 33 ( 5.8) 35 ( 3.8) 31 ( 5.1) 271 ( 2.0)1 275 ( 2.0)1 281 ( 3.5) Nation 42 (10.1) 30 ( 4.4) 28 ( 7.5) 249 ( 4.0)1 256 ( 3.4)1 267 ( 7.3)1 Other State 33 ( 3.2) 27 ( 2.3) 41 ( 3.7) 274 ( 2.3) 279 ( 2.2) 283 ( 1.9) Nation 36 ( 2,9) 26 ( 1.2) 38 ( 2.9) 252 ( 3.0) 261 ( 2.1) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size Is insufficient to permit a reliable estimate (fewer than 62 students). 1 124 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A1S I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Several Times a W eek About Once a Week Lass Than %moldy TOTAL Poventage and Proeciency Pawls, &id Proliclancy Paraanlaga and Pndidency state 33 ( 2.2) 29 ( 1$) $7 ( 2.4) 269 ( 1.5) 275 ( 1.3) 282 ( 1.5) Nation 3$ ( 2.4' 25 ( 1.2) 37 ( 2.5) 253 ( 261 ( 1.4) 272 ( 1.9) PARENTS EDUCATION HS non-gr*duate State 41 ( 5.1) 11.11.11 39 ( *4* ( 4.8) 20 ( 4.7) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) HS gi'aduate state 35 ( 3.2) 29 ( 2.4) 37 ( 3.0) 257 ( 2.0) 285 ( 1.7) 270 ( 2.0) Nation 40 ( 3.2) 29 ( 22) 32 ( 3.8) 247 ( 2.7) 258 ( 24) 262 ( 2.2) Some college State 33 ( 2.5) 30 ( 2.0) 37 ( 2.7) 278 ( 2.1) 284 ( 2.2) 28a ( 2.1) Nation 34 ( 3.4) 28 ( 2.2) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) College graduate State 32 ( 2.1) 29 ( 1.8) 39 ( 2.4) 279 ( 2.1) 282 ( 2.1) 291 ( 1.7) Nation 33 ( 2.8) 22 ( 1.8) 41 ( 2.6) 284 ( 2.8) 273 ( 2.5) 285 ( 2.3) GENDER MmIe State 34 ( 2.3) 31 ( 1.8) 36 ( 2.4) 288 ( 2.1) 277 ( 1.6) 283 ( 1.9) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 263 ( 2.3) 274 ( 2.4) Female State 33 ( 2.5) 28 ( 1.7) 39 ( 2.8) 271 ( 1.7) 273 ( 1.8) 281 ( 1.8) Nation 37 ( 2.5) 25 ( 15) 38 ( 2.8) 253 I. 2.1) 259 ( 1.8) 280 ( 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 NAEP TRIAL STATE ASSESSMENT 125 Minnesota TABLE Al8 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT Oen a Calcdator Teacher Expia Ins Calculator Use Yes No Yes No TOTAL Parcentege and Proficiency ad ( 02) 276 ( 0.6) 97 ( OA) 263 ( 1.3) 99 ( 02) 279 ( 0.8) 96 ( 0.3) 270 ( 1.5) 93 ( 2$) 11,011, 11.1 1113 ( 1 ) 237 ( 2.8) 96 ( 1.9) 241 ( 3.7) 92 ( 1.2) 245 ( 2.7) 100 ( 0.0) 267 ( 4.6) 99 ( 0.9) 282 ( 5.3)1 99 ( 0.4) 277 ( 1.7) 99 ( 1.0) 281 ( 3.8)s 98 ( 0.5) 276 ( 1.6) 96 ( 1.3) 257 ( 3.9)1 99 ( 0.4) 279 ( 1.3) 97 ( 0.5) 263 ( 1.7) Percentage and Proficiency 1 ( 0.2) 3 ( 0.4) 234 ( 3.8) 1 ( 0.2) 2 ( 0.3) 7 ( 2,5) ( .41 7 ( 1 ( 4 ( 1.9) 8 ( 1.2) ( «4) 0 ( 0.0) 1 ( 0.9) 1 ( 1,0) 2 ( OS) 4 ( 1.3) ( 1 ( OA) ( ***) 3 ( 03) 233 ( 5.4) Percenteoe and Proficiency 51 ( 2.1) 274 1.3) 49 (2.3) 258 ( 1.7) 50 ( 2.1) 277 ( 1,1) 48 ( 2.6) 268 ( 1.5) 87 ( 9.6) Mr* ( 114111 53 ( 4.9) 235 ( 3.8) 58 ( 8.0) *** 63 ( 4.3) 243 ( 3,4) 48 ( 8.4) .41 52 ( 4.8) ***) 62 ( 3.2) 273 ( 2.5) 45 (12.2) 278 ( 2.5)1 48 ( to) 274 ( 2.4)1 42 ( 8.7) 251 ( 4,8)1 52 ( 3.3) 277 ( 1.7) 50 ( 2.7) 258 ( 2.1) Percenteoa and Proficiency 40 ( 2.1) 276 ( 1.1) 51 ( 2.3) 208 ( 1$) 50 ( 2.1) 280 ( 1.1) 54 ( 2.6) 273 ( 1.8) 33 ( 9.15) ***) 47 ( 4.9) 239 ( 2.7) 42 ( 0.0) a4,1 37 ( 4.3) 245 ( 2.9) 52 ( 6.4) 4,41 46 ( 4.8) ( 48 ( 3.2) 282 ( 2.2) 55 (12.2) 285 ( 8.4)1 54 ( 6.0) 277 ( 2.0)1 58 ( 8.7) 261 ( 4.4)1 46 ( 3.3) 280 ( 1.8) 50 ( 2.7) 268 ( 2.0) State Nation RACE/ETHNICITY Mgt* State Nation Black State Nation Hispanic State Nation Asian State Nation TYPE OF COMMUNITY Advartaged urban State Nation Extreme rural State Nation Mar 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 sin is insufficient to permit a reliable estimate (fewer than 62 students). 