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DOCUMENT RESUME ED 330 574 SE 052 084 TITLE The State of Mathematics Achievement in North Dakota: 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, ard 40 separate reports for 37 states, DC, Guam, and t4e 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/PC05 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Ziunior High Schools; *Mathematics Achievement; Mathe atics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS National Assessment of Educational Progress; *North Dakota; *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 North Dakota, 2,485 students in 106 public schools were assessed. This report describes the mathematics proficiency of North Dakota 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 commmity, 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, North Dakota students had an average proficiency of 281 compared to 261 nationwide. Many fewer students (North Dakota-24%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJ(/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics A It! e t in NORTH DAKOTA The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD 1114Fc p,v,15, r: ,../ti."..Lh. U S OEPARTIAENT Of EDUCATION OthIe I ahona, Researrn anti trnpro.ement PU TIONAL RESOURCES INFORMATION CENTER (ERIC' r1 .f. clot ument nes Peen reproduce(' as re(0,,,rpcf from the person or oroanastron orky,nat,oc Mno, chenge5 nave Deer, made to "prove ,rproducIron quairty PortIS of .reor opin.oris stared, f1t3 cfoe,j Mera tlo not ne,. etssa,,ir ,ecvesent ort.cat OE RI 04.444.,f, (V Prepared by Educational Testing Service under Contract wb 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 OsIAEll. is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. Since 1%9, assessments have been conducted periodically in reading. mathematics. science, writing. history/geography. and other fields. By making objective information on student performance available to policymakers at the national, state, and local levels. NAEP is an integral part of our nation's evaluation of the condition aid progress of education. Only information related to academie achievement is collected under this program. NAEP guarantivs the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics. the U.S. Department of Education, The Commissioner of Education Statistics is responsible. by law, for carrying out the NAEP project through competitive awards to qualified organizations. NAEP reports directly to the Commissioner, who is also responsibie for providing continuing reviews, including validation studies and solicitation of public comment. on NAEP's conduct and usefulness. In 1988. Congress ,reated the Natio.ial Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The board is responsible for selecting the subject areas to be assessed, which may include adding to thosespecified 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 Nat'mal 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 Coordinater 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 Sc 'soot History Teacher Cairo-Durham High School Caiio. New York Parris C. Battle Teacher Horace Mann Elementary School Miami, Florida Mary R. Blanton Attorney Cromwell. Porter. Blanton & Blanton Salisbury. North Carolina Boyd W. Boeh lje Attorney Gauss. Klyn. & Boehlje Pella, Iowa Linda R. Bryant Teacher Greenway Middle School Teaher Center Piushurgh. Pennsylvania Honorabk Michael N. Castle Governor of Delaware Carvel State Office Building Wilmington. Delaware Honorable Naomi K. Cohen State of Connecticut House of Representatives Legislative Office Building Hart ford. Connecticut Chester E. Finn. Jr. Professor of Education and Public Policy Vanderbilt University Washington. D.C. Michael S. Glode Wyoming State Board or Education Saratoga. Wyoming Christine Johnson Principal Abraham Lincoln High School Denver, Colorado John Lindley Principal South Colby Liementary School Port Orchak . Washington Carl J. Moser Director of Schools The Lutheran Church Missouri Synod International Center St. Louis, Missouri Mark D. Musick President Southern Regional Education Board Atlanta, Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith, Arkansas Matthew W. Prophet, Jr. Superintendent Portland Oregon School District Portland, Oregon Honorable William T. Randall Commissioner of Education State Department of Education Denver. Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington, D.C. Honorable Richard W. Riley Attorney Nelson, Mullins. Riley and Scarborough Columbia. South Carolin.. Thomas Topuzes Attorney Law Offices of Frank Rogozienski Coronado, California Herbert J. Walberg Professor ot Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and Improvement (Ex-Officio) U.S. Department of Education Washington. D.C. Roy Truby Executive Director. NAGB Washington. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The SIM of Mathemades Achievement in NORTH DAKOTA The Trial State Assessment at Grade Fight Report No: 21-ST.02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education 4 U.S. Department of Education Lamar Alexander &crusty Office of Educational Researcb and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson 1. 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. Far 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 Bmnch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800424-1616 (in the Washington, D.C. metropolitan area call 202-219-1651). Meaty of Cowen, Catalog Card Number 91-61478 ISBN: 048685-14-9 The work upon which this publication is based was performed for the National Center forEducation Statistics, Office of Educatiotul Research aad Improvement, by Educational Testing Service. Education' Toting Service is sa equal opponunity/affinnative scrim employer Edmeetional Tessin" Service, EFS, and (P) are registered tradentarks of Educational Thsting Table of Contents EXECUTIVE SUMMARY 1 INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of North Dakota 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in North Dakota Public Schools? 17 Chapter 1. Students' Mathematics Performance 18 Levels 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 29 Gender 31 Content Area Performance 33 6 THE 1990 NAEP TRIAL STATE ASSESSMENT in PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics? 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Slim/nary 48 Chapter 4. How Is Mathematics Instruction Delivered? 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objects 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used? 60 The Availability of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics' 67 Educational Background 68 Summary 71 Chapter 7. The Conditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Hours of Television Watched per Day 75 Student Absenteeism .76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 7 iv THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national av..e,,srnents that NAEP has conducted since its inception. As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Progyam in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to represent the eighth-grade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored SO percer 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 North Dakota 41111.1.11M. 0.1, In North Dakota, 106 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this saelple of schools were representative of 103 percent of the eighth-grade rublic-school students in North Dakcta. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 1 percent of the eighth-grade public-school population was classified as limited English Proficient (LEP), while 8 percent had an Individualized 2ducation Plan (IEP). An 1EP is a plan, mitten for a student who has lseen detennined 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 exe-ided 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 judgeli incapable of partici, ating 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 tctal, 2,485 eighth-grade North Dakota public-schooi students were assessed. The weighted student participation rate was 96 percent. This means that the sample of students who took part in the assessment was representative of 96 percent of the eligible eighth-grade public-school student population in North Dakota. Students' Mathematics Performance The average proficiency of eighth-grade public-school students from North Dakota on the NA113 mathematics scale is 281. This proficieney is higher than that of students across the nation (261). Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAFP scale. 9 2 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota In North Dakota, 100 percent of the eighth graders, compered to 97 percent in the nation, appear to have &Nuked skills involv:ng simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in North Dakota (24 percent) and '2 percent in the nation appear to have acquired reaaoning and problemTaolving 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; ard Algebra and Functions. Students in North Dakota performed higher than students in the nation in all of these five content areas. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the North Dakota eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In North Dakota: White students had higher average mathematics proficiency than did Hispanic or American Indian students. Further, a greater percentage of White students than Hispanic or American Indian students attained level 300. The resuits by type of community indicate that the average mathematics performance of the North Dakota students attending schools in advantaged urban areas was about the same as that of students attending schools in extreme rural arras and areas classified as "other". In Noah Dakota, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 33 points higher than that of students whose parents did not graduate from high school. The results by gender show that eighth-grade males in North Dakota had a higher average mathematics proficiency than did eighth-grade females in North Dakota. In addition, a greater percentage of males than females in North Dakota attained level 300. Compared to the national results, females in North Dakota performed higher than females across the country; males in North Dakota performed higher than males across the country. THE 1990 NAEP TRIAL STATE ASSESSMENT 3 North Dakota 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 North Dakota are as follows: Less than half of the students in North Dakota (43 percent) were in schools where mathematics was identified as a special priority. This is a smaller percentage than that for the nation (63 percent). In North Dakota, 48 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 North Dakota were taking eighth-grade mathematics (73 percent) than were taking a course in pre-algebra or algebra (25 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 North Dakota spent 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. 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 1 1 4 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota In North Dakota, 18 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 35 percent of the students were taught by teachers who got only some or owe of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In North Dakota, 23 percent of the students never used a calculator to work problems in class, while 46 percent almost always did. In North Dakota, 19 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. More than half of the students (69 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 North Dakota 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 North Dakota (14 percent) watched one hour or less of television each day; 6 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 5 North Dakota 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-wade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands i 3 ME 1990 NAEP TRIAL STATE ASSESSMENT 4 7 North Dakota This report describes the performance of the eighth-grade public-school students in North Dakota 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 North Dakota. Part One describes the mathematics performance of the eighth-grade public-school students in North Dakota, the Central region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in North Dakota, the Central region, and the nation. Overview of the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Ed-;cational 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 (1)(2)(C)(1) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(1))) As a result of the legislation, the 1990 NAEP piogram included a Trial State Assessment Program in eighth-grade mathematics. National assessmenti 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 .ichool 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. 1 4 8 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota The Trial State Assessment was based on a set of mathematics objectives newly developed for the prop.= and patterned after the consensus process described in Public Law 98-511, Section 405 (E), which authorized NAEP through June 30, 1988. Anticipating the 1988 legislation that authorized the Trial State Assessment, the federal government arranged for the National Science 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 pees 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 North Dakota, 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 North Dakota are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nationally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAEP program was necessary because the voluntary 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 Mathematics. Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Cour,cil of Teachers of Mathematics, 1989). rs'ti THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota RACE/ETHNICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Procedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for North Dakota. 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 vend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defmed as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the eMent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for repotting. 6 10 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota GENDER Results are reported separately for males and females. REGION The United States has been divided into four regions: Northeast, Southeast, Central, and West. States included in each region are shown in Figure 1. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Vvginia will be to the Southeast. FIGURE 1 I Regions of the Country NORTHEAST SOUTHEAST CENTRAL WEST Connecticut Mabama Alaska Delaware Arkansas indiana Arizona District of Columbia Florida Iowa California Maine Georgia Kansas Colors** illarybind Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana New Jersey North Carolina Nebraska Nevada New York South Carolina Noah Dakota New Mexico Pennsytvania Tennessee Ohio Oklahoma Rhode island Virginia South Dakota Oregon Vermont West Vit Ifni& Wisconsin Texas Vnia Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota Guide Lies for Analysis This report describes and compares the mathematics profkiency 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 tbe 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 magni*ude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample is strong enough to conclude that the means or proportions are really different for those groups in the population. If the evidence is strong (i.e., the difference is statistically significant), the report describes the group means or proportions as being different (e.g., one group performed higher than or lower than another group) -- regardless of whether the sample means or sample proportions appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the difference is not statistically significant), the means or proportions are described as being about the same -- again, regardless of whether the sample means or sample proportions appear to be about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the apparent magnitude of the difference between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain the value zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. When three or more gyoups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are discussed in greater detail in the Procedural Appendix. 1 8 12 THE 1990 NAEP TRIAL STATE ASSESSMENT It is aho important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intrvals about the mean of a particular population of interest. Comparing such confidence intervals fortwo 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 pacentage of students in the combined group taking either algebra or pre-algebra is given and compared to the percentage of students enrolled in eighth-grade mathematics. However, the tables that accompany that text report percentages and proficiencies separately for the three groups (algebra, pre-algebra, and eighth-grade mathematics). The combined-group percentages reported in the text and used in all statistical tests are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the percentage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each 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 siatistical tests that are reported in the text (based on unrounded numbers). ;.4 THE 1990 NAEP TRIAL STATE ASSESSMENT 13 North Dakota Profile of North Dakota EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in North Dakota, 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 North Dakota Eighth-Grade I Public-School Students PERCENTAGE OF STUDZNTS 1990 NAEP TRIM. STATE ASSESSMENT North Dakota Central Nation DEMOGRAPHIC SUBGROUPS Porcentaga Percentage Percentage Rac&Ethnlclty White Of ( 1.4) 79 ( 2.6) 70 ( 0.5) Slack ( 0.3) 13 ( 3.2) 18 ( 0.3) Hispanic 3 ( 0.4) 5 ( 1.0) 10 ( 0.4) Asian 1 ( 0.4) ( 0.4) 2 ( 0.5) American Indian 5 ( 12) ( 0.4) 2 ( 0.7) Type of Community Advantaged urban 9 ( 0.4) 3 ( 3.1) 10 ( 3.3) Disadvantaged urban 3 ( 0.4) 10 ( 4.3) 10 ( 2.8) Extreme rural 37 ( 2.5) ( 6.0) 10 ( 3.0) Other 50 ( 2.3) 79 ( 7.7) 70 ( 4.4) Parents Education Did not finish high school 4 ( 0.7) ( 0.9) 10 ( 0.8) Graduated high school 24 ( 1.3) 33 ( 2.1) 2S ( 1.2) Some education after high school 19 ( 0.8) 19 ( 0.9) 17 ( 0.9) Graduated college 49 ( 1.3) 35 ( 1.8) 39 ( 1.9) (Wider Male 51 ( 1.8) SO ( 1.4) 51 ( 1.1) Female 49 ( 1.8) 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 percentages for RaceiEthnicity 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 2 0 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for North Dakota schools and students sampled for the 1990 Trial State Assessment. In North Dakota, 106 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that au of the eighth-grade students in this sample of schools were representaive of 100 perotnt of the eighth-grade public-school students in North Dakota. TABLE 2 I Profile of the Population Assessed in I North Dakota EIORTN-ORADE PUBLIC soma. PARTICIPATION Weighted school participation rate before substitution 018% Weighted school participation rate after substitution 100% Number of schools originally sampled Number of schools not eligible Number of schools in original sample participating Number of substitute schools provided Number of suostitute schools participating Total number of participating schools 111 5 8 106 THE 1990 NAEP TRIAL STATE ASSESSMENT EIONTH-ORADE PUBL/C-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups WI% Number of students selected to participate In the assessment 2,727 Number of students withdrawn from the assessment 58 Percentage of students who were of Limited English Proficiency 1% Percentage of students excluded from the assessment due to Limited English Proficiency 0% Percentage of students who had an individualized Education Plan 8% Percentage of students excluded from the assessment due to individualiTed Education Plan status 3% Number ot Students to be assessed 2,578 Number of students assessed 2,485 IS North Dakota In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 1 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 8 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the. student and descaes a program of activities and/or =Wed 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 &Ideation Plan and (in either, ease) 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, 2,485 eighth-grade North Dakota public-school students were assessed. The weighted student participation rate was 96 pexcent. This means that the sample of students who took part in the assessment was representative of 96 percent of the eligible eighth-grade public-school student population in North Dakota. 22 16 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in North Dakota Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometr2; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAEP mathematics scale, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficiency of eighth-wade public-school students in North Dakota. Chapter 1 compares the overall mathematics performance of the 'students in North Dakota to students the Central region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 sumniarizes 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. 11 3 THE 1990 NAEP TRIAL STATE ASSESSMENT 17 0101441. CHAPTER 1 North Dakota .Ir semwemeoerre Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from North Dakota on the NAEP mathematics scale is 281. This proficiency is higher than that of students across the nation (261).2 FIGURE 2 Average Eighth-Grade Public-School I Mathematics Proficiency NAEP Mathematics Scale 200 225 250 275 300 500 Averags Proficiency N. PPol N. North Dakota Central Nation The standard errors are presented in parenthebes. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by I-H). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certairity there is a real difTerence in the average mathematics proficiency between the two populations of interest 2- 4 18 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota 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 desclibe the nature of students' proficiency in water detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAEP scale. To defme the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While derming proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presentedhere. Definitions of the four levels of mathematics proficiency are given in Figure 3. lt is important to note that the definitions of these levels are based solely on student perfonnance on the 1990 mathematics assessment. The levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In North Dakota, 100 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in North Dakota (24 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 North Dakota, Central region, and national results for each content area. Students in North Dakota performed higher than students in the nation in all of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 North Dakota FIGURE 3 Levels of Mathematics Proficiency LEVEL 200 111 Simple Addftive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and subtraction problems with and without regrouping. Using a calculator, they can extend these abilities to multiplication and division problems. These students can identify solutions to one-step word probleMs and select the greatest four-digit number in a list. In measurement, these students can read a ruler as well as common weight and graduated scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simpie figures. In data analysis, they are able to read simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numerical sentences and eudend simple pattern sequences. LEVEL 250 Simple Multiplicative Reasoning and Two-Step Problem Solving Students at this levet 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 es 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, arid recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an initial understanding of basic terms and propertios, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and probability. In algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions. 2 6 20 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota FIGURE 3 I Levels of Mathematics Proficiency (continued) 1 LEVEL 300 Reasoning and Problem Solving involving Fractions, Decimals, 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 cornmOn fractions and decimals, Including p4ctorial representations. They can Interpret the meaning of percentr less than and greater than 100 and apply the concerts of percentages to solve simple problems. These students demonstrate some evidenca 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 aculate 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 number and algebraic understanding to include some properties of exponents. They can recognize scientific notation on a calculator and make the *ransition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles to solve problems. They can find the circumferences of circles and the surface areas of solid figures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirect measurement. These students also can apply their knowledge ot the properties of geometric figures t 've problems, suth 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 relator% 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. r, **, 4. I THE 2990 NAEP TRiAL STATE ASSESSMENT 21 North Dakota FIGURE 4 I Levels of Eighth-Grade Public-School Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation 0 20 40 eo 80 o ( 0.4) 0 ( 0.2) 0 ( 0.2) 24 ( 1.7) 12 ( 2.5) 12 ( 1.2) ( 1.4) 70 ( 3.2) 64 ( 1.6) 100 ( 0.2) 98 ( 0.9) 97 ( 0.7) / 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 9 5 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. 26 22 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota 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 4111411161"1. , 0 200 225 250 275 Average Profkimicy 296 ( 1.1) 270 ( 2.7) 266 ( 1.4) 260 ( 1.9) 293 ( 3.4) 258 ( 1.7) 276 ( 1.3) 262 ( 3.1) 259 ( 1.4) 2136 ( 1.5) 265 ( 3.2) 262 ( 1.8) 275 ( 1.1) 283 ( 2.1) 260 ( 1.3) 300 500 Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percen confidence interval, denoted by I-0-9. If the confidence intervals for the populations not overlap, there is a statistically significant difference between the populations. rs (3 A. 4 7 THE 1990 NAEP TRIAL STATE ASSESSMENT 23 North Dakota CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY The Trial State Assessment results can be compared according to the different racial/ethnic groups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Hispanic, and American Indian students from North Dakota are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Hispanic or American Indian students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Hispanic or American Indian students attained level 300. 3 0 24 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota FIGURE 6 I Average Eighth-Grade Public-School 1 Mathematics Proficiency by Race/Ethnicity NAEP ilathensalitts Scala 0 200 225 250 275 300 500 -% : \\ sPw!'s Average Prong/way 1.4001 1-4Nowe North Dakota White Hispanic American Indian Central White Hispanic American Indian Nation White Hispanic American Indian 4101.'50 The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence interval, denoted by P.4-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 31 THE 1990 NAEP TRIAL STATE ASSESSMENT 2$ North Dakota ME WOWS REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARD 1 Mathematics Proficiency by Race/Ethnicity LEVEL 300 state White Hispanic Amer. Indian Raglan White Hispanic Amer. Indian MOM White Hispanic Amer. Indian LEVEL 250 State White Hispanic Amer. Indian RefPlen White Hispanic Amer. Indian Nation White Hispanic Amer. Indian LEVEL 200 State White Hispanic Amer. Indian Re9ion White Hispanic Amer. Indian Nation White Hispanic Amer. Indian Porcantago 20 ( 1.8) 5 ( 4.4) 0 ( 0.7)1 14 ( 2.8) .) 15 ( 1.5) 3 ( 1.1) 1 ( 2.3)1 92 ( 0.7) 52 ( 9.0) 39 ( 7.1)1 7$ ( 3.1) ( "-I ) ( 74 ( 1.8) 41 ( 4.5) 45 (16.0)1 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 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! 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 topermit a reliable estimate (fewer than 62 students). 3 2 26 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TYPE OF COMMUMTY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, extreme rural arras, and areas classified as "other". (These are the "type of community" goups in North Dakota with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the North Dakota students attending schools in advantaged urban areas wu 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 NAEP Mathematics $cale 0 200 225 250 275 300 500 Average Proficiency North Dakota Advantaged urban Extreme rural Other Central Advantaged urban Extreme rural Other Nation IA) ,s( 24) an 104 low ( tisi .( SA) il40041 Advantaged urban Extreme rural Other $11 211111 ( ( 3.8)1 4.1)I 1-0) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 33 THE 1990 NAEP TRIAL STATE ASSESSMENT 27 North Dakota FIGURE 9 LEVEL 300 Stat. Adv. urban Ext. rural Other Region Adv. urban Ext. rural Other Nation Adv. urban Ext. rural Other LEVEL 250 atm Adv. urban Ext. rural Other Roirion Adv. urban Ext. rural Other Nation Mv. urban Ext. rural Other LEVEL 200 State Adv. urban Ext. rural Other Region Adv. urban Ext. rural Other Nation Mv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community 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-I). If the confidence intervals for the populations do not overlap, there is a stafistically 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 152 students). 