126 1HE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE Al8 (continued) Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL. STATE ASSESSMENT - Own a Calculator . Teacher E.xplakts Calculator Use Yes , , No YeS No TOTAL State Nation PARENTS' EDUCATION NS non-graduate State Nation HS graduate State Nation Sono college State Nation College graduate State Nation GENDER Male State Nation Female State Nation Percentage and Proadency 99 ( 0.2) 276 ( 0.8) 97 ( 0.4) 263 ( 1.3) 93 ( 2.0) 256 ( 3.2) 92 ( 1.6) 243 ( 2.0) 98 ( 0.5) 264 ( 1.4) 97 ( 0.6) 255 ( 1.5) 99 ( 0.4) 283 ( 1.2) 98 ( 0.9) 268 ( 1.8) 99 ( 0.3) 285 ( 1.1) 99 ( 0.2) 275 ( 1.6) 98 ( 0.3) 277 ( 1.1) 07 ( 0.5) 264 ( 1.7) 99 ( 03) 178 ( 1.0) 97 ( 0.5) 282 ( 1.3) Permits.. PeresKaga and and and Preaching. Protkiancy Prolkkoncy ( 0.2) ( ***) 3 ( 0.4) 234 ( 31) 7 ( 2.0) 444 ( 444) 8 ( 1.8) ( *) 2 ( 0.5) 3 ( 0.6) 444 ( 444) ( 0.4) 444 ( 4") 4 ( 0,9) 4" 444) 1 ( 0.3) 444 ( 4") 1 ( 02) 444 ( ) 2 ( 0.3) 1 ( 0.3) 444 ( 4") 3 ( 0.5) 51 ( 2.1) 274 ( 1.3) 49 ( 2.3) 258 ( 1.7) 51 ( 4.9) 53 ( 4.8) 242 ( 2.9) 53 ( 3.1) 262 ( 2.0) 54 ( 3.0) 252 ( 1.9) 52 ( 2.8) 280 ( 1.5) 48 ( 3.2) 265 ( 2.4) 49 ( 2.2) 283 ( 1.6) 46 ( 2.6) 268 ( 2.2) 54 ( 2.3) 274 ( 1.7) 51 ( 2.6) 258 ( 2.1) ( 2.3) 273 ( 1,4) 47 ( 2,5) 258 ( 1.7) 49 ( 2.1) 278 ( 1.1) 51 ( 2.3) 266 ( 1.5) 49 ( 4.9) - 47 ( 4.6) 243 ( 2.5) 47 ( 3.1) 266 ( 1.9) 46 ( 3.0) 258 ( 2.0) 48 ( 2.8) 288 ( 1.7) 52 ( 3.2) 268 ( 22) 51 ( 2.2) 287 ( 1.5) 54 ( 2.8) 280 ( 1.9) 46 ( 2.3) 279 ( 1.6) 49 ( 2.6) 269 ( 2.1) 52 ( 2-3) 27$ ( 1.3) 53 ( 2.5) 263 ( 1.8) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 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 Minnesota TABLE A19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Worthig Problems Class Doing Problems at Horne Taking Quizzes or Tests Almost Always Never Almost Always NeVer Almost Always , Never TOTAL Percintep and Proliciency Pereentso and Proficiency Patentee, and Proficiency Patents', and Preticiency Percents. and Proficiency Percentsgs and Proficiency State 46 ( 1.5) 20 ( 1.6) ( 1.3) 15 ( 0.8) 21 ( 1.5) 31 ( 1.6) 269 ( 1.2) 286 ( 1.2) 275 ( 1.3) 277 ( 1.7) 272 ( 2.1) 286 ( 1.2) Nation 43 ( 1.5) 23 ( 1.9) 90 ( 1.3) 19 ( 0.9) 27 ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) RACE/ETHNICITY WM. State 44 ( 1.6) 21 ( 1.6) 29 ( 1.4) 15 ( 0.9) 21 (1.6) 33 ( 1.7) 272 ( 1.1) 286 ( 1.3) 277 ( 12) 279 ( 1.8) 275 ( 1.8) 287 ( 1.2) Nation 4$ ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 25 ( 1.6) 32 ( 2.3) 262 ( 1.7) 278 ( 1.3) 270 ( 1.7) 269 ( 2.3) 263 ( 2.6) 279 ( 1.2) Slack State 65 ( 6.8) 17 ( 5.4) 19 ( It* ( 3.5) 11+1) 41 (10.1) **.) 16 ( ( 4.3) Nation 57 ( 3.2) 20 ( 3.9) 31 ( 2.0) 18 ( 1.9) 38 ( 3.3) 24 ( 3.1) 232 ( 2.4) 249 ( 4.0) 233 ( 3.3) 248 ( 5.5) 230 ( 3.6) 251 ( 4.1) Hispank State 52 ( 4.8) 4*4(444) 4 ( 1.3) 44t4 ) 31 ( 4.4) 20 *** ( 4.2) **4) Nation 51 ( 2.9) 16 ( 3.5) 26 ( 32) 21 ( 2.1) 2$ ( 2.7) 22 ( 3.1) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1) 237 ( 3.2y 256 ( 4.2) Asian State 49 ( 5.0) 19 ( INN 5.0) ief ) 27 4.6) ( *es) 10 ( 3.6) 15 ( 5.2) 21 ( ( 5.3) ***) Nation 35 ( 6.3) ***) 29 ( 5.8) 30 ( 8.3) ***) 23 ( *4. 4.4) 23 ( 5.8) 48 ( 444 8,4) *44) TYPE Of COMMUNITY Advantaged urran State 46 ( 269 ( 3.1) 3.0) 17 ( 289 ( 2.8) 2.7)1 33 ( 272 ( 2.9) 2.6) 11 ( *4. 1.2) 23 272 ( 3.0) ( 4.8) 28 ( 292 ( 3.0) 2.1) Nation 51 ( 5.4) 23 (10.7) 32 ( 6.1) 15 ( 2.4) 31 ( 3.8) 28 ( 91) 270 ( 4.7)1 274 ( 4.9)f 281 ( 7.8)1 285 ( 4.2)1 Extreme nral State 42 ( 3.1) 22 ( 3.6) 27 ( 1.5) 14 ( 1.8) 14 ( 1 .8)' 34 1 2.5) 271 ( 1.8) 285 ( 2.2)1 271 ( 2.3) 275 ( 3.5)1 271 1 2.6)1 287 ( 2.7)1 Nation 46 ( 246 7.4) 4,3)1 29 ( OS) 268 ( 6.1)1 20 ( 2.5) 23 ( 263 ( 3.9) 4,4)1 24.. ( 6.6) 37 ( 270 ( 8.3) 4.0)1 00w State 45 ( 2,4) 19 ( 2.9) ( 2.3) 16 ( 1.6) 22 ( 2.7) 32 ( 3.1) 273 ( 2.0) 286 ( 2.0) 279 ( 1.9) 283 ( 2.0) 277 ( 2.2) 286 ( 1.7) Nation 48 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1.8) 29 ( 2.1) 254 ( 2.1) 272 ( 1.8) 263 ( 2.3) 263 ( 2.8) 253 ( 2.7) 275 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 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). 128 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A19 I Students' Reports on the Use of a Calculator (continued) 1 for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRLAL STATE ASSESSMENT taticleldng Pr°134ms 6- Class Doing Problems at Nome .. Taidng Quiztes or Toots Almost Always - Never Almost Always Never Almost Always Never TOTAL Percentage and Proficiency Palmtop' end Proaciency Percentage and ProNciancy Percentage and Proficiency Percentage and Proficiency Percentage and Profit Norm State 45 ( 1.5) 20 ( 1.13) 29 ( 1.3) 15 ( 0.8) 21 ( 15) 31 ( 1.6) 2e9( 1.2) 285 ( 1.2) 275 ( 1.3) 277 ( 1.7) 272 ( 2.1) 236 ( 1.2) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.5i 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) PARENTS EDUCATION NS non-graduate State 51 ( 6.0) 19 ( 3.6) 38 ( 5.5) 16 ( 41.5) 24 ( 5.8) 25 ( 4.3) ( ( ( ( ( ( Nation 54 ( 3.3) 19 ( 3.8) 26 ( 3.1) 22 ( 2.6) 32 ( 3.8) 24 ( 3.2) 240 ( 2.3) 244 ( 3.8) 244 ( 4.2) 237 ( 2.3) 251 ( 4.6) NS gradual. State 49 ( 2.0) 16 ( 1.7) 23 ( 1.9) 16 ( 1.4) 22 ( 2.2) 26 ( 2.1) 293 ( 2.0) 273 ( 2.3) 261 ( 2.4) 270 ( 3.5) 260 ( 2.7) 275 ( 1.8) Nation 52 ( 2.5) 20 ( 2.4) 29 ( 1.9) 18 ( 1.5) 20 ( 1.8) 27 ( 2.2) 249 ( 1.4) 265 ( 2.7) 250 ( 2.4) 258 ( 2.4) 24$ ( 2.8) 265 ( 2.0) Som. college State 42 ( 2.2) 24 ( 1.9) 27 ( 2.2) 12 ( 1.3) 1$ ( 2,0) 39 ( 25) 276 ( 1.7) 280 ( 2.4) 280 ( 2.0) 282 ( 3.5) 277 ( 3.0) 290 ( 2.0) Nation 46 ( 2.8) 26 ( 2.8) 28 ( 2,0) 20 ( 1.9) 26 ( 2.4) 35 ( 2.5) 258 ( 2.1) 272 ( 2.5) 287 ( 3.0) 260 ( 3.2) 255 ( 3.6) 275 ( 2.0) Co neg. graduate State 43( 1.9) 22 ( 2.3) 33 ( 2.0) 14 ( 1.0) 22 ( 1.9) 33 ( 2.1) 278 ( 1.7) 291 ( 1.7) 283 1.8) 287 ( 2.1) 282 ( 3.0) 293 ( 1.5) Nation 45( 1.9) 25 ( 2.4) 33 ( 2.0) 16 ( 1.4) 26 ( 1.6) 33 ( 2.7) 265( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 266 ( 2.6) 285 ( 2.0) GENDER Male State 48 ( 1.8) 17 ( 1.4) 28 ( 1.7) 17 ( 1.2) 20 ( 1.6) 28 ( 1.8) Zr0 ( 1.5) 287 ( 2.2) 275 ( 1.8) 276 ( 2.7) 272 ( 2.6) 238 ( 1.8) Nation 50( 1.7) 20 ( 2.0) 29 ( 1.6) 19 ( 1.3) 27 ( 1$) 26 ( 2.1) 255( 1.9) 275 ( 2.2) 264 ( 2.8) 263 ( 2.5) 256 ( 3.0) 277 ( 1.9) Female State 42 ( 2.1) 23 ( 2.1) 29 ( 1.5) 12 ( 1.2) 23 ( 2.0) 35 ( 2.1) 268 ( 1.5) 283 ( 1.4) 275 ( 1.6) 279 ( 2.0) 271 ( 2.3) 284 ( 1.5) Nation 46 ( 2,0) 26 ( 2.1) 32 ( 1.6) 18 ( 1.2) 27 ( 1.8) 33 ( 2.1) 252 ( 1.7) 209 ( 1.8) 259 ( 1.7) 263 ( 2.4) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). ,? 