100 3 4 28 THE 1990 NAEP TRIAL STATE ASSESSMENT 3D ( 5.6) 24 ( 3.0) 24 ( 2.3) min ( 13 ( 2.9) 28 ( 4.8)t 8 ( 2.3)1 12 ( 1.2) 93 ( 32) ( 3.2) ( 1.5) ( ***) 73 ( 4.2) 93 ( 4.6)1 58 ( 8.2)1 84 ( 2.3) 100 ( 0.0) 90 ( OS) 100 ( 0.2) ( ***/ mix ( ) Oil ( 0.9) 100 ( 0,0) 97 ( 2.8)1 97 ( 1.0) North Dakota PARENTS' EDUCATION LEVEL Previous NAEP findings have shown that students whose parents are better educated tend to have higher mathematics proficiency (see Figures 10 and 11). In North Dakota, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 33 points higher than that of students who reported that neither parent waduated from high school.. As shown in Table 1 in the Introduction, a larger percentage of students in North Dakota (49 percent) than in the nation (39 percent) had at least one parent who gaduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 4 percent for North Dakota and 10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School Mathematics Proficiency by Parents' Education NAEP Mathornotico Seal* 200 225 250 275 300 500 AVrage Proficiency NI North Dakota HS non-graduate HS graduate Some college College graduate Central S non-gradllate HS graduate Some college College graduate Nation 141$ HS non-graduate Fro HS graduate /44 Some college HI College graduate The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confide= interval, denoted by 1-1-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). :3 5 THE 1990 NAEP TRIAL STATE ASSESSMENT 29 North Dakota 11410111 REPOK FIGURE II I Levels of Eighth-Grade Public-School CARO 1 Mathematics Proficiewy by Parents' Education LEVEL 300 State HS non-grad. HS graduate Some college College grad. Ploclk In HS non-grad. HS graduate SOMe C011ega College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 Mita HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS nongrad. HS graduate Some college College grad. 20 40 00 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 H-i). 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. 0" Sample size is insufficient to permit a reliable estimate (fewer then 62 students). 2 ( 3.5) 14 ( 3.2) 25 ( 3,5) 32 ( 2.4) ( ( 3.9) 14 ( 3.4) 17 ( 1 ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.9) 00 ( 7.5) 03 ( 2.9) 114 ( 1.1) ( "4) $5 ( 4.1) 76 ( 5,1) 79 ( 3.9) 37 ( 4.6) 1541 ( 2.7) 71 ( 2.6) 7S ( 2.0) 09 ( 0.9) SS ( 0.8) 100 ( 0.1) 100 ( 0.0) 61(1.2) 100 ( 0.0) 09 ( 0.9) 100 :4; 30 THE 1990 NALP TRIAL STATE ASSESSMENT ( 1.9) 07 ( 0.8) SO ( 0.7) 90 ( 0.7) North Dakota GENDER As shown in Figure 12, eighth-grade males in North Dakota had a higher average mathematics proficiency than did eighth-grade females in North Dakota. Compared to the national results, females in North Dakota performed higher than females across the country; males in North Dakota performed higher than males across the country. FIGURE 12 I Average Eighth-Grade Public-School 1 Mathematics Proficiency by Gender NAEP Mathematics Scat. 200 225 250 275 300 500 Alamo Probe Nosy North Dakota male 101 ( 14) Female 170 Clehtfal I-404 . Maile Sr, 363), Female 24): Nation /44 Male Sit 14) Pt4 Female 150 ( 14) The standard errors are presented m parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 1 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in North Dakota who attained level 200. The percentage of females in North Dakota who attained level 200 was greater than the percentage of females in the nation who attained level 200. Also, the percentage of males in North Dakota who attained level 200 was greater than the percentage of males in the nation who attained level 200. 37 THE 1990 NAEP TRIAL STATE ASSESSMENT 31 North Dakota FIGURE 13 I Levels of Eighth-Grade Public-School 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 0 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within ± 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-4-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained th level. 32 ME 1990 NAEP TRIAL STATE ASSESSMENT 27 ( 2.3) 21 ( 2.0) 14 ( 4.8) 9 ( 2.3) 14 ( 1.7) 10 ( 1.3) 90 ( 1.5) 87 ( 2.2) SS ( 3.3) 71 ( 4.0) 14 ( 2.0) 64 ( 1.8) 100 ( 0.3) 90 ( 0.3) 00 ( 0.8) se ( 1.2) 97 ( 0.9) 97 ( 0.8) North Dakota In addition, a greater percentage of males than females in North Dakota attained level 300. The percentage of females in North Dakota who attained level 300 was water than the percentage of females in the nation who attained level 300. Also, the percentage of males in North Dakota 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 summar5r of content area peiformance by race/ethnicity, type of community, parents' education level, and gender. THE 1990 NAEP TRIAL STATE ASSESSMENT 33 North Dakota TABLE 3 I Eighth-Grade Public-School Mathematics i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1980 NAEP TRIAL STATE ASSESSMENT Numbers and Operations M easuremaft _ Geome try Data Analysis' Statistics. and Probability - Algebra and Functions _ TOTAL Proficiency Proficienzy Proficiency issoficiency Padiclioney State 28e ( 1.1) 200 ( 1.9) 278 ( 1.3) 286 f 1.5) 275 ( 1.1) Region 270 ( 2.7) 203 ( 3.4) 252 ( 3.1) 265 ( 3.2) 253 ( 2.1) Nation 200 ( 14) 258 ( 1.7) 25a ( 1.4) 262 ( 1.8) 260 ( 1.3) RA44/ETBNICITY White State 289( 1.1) 284 ( 1.5) 280 ( 1.3) 289 ( 1.1) 2/8 ( 0.9) Region 270 ( 2.9) 271 ( 3.7) 268 ( 3.0) 273 ( 3.1) 259 ( 2.3) Nation 273 ( 1.0) 267 ( 2.0) 267 ( 1.5) 272 ( 1.8) 208 ( 1.4) Hispank State Region 258 ( *low ( 4.9) 239 ( ( 7.1) 114) 248 (( 6.0 253 (( 7.0) 4+1 243 ( *44 5.7) Nation 243 ( 2.7) 238 ( 3.4) 243 ( 34) 239 ( 3.4) 243 ( 3.1) American Wien State Region 248 ( 3.2)1 *.p.) 234 ( 5.3)1 248 ( ( 3.4)1 44,) 242 ( *** 5.5)1 234 ( *** 4.7)1 Nation 249 ( 7.8)1 247 ( 0.8)1 248 ( 8.0)! 242 ( 5.2)1 242 ( 4.9)s TYPE OF CO4IMUNITY Advantaged urban State 284 ( 2.4) 293 ( 3.2) 279 ( 2.4) Region 1144 ( *MR) *V* ( ( Nation 283 ( 3.2)1 281 ( 3.2)1 277 ( 5.2)1 285 ( 4.8)1 277 ( 4.8)1 Extreme rural State Region 285 ( *414 ( 2.3) ***) 279 ( ( 3.7) 277 ( 2.5) 283 ( ( 3.3) *41 273 ( 2.4) *gm.) Nation 258 ( 4.3)1 254 ( 4.2)! 253 ( 44)1 257 ( 5.0)1 258 ( 4.8)1 Other State 288 ( 1.2) 280 ( 2.4) 278 ( 1.8) 287 ( 1.7) 277 ( 1.4) Region 273 ( 3.5) 268 ( 4.3) 254 ( 3.7) 267 ( 4.1) 285 ( 2.5) Nation 266 ( 1.9) 257 ( 2.4) 259 ( 1.7) 281 ( 2.2) 261 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the .sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 4 0 34 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE 3 I Eighth-Grade Public-School Mathematics (continued) i Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1000 NAEP TRIAL S T A T E ASSESSMENT Numbers and O p e r a t i o n s 1 1 . 2 1 1 1 1 " 1 " " " a n s " Data Ariatysk, l i b a s t k t and Probability Al"lbrRatotiansa and TOTAL State Region Nation PARENTS' EDUCATION ItS non-waduate State Region Nation NS graduat State Region Nation Som college State Region Nation College graduate State Region Nation (WNW' Male State Region Nation Female State Region Nation PrOckincy Praildancy PrOckstry Proldency Prvaltalmay 280 ( 1.1) 260 270 ( 2.7) 2133 3.4 206 ( 1.4) 258 1.7 270 13) 295 ( 262 3.1) 205( 3.2 259 1.4) 262 ( 141 275 1.1 2113 2.1 200 13 263 1 4.7) 24f ( 5.8) 253 i 3.2) 40 ( $.5) 22 i LI ... ...) ... ( .4.) ...) *MO On 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) 240 ( 3.1) 242 ( 3.01 278 ( 2.3) 274 ( 3.8) 268 ( 2.1) 278 ( 3.0) 289 ( 2.5) 2518 ( 3.8) 251 ( 3.4) 260 ( 3.21 leg 1 24 259 ( LS) 241 ( 2.1) 252 ( 1.9) 253 ( 22 253 2.0) 289 ( 2.4) 200 ( 2.6) 279 ( 2.4) 2011 ( 22 276 ( 22) 275 ( 3.2) 270 ( 5.7) 264 ( 4.9) 273 ( 4.7 NO i Ei 270 ( 1.5) 264 ( 2.7) 202 ( 2.0) 289 ( 2.4 292 ( 1.5) 2137 ( 2.4) 285 ( 1.5) 21;0 ( 1.7) 263 1.5) 277 ( 42) 270 ( 4.4) 270 ( 4.3) 273 ( 4.5) 271 3.1) 27$ ( 13) 272 ( 2.0) 270 ( 1.6) 276 ( 2.2) 273 1.7) 289 ( 1.7) 271 ( 3.9) 206 ( 2.0) 283 ( 1.8) 270 ( 2.7) 266'( 1.4) 288 ( 2.2) 267 ( 4.8) 262 ( 2.3) 274 ( 2.3) 259 ( 3.4) 253 ( 1.6) 279 ( 1.6) 264 ( 3.7) 200 ( 1.7) 276 ( 1.7) 200 ( 3.1) 25$ ( 1.5) 290 ( 1.6) 265 ( 3.4) 262 ( 2.1) 281 ( 1.8) 265 ( 4.0) 261 ( 1.9) 276 ( 1.3) 263 ( 2.2) 200 ( 1.6) 275 ( 1.7) 262 ( 2.8) 260 ( 14) The standard errors of the estimated StatistiCS appear in parentheses, It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 41 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 North Dakota NE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, arl students. To gather such information, the students participatAng 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, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. 4 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 37 North Dakota Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in Amaican schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work bestto 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 televixion than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 4 3 38 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota 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 poicymakers 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 North Dakota public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: Less than half of the eighth-grade students in North Dakota (43 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. 3 Curtis McKnight, et al., The Underachieving Curriculum Assessing U.S. School Mathematics from an International Perspective, A National Report on the Second International Mathematics Study (Champaign, IL: Stipes Publishing Comp.,. , 1987). Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematics Education (Washington, DC: National Academy Press, 1989). 4 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 North Dakota In North Dakota, 48 percent of the students could take an algebra course in eighth grade for high school course placement or credit. More than half of the students in North Dakota (65 percent) were taught mathematics by teachers who teach only one subject. About one-quarter (30 percent) of the students in North Dakota were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was more prevalent across the nation (63 percent). TABLE 4 1 Mathematics Policies and Practices in North Dakota Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Ngsrdi DaicOa I Cerdrai Nation Percentage of eighth-grade students in public schools that Identified MathOrnatks as receiving special emphasis in school-wide goals and objectives, Instruction, In-service training, etc. Percentage of eighth-grade public-school students who are offered a course in algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who teach only mathematics Percentage of eighth-grade students in public schools who are assigned to a mathematics class by Risk ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics instruction per iveek Percentage Peroantege Pimento. 43 ( 3.2) T2 (13.8) En ( 5.9) 4$ ( 2.0) 09 (18.4) 78 ( 42) OS ( 2.9) 87 ( 7.8) 91 ( 3.3) 30 ( 2.0) 00 ( 5.7) 63 ( 4.0) 44 ( 2.3) 25 ( 8.8) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certsbuy that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. 5 40 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in North Dakota are taking mathematics courses. Based on their responses, shown in Table 5: A greater percentage of students in North Dakota were taking eighth-grade mathematics (73 percent) than were taking a course in pre-algebra or algebra (25 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-atgebra or algebra. Students in North Dakota who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pm-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class i They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL. STATE ASSESSMENT North Dakota Centre! Nation What kind of mathematics class are you Percentage Percentage Percentage and and and taking this year? Proficiency Proficiency Proficiency Eighth-grade mathematics 73 ( 2.0) 58 ( 4.8) 62 ( 2.1) 277 ( 1.4) 255 ( 3.1) 251 ( 1.4) Pr...algebra 17 ( 1.9) 22 ( 4.3) 19 ( 1.9) 289 ( 2.4) 278 ( 3.1)1 272 ( 2.4) Algobra 8 ( 1.0) 15 ( 2.8) 15 ( 1.2) 307 ( 4.4) 289 ( 5.4) 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The 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. 4 6 THE 1990 1 s:AEP TRIAL STATE ASSESSMENT 41 North Dakota Further, fivm Table AS in the Data Appendix:` About the same percentage of females (26 percent) and males (24 percent) in North Dakota were enrolled in pre-algebra or algebra courses. In North Dakota, 26 percent of White students, 10 percent of Hispanic students, and 20 percent of American Indian students west enrolled in pre-algebra or algebra courses. Similarly, 21 percent of students attending schools in advantaged urban areas, 24 percent in schools in extreme rural areas, and 27 percent in schools in areas classified as "other" were enrolled in pre-algebra or algebra COMM. 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 North Dakota spent 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 IS 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 North Dakota, 1 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 North Dakota 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* educauon level, and gender, 4 7 42 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota The results by race/ethnicity show that 2 percent of White students, 0 percent of Hispanic students, and 0 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, I percent of White students, 0 percent of Hispanic students, and 0 percent of American Indian students spent no time doing mathematics homework. In addition, 11 percent of students attending schools in advantaged urban areas, 0 percent ixt schools in extreme rural areas, and 1 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 0 percent of students attending schools in advantaged urban areas, 3 percent in schools in extreme rural areas, and 0 percent m schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT North Dakota Central Nation Percentage and Proficiency 1 ( 0.8) ..**) Percentage and Proficiency 1 ( 0.8) .44 ( *** Percentage snd Proficiency ( 0.3) About how much time do students spend on mathematics homework each day? None 15 mimeos 37 ( 2.6) 34 ( 7.1) 43 ( 42) 279 ( 2.2) 255 ( 4.7) 258 ( 2.3) 30 minutes 51 ( 3.7) 48 ( 9.6) 43 ( 4.3) 283 ( 1.8) 272 ( 3.5) 286 ( 2.8) 43 minutes 10 ( 1.6) 13 ( 6.0) 10 ( 1.9) 282 ( 3.7) 281 (12.5)I 272 ( 5.7)1 An hour or more 2 ( *4* 0.3) *** ) 6 ( 2,3) «.-*) 4 ( 278 ( 0.9) 5.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value f r the entire population is within ± 2 standard errors of the estimate for the sample. I. Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). LIS THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Percentage Percentage Percentage and and and Preiciamy Preddency Prat Wray 9 ( 0.6) 7 ( 1.4) 9 C 0.6) 287 ( 2.8) «K. ( 44) 251 ( 2.5) 31 ( 1.4) 34 ( 4.8) 31 ( 2.0) 284 ( 4.4) 269 ( 3.8) 264 ( 1.9) 33 ( 1.4) 32 ( 2.3) 32 ( 12) 280 ( 1.5) 264 ( 3.6) 263 ( 1.9) 10 ( 1.1) 15 ( 1.2) 16 ( 1.0) 27$ ( 2.3) 265 ( 4.0) 266 ( 1.9) 12 ( 0.7) 12 ( 3.4) 12 ( 1.1) 279 ( 3.0) 262 ( 8.2)1 258 ( 3.1) ............... North Dakota 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 1090 MEP TRIAL STATE ASSESSMENT North Dakota Central Nation About how much time do you usually spend each day on mathematics homework? None 16 minutes 30 mimdes 45 minutes An how or more 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 North Dakota, relatively few of the students (9 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 North Dakota 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, 9 percent of Hispanic students, and 22 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 9 percent of White students, 9 percent of Hispanic students, and 6 percent of American Indian students spent no time doing mathematics homework. 