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 Minnesota TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL "Calculator-Use" "Calculator-Use" STATE ASSESSMENT High Group Other Group TOTAL Panantafe and Pnatiancy Paraantaga and Proficlincy State 50 ( 1.0) 50 ( 1.0) 252 ( 1.0) 200 ) 1.2) Nation 42 ( 1.3) 56 ( 1.3) 272 ( 1,8) 255 ( 1.5) RACE/ETHNICITY White State SOf 1.0) 50 ( 1.0) 284 ( 1.0) 273 ( 1.2) Nation 44 ( 1.4) 56 ( 1.4) 277 ( 1.7) 263 ( 1.7) Black State 40 ( 5.1) ( *1.1 ft** ( N ation 37 ( 3.4) 63 ( 3.4) 246 ( 3.9) 231 ( 3.0) Hispanic State 60 ( 6.2) Nation 36 ( 4.2) 54 ( 4.2) 254 ( 4.6) 238 ( 10) Asian State 45 ( 7.4) 41,141. 4+1 Nation 50 ( 4.5) SO ( 4.8) 0* ( TYPE OF COMMUNITY Advantaged urban State 51 ( 2.3) 49 ( 2.3) 280 ( 1.9) 270 ( 2.8) Nation 50 ( 3.8) 50 ( 3.8) 288 ( 4.9)! 275 ( 4.4)! Extreme rural State 51 ( 2.6) 49 ( 2.6) 282 ( 1.7) 270 ( 2.3)1 Nation 39 ( 5.6) 81 ( 5.6) 269 ( 4.4)! 248 ( 4.3)1 Other State 50 ( 1.7) 50 ( 1.7) 285 ( 1.5) 273 ( 1.7) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value fur the entire populauon is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample sue is insufficient to permit a reliable estimate (fewer than 62 students). 130 1 f' 77.1 .- THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO INAEP TRIAL STATE ASSESSMENT High "Ca lculator-Usa" Group Other "Calculator-Use Grow TOTAL. Percentage and Proficiency Percentage and Proficiency State 50 ( 1.0) 50 ( 1.0) 262 ( 1.0) 249 ( 12) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.8) 255 ( 15) PARENTS EDUCATION HS non-graduate State 48 ( 5.8) 54 ( 5.8) .44 ) Nation 34 ( 3.3) 68 ( 3.3) 248 ( 4.4) 242 ( 2.4) HS graduate State 48 ( 2.0) 54 ( 2.0) 270 ( 1.6) 259 ( 2.0) Nation 40 ( 22) 00 ( 2.2) 283 ( 2.0) 249 ( 1.8) Some collage State 54 ( 2.8) 46 ( 2.6) 289 ( 1.5) 277 ( 2.1) Nation 4$ ( 2.2) 52 ( 2.2) 277 ( 2.6) 258 ( 2.5) College graduate State 53 ( 1.8) 47 ( 1.8) 290 ( 1.3) 279 ( 1.9) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER Male State 46 ( 1.5) 54 ( 1.5) 284 ( 1.6) 269 ( 1.3) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 53 ( 1.4) 47 ( 1.4) 280 ( 1.1) 269 ( 1.7) Nation 45 ( 1.8) 55 ( 1.8) 289 ( 1,7) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 131 Minnesota TABLE A24 I Students' Reports on lyp cb of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE P4.4ATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Four Types I TOTAL Percentage and Proficiency Percentage and Proficiency Percentage seW !cadency State 12 ( 0.7) 31 ( 0.7) 57 ( 1.0) 258 ( 1.9) 274 ( 1.3) 281 ( 0.9) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1 3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) RACE/ETHMICITY white State 10 ( 0.6) 31 ( 0.8) 59 ( 1.0) 282 ( 2.2) 278 ( 1.1) 282 ( 0.9) Nation 18 ( 1.1) 29 ( 1.3) 56 ( 1.5) 251 ( 2.2) 288 ( 1.5) 276 ( 1.7) Slack State 26 ( 8.8) .4. ....) ( .41 39 ( 6.6) Nation 31 ( 1.9) 38 ( 2.2) 33 ( 2.4) 232 ( 3.2) 233 ( 32) 24.5 ( 3.3) Hispanic State 20 ( 4.1) 35 ( 5.8) 45 ( 8.1) ( .") Nation 44 ( 3.0) 30 ( 2.4) 28 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) Asian State 38 ( 8.5) firir --*) 28 ( 5.3) ) 34 ( 7.2) ree ( eee) Nation 28 ( 6.0) .44 ( .4.) 33 ( 5.8) ree ( ere) 38 ( 4.2) ree ( ere) TYPE OF COMMUNITY Advantaged Winn State 34 ( 2.2) 50 ( 2.8) 276 ( 2.3) 281 ( 2.0) Nation 13 ( 3.8) 26 ( 2.1) 61 ( 4.9) 4-9 ( *44 287 ( 3.6)1 Extreme nral State 27 ( 1.6) 63 ( 1.8) 274 2.4) 281 1.9) Nation 17 ( 4.9) 33 ( 3.2) 50 ( 5.1) ( 253 ( 4.3)! 263 ( 5.6)) Other State 10 ( 0.9) 31 ( 1.3) 60 ( 1.6) 285 ( 3.2) 277 ( 1.9) 282 ( 1.4) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 1.5) 244 ( 2.8) 252 ( 2.2) 272 ( 1.7) 11111MIIMMINIMIlinm.MMEMIIM.MFlp.lk The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of inter...st 'he value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Ti.:erpLL 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 e . 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A24 I Students' Reports on Types of Reading (c°ntinued) Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL 1 STATE ASSESSMENT Zero to TWo Typos Thre Types Four Typos TOTAL Pereentage and Praciency Percentage and Proactency Percentage and Proectency State 12 ( 0.7) 31 ( 0.7) 57 ( 1.0) 258 ( 1.9) 274 ( 1.3) 281 ( 0.9) Nation 21 ( 1,0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) PARENTS' EVOCATION NS non-gradua State 36 ( 4.7) ( 5.1 36 ( 4.6) Off ( *RR ) ( *Olt ) *4- Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 246 ( 3.3) KS gradtato State 14 ( 1.4) 37 ( 1.7) 49 ( 1.8) 253 ( 3.4) 263 ( 1.7) 269 ( 1.7) Nation 26 ( 2.2) 33 ( 1.9) 40 ( 1.7) 246 ( 2.2) 253 ( 2.7) 260 ( 2.1) Some cotlogo State 9 ( 1.2) 27 ( 1.7) 64 ( 1.9) (433 ( 2.2) 284 ( 1.4) Nation 17 ( 1.5) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduate State 6 ( 0.9) 30 ( 1 2) 64( 1.4) 272 ( 3.7) 280 ( 1.9) 288 ( 1.2) Nation 10 ( 0.8) 28 ( 1.8) 62 ( 2.0) 254 ( 2.8) 269 ( 2.5) 280 ( 1.8) GENDER State 12 ( 1.0) . , 2) 56 ( 1.3) 258 ( 2.8) 274 t t.6) 282 ( 1.3) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Femal State 12 ( 1.0) 30 ( 1.3) 59 ( 1.5) 258 ( 2.9) 273 ( 1.6) 280 ( 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 -I-. 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 133 Minnesota TABLE A25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT One Hour or Less Two Hours Three Hours Four to Five Hours Six Hours or Moro TOTAL Parcentage and Proficiency Percentage and ft:Adam Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 15 ( 0.8) 27 ( 0.8) 26 ( 0.9) 25 ( 0.7) ( 05) 281 ( 1.7) 281 ( 1.5) 277 ( 1.1) 271 ( 1.4) 260 ( 2.3) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 ( 1.1) 18 ( 1.0) 209 ( 2.2) 268 ( 1.8) 265 ( 1.7) 280 ( 1.7) 245 ( 1.7) 1ETHNICITY we State 15 ( 0.9) 27 ( 0.8) 27 ( 0.9) 25 ( 01) ( 0.5) 283 ( 1.5) 283 ( 1.4) 279 ( 1.2) 274 ( 1.4) 264 ( 2$) Nation 13 ( 1.0) 23 ( 1.2) 24 ( 1.1) 27 ( 1.4) 12 ( 1.2) 276 ( 2.5) 275 ( 2.2) 272 ( 1.9) 287 ( 1.7) 253 ( 2.6) Black State 3 ( 1.9) ***) 18 ( 3.8) 54 ( 5.4) ( ...) Nation 6 ( 0.8) 13 ( 1.7) 17 ( 2.1) 32 ( 1.8) 32 ( 22) 239 ( 7.0) 239 ( 5.0) 239 ( 4.0) 233 ( 2$) Hispanic State 16 ( 4.1) 22 ( 4.5) ...) 29 ( 4.8) **) 23 (- 4.3) 441 10 ( 3.4) Nation 14 ( 2.4) 20 ( 2.5) 19 ( 2.1) 31 ( 3.1) 17 ( 1.7) ( ".) 245 ( 3.2) 242 ( 5.6) 247 ( 3.5) 236 ( 3.8) Asian State 12 ( ***) 20 ( 5*. ( 3.7) 04-5) 22 ( 4.5) ( Nation 18 ( 5.0) 24 ( "e ( 4.2) "*) 22 ( .0. ( 3.1) ...) 23 ( 4.7) 43 ( ( 4.0) IN* ) TYPE OF COMMUNITY Advantaged urban State 19 ( 279 ( 1.7) 2.4) 29 ( 282 ( 1.1) 2.6) 23 ( 277 ( 1.5) 2.2) 22 ( 274 ( 1.5) 2.5) 8 ( *** 1.1) ***) Nation 18 ( 1.4) 21 ( 1.8) ...) 