44 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota In addition, 13 percent of students attending schools in advantaged urban areas, 12 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, 7 percent of students attending schools in advantaged urban areas, 8 percent in schools in extreme rural areas, and 10 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 variouscontent areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics contentareas 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 ttpic: 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, Curricuhon and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). t THE 1990 NAEP TRIAL ST/UT ASSESSMENT 45 North Dakota 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 teachtrs placed heavy instructioral 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 North Dakota 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 North Dakota Central Nation Teacher "emphasis" categories by Perambee Panantage Parassiap and and content areas PM Money Praticiany Praia Way Numbers and Operations Heavy emphasis 49 ( 1.2) 54 ( 1.2) 49 ( 3.11) 283 ( 1.9) 264 ( 4.3) 260 ( 1.8) Little or no emphasis 10 ( 0.8) 13 ( 4.5) 15 ( 2.1) 295 ( 2.4) 285 ( 6.8)1 287 ( 3.4) Measurement Heavy emphasis 13 ( 29) 18 ( 5.7) 17 ( 3.0) 277 ( 5.0)1 247 (125)1 250 ( 5.6) Little or no emphasis 3$ ( 13) 42 ( 9.7) 33 ( 4.0) 204 ( 3.1) 270 ( 7.7)1 272 ( 4.0) Geometry Heavy emphasis 23 ( 3.0) 26 ( 7.0) 28 ( 3.8) 260 ( 1.8) 261 ( 7.9)1 260 ( 3.2) Little or no emphasis 20 ( 1.8) 35 ( 7.2) 21 ( 3.3) 279 ( 1.8) 261 ( 9.0)1 264 ( 5.4) Data Analysis, Statistics. and Probability Heavy emphasis 9 ( 2.6) 12 ( 2.5) 14 ( 2.2) 286 ( 3.7)1 282 ( 75) 269 ( 4.3) Little or no emphasis 74 ( 2.6) 57 ( 8.8) 53 ( 4.4) 286 ( 1.4) 264 ( 5.6)1 261 ( 2.8) Algebra and Functions Heavy emphasis 56 ( 3,4) 50 ( 7.6) 46 ( 3.6) 281 ( 1.2) 213 ( 3,6) 275 ( 2.5) Little or no emphasis 9 ( 1.9) 19 ( 3.9) 20 ( 3.0) 266 ( 4.6)1 242 ( 5.5)1 243 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAB!' TRIAL STATE ASSESSMENT 47 North Dakota 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: Less than half of the eighth-grade students in North Dakota (43 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In North Dakota, 48 t of the students could take an algebra course in eighth grade for hi -school course placement or credit. A greater percentage of students in North Dakota were taking eighth-grade mathematics (73 percent) than were taking a course in pre-algebra or algebra (25 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 North Dakota spent 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 North Dakota, relatively few of the students (9 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 North Dakota 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 NA EP TRIAL STATE ASSESSMENT North Dakota CHAPTER 4 riX042:-4 ORM BR BlUR IN mumansalsoras sss sr emir is 111101111111111.111,1.11 111111111111101114111 11112111111111111111111111111 811111 .,110111.11111.11 '4711111111111111'011111111 -11111111,1rAmai isimeamss All aesess How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning or for those who come from different cultural backgrounds is an important aspect of teaching.' An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. 6 National Council of Teachers of Mathematics. Professional Standards /or the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). tPf THE 1990 NAEP TRIAL STATE ASSESSMENT 49 North Dakota From Table 9 and Table A9 in the Data Appendix: In North Dakota, 18 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 35 percent of the students were taught by teachers who got only some or norm of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In North Dakota, 23 percent of students attending schools in advantaged urban areas, 20 percent in schools in extreme rural areas, and 17 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in North Dakota, 40 percent of students attending schools in advantaged urban arms, 37 percent in schools in extreme rrral areas, and 31 percent in schools in areas classified as "othes" were in classrooms where only some or no resources weir available. Students whose teachers got all the resources they needed had mathematics achievement levels similar to those whose teachers got only some or none of the resources they needed. TABLE 9 I Teachers' Reports on the Availability of I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT North Dakota Central Nation Which of the following statements is true about how well supple° you are by your school system with the instructional Percentage Percentage Percentage and and and materials and other resources you need to teach your class? Pro Money Proficiency Proficiency get all the resources I need. 18 ( 2.7) 8 ( 2.4) 13 ( 2.4) 279 ( 3.2) ,.... ( 4411 285 ( 4.2) I get most of the resources I need, 48 ( 2.9) 45 ( 7.8) 56 ( 4.0) 282 ( 1.7) 271 ( 2.2)1 265 ( 2.0) I get some or none of the resources I need. 35 ( 3.4) 47 ( 7.3) 31 ( 4.2) 282 ( 1.8) 269 ( 3.5) 281 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors oi 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 insufricient to permit a reliable estimate (fewer than 62 students). r t) 50 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yielded many insights into th c. 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 North Dakota (38 percent) worked mathematics problems in small groups at least once a 'week; some never worked mathematics problems in small groups (18 percent). The largest percentage of the students (74 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (5 percent). In North Dakota, 79 percent of the students were assigned problems from a mathematics textbook almost every day; 5 percent worked textbook problems about once a week or less. Less than half of the students (37 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 Currkulum: Eighty-second Yearbook of the National Society for the Study of Education (Chicago, IL: University of Chicago Press, 1983). 5 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 51 North Dakota TABLE 10 I Teachers' Reports on Patterns of Mathematics 1 Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 111150 NAEP TRIAL STATE ASSESSMENT North Dakota Centel Won About flow often do students work problems In smelt groups? Al least once a week Lm than once a week Never About how often do students use objects like rulers, counting blocks, or geometric solids? At least once a week Lass than one* a week Never Pmentage Parvartaga Paroanals and and and Pratidancy flesildencv .111181antY 38 ( 3.3) 50 ( 7.8) 50 ( 4.4) 291 ( 2.5) 25$ ( 4.1) NO ( 2.2) 43 ( 3.7) 43 ( 5.6) 43 ( 4.1) 254 ( 1.5) NB ( 4.0)1 264 ( 2.3) 1$ ( 2.1) 7 ( 4.3) 8 ( 2.0) 279 ( 2.5) 14,4. ( *mil 277 ( 5.4)1 Percentage Percentage Percentage and and and Proficiency Proficiency Proficiency 21 ( 2.7) 279 ( 1.3) 15 ( 5.1) 255 ( 4.9)1 22 ( 3.7) 254 ( 3.2) 74 ( 281 ( 5 ( 2.9) 1.5) 0.9) ..**) 811 264 ( 4 (( 8.0) 3.3) 2.3) 69 ( 263 ( 9 ( 282 ( 3.9) 1.9) 2.8) 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. 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), 5 7 52 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE 11 I Teachers' Reports on Materials for I Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1,00 NAEP TRIAL STATE ASSESSMENT North Dakota Central Nation About how often do students dO problems from textbooks? Parcanta. and Pislidenly Percentage and Madam Percentage and Proficiency Almost every day 79 ( 3.3) 02 ( 5.13) 82 ( 3.4) 282 ( 1.1) 2010 ( 32) 267 ( 1.8) Several times a week 10 ( 3.4) 32 ( 42) 31 ( 3.1) 200 ( 5.0)1 252 ( 5.3) 254 ( 2.9) About once a week or less 5 ( 0.3) 0 ( 2.7) 7 ( 1.8) ORM ( OM) 200 ( 5.1) About how often do stuaents do problems Percentage Percentage on worksheets? and and and Proficiency Proddency Proldency At least several times a week 37 ( 2.5) 21e ( 2.1) 38 ( 8.3) 252 ( 5.5)1 34 ( 3.8) 258 ( 2.3) About once a week 34 ( 3.3) 23 ( 43) 33 ( 3.4) 281 ( 1.0) 201 ( 8.1) 200 ( 2.3) Less than moldy 29 ( 2.7) 39 ( 7.0) 32 ( 3.0) 280 ( 2.3) 270 ( 4.1) 274 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determination of the variability of thir 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 North Dakota COLLABORATING IN SMALL GROUPS In North Dakota, 50 percent of the students reported never working mathematics problems in small groups (see Table 12); 19 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 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT north Dakota Central Ration Patents. and ProficiancY Percentage and Proficiency Percentage and Proficiency How often do you work in small groups in your mathematics class? At least once a week 19 ( 1.6) 23 ( 4.6) 28 ( 2.5) 282 ( 1.7) 266 ( 6,S) 254 ( 2.7) Less than once a week 31 ( 1.2) 32 ( 3.3) 28 ( 1.4) 283 ( 1.8) 2811 ( 3.0) 267 ( 2.0) Never 50 ( 2.0) 45 ( 6.3) 44 ( 2.9) 250 ( 1.5) 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 standard errors of the estimate for the sample. Examining the subripulations (Table A 12 in the Data Appendix): In North Dakota, 10 percent of students attending schools in advantaged urban areas, 16 percent in schools in extreme rural areas, and 22 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 19 percent of White students, 27 percent of Hispanic students, and 24 percent of American Indian students worked mathematics problems in small goups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (18 percent and 20 percent, respectively). 54 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota USING MATHEMATICAL OFJECTS Students wexe 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; About one-quarter of the students in Nvrth Dakota (30 percent) never used mathematical objects; 24 percent used these objects at least once a week. Mathematical objects were used at least once a week by 16 percent of students ;Mending schools in advantaged urban areas, 25 percent in schools in extreme rural areas, and 25 pexcent in schools in areas classified as "other". Males were more likely than females to use mathematical objects in their mathematics classes at least once a week (29 percent and 19 percent, respectively). In addition, 24 percent of White students, 34 percent of Hispanic students, and 28 percent of American Indian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATH DAMS PROFICIENCY 1990 NAP TRIAL STATE ASSESSMENT North Dakota Nation How often do you work with objects like rulers, counting blocks, or geometric solids in your mathemaVcs class? At least once a week Less than once a mek Percentage Percentage and and Prelidency Prolidency 24 ( 1.4) 23 ( 2.9) 278 ( 1.7) 280 ( 3.5) Percentage mid Proldency 28 ( 1.8) 258 ( 2.8) 45 ( 1.5) 38 ( 2.5) 31 ( 12) 284 ( 1.8) 272 ( 2.9) 289 ( 1.5) 30 ( 1.4) ei ( 4.0) 41 ( 2.2) 280 ( 1.9) 282 ( 2.8) 259 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. GO THE 1990 NAEP TRIAL STATE ASSESSMENT 55 North Dakota MATERIALS FOR MA THEMATICS INSTRUCTION The percentages of eighth-grade public-school students in North Dakota who frequestly 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 M4 in the Data Appendix): Many of the students in North Dakota (80 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of the students in the nation. Textbooks were used almost eves), day by 79 percent of students attending schools in advantaged urban areas, 84 percent in schools in extreme rural areas, and 76 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 1080 NAEP TRIAL STATE ASSESSMENT North Dakota How often do you do mathematics problems from textbooks In your Percentage Percentage Percontap mathematics class? and Proficiency and Proadency and Proficiency Almost every day 80 ( 1.2) 74 ( 4.7) 74 ( 1.9) 284 ( 1.1) 271 ( 22) 267 ( 1.2) Several times a week 11 ( 0.9) 15 ( 1.8) 14 ( OA) 268 ( 3.7) 2.50 ( 4.2) 252 ( 1.7) About once a week or less 9 ( 0.8) 11 ( 4.3) 12 ( 1.8) 275 ( 2.5) 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. Cl 56 THE 19 $,J NAEP TRIAL STATE ASSESSMENT North Dakota And, for the frequency of worksheet usage (Table 15 and Table Al 5 in the Data Appendix): Less than half of the students in North Dakota (36 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 25 percent of students attending schools in advantaged urban areas, 38 percent in schools in extreme rural areas, and 37 percent in schools in areas classified as "other". TABLE I S I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAEP TRIAL STATE ASSESSMENT Noels Dakota Central Nation How often do you do mathematics problems on worksheets in your vor. Parcentage Percentage Porcantage mathematics class? and ProNciency and Proficiency and ProficiencY AI least several Untes a tweet 36 ( 1.0) 36 ( 80) 38 ( 2.4) 278 ( 2.0) 257 ( 4.9) 253 ( 22) About once a week 24 ( 1.8) 23 ( 2.3) 25 ( 12) 280 ( 1.8) 264 ( 2.6) 281 ( 1.4) Less than woo* 40 ( 2.4) 40 ( 5.6) 37 ( 2.5) 284 ( 1.5) 273 , 4.0) 272 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 94 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standaisi 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 North Dakota TABLE 16 Comparison of Students' aad Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS - 11190 'MEP TRIAL STATE ASSESSMENT - North Dakota Centra l 1 Nation Patterns of classroom Instruction Percentage of students atm work mathematics problems k? small Imps At least once a week Less than once a week Never Percentage of students Who use objects OM Men, counting blocks, or geometric solids At least once a week Lees than once a week Never 1 Materials for mathematics instruction i Percentage of students Ma use a mathematics textbook Almost every day Several times a week About once a week or less Percentage of students who we a mathematics wolitshset At least several tunes a week About once a week Less than weekly 411. The standard errors or the estimated 1-....tistics 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. Peremenee Pereertago Iteneente. Siletents Toad** Sludents Umbers Students Towhees 19 ( 1.0) 38 ( 3.3) 23 ( 42) 50 ( 72) 28 ( 2.5) 50 ( 4.4) 31 ( 12) 43 ( 3.7) 32 ( 3.3) 43 ( 8.8) 28 ( 1.4) 43 ( 4.1) 60 ( 2.0) 18 ( 2.1) 45 ( 0.3) 7 ( 4.3) 44 ( 2.9) 0 ( 2.0) 24 ( 1.4) 21 ( 2.7) 23 ( 2.9) 15 ( 5.1) 28 ( 1.8) 22 ( 3.7) 45 ( 1.5) 74 ( 2.9) 3$ ( 2.5) 81 ( 6.0) 31 ( 1.2) 09 ( 3.9) 30 ( t.4) 5 ( 0.9) 41 ( 4.8) 4 ( 2.3) 41 ( 2.2) 9 ( 22) Percentage Percentage Percentage Students Teachers Students Teachers Students Teachers 80 ( 1.2) 7 ( 3.3) 74 ( 4.7) 02 ( 5.6) 74 ( 1.9) 62 ( 3.4) 11 ( 0.0) 16 ( 3.4) 15 ( 1.6) 32 ( 4.2) 14 ( 0.8) 31 ( 3.1) 9 ( 0.8) 5 ( 0.3) 1.1 ( 4.3) 6 ( 2.7) 12 ( 12) 7 ( 1.8) 36 ( 1.9) 37 ( 2.5) 36 ( 6.0) 38 ( 8.3) 36 ( 2.4) 34 ( 3.8) 24 ( 1.8) 34 ( 3.3) 23 ( 2.3) 23 ( 4.8) 25 ( 1.2) 33 ( 3.4) 404 2.4) 29 ( 2.71 40 ( 5.6) 39 ( 7.0) 37 ( 24) 32 ( 58 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery practices and resources. ^noears that mathematics textbooks and worksheets continue to play a major role in mathematics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachers: Less than half of the students in North Dakota (38 percent) worked mathematics problems in small groups at least once a week; some never worked in small groups (18 percent). The largest percentage of the students (74 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (5 percent). In North Dakota, 79 percent of the students were assigned problems from a mathematics textbook almost every day; 5 percent worked textbook problems about once a week or less. Less than half of the students (37 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 North Dakota, 50 percent of the students never worked mathematics problems in small groups; 19 percent of the students worked mathematics problems in small groups at least once a week. About one-quarter of the students in North Dakota (30 perrent) never used mathematical objects; 24 percent used these objects at least once a week. Many of the students in North Dakota (80 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 North Dakota (36 percent) used worksheets at least several times a week, compared to 38 percent in the nation. THE 1990 NAEP TRIAL STATE ASSESSMENT 59 North Dakota 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 we them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks.' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. National Assessment of Educational Progress, Mathematics Objectives. 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). lid 60 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota Table 17 provides a profile of North Dakota eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 39 percent of the students in North Dakota had teachers who allowed calculators to be used for tests. About the same percentage of students in North Dakota and in the nation had teachers who permitted unrestricted use of calculators (24 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of North Dakota Policies on Calculator Use PERCENTAGE OF STUDENTS _ 1000 MEP TRIAL STATE ASSESSMENT North Dakota Control Nation Percentage of eighth-grade students in public schools whose teachers permit the unrestricted use of calculators Percentage of eighth-grade students in public schools whose teachers permit the use of calculators for tests Percentage of eighth-grade students in public schools whose teachers report that students have access to calculators owned by the school Peratittop Percentage Percentile 24 ( 3.3) 27 ( 8.1) 16 ( 3.4) 39 ( 3.4) 44 ( 7.9) 33 ( 4.5) 37 ( 2.6) SS ( 6.2) 56 ( 4.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THZ 1990 NAV' TRIAL STATE ASSESSMENT 61 North Dakota THE AVAILABILITY OF CALCULATORS In North Dakota, most students or their families (100 percent) owned calculators (Table 18); however, fewer students (49 percent) had teachers who explained the use of calculators to them. From Table Al8 in the Data Appendix: In North Dakota, 48 percent of White students, 64 percent of Hispanic students, and 61 percent of American Indian students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (47 percent and 50 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT North Dakota Central Nation =O1M- Do you or your family own a calculator? Yes Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes ercentage Percontaga Percentage and and and Proficiency Proficiency Profidency 96 1 0.6) 266 ( 2.5) 2 ( 0.6) 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( 3.8) Percontage Pertentage Percontage and and and Proficiency Proficiency Proficiency 49 ( 1.7) 279 ( 1.7) 51 ( 1.7) 284 ( 1.3) 56 ( 4.9) 49 ( 2.3) 263 ( 3.0) 258 ( 1.7) 44 ( 4.9) 51 ( 2.3) 269 ( 3.4) 266 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can tic 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 esumate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). G7 62 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota 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, stty' 'ts were asked how frequently (never, sometimes, almost always) they used cak.t. _ors for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In North Dakota, 23 percent of the students never used a calculator to work problems in class, while 46 percent almost always did. Some of the students (12 percent) never used a calculator to work problems at home, compared to 31 percent who almost always used one. Less than half of the students (34 percent) never used a calculator to take quizzes or tests, while 23 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IWO NAEP TRIAL STATE ASSESSMENT North Dakota Central Nation Percentage and Proficiency Pamentage and Naticiancy Percentage and Proficiency How often do you use a calculator for the following tasks? Working problems Hi dass Almost always 48 ( 1.6) 51 ( 3.8) 48 ( 1.5) 277 ( 13) 260 ( 2.8) 254 ( 1.5) Never 23 ( 1.6) 18 ( 3.6) 23 ( 1.9) 288 ( 1.4) 270 ( 4.1)! 272 ( 1.4) Doing problems at home Almost always 31 ( 1.4) 35 ( 2.2) 30 ( 1.3) 261 ( 1.5) 266 ( 2.8) 261 ( 1.8) Never 12 ( 0.9) 16 ( 2.1) 191 0.9) 282 ( 1.9) 263 ( 3.3) 263 ( 1.8) Taking quizzes or tests Almost always 23 ( 1.2) 29 ( 4.5) 27 ( 1.4) 277 ( 1.9) 280 ( 4.0) 253 ( 2.4) Never 34 ( 1.7) 22 ( 4.8) 30 ( 2.0) 269 ( 1.2) 271 ( 3.4)i 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 .1. 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 63 North Dakota WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate w.iether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items ii the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the comet 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 thv were presented. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A greater percentage of students in North Dakota weir in the High group than were in the Other group. About the same percentage of males and females were in the High group. In addition, 57 percent of White students, 54 percent of Hispanic students, and 32 percent of American Indian students were in the High goup. TABLE 20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT North Dakota emirs, Nation , "CaInulator-use" group IL High Other Percentage and Pro &dewy Percentage Percentage and and Proficiency Prolkiency 58 ( 1.5) 48 ( 1.8) 42 ( 1.3) 286 ( 1.6) 272 ( 3.4) 272 ( 1.8) 44 ( 14) 54 ( 1.8) 56 ( 1.3) 275 ( 1.8) 280 ( 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. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 North Dakota 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 tmphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 39 percent of the students in North Dakota had teachers who allowed calculators to be used for tests. About the same percentage of students in North Dakota and in the nation had teachers who permitted unrestricted use of calculators (24 percent and 18 percent, respectively). In North Dakota, most students or their families (100 percent) owned calculators; however, fewer students (49 percent) had teachers who explained the use of calculators to them. In North Dakota, 23 percent of the students never used a calculator to work problems in class, while 46 percent almost always did. Some of the students (12 percent) never used a calculator to work problems at home, compared to 31 percent who almost always used one. Less than half of the students (34 percent) never used a calculator to take quizzes or tests, while 23 percent almost always did. 71 66 THE 1990 NAEP TRIAL STATE MSESSM ENT North Dakota CHAPTER 6 Who Is Teaching Eighth-Grade Mathematics? In recent years, accountability for educational outcomes has become an issue of increasing importance to federal, state, and local governments. As part of their effort to improve the educational process, policymakers have reexamined existing methods of educating and certifying teachers.° Many states have begun to raise teacher certification standards and strengthen teacher training programs. As shown in Table 21: In North Dakota, 19 percent of the students were being taTIght by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. More than half of the students (69 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 (91 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate. This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). 7 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 67 North Dakota TABLE 21 I Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 10110 NAEP TRIAL STATE ASSESSMENT North Dakota Central Nation Percentage of students whose mathematics teachers reported having the following degrees Percentage Percentage Percentage Bachelor's degree 81 ( 1.9) 48 ( 9.1) 56 ( 4.2) Master's or specialist's degree 19 ( 1.9) 48 ( 8.8) 42 ( 4.2) Doctorate or professional degree 0 ( 0.0) 4 ( 2.7) 2 ( 1.4) Percentage of students whose mathematics teachers have the Mowing types of teaching certificates that are recognized by North Dakota No regular certification ( 0.2) 4 ( 2.7) 4 ( 1.2) Regular certification but less than the highest available 30 ( 4.1) 25 ( 7,3) 29 ( 4.3) Highest certification available (permanent or long-term) 69 ( 4.1) 71 ( 7.3) 60 ( 4.3) Percentage of students *hose mathematics teachers have the following types of teaching certificates that are recognized by North Dakota Mathematics (middle school or secondary) 91 ( 1.6) 77 ( 4.5) 84 ( 22) Education (elementary or middle school) 5 ( 1.4) 17 ( 75) 12 ( 2.6) Other 3 ( 0.6) 7 ( 4.8) 4 ( 1,5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds more specifically, their undergraduate and graduate majors and their in-service training. 73 58 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In North Dakota, 61 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in North Dakota (15 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and 1 Graduate Fields of Study PERCENTAGE OF STUDENTS 1a00 NAEP TRIAL. STATE ASSESSMENT North Dakota Central Nation What was your undergraduate major? Percentage Percentage Percentage Mathematics 61 ( 3.0) 57 ( 7.1) 43 ( 3.9) Education 28 ( 2.8) 29 ( 6.4) 36 ( 3.8) Other 11 ( 1.1) 14 ( 5.4) 22 ( 3.3) -1 What was your graduate major, Percentage Percentage Percentaga Mathematics 15 ( 1.5) 34 ( 9.1) 22 ( 3.4) Education 28 ( 2.9) 34 ( 6.2) 38 ( 3.5) Other or no graduat level study 57 ( 3.3) 32 ( 6.6) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses, 1t can be said with about 95 percent certainty that, for eaLh 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 69 North Dakota Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In North Dakota, 25 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-semice training. Some of the students in North Dakota (20 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students bad mathematics teachers who spent no time on similar in-service training. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS WOO NAEP TRIAL STATE ASSESSMENT North Dakota Cintral Nation During the last year, how much time in total have you spent on in-service education in mathema:ics or the teaching of mathematics? Nona Ono to 15 hours 16 hours or more Percentage Percentage Percontago 20 ( 2.4) ( 1.3) 11 ( 2.1) 55 ( 3.8) 71 ( 5.4) 51 ( 4.1) 25 ( 2.0) 28 ( 5.0) ( 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. P*7J THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota 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 cuniculum 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 gratifications and practices may point to areas worth further exploration. There is no guarantc.: 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 informaticn about teachers' educational backgrounds and experience reveals that: In North Dakota, 19 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. More than half of the students (69 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 North Dakota, 61 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Some of the eighth-grade public-school students in North Dakota (15 percent) were taught mathematics by teathers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. '° Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Differences An International Assessment of Mathematics and Science (Prmceton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, '958). lna V.S. Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement NAEP's 1990 Assessment of the Nation and the Tnal Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 71 North Dakota In North Dakota, 25 percent of the eighth-grade public-scliool students had teachers who spurt 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 Nozth Dakota (20 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathmatics teachers who spent no time on similar in-service training. '77 72 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota CHAPTER 7 The Conditions Beyond School that Facilitate Mathematics Learning and Teaching Because students spend much more time out of school each day than they do in school, it is reasonable to expect that out-of-school factors greatly influence students' attitudes and behaviors in school. Parents and guardians can therefore play an important role in the education of their children. Family expectations, encouragement, and participation in student learning experiences are powerful influences. Together, teachers and parents can help build students' motivation to learn and can broaden their interest in mathematics and other subjects. To examine the relationship between home environment and mathematics proficiency, students participating in the Trial State Assessment were asked a series of questions about themselves, their parents or guardians, and home factors related to education. THE 1990 NAEP TRIAL STATE ASSESSMENT 73 North Dakota AMOUNT OF READLNG 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 I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT North Dakota Cantral Nation 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 typos Three types Four types parcemage and Proficiency Percentage and Prod,* fancy Percent Ago and Proadency 10 ( 1.0) 19 ( 2.1) 21 ( 1.0) 281 ( 3.5) 250 ( 3.4) 244 ( 2.0) 30 ( 1.2) 31 ( 2.2) 30 ( 1.0) 280 ( 1.8) 265 ( 3.6) 258 ( 1.7) 60 ( 1.3) 50 ( 1.8) 48 ( 1.3) 285 ( 0.9) 272 ( 2.1) 272 ( 1.5) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. The data for North Dakota reveal that: Students in North Dakota 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 North Dakota A smaller percentage of Hispanic and American Indian students had all four types of these reading materials in their homes than did White students. About the same percentage of students attending schools in 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 Tri,u State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 19e0 NAEP TRIAL STATE ASSESSMENT North Dakota Central Nation How much television do you usually , watch each day? Percentage Plvtlelency Percentage PruNdency Percentage 1111d Proficiency One hour or less 14 ( 0.9) 11 ( 1.6) 12 ( 0.8) 289 ( 2.0) 270 ( 3.5) 269 ( 2.2) Two hours 27 ( 1.2) 22 ( 1.7) 21 ( 0.9) 283 ( 1.3) 274 ( 3.2) 268 ( 1.8) Three hours 26 ( 12) 25 ( 2.4) 22 ( 0.8) 282 ( 1.6) 271 ( 4.0) 265 ( 1.7) Four to five hours 28 ( 1.3) 27 ( 3.0) 28 ( 1.1) 279 ( 2.3) 261 ( 2.9) 260 ( 1.7) Sbc hours or, more 8 ( 0.7) 14 ( 1.6) 18 ( 1.0) 284 ( 3.1) 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.: 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 75 North Dakota From Table 25 and Table A25 in the Data Appendix: In North Dakota, 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 North Dakota (14 percent) watched one hour or less of television each day; 6 percent watched six hours or more. About the same percentage of males and females tended to watch six or more hours of television daily. However, a smaller percentage of males than females watched one hour or less per day. In addition, 6 percent of White students, 8 percent of Hispanic students, and 14 percent of American Indian students watched six hours or more of televirim each day. In comparison, 15 percent of White students, 10 percent of Hispanic students, and 9 percent of American Indian students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix: In North Dakota, average mathematics proficiency was lowest for students who missed three or more days of school. About half of the students in North Dakota (50 percent) did not miss any school days in the month prior to the assessment, while 14 percent missed three days or more. In addition, 13 percent of White students, 20 percent of Hispanic students, and 33 percent of American Indian students missed thret. or more days of school. 