30 ( 4.3) 6 ( *** ( 2.0) ***) Extreme rural State 13 ( 1.4) 25 ( 1.8) 291 2.3) 27 ( 1.9) 7 ( 1.0) 282 ( 4.0)1 281 ( 2.5) 274 ( 1.9)1 272 ( 2.8) Nation 14 ( 3.3) 19 ( 2.6) 26 ( 2.7) 19 ( 3.8) 256 ( 3.6)1 Other State 15 ( 1.4) 28 ( 1.4) 27 ( 1.2) 24 ( 1.1) 2as 1.7) 282 ( 2.5) 279 ( 2.0) 273 ( 1.9) Nation 12 ( 1.0) 21 ( 1.0) 23 ( 1.2) 27 ( 1.2) 17 ( 1.4) 268 ( 2.6) 269 ( 2.3) 265 ( 2.1) 259 ( 2.2) 246 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 I 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A25 1 Students' Reports on the Amount of Time Spent (continued) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL One Hour or Four to Five Six Hours or STATE ASSESSMENT Lass Two IRA's Throe Hours Hours Mon - - TOTAL Pen:~ and Proficiency Peroenlass and Proficiency Parcentage and Proficiency Penalise and Proficiency Pereentsp and Prefidency State 16 ( 0.6) 27 ( 0.8) 26 ( 0.9) 25 ( 0.7) 7 ( 04) 281 ( 1.7) 201 ( 1.5) 277 ( 1.1) 271 ( 1.4) 200 ( 2.3) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 ( 1.1) 18 ( tO) 209 ( 22) 286 ( 1.8) 265 ( 1.7) 200 ( 13) 245 ( 13) PARENTS' EDUCATION HS non-graduate State 11 ( 3.2) ( **lb ) 19 ( 4.7) *4.1 22 ( 4.3) 41 ( 4.7) 8 ( 3.2) 4.01 Nation 12 ( 2.2) e.*) 20 ( 3.1) 21 ( 2.8) 28 ( 244 ( 2.9) 3.2) 20 ( 2.4) 444) HS graduate State 13 ( 1.3) 24 ( 14) 25 ( 1.9) 31 ( 1.8) 8 ( 1.1) 263 ( 3.4) 268 ( 2.0) 265 ( 2.5) 262 ( 2.3) 41411 ( Nation 8 ( 1.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 1 9 ( 1.6) 249 ( 4.7) 257 ( 2.8) 259 ( 3.2) 253 ( 2.5) 248 ( 3.0) Some college State 15 ( 1.9) 30 ( 1.6) 2$ ( 1.7) 21 ( 1.7) 8 ( 1.2) 288 ( 2.4) 282 ( 2.1) 285 ( 2.0) 279 ( 2.1) 044 ( *** Nation 25 ( 2.4) 23 ( 2.6) 28 ( 2.2) 14 ( 1.5) 27$ ( 2.7) 269 ( 3.5) 267 ( 2.5) 242 ( 3.4) College graduate State 17 ( 1.4) 29 ( 1.3) 20 ( 1.3) 23 ( 1.6) 5 ( 0.6) 290 ( 1.8) 292 ( 1.5) 283 ( 1.7) 277 ( 2.0) Nation 17 ( 1.3) 22 ( 1.6) 23 ( 1.1) 25 ( 1.5) 12 ( 1.1) 282 ( 2.6) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 3.2) GENDER Male State 12 ( 1.1) 25 ( 1.1) 26 ( 1.4) 28 ( 1.3) 8 ( 0.9) 280 ( 2.3) 282 ( 1.8) 277 ( 1.8) 273 ( 1.8) 260 ( 3.1) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 2. ( 1.3) 17 ( 1.5) 269 ( 3.3) 267 ( 2.6) 267 ( 2.2) 262 ( 21) 248 ( 24) Female State 18 ( 1.3) 28 ( 1.2) 27 ( 14) 23 ( 1.1) 5 ( 0.7) 282 ( 2.2) 279 ( 2.0) 277 ( 1.3) 267 ( 12) **. *** Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 1.6) 15 ( 1.2) 269 ( 2.8) 269 ( 2.2) 264 ( 1.8) 258 ( 1.9) 241 ( 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). I Liu THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Minnesota TABLE A26 I Students' Reports on the Number of Days of i School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL. STATE ASSESSMENT None One or Two Days Three Days or More TOTAL Porcantiga and Prodidancy Percentage and Proficiency Ravening, and Prolidency State 44 ( 1.0) 38 ( 1.0) 20 ( 0.9) 230 ( 1.0) 278 ( 1.3) 285 ( 1A) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 286 ( 1.5) 250 ( 1.9) RACE/ETHNICITY White State 44 ( 1.0) 38 ( 1.1) 20 ( 0.9) 282 ( 1.0) 280 ( 1.3) 269 ( 1.2) Nation 43 ( 12) 34 ( 1.2) 23 ( 12) 273 ( 1.8) 272 ( 1.7, 258 ( 2.1) Black Sta te 32 ( 8.0) 0-0. 34 ( 4.4) 33 ( 7.2) Nation 58 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 27 ( 5.2) 29 ( 8.1) ( *44(44*) Nation 41 ( 3.3) 32 ( 2.2) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) Asian State 49 ( 4.7) 39 ( 5.0) *** ( "*) 11 ( 3.6) *** ( *44) Nation 62 ( 5.6) 287 ( 4.7)1 27 ( 5.3) *** ( 11 ( 4.9) TYPE OF COMMUNITY Advantaged urban State 37 ( 2.5) 41 ( 2.2) 22 ( 1.3) 280 ( 2.4) 280 ( 3.2) 26a ( 2.1) Nation 47 ( 2.3) 284 ( 4.4)1 38 ( 2.8) 279 ( 4.5)1 15 ( 3.7) ***) Extrema rural State 43 ( 1.8) 38 ( 1.8) 19 ( 2.1) 278 ( 1.8) 279 ( 2.5) 263 ( 2.4)1 Nation 43 ( 4.4) 32 ( 4.2) 25 ( 3.9) 257 ( 4.1)1 284 ( 5.8)1 Otfiar State 48 ( 1.8) 33 ( 1.5) 19 ( 1.5) 282 ( 1.5) 279 ( 1.7) 270 ( 2.4) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 285 ( 2.2) 266 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent txrtainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permlt reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A26 I Students' Reports on the Number of Days of (continued) 1 School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY [STATE ASSESSMENT 1990 NAEP TRIAL None One or Two Days Three Days or More TOTAL Percentage and Proficiency Percentage and ProlIdency Pstrantage and Praficioney State 44 ( 1.0) 30 ( 1.0) 20 ( 0.9) 280 ( 1.0) 278 ( 1.3) 265 ( 1.4) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 266 ( 1$) 250 ( 1.9) PARENTS EDUCATION HS non-graduate State 28 ( 5.0) ...) 33 ( 5.2) ...) 38 ( 4.3) Nation 36 ( 3.2) 26 ( 3.1) 38 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) HS graduate State 40 ( 1.8) 36 ( 1.8) 24 ( 1.8) 266 ( 1.5) 267 ( 1.9) 257 ( 2.7) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 2.0) 257 ( 2.8) 249 2.4) Some college State 46 ( 2.2) 35 ( 2.3) 18 ( 1.6) 286 ( 1.3) 283 ( 22) 273 ( 2.4) Nation 1.8) 37 ( 1.6) 23 ( 1.6) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) College graduate State 47 ( 1.6) 37 ( 13) 17 ( 1.0) 288 ( 1.2) 286 ( 1.5) 275 ( 23) Nation 51 ( 1.6) 33 ( 1.2) 16 ( 1.3) 275 ( 2.1) 277 ( 1.7) 265 ( 3.1) GENDER Male State 44 ( 1$) 36 ( 1$) 20 ( 1.1) 280 ( 1.4) 280 ( 1.6) 264 ( 2.3) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 1.4) 266 ( 2.0) 267 ( 2.1) 250 ( 2.6) Female State 43 ( 1.5) 36 ( 1.3) 20 ( 1.2) 280 ( 1.1) 276 ( 1.6) 268 ( 1 6) Nation 43 ( 1.4) 32 ( 1.1) 25 ( 1.3) 264 ( 2.3) 266 ( 1.7) 250 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. '1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 142 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 Minnesota TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE MSESSMENT Strongly Agree Aare. Undecided, Disagree, Sirongiy Disagree _ TOTAL Pavan lags NW Pro &dem Pernentar and Prolkdanqt Panwdapo and Madam State 20 ( 1.3) 51 ( 1.3) 23 ( 1.2) 269 ( 1.3) 276 ( 1.1) 263 ( 1.3) Nation 27 ( 4.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) RACE/ETHNICITY White State 26 ( 1.4) SO ( 1.3) 24 ( 1.3) 291 ( 1.3) 278 ( 1.1) 265 ( 1.1) Nation 20 ( 1,6) 48 ( 1.3) 26 ( 1$) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Black State 26 ( 3.7) 46 ( .44 ( 5.3) 444) 26 ( 5.2) Nation 32 ( 2.5) 52 ( 2.3) 16 ( 1.9) 247 ( 4.1) 233 ( 3.3) 227 ( 4.2) Hispanic State 20 ( 3.8) SO ( 5.6) .44 ( 20 1-dr ( 5.3) ***) Nation 24 ( 2,5) 46 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 236 ( 3.8) Asian State 23 ( 4.9) 441 55 ( sa) 17 iHr ( 4.8) ( 0+1 Nation 29 ( 5.5) 53 ( 5.6) 17 444 ( 4.9) ( .441 TYPE OF COMMUNITY Advantaged urban State 24 (,1.9) 54 ( 1.8) 23 ( 1.4) 292 ( 2.2) 27$ ( 2.5) 261 ( 2.5) Nation 17 ( 3.2) 55 ( 280 ( 2.4) 4.1)1 23 .4* ( 4.2) Extreme rural State 24 ( 2.8) 52 ( 3.1) 25 ( 2.8) 292 ( 3.0)/ 274 ( 1.5) 203 ( 2$)1 Nation 34 ( 270 ( 2.8) 3.9)1 49 ( 252 ( 2.2) 4.1)1 17 1,44 ( 1.4) ( Odor State 28 ( 2,5) 50 ( 1.9) 21 ( 1.9) 290 ( 2.2) 278 ( 1.9) 267 ( 1.7) Nation 27 ( 1.4) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate deterrnMation of the variability of this estimated mean proficiency. *** Sample size is insufricient to permit a reliable estimate (fewer than 62 students). 