81 76 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota Similarly, 14 percent of students attending schools in advantaged urban areas, 15 percent in schools in extreme rural areas, and 15 percent in schools in areas classified as "other" missed three or more days of school. TABLE 26 1 Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 MEP TRIAL ST4,:': ASSESSMENT North DMota Central Nation IDA How many days of school did you miss last month? 000 Of two days Three days or more Percentiles Permit.. and and Profit:fancy Praddancy SO ( 1.2) 285 ( 12) 38 ( 1.2) 281 ( 1.3) 14 ( 1.0) 269 ( 2.9) 47 ( 1.7) 269 ( 2.5) 30 ( 2.0) 271 ( 3.4) 23 ( 2.0) 252 ( 3.3) Panontage and Proliclincy 45 ( 1.1) 265 ( 1.8) 32 ( 0.9) 266 ( 1.6) 23 ( 1.1) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 77 North Dakota ..;IUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, leaning mathematics should require students not only to master essential skills and concepts but also to develop confidence in their mathematicai abilities and to value mathematics as adiscipline.' 2 Students were asked if thr 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 .viving everyday problems. A student "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongly agree" were given a value of I (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's responses were averaged over the five statements. The students were then as&igned a perception index according to whether they tended to strongly agree with the statements (an index of 1), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree. or to strongly disagree with the statements :an index of 3). Table 27 provides the data for the students' attitudes toward mathematics as defmed by their perception index. The following results were observed for North Dakota: Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. About one-quarter of the students (29 percent) were in the "strongly agree" cate:ory (perception index of 1). This compares to 27 percent across the nation. Some of the students in North Dakota (20 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception index of 3). " National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematks (Reston, VA: National Council of Tearherr of Mathematics, 1989). Cr) 3 78 THE 1990 NAEP TRIAL STATE ASSURMENT North Dakota TABLE 27 1 Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - MO MEP TRIAL STATE ASSESSMENT North Dakota Central Nation Student "perception index" groups Percentage and Proeciency Percentage and Proficiency Percentage and Praffelency Strongly agree 29 ( 1,5) 25 ( 1.6) 27 ( 1.3) ("perception Index" of 1) 293 ( 1.5) 272 ( 3.5) 271 ( 1.9) Agree 50 ( 1.4) 50 ( 1.8) ( 1.0) ("Perception index" ot 2) 280 ( 1$) 267 ( 3.1) 262 ( 1.7) Undecided, disagree, strongly disagree 20 ( 1.1) 25 ( 2.2) 24 ( 1.2) ("perception index" of 3) 268 ( 2.2) 256 ( 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 North Dakota who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the res,ilts for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who hz.d zero to two types. S 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 79 North Dakota Some of the eighth-grade public-school studesits in North Dakota (14 percent) watch.ed one hour or less of television each day; 6 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. About half of the students in North Dakota (50 percent) did not miss any school days in the month prior to the assessment, while 14 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. About one-quarter of the students (29 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. r 80 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon which the assessment was based, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Edu......-;;,,nal Testing Service. The development of the Trial State Assessment Program benefitted from the involvement of hundreds of representatives from State Education Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the program. Assetement Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spiral matrix design a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The first step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. C5 0 THE 3990 NAEP TRIAL STATE ASSESSMENT 81 North Dakota 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 thnee blocks of cognitive mathematics items. Student3 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 he 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 thebooklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based cor iensus 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 (sec Figure A2). Data Analysis and Scales Once the assessments had bem conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on students' performance on the set of mathematics items they received. IR T provides a common scale on which performance can be reported for the nation, each jurisdiction, and suhpopulations, 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 Educational Progress. Mathematics Objectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). 82 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota FIGURE Al I Content Areas Assessed Numbers and Operations This content area focuses on students' understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-world situations, as well as computational and estimation situations. Understanding numerical relationships as expressed in ratios, proportions, and percents is emphasized. Students' abilities in estimation, mental computation, use of calculators, generalization of numerical patterns, and verification of reSults are also included. Measurement This content area focuses on students' ability to describe real-world objects using numbers. Students are asked to identify attributes, select appropriate units, apply measurement concepts, and communicate measurement-related ideas to others. Questions are included that require an ability to read instruments using metric, customary, or nonstandard units, with emphasis on precision and accuracy. Questions requiring estimation, measurements, and applications of measurements of length, rime, money, temperature, mass/weight, area, volume, capacity, and angles are also included in this content area. [Geometry M=IMINM This content area focuses on students' knowledge of geometric figures and relationships and On their skills in working with this knowledge. These skills are important at all levels of schooling as well as in practical applications. Students need to be able to model and visualize geometric figures in one, two, and three dimensions and to communicate geometric ideas. In addition, students should be able to use informal reasoning to establish geometric relationships. Data Analysis, Statistics, and Probability This content area focuses on data representation and analysis across all disciplines and reflects the importance and prevalence of these activities in our society. Statistical knowledge and the ability to interpret clata 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 algedraic 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 underatanding: it in.rolves 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. CI C) THE 1990 NAEP TRIAL STATE ASSESSMENT 83 North Dakota FIGURE A2 I Mathematical Abilities The following three categones of mathematical abilities are not to be constru' as hierarchical. For example, problem 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 evidence that they can recognize, label, and generate examples and counterexamples of concepts: can use and interrelate models, diagrams, and varied representations of concepts; can identify and apply principles: know and can apply facts and definitions: can compare, contrast, and integrate related concepts and principles: can recognize, interpret, and apply the signs, symbols, and terms used to represent cOncepts; and can interpret the assumptions and relations involving concepts In mathematical settings. Such understandings are essential to performing procedures in a meaningful way and applying them in problem-solving situations. Procedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to select and apply appropriate procedures correctly, verify and justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors inherent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have been created as tools to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncomputational skiffs such as rounding and ordering. Problem Solving In problem solving, students are required to use their reasoning and analytic abiliti , when they encounter new situations. Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, data, models, and relevant mathematics; generate, extend, and modify procedures: use reasoning (i.e., spatial, inductive, deductive, statistical, and proportional); and judge the reasonableness and correctness of solutions. 84 THE 19g0 NAEP TRIAL STATE ASSESSMENT North Dakota A scale ranging from 0 to 500 was created to report perfonnance for each content area. Each content-atea scale was based on the distribution of student performance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In contnist, the NAEP scale anchoring is accomplished by describing what students at selected leveh 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 defmed, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would therefore have been highly speculative. To define performance at each of the four levels on the scale, NAEP analyzed sets of mathematics item i pm the 1990 assessment that discriminated well between adjacent levels. The criteria fir selecting these "benchmark" items were as follows: To d line performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To define performance at each of the higher levels on the scale, items were chosen that were: a) answered cornctly by at least 65 percent of students whose proficiency was at or near that level; and b) answered incorrectly by a majority (at least 50 percent) of the students performing at or near the next lower level. The percentage of students at a level who answered the item correctly had to be at least 30 points higher than the percentage of students at the next lower level who answered it correctly. no THE 1990 NAEP TRIAL STATE ASSESSMENT 85 North Dakota Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated propoition 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-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or work.heets were used, the instructional emphasis placed on different mathematical topics, ar -I the use of various instructional approaches. Because of the nature of the sampling far the Trial State Assessment, the responses to the mathematics teacher questionr aire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. Since t'lere were msufficient 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. ;)..1 86 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 Tomas Golf lab 0 Lake, 7. Linda had thus imot Wm all the use elm sad data difkust bells u shwa 'ems II she Mb aid box with dee bad a/ hark 'haw.. which hos will hare as Mew belie ka it? 0> The los with the lamas hatia tD The baa lush she pall beLlo tD The lax with tht tubber bah ti) You us% telL EXAMPLE 2 SOUS OF PANT PtCSED AT FARAWAY FARMS ;441 Th W Thari Ow Mk we* Otesget Lamm Geopefsat IMMO C. How sway boxes at asetases wele sada as Thttudayi CD SS C1Ct 60 OD 70 OD so CD 90 CO I don't know. Grade 4 Overall Percentage Percentage Correct Ng 65 91 Grade 4 Overall Percentage Percentage Correct g9g 224 75 91 Correct: 73% for Anchor Levels: 202 100 Grade 8 Overall Percentage Percentage Correct 222 76 87 P2 Corrv t % for Anw. Levels: 100 Correct: 89% for Anchor Levels: 1t2 96 100 THE 1990 NAEP TRIAL STATE ASSESSMENT 87 North Dakota FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 250: Simple Multiplicative Reasoning and Two-Stop Problem Solving EXAMPLE 7. What 15 the vatuc of a + $ when a 3 Answer EXAMPLE 2 Kat MILCIt ARM MALTS Calor et Pommy 37 S3 Tbe tabk Avec skines ihe setolo at Ferny id bais VAN.On do dick below, oaks e Ode mph to Wesson do doe in tbe obis Labe sob pen id the assie look ends sbe ammo heir sides Dsd you use the takulatess on ibo ;tunic.* Ws 0 hie EXAMPU 3 6. koala= Is pecking heathens taw boxes Eath box hofds 6 baseballs She hes 24 belb. Much number sentence will help Ma rind out how many boxes she will need; Cro 24 6 w 0 cp 24 6 w 0 cer 24 + 6 w, 0 cr 24 x 6 w 0 (I!) I don't know. Grade 8 Overall Percentage Correct 78% Percentage Correct for Anchor Levels: 222 211/ 121 25 59 95 95 Grade 8 Overall Percentage Correct: 73% Percentage Correct for Anchor Levels: Mt &IQ N12 21 58 92 22 Grade 8 Overall Percentage Correct 77% Percentage Correct for Anchor Levels: ZQQ ZQ i§g 37 71 95 100 c 3 88 THE 1990 NAEP TRIAL srATE ASSESSMENT North Dakota FIGURE A3 J Example Items for Mathematics Proficiency Levels (continued) Level 300: Reasoning and Problem Solving invoMng Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE 1 ID. Mikhail du foliewtse shows tbe weigh a Ilsprag flu above mangle ova liae OD EXAMPLE 2 In the NNW tenr* dui elm bethlias. aw IS kes loot stqweseeld s leek me&dlt Wits Jaw lithe use Leak* suet 5 hes hap% would be repssentat L Arale weld kw way Ada bight CP 4D I SI 7 coy Oil rsu 11 doe ealetileiet e* die eiitatioet Vas C) No Grade 8 Overall Percentage Correct 80% Percentwi Correct for Anchor Levels: 221 122 33 49 77 90 Grade 12 Overall Percentage Correct 75% Percentage Cava for Anchor livels: 222 2i14 48 79 95 Grade 8 Overall Percentage Correct 59% Percentage Correct for Anchor Levels: 2tX1 2C0 222 17 46 86 99 !j4 BEST COPY AVAILABLY THE 1990 NAEP TRIAL STATE ASSESSMENT 89 Nonit Dakota FIGURE i' f Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving InvoMng Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability EXAMPLE 1 IP Questions 16-17 tofu to tbs We* uti :sumo oi dotstiores. S 2 16. It this pouts') oi dot-biutts tsecAttsuod. ).01 sassy dots toil be in the )00th hprel GD CD 101 CD 199 21D 200 CD 201 EXAMPLE 2 17. Explain bow sou food yew soswct to Surstion 16. Anetwor Grade 8 Overall Percentage Correct 34% Percentage Correct for Anchor Levels: 2911 NS/ 13 19 53 88 Grade 12 Overall Percentage Correct: 49% Percentage Correct for Anchor Levels: ;22 Ug 1.14 22 48 90 Grade 8 Overall Percentage Correct: 15% Percentage Correct for Anchor Levels: 2212 kftg Z242 IN 1 4 28 74 Grade 12 Ovrall Percentage Correct: 27% Percentage Correct for Anchor Levels: Al4 gri9 2S/4 3 22 74 90 THE 1990 NAEP TRIAL SPATE ASSFSSMENT North Dakota SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-gade mathematics teachers or from a sample of schools, it is consistent with NAEP's goal of providing infonnation about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) air estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAEP) arc subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. like almost all estimates based on assessment measum, NAFP's total group and subgroup proficiency estimates are subject to a second source of mcertainty, in additionto sampling error. As previously noted, each student who participated in the Trial State Assessment was administered a subset of questions from the total set of questions. If each student had been administered a different, but equally appropriate, set of the assessment questions -- or the entire set of questions -- somewhat different estimates of total group and subgroup proficiency might have been obtained. Thus, a second source of uncertainty arises because each student was administered a subset of the total pool of questions. THE 1990 NAEP TRIAL STATE ASSESSMEN1. 91 North Dakota In addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistir. (such as the proportion of students answering a background question in a certain way or the proportion of students in certain racial/ethnic groups) reflect only sampling error. NAEP uses a methodology called the jackknife procetlure to estimate these standard errors. Drawing Inferences from the Results One of the goals of the Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory bas,:l on the particular sample of students assessed. One uses the results from the sample -- taking into account the unt rtainty associated with all samples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population means and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or tfaritory) 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 e- tire 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 oeltentages, provided that the percentages are not extremely large (greater than 9d 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 thtervals are quite complicated. 92 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota 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 usualO spend each day on matherratks 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 mathematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is hiLher, 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 a statement about the entire population, not about the particular sample that was assessed. The data from the sample are used to make inferences about the population as a whole. As discussed in the previous section, each estimated sample mean proficiency (or proportion) has a degree of uncertainty associated with it. It is therefore possible that if all students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a rea/ difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of umertainty called the standard error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the manner in which the standard error for an individual group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups ± 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between groups in the population. If the interval does not contain Zell), the difference between groups is statistically significant (different) at the .05 level. ns THE 1990 NAEP TRIAL STATE ASSESSMENT 93 North Dakota As an example, suppose that one were interested in detesmining whether the average mathematics proficiency of eighth-pade females is higher than that of eighth-grade males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard errors for females and males were as follows: Group Average Proficiency Standard Error Female 259 2.0 Mak: 255 2.1 The difference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is Nri.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 -!.8 and 9.8). Thus, one should conclude that there is insufficiept evidence to claim a difference in average mathematics proficiency between the population ...f eighth-glade 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 presereed. .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 appropriate when the statistics being compared come from independent samples. For certain comparisons in the report, the groups were not independent. In those eases, a different (and more appropriate) estimate of the standard error of the difference was used. 94 THE. 1990 NAEP TIUAL STATE ASSESSMENT North Dakota The procedures described in this section, and the certainty ascribed to intervals (e.g., a 95 percent confidence interval), are based on statistical theory that assumes that only one confidence interval or test of statistical significance is being performed. However, in each chapter of this report, many different groups are being compared (i.e., multiple sets of confidence intervals are being analyzed). When one considers sets of confidence intervals, statistical theory indicates that the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. If one wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Detel mined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Thrcughout this report, estimates of staward 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 ermrs -- should be interpreted cautiously. Further details concerning procedures for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defined by race/ethnicity and type of school 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 mults. As a result, data are not provided for Cie subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size 62 students was required. This number was determined by computing the ;ample size required to detect an effect size of .2 with a probability of .8 or greater. 100 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 North Dakota The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or territory, divided by the standard deviation of thc proficiency in the total population. If the true difference between subgroup and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical repolt Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "almost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below. Percentage Dascription 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 89 Many 89 < p < 100 Almost all p = 100 AR IC i 96 THE 1990 NAEP TRIAL STATE ASSESWENT North Dakota 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 North Dakota TABLE AS I Students' Reports on the Mathematics Class I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1910 NAEP TRIAL Elghth-grade STATE ASSESSMENT Mathematics Pre-alilihrit Atilibbni TOTAL. and Preliciency Percentage and Proliciency Percenielle and Preeciency State 73 ( 2.0) 17 ( 1.9) 8 ( 1.0) 277 ( 1.4) ( 2.4) 307 ( 4.4) Nation d2 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 298 ( 2,4) RACE/ETHNICITY White State 73 ( 2.1) 17 ( 2.0) 9 ( 1.2) 280 ( 1.1) 291 ( 2.4) 308 ( 4.7) Nation 59 ( 2.5) 21 ( 2.4) 17 ( 1.5) 259 ( 1.6) 277 ( 2.2) 300 ( 2.3) Hispanic State SO ( 6.1) 10 ( 4.3) 0 ( 0.0) *OM ***) Nation 75 ( 4.4) 8 ( 1.5) 240 ( 2.4) MM. 11,411 ( American Indian State 78 ( 4.8) 1 ( 1.2) 240 ( 4.1)i *411) Nation 84 ( 5.7) 8 ( 72) ...) *** ( 2.7) TYPE OF COMMUNITy Advantaged urban State 79 ( 279 ( 3.6) 4. ***) 14 ( *** 3.2) Nation 55 ( 9.4) 22 ( 7.9) 21 ( 4.4) bdranse rural 269 ( 2.5)1 m) State 75 ( 5.2) 19 ( 4.9) 5 ( 2.2) 279 ( 3.2) 286 ( 2.1)1 277 ( 2.5)' Nation 7'4 ( 24$. ( 4.5) 3.1)1 14 ( ( 5.0) 7 ( 2.2) Other State 70 ( 276 ( 1.9) 1.0) 18 ( 291 ( 1.3) 4.3) 10 ( ( 0.9) .4) Nation 61 ( 2.2) 20 ( 2.1) 18 ( 1.4) 251 ( 2.0) 272 ( 2.8) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "* Sample sin is insufficient to permit a reliable estimate (fewer than 62 students). r 98 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE AS I Students' Reports on the Mathematics Class (ccetinued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Eighth-grade Mathematics .,.__ Pre-algebra Algebra . TOTAL. porcantdlle and Pre *dem Percentage and Pradalency Ponandap and Pradahwicy State 73 ( 2.0) 17 ( 1.9) ( 1.0) 277 ( 1.4) 289 ( 2.4) 201 ( AA) Nation 62 ( 2.1) 19 ( 1.9) "5 ( 1.2) 251 ( 1.4) 272 ( 2.4) 290 ( 24) PARENTS EDUCATION HS nee-graduate State 67 ( 7.7) 259 ( 4.4) 14. 045 14 ( 7.8) Nation 77 ( 3.7) 241 ( 2.1) 13 ( 3,4) 4.14 ( .11 3 ( 1.1) .1m ) NS graduat State 81 ( 3.8) 270 ( 2.8) 12 ( 2.9) 282 ( 3.5)1 5 ( 1.7)) Nation 70 2.8) 18 ( 2.4) 8 ( 1.1) 249 ( 1.9) 288 ( 3.5) 277 5.2) Same college State 73 ( 2.9) 279 ( 1.9) 20 ( 2.7) 290 ( 5.0) 8 ( 1.1)) Nation 60 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2.1) 276 ( 2.8) 295 ( 3.2) College graduate State 89 ( 2.2) 1$ ( 1.9) 11 ( 1.1) 263 ( 1.4) 294 ( 3.0) 316 ( 4.0) Nation 53 ( 2.7) ( 2.3) 24 ( 1.7) 259 ( 1.5) 276 ( 2.6) 303 ( 2.3) GENDER Male Sta,e 74 ( 2.5) 15 ( 2.2) 9 ( 1.1) 280 ( 1.6) 293 ( 2.7) 314( 6.0) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 2.5) Female State 72 ( 2.0) 18 ( 2.1) ( 1.4) 274 ( 1.6) 285 ( 3.5) 300 ( 5.7) Nation 61 t, 2.6) 20 ( 2.3) 15( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear in parentheses. it can be said with about 95 percent certainty that, for each population of interest, the value "or the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). N THE. 1990 NAEP TRIAL STATE ASSESSMENT 99 North Dakota TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTP.GE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1460 NAEP TRIAL STATE ASSESSMEKi None 15 Minutes 30 Minutes 45 Merman An Houror] More TOTAL Perventage and Profidency 1 ( 0.8) ( 03) «4 .) 1 ( 0.9) *MR ( eel 1 ( 0.3) +.) 0 ( 0.0) ( "") 1 ( 0.8) **** ".) 0 ( 0.4) *** (.") o ( 0.0) ** ***) 0 ( 0.0) 3 ( 2.1) ( `") 0 ( 0.0) ** ( ".) 0 ( 0.4) *** ( ***) ( 0.4) ( Percentage and Proficiency 37 ( 2.6) 279 ( 2.2) 43 ( 42) 25C ( 2.3) 38 ( 2.9) 283 ( 1.2) 39 ( 4.5) 206 ( 2.2) 39 ( 8.9) 041 46 ( 7.6) 245 ( 3.0)1 51 (12.0) 74 (31.9) Mit 11141 39 ( 82) 61 (11.3) 273 ( 3.1)1 35 ( 5.3) 277 ( 5.6) 68 (14.9) 253 ( 5.4)1 36 ( 2.9) 281 ( 1.6) 37 ( 4.3) 256 ( 3.1) Percentage and Preficiencar 51 ( 3.7) 283 (1.6) 43 ( 4,$) 296 ( 2.6) 52 ( 3.9) 285 ( 1.5) 45 ( 5.1) 270 ( 2.7) 43 ( 8.9) ...) 34 ( 8.8) 251 ( 4.2)1 21 ( 7.3) 22 (28.2) 28 ( 1.7) 32 ( 8.6) ( "") 51 ( 7.9) 286 ( 2.7)1 14 (10.9) 54 ( 3.3) 281 ( 1.6) 49 ( 5.1) 265 ( 2.5) Percentage and Prolidency 10 ( 1.6) 262 ( 3,7) 10 ( 1.9) 272 ( 5.7)1 9 ( 13) 289 ( 4.3) 11 ( 2.4) 277 ( 7,8)1 18 ( 4.2) 13 ( 2.9) iv* 2!) ( 8.8) 0 ( 0.0) 21 ( 2.2) ( 3.4) 10 ( 3.7) 266 ( 7.8)1 ( 5.6) 9 ( 1.3) 293 ( 7.7) 10 ( 2.4) 278 ( 8.8)1 Percentage and Prondoncy 2 ( 93) 4 ( 0.9) 278 ( 5.1)1 2 ( 0.3) 44* ( .41 4 ( 0.9) 279 ( 5.8)1 0 ( 0.0) «HI ( 2.1) .41 *** ( ***) 4 ( 4.8) ( "") 11 ( 4.2) 0.0) t 0 0. 1 ) ite-41 ( *fit) 10 7.3) 1 ( 0.1) 4( 1.1) 282 (11.6)1 State Nation RACE/ETHNICITY White State Nation Hispanic State Nation American Ind lan State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extreme noel State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each popufation 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). IC 5 100 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A6 Teachers' Reports on the Amount of Time (mutinued) Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMEXT _ None 15 Minutes _ X Minutes 46 Minutes . An Hoar or More TOTAL State Nation PARENTS EDUCATION 141 non-grackiate State Nation H3 graduate State Nation Some collage State Nation Cc4lege graduate State Nation GENDER Male State Nation Female State Nation Penedo, end Prefickncy 6 ( 4.0) ( ( 0.6) 16. 1 0.6) 0.5) 2 ( 1.3) ***) ( 0.9) *** ( ***) 1 ( 0.6) ( ( .") Palmtop and Proency 37 2.8) 279 2.2) 43 (4.2) 258 ( 2.3) 27 ( 6.3) 444 ( 11411 49 ( 8.3) 240 ( 2.8) 35 ( 3.9) 43 ( 5.2) 249 ( 3.1) 35 ( 4.0) 279 ( 2.7) 44 ( 5.4) 265 ( 2.6) 39 ( 2.7) 286 ( 2.4) 40 ( 4.7) 285 ( 2.5) 36 ( 3.2) 282 ( 2.0) 44 ( 4.4) 257 ( 2.9) 35 ( 3.2) 275 ( 2.9) 41 ( 4.4) 255 ( Perventage and Prolialency 51 ( 3.7) 283 ( 1.8) 43 ( 43) 208 ( 2.6) 80 ( 8 .0) *44 ( 40 ( 8.1) 248 ( 31) 53 ( 5.7) 277 ( 2.6) 44 ( 5.6) 258 ( 2.7) b5 ( 4.7) 288 ( 2.7) 43 ( 5.8) 270 ( 3.6) 48 ( 3.4) 288 ( 1.8) 44 ( 4.1) 277 ( 3.0) 51 ( 3.7) 285 ( 2.0) 43 ( 4.3) 268 ( 2.9) 50 ( 4.4) 281 ( 1.9) 43 ( 4.7) 254 ( 2.8) Perceitege and Prelidency 10 ( 1.8) 282 ( 33) 10 ( 1.8) 272 ( 5.7)1 18 ( 6.4) 8 (1.7) ***) 11 ( 3.4) 40R WO* ) 9 ( 3.4) ( *el 7 ( 22) Mr* ***) ( 2.1) 9411 ( 1,111?) 10 ( 1.3) 298 ( 5.1) 11 ( 2.3) 287 ( 6.1)1 9 ( 1.1) 290 ( 7.0) 9 ( 1.9) 273 ( 7.3)1 11 ( 2.7) 275 ( 6.0)1 11 ( 2.0) 272 ( 5.7)1 Percentage and Proficiency 2 ( 02) 4 ( 0.9) 276 ( 5.1)1 0 ( 0.0) «4 ( 441 4 ( 1.3) 1 ( 0.5) 3 ( 1.0) ( 0,1 4 ( 1.0) we* ( 2 ( 0.5) ( *Mr) 5 ( 1.3) *". ( 1 ( 0.5) 41 5 ( 1.3) 279 ( 7.7)1 2 ( 0.8) ( 4 ( 0.9) ( ) The standard errors of the estimated statistics appea; in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the vaivy for the entire population i: 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). 1 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 101 North Dakota TABLE A7 I Students' Reports on the Amount ef Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1110 NAEP TRIAL STATE ASSESSMENT Nene 15 Minutes _ 30 Minutes a Minutes _ An Hour or Mare TOTAL Percentage and Preildency ( 0.6) 267 ( 2.6) ( 0.8) 251 ( 2.8) 9 ( 0.7) 290 ( 2.7) 10 ( 1.0) 256 ( 3.4) 9 ( 43) MI* 12 ( 1.8) . .41 6 ( 1.3) 44. 13 ( 5.3) *4* ( 7 ( 1.4) b ( 2$) *44) 8 ( 0.9) 290 ( 2.1) ( 2.3) IhNI ( SIM 1 0 ( 0.9) 284 ( 3.9) 9 ( 1.0) 250 ( 3.8) Percentage and Preedency 31 t4) 284 ( 1.4) 31 2.0) 264 ( 1.9) 33 ( 1.5) 285 ( 1.5) 33 ( 2.4) 270 ( 1.9) 15 ( 5.8) *44(444) 27 ( 3.0) 246 ( 3.6) 14 ( 4.8) 144(444) 30 (10.0) **it ( .114) 36 ( 4.7) *Mb ( 4** 41 (123) 278 ( 3.0)4 30 ( 2.0) 285 ( 23) 36 ( 4.6) 260 ( 3.5)1 30 ( 2.2) 233 ( 2.0) 30 ( 1.8) 263 ( 2.3) Percentage and Pandang 83 ( 1A) 280 ( 1.5) 32 ( 1.2) 2.13 ( 1.9) 32 ( 1.5) 283 ( 1.4) 32 ( 1.3) 270 ( 2.1) 46 ( 9.5) 30 ( 2.8) 243 ( 3A) 36 ( 63) ( "") 32 ( 4.8) 444 ( ANN ) 31 ( 6.6) 280 ( 4.6)1 33 ( 2.0) 278 ( 2.1) 31 ( 2.9) 25$ ( 5.1)1 34 ( 1.7) 283 ( 1.9) 32 ( 1.3) 264 ( 2.3) Percentage and Madam 18 ( 1.1) 278 ( 2.3) 16 ( 1.0) 208 ( ta) 15 ( 1.0) 282 ( 22) 15 ( 0.9) 277 ( 2.2) 21 ( 7.0) go+, 17 ( 2.1) 241 ( 4.3) 22 ( 3.0) ( *el 24 (142) 12 ( 3.9) 12 ( 3.3) (444*4*) 17 ( 15) 276 ( 3.9) 18 ( 3.8) 4.0 ( **I) 16 ( 1.6) 279 ( 2.7) 15 ( 1.1) 267 ( 2,1) Percentage and Preaching, 12 ( 0.7) 279 ( 3.0) 12 ( 1.1) 256 ( 3.1) 11 ( 0.9) 284 ( 2.1) 11 ( 1.3) 268 ( 33) 9 ( 4.6) ( 4.1 14 ( 1.7) .44) 6 ( 6.4) ***) OM* ( 7 ( 3.4) 12 ( 1.2) 273 ( 6.4) 7 ( 2.7) «. 10 ( 1.1) 279 ( :47) 13 ( 1.1) 258 ( 3$) State Nation RACE/ETNNICITY Whits State Nation Nispank State Nation American hiclian State Nation TYPE Of COMMUNITY Advantaged urban State Nation Extrante rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 117 102 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A7 I Students' Reports on the Amount of Time They (continued) I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Wades 45 Minutes An Hour or More TOTAL Perantage and Profidency Percettage and Proficiency Percentage and Protiodency Parcentage and Proficiency Percentage and lontficiency State ( 0.0) 31 ( 1.4) 33 ( 1.4) 16 ( 1.1) 12 ( 0.7) 287 ( 2.5) 284 ( 1.a) 280 ( 1.5) 218 ( 2.3) 279 ( 3.0) NatIon 9 ( 0.8) 31 ( 2.0) 32 ( 12) 16 ( 1.0) 12 ( 1.1) 251 ( 2.8) 284 ( 1.9) 2.3 ( 1.9) 208 ( 1.9) 258 ( 3.1) PARENTS EDUCATION 14S nongraduate State 12 ( 5.0) *44) 40 ( 7.4) 28 ( - ( 5.7) 15 ( 4.8)4 4 ( - ( 2.1) ..) Nation 17 ( 3.0)-) 26 ( 248 ( 3.3) 4,0) 34 ( 246 ( 4.4) 2.6) 12 ( 2.5)) 10 ( 2.2)) NS graduate State 7 ( 1.6) 28 ( 2.4) 33 ( 2.8) 19 ( 2.4) 13 ( 1.9) 278 ( 3.2) 210 ( 2.7) 270 ( 4.5) 271 ( 4.8) Nation 10 ( 1.7) 33 ( 22) 31 ( 1.9) 16 ( 1.4) 11 ( 1.5) 240 ( 4.2) 259( 3.2) 254 ( 2.4) 256 ( 2.8) 244 ( 3.4) Some college State 9 ( 1.7) 28 ( 2.6) 32 ( 22) 49 ( 2.7) 12 ( 1.7) *I* ( *1! ) 285 ( 2.7) 280 ( 2.8) 282 ( 3.9) 284 ( 4.2) Nation 9 ( 12)) 30 ( 286 ( 2.7) 3.0) 3$ ( 266 ( 2.1) 2.8) 14 ( 274 ( 1.8) 3.5) 11 ( 1.5) ) College graduate State 10 ( 1.0) 33 ( 1.6) 34 ( 1.7) 13 ( 1.4) 10 ( 1.2) 294 ( 3.7) 289 ( 2.0) 289 ( 1.7) 285 ( 3.3) 287 ( 3.3) Nation 7 ( 0.9) 31 ( 3.4) 31 ( 2.0) 18 ( 12) 14 ( 1.9) 285( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Mato State 11 ( 1.0) 35 ( 1.7) 30 ( 1.4) 14 ( 1.2) 10 ( 1.1) 287 ( 3.6) 287 ( 1.7) 283 ( 2.5) 283 ( 2.4) 278 ( 4.8) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.0) 264 ( 2.8) 266 ( 2.4) 285 ( 3.0) 258 ( 4.1) Fong'. State 6 ( 1.0) 27 ( 1.7) 37 ( 2.1) 17 ( 1.6) 13 ( 1.2) 286 ( 3.0) 280 ( 1.8) 277 ( 1.9) 274 ( 3.5) 280 ( 3.5) Nation 7 ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 248 ( 4.1) 263 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) ....--. The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value 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). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT 103 North Dakota TABLE A8 I Teachers' Reports on the Emphasis Given To Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP 'TRIAL STATE ASSESSMENT Numbers and Operadons Measurement i Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Utile or No Emphasis Heavy Pnphasis Little or No Emphasis TOTAL Parnontage end Preedinay 49 ( 283 ( 1.9 49 ( 3.8 280(1.8 Farcentage and Praidancy 0.8) 295 2.4) 15 2.1) 287 34) Paraintage and Pranciency 277 5.0 17 9.0 250 8.8) State Nation Hafftfia.,_,_IICITY Wine State 4$ ( 3.1) 11 ( 0.8) 13 ( 2.8) 288 ( 1.8) 298 1.9) 280 ( 50)4 Nation 46 ( 3.7) 18 2.4) 14 ( 3.4) 267 ( 2.2) 289 3.5) 259 ( 8.9)4 Hispanic State 52 ( 8.8) 8 4.2) 9 ( 3.5) *NI ( **I n ..) Nation 47 ( 8.7) 8 2.2) 23 ( 4.1) 246 ( 4.8) ") ( ***) American Indian State 60 ( 9.9) 0 0.0) 12 ( 4,5) 242 ( 2.7)1 *a. *441 Nation 84 (18.5) 6 8.9) 7 ( 8.7) ( a" "41) a ( aa.) TYPE OF COMMUNITY 'alvantaged urban State 21 ( 4.7) 27 ( 4.7) 0 ( 0.0) ( *4 ) *MI ( ) Natpn 28 (13.0) 18 ( 4.2) .404) Extrema rural State 51 ( 7.2) 3 ( 0.7) 6 ( 1.8) 284 ( 3.6) 296 ( 2.5)1 263 ( 7.5)1 Nation 53 (12.4) 257 ( 7.1)1 .04 ( 3.6) 6 ( 4.9) Maw State 51 ( 3.4) 12 ( 1.1) 17 ( 4.3) 233 ( 1.7) 293 ( 3.3) 278 ( 6.3)1 Nation 52 ( 4.1) 16 ( 2.7) 16 ( 3.9) 260 ( 2.3) 286 ( 3.6) 253 ( 7.1)1 Parcanfroa Paroaedsge Pannalags and and and Praliakinew Pralidonay Praisiannt 35( 23 ( 284 3.1 280 1.8 279 1.8 33 4.0 28 SA 21 3.3 272 ( 4.0 280 3.2 254 5.4 33 ( 3.2) 24 ( 32) 19 ( 1.9) 290 ( 21) 281 ( 1.7) 283 ( 2.0) 30 ( 4.7) 27 ( 4,4) 22 ( 34 ) 277 ( 4.3) 265 ( 3.3) 273 ( 55) 46 ( 85) 23 ( 5.9) 6 ( 2.7) ( 34 ( 5.8) 27 ( 6.8) 18 ( 5.5) 255 ( 4.4)1 ( ***) ( 11") 62 (10.0) 11 ( 5.8) 301 95) .4* ( *a) ( t.s.) mai 13 (15.5) 113 (19.7) 6 (10.4) ( ahra) aaa ( aat) ( ) 20 ( 6.4) 40 ( m 8.5) 3$ ( 267 ( 9.4) 4.9)1 39 ( 7.4) 18 ( 4.8) 276 ( 5.0)1 279 ( 2.4)1 32 (41.7) 9 ( 8.1) 265 ( 9.1)1 ( 28 ( 2.4) 27 ( 4.4) 288 3.1) 281 ( 2.9) 34 ( 5.3) 28 ( 4.8) 270 ( 4.6) 200 ( 3.9) ( 2.4) ( 441 13 ( 3.2) 19 ( 4.6) 257 ( 1.9)1 18 ( 7.9),) 21 ( 1.6) 286 ( 2.5) 24 ( 4.3) 285 ( 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. 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). C 104 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A8 I Teachers' Reports on the Emphasis Given to (continued) i Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRIAL STATE ASSESSMENT Numbers and Operation Monurement Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis tittle or No Emphasis iPsrantago TOTAL and Profeioney 49 ( 3.2) 233 ( 1.9) 49 ( 3.8) 200 ( 1.8) 40 ( 7.7) *we .,) 60 ( 6.9) 251 ( 3.4) 50 ( 5.0) 275 ( 3.5) 55 ( 4.3) 259 ( 2.9) 50 ( 4.4) 284 ( 3.8) 4? ( 4.4) 265 ( 2.6) ( 3.0) 289 ( 2.2) 44 ( 4.1) 269 ( 2.8) 48(3.7) 285 ( 1.8) 48 ( 4.1) 261 ( 2.5) 50 ( 3.4) 280 ( 3.0) 51 ( 3.9) 260 ( 2.0) Pareaniago and Pro Scieney 10 ( 0.8) 295 ( 15 ( 2.1 237 ( 3.4 3.9) 7 ( 2.3) ( 9 ( 22) **raj 11 ( 2.8) **. 9 ( 1.6) 01* ( ffret) 17 ( 3.3) 284 ( 4.1)1 12 ( 1.3) 298 ( 3.9) 19 ( 2.4) 298 ( 3.4) 10 ( 13) 300 ( 5.8) 14 ( 2.1) 287 ( 4.4) 11 ( 1.4) 290 ( 3.9) 15 ( 2.4) 288 ( 3.3) Ponontage and Proteiancy 13 ( 2.6) 277 ( 5.0)1 17 ( 3.0) 250 ( 5.6) 19 ( 7.2) 414r4f **41) 22 ( 5.3) ( 4 14 ( 3.8) 270 ( 7.0)1 17 ( 3.9) 251 ( 13 ( 2.9) ***) 12 2.7) 441 11 ( 2_5) 237 ( 6.8)1 16 ( 3.3) 264 ( 7.2)1 11 ( 1.7) 285 ( 4.5) 17 ( 3.3) 258 ( 6.7) 14 ( 3.8) 270 ( 8.6)1 17 ( 3.2) 241 ( 5.4) Pareadago and Pro Waxy 35 ( 3.3) 234 ( 33 ( 4.0 272 ( 4.0 29 ( 6.2) «in 25 ( 5.3) 31 ( 5.1) 276 ( 6.3) 27 ( 5.0) 253 ( 4.7)4 38 ( 4.8) 287 ( 5.0) 39 ( 5.5? 279 ( 4.5) 35 ( 2.8) 291 ( 3.9) 37 ( 3.8) 283 ( 3.8) 36 ( 3.4) 291 ( 3.6) 32 ( 3.9) 275 ( 4.8) 34 ( 3.8) 275 ( 4.6) 35 ( 4.3) 268 ( 4.1) Pareentage and Pre Wow/ 23 ( 3.0) 280 ( 1.8) 28 ( 3.8) 260 ( 3.2) 18 ( 5.5) *41 -32 ( 6.3) 25 ( 4.7) 267 ( 3.1)1 27 ( 4.5) 255 ( 4.2) 24 ( 3.8) 278 ( 3.1) 27 ( 5.0) 262 ( 4.8)1 23 ( 3.1) 291 ( 2.9) 26 ( 3.4) 270 ( 3.8) 23 ( 2.9) 231 ( 3.1) 29 ( 4.1) 263 ( 3.8) 24 ( 3.8) 280 ( 3.3) 27 ( 3.9) 256 ( 3.3) Pareentago and Pm/Wow' 20 ( 1.8) 279 ( 1.8) 21 ( 3.3) 264 ( 5.4) 26 ( 5.9) trilv Mel 20 ( 6.7) ( 41 19 ( 3.4) 266 ( 4.3)4 24 ( 5.1) 246 ( 4.8)1 20 ( 2.7) 282 ( 4.6) 23 ( 4.1) 270 ( 4.7) 19 ( 1.7) 291 ( 3.5) 21 ( 2.9) 280 ( 6.4) 21 ( 2.2) 282 ( 2.9) 20 ( 3.3) 266 ( 8.8) 18 ( 2.0) 276 ( 3.4) 23( 3-5) 263 ( 5.0) State Nation PARENTS' EDUCATION NS non-graduate State Nation ItS graduat State Nation Some wiles!' State Nation Co Neg. graduate State Nation GENDER Mats State Nation Fans** 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 populat..in is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphas-is" 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). I 1 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 105 North Dakota TABLE AS I Teachers' Reports on the Emphasis Given To (ccintinucd) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT .. Data Analysis, Statistics, and ProbabilitY Algebra and Functions , Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL State Nation RACE/ETNNWITY MN. State Nation Hispanic State Nation Anvrican Indian State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extreme rural State Nation Other State Nation Peroentage and Proicioncy 9 2.6) 296 3,7)1 14 2.2) 264 4.3) 8 ( 2.9) 292 ( 4.1)1 14 ( 2.4) 276 ( 4.1) 8 ( 2.5) 15 ( 4.1) 27 ( 6.6) *4* 3 ( 42) 8 ( 0.9) 276 ( 4.0) 5 ( 5.4) 1114. *** 1 1 ( 4.7) 289 ( 4,7)1 15 ( 2.9) 267 ( 4.7) peramtap Peradnisp Percedsid and and and fortiidmitgr lorsiciency Prolkiercy 74 ( 2.6) 2.6 ( 1.4) 53 ( 4.4) 261 ( 2.0) 76 ( 2.5) 268 ( 1.3) 53 ( 5.0) 271 ( 3.1) 78 ( 8.0) 56 ( 6.3) 246 ( 4.4) 24 ( 7.3) 0-0") 82 (29.1) ..**) It** ( ) 65 (19.4) 284 ( 7.4)1 78 ( 4.6) 287 ( 2.6) 65 (18.9) 254 ( 6.7)1 70 ( 3.4) 285 ( 1.6) $3 ( 52) 260 ( 3.4) 56 $.4) 281 1.2) 45 3.6) 275 2.5) 57 ( 3.3) 283 ( 1.3) 48 ( 4.2) 261 ( 3.0) 52 ( 82) .44 46 ( 5.9) 257 ( 4.0)1 42 (10.5) M.* ( *4) 16 (21.5) 4,44 ( 79 ( 4.7) 41 ( $.9) 296 ( 7.9)I 54 ( 7.3) 276 ( 1.8) 33 ( al) ( 4.1P 56 ( 3.7) 283 ( 1.9) 47 ( 4.3) 276 ( 2.8) ( 1.0) 266 ( 4.6)1 20 ( 3.0) 243 ( 3.0) 9 ( 2.1) 272 ( 4.2)1 18 ( 2.8) 251 ( 3.3) 9 ( 5.5) 18 ( 42) *Mr ( *MI 8 ( 4,1) *04) 67 (51.6) o ( 0.0) 12 5.2) 269 ( 8.0)1 42 (16.0) 241 ( 5.9)1 8 ( 0.9) 270 ( 4.6) 17 ( 3.3) 245 ( 4.4)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 106 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A8 I TeaLhers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1080 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Algebra ioxl Ravel loos Heavy EmPhasis Little or No Empbasis 1 Little or No vy Emphasis . Hea Emphasis .. TOTAL Paramtaga sad Pro Many Perventare and Prediciancy Parentage and .rfaitaktany Parrantnee and Proldanay State 0 ( 2.0) 74 ( 2.6) 58 ( SA) 9 ( 1.9) 298 ( A.7)1 288 ( 1.4) 281 ( 1.2) 216 ( 4.6)1 Nation 14 ( 2.2) 53 ( 4.4) 46 ( 3.6) 20 ( 3.0) 209 ( 4.3) 261 ( 24) 275 ( 2.5) 243 ( 3.0) PARENTS' EDUCATION HS noograduator State 17 ( 8.5) 86 ( $.1) *4i 54 ( 7.9) ( *41 Nation 9 ( .44 3.0) 53 240 ( 7.7) ( 6.2) 28 ( .44 ( 5.2) 29 ( 8.9) KS graduate State 10 ( 44, 3.6) 4.**) 73 280 ( ( 4.2) 3.3) 50 ( 269 ( 5.5) 3.2) 12 ( 3.5) e«.) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 261 ( 6.0)1 247 ( 2.9) 265 ( 3.5) 239 ( 3A) Some college State 8 ( 2.7) 76 290 ( ( 2.8) 2.6) 59 ( 282 ( 4.4) 2.8) 7 ( 2.0) «fre «in Nation 13 ( 2.5) 57 ( 5.8) 48 ( 4.8) 17 ( 3.1) 270 ( 3.7) 278 " 3.0) 1111* Canasta graduat. State 9 ( 2.4) 74 ( 2.6) 59 ( 2.9) 7 ( 1.4) 296 ( 3.5)1 292 ( 1.8) 290 ( 1.6) 282 ( 4.7) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 18 ( 2.4) 282 ( 4.5) 275 ( 3.8) 283 ( 3.0) 249 ( 4.0) GENDER Male State ( 1.6) 76 ( 2.3) 56 ( 3.8) 7 ( 1.9) 293 ( 4.3)1 290 ( 1.7) 281 ( 1.8) 265 ( 6.6)1 Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.8) 275 ( 5.8) 260 ( 3.5) 278 ( 3.2) 243 ( 3.0) Female State 11 ( 3.8) 71 ( 3.7) 57 ( 3.6) 10 ( 2.5) 281 ( 5.0)1 282 ( 1.8) 281 ( 1.7) 270 ( 6.8)1 Nation 16 ( 2.4) 53 ( 4.5) 48 ( 3.6) 18 ( 2.9) 263 ( 4.4) 262 ( 2.8) 274 ( 2.7) 244 ( 3.9) 11111011.MIl 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. I Interpret with cr,ution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT 107 North Dakota TABLE A9 I Ttachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL I Oet AU the Resources I Mot Most of the I Get Some or None of STATE ASSESSMENT Need Routines I Need the Resoirces I Need TOTAL and Proficiency Percentage and Proficiency State 18 ( 2.7) 4 ( 2.9) 279 ( 3.2) 282 ( 1.7) Nation 13 ( 2.4) 56 ( 4.0) 265 ( 4.2) 265 ( 2.0) RACE/ETHNICITY White State 17 ( 2.7) 48 ( 2.7) 281 ( 2.8) 285 ( 1.1) Nation 11 ( 2.5) 58 ( 4.6) 275 ( 3.5)1 270 ( 2.3) Hispenin State 33 ( 7.3) 41 ( 9.2) Nation 23 ( 7,6) 44 ( 4.9) 246 ( 7.7)! 250 ( 2,9) American Indian State 3 ( 1.4) "41 50 (11.5) 0+4 Nation 6 ( *** 7.4) 72 (26.8) TYPE Of COMMUNITY Advantaged urban State ( 1144 37 ( 4.6) ***) Nation 38 ( 9.2) 59 ( 8.9) 272 ( 8.5)1 288 ( 1.3)1 Extreme rural State 20 ( 6.3) 43 ( 6.8) 287 ( 1.7)1 276 ( 3.7) Nation 2 ( 44,4, 2.6) 54 (10.4) 260 ( 8.8)1 Other State 17 ( 3.3) 53 ( 3.3) 272 ( 3.5)1 286 ( 1.3) Nation 11 ( 2.9) 58 ( 5.4) 265 ( 3.9)1 264 ( 2.1) Percentage and ProRcHetcy 35 ( 3.4) 282 ( 1.8) 31 ( 4.2) asi ( 2.9) 35 ( 3.5) 285 ( 1.7) 30 ( 4.6) 267 ( 3.3) 26 ( 7.0) 1111ht 111P1 31 ( 7.7) 244 ( 3.0)1 47 (10.9) 24$ ( 1$) 22 (20.7) 4,4* 40 ( 3.0) ***) 4.) 37 ( 8.5) 282 ( 3.5)1 43 (10.3) 257 ( 5.0)1 31 ( 2.8) 280 ( 1.2) 31 ( 5.6) 263 ( 4.2) The standard errors of the estimated statistics appear in parentheses. ft can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 108 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dak9ta TABLE A9 I Teachers' Reports on the Availability of (continued) I Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 NAEP TRIAL I Ost AN the Roams* 1 I Get Most of the I OM Some or Nona of STATE ASSESSMENT Mod Resources I Need the Respires* I Nomad TOTAL Prolding ParcoNage ant Nr8Sokacy Iherosslap PreNdaNcy State 18 ( 2.7) 411 ( 88(3.4) 279 ( 3.2) 262 ( 1.7 282 ( 14) Nation 13 ( 2.4) 31 ( 4.2) 265 ( 42) 205 ( 2.0) 261 ( 2M PARENTS' ECKMATION NS non-graduate State 18 ( 6.8) ( 52 ( 7.7) 30 ( 65) .4* ( Nation 8 ( 2.8) 54 ( b.7) 38 ( 63) he* ( eel 244 ( 2.7) 249 ( 3.5)4 NS graduats State 17 ( 3.7) 43 ( 4.3) 40 ( 5.7) ( 4.9)1 274 ( 4.0) 215 ( 3.2) Nation 10 ( 23) 54 ( 4.9) 36 ( 4.9) 253 ( 4.8)1 250 ( 1.9) 258 ( 2.8) Some collsgs State 20 ( 3.8) 49 ( 3.9) 31 ( 3.7) 293 ( 5.4) 264 ( 1.9) 282 ( 33) Nation 52 ( 4.3) 25 ( 4.1) Off ( 289 ( 2.5) 267 ( 3.8) Collage graduato State 17 ( 3.0) 49 ( 3.1) 34 ( 3.1) 285 ( 2.0) 289 ( 1.9) 269 ( 13) Nation 15 ( 2.9) 58 C 4.9) 30 ( 5.1) 278 ( 5.4)4 2/6 ( 2.2) 273 ( 3.7) GENDER Usti State 18 ( 2.9) 49 ( 3.5) 35 ( 3.8) 281 ( 3.1) 28$ ( 2.0) 284 ( 2.2) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4.0) 264 ( 5.0)1 255 ( 2.5) 264 ( 3.3) Facials State 20 ( 2.8) 48 ( 2.9) 34 ( 3.6) 277 ( 4.2) 279 ( 2.6) 279 ( IA) Nation 13 ( 24) 55 ( 4.4) 32 ( 4.7) 286 ( 3.9) 284 ( 2.0) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 109 North Dakota TABLE Al Oa I Teachers' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP MAL STATE ASSESSMENT , At Least Once a Weak Leas Than Ones a Week Now TOTAL Percentage and Preadency Peramtage and proderia Percentage and Prelidencg State 38 ( 3.3) 3.1) 18 ( 2.1) 281 ( 2.5) 284 1.5) 279 ( 2.5) Nation 50 ( 4A) 43 4.1) 8 2.0) 200 ( 2.2) 284 ( 2.3) 277 sAp RACEMTHNOTY State 37 ( 3.3) 44 ( 3.7) 19 ( 2.2) 285 ( 1.7) 288 ( 1.5) 280 ( 2.0) Nation 49 ( 4.8) 43 ( 4.5) ( 2.3) 205 ( 2.7) 271 ( 22) 285 ( 4.9)I NkpartIc State 38 ( 44, ( 8.3) *44) 44 ( OA) 0.fr.) 18 ( 5.2) 1111 Nation 64 ( 246 ( 7.2) 2.5) 32 ( 6.9) 247 ( 8.3)1 4 ( 1.4) ..**) American Wien State 80 (10.4) 33 ( 0.3) 248 ( 4.8)1 ( 4.0) ,.) Nation 18 (24.3) 80 (27.2) 2 ( 32) ( TYPE Of COMMUNITY Advantaged urban State 32 ( 4.2) 40 ( 6.4) 28 ( 2.2) Nation 39 (22.9) 41 (17.9) 273 ( 6.0)1 20(12.2) ..**) Extrema rural State 37 ( 7.2) 51 ( 8.8) 12 ( 4.5) 278 ( 4.9)1 285 ( 2.6)1 275 ( 52)1 Nation 35 (14.8) 56 (17.1) ( 9.8) 255 ( 55)1 258 ( 5.9)! ( Other State 42 ( 4.3) 42 ( 3.4) 18 ( 1.8) 283 ( 2.8) 283 ( 1.4) 281 ( 2.5) Nation 50 ( 4.4) 44 ( 4.5) 8 ( 1.8) 260 ( 2.4) 264 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the simple does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than (2 students). 1 110 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE AlGa I Teachers' Reports on the Frequency of Small (mtinued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT , . At Least Once a Week "i Less Mum Once a Week . Moo r TOTAL 640:0661140 and peldiale081 36 ( 261 ( 2.5 50 ( 4A 200 ( 2.2 Pqramiage aW Pre4kinney 43 ( 3.7) 204 1.5! 43 (4.1) 264 (2.3) Panatela and Maslow 16 ( 2.1) 279 ( 24) ( 2.0 277 ( 5A)I State Nation PARENTS EDUCATION NS non-graduate State 44 ( 8.5) 35 ( 7.6) 22 MIN/ ( 7.5) ( 111 Nation 60 ( 8.4) 39 ( 6.5) /.4) 244 ( 3.2) 244 ( 3.2)1 Ns* ( Mel NS graduate State 39 ( 5.1) 44 ( 8.0) 17 ( 3.4) 273 ( 4.5) 275 ( 2.9) 268 ( 5.2) Nation 49 ( 4.8) 45 ( 5-1) 0 ( 2.5) 252 ( 2.8) 257 ( 2.7) Some college State 41 ( 4.2) 41 ( 4.2) 17 ( 2.7) 283 ( 3.8) 285 ( 22) 262 ( 3.2) Nation 51 ( 52) 42 ( 5.1) 7 ( 2.3) 266( 3 1) 268 ( 32) College graduat State 37 ( 3.3) 44 ( 3.4) 19( 2.1) 288 ( 2.3) 291 ( 1.8) 286 ( 2.9) Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.8) 278 ( 3.0) 285 ( 4.9)1 GENDER Mali State 37 ( 3.5) 45 ( 3.9) 18 ( 2.1) 284 ( 2.8) 287 ( 1.8) 281 ( 2.4) Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 265 ( 3.1) 278 ( 5.3)4 Female State 39 ( 3.7) 42 ( 3.6) 19 ( 2.9) 277 ( 3.3) 281 ( 1.9) 276 ( 3.3) Nation 50 ( 4.7) 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 8.6)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), THE 1990 NAEP TRIAL STATE ASSESSMENT II I North Dakota TABLE AlOb I Teachers' Reports on the Use of Mathematical i Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STAT SESSMENT E AS I., At Least Once a Week Laos Thin Once a Weak - Never TOTAL State Nation RACE/ETHNICITY White State Nation Mica* State Nation American Wien State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extreme rural State Nation Other State Nat , Ihnotags awl Proficiency 21( 2.7) 279 ( 1.3) 22 ( 3.7) 254 ( 3-2) 20 ( 2.8) 283 ( 1.3) 17 ( 4.0) 261 ( 3.8)1 26 ( 6.6) 39 ( 7.5) 247 ( 3.8) 34 ( 8.8) M101 ( *NI 78 (34.6) o ( 0.0) 23 (14.4) Te, 22 ( 7.0) 275 ( 2.4)1 27 (14.9) at44 .41 20 ( 2.1) 282 ( 1