138 THE 1990 NAEP TRIAL STATE ASSESSMENT Minnesota TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19.0 NAEP TRIAL STATE ASSESSMENT Strongly Agree , Agree _ Undecided, Disagree, Strongly Disagree TOTAL Peroentage and Prolidency Percentage and Proficiency Percentage and Proficiency State 26 ( 1.3) 51 ( 1.3) 23 ( 1.2) 289 ( 1.3) 276 ( 1.1) 263 ( 1.3) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) PARENTS' EDUCATION HS non-graduate State 16 ( 4.2) 43 ( 5.0) 4.2 ( 5.6) *4r* e*) *It ( Mt) di 4.14) Nation 20 ( 2.6) 50 ( 3.3) 30 ( 3.6) ,i,-4- ( ii...) 243 ( 2.6) 238 ( 4.3) HS graduate State 21 ( 1.7) 51 ( 1.8) 2$ ( 2.1) 275 ( 2.1) 265 ( 1$) 255 ( 2.2) Nation 27 ( 2.1) 47 ( 2.3) 26 ( 2.0) 262 ( 2.7) 255 ( 2.3) 245 ( 2.4) Some college State 27 ( 2.3) 51 ( 2.2) 22 ( 2.0) 296 ( 2.3) 280 ( 1.5) 274 ( 1.8) Nation 28 ( 2.5) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 287 ( 1.9) 258 ( 3.2) College graduate State 30 ( 1.7) 52 ( 2.1) 18 ( 1.4) 295 ( 1.5) 284 ( 1.41 288 ( 2.1) Nation 30 ( 2.3) 51 ( 1.6' 19 ( 1.8) 280 ( 2.41 274 ( 2.2) 266 ( 2.5) ()ENDER Male State 29 ( 1.3) 48 ( 1.5) 23 ( 1.4) 289 ( 1.7) 276 ( 1.6) 262 ( 2.0) Nation 28 ( 1.5) 48 ( 1.2) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Female State 23 ( 1.8) 53 ( 1.7) 24 ( 1.5) 288 ( 1.5) 275 ( 1.3) 263 ( 1.6) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 289 ( 2.1) 262 ( 1.8) 252 ( 1.9) The stanciard 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 was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing Service (En), Westat, and National Computer Systems (NCS). The program benefitted from the contributions of hundreds of individuals at the state and local levels Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Finally, 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 considesable contributions to the program, especially its management of the National Assessment Planning Project. That project resulted in the mathematics framework and objectives for the asseument and recommendations about reporting the results of the program. In particular, we note the significant contributions of Ramsay Se Idea, Director of the State Education Assessment Center for the CCSSO and the members of the Steering, Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people from school districts, colleges and universities, and State Education Agencies worked tirelessly to help ETS staff develop the assessment and a framework for interprefing the results. Under the NAEP contract to Ers, Archie Lapointe sesved as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mazzeo, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffler, state smices. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and proeff.sing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zabac.k. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the results of its assessed students. To meet this challenge, a computerized report generatical system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Korner wrote the text for the report. Kent Ashworth was responsiNe 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. 1 '5 U.S. GOVERNMENT PRINTING OFFICE : 1991 0 - 293-276 QL 8 (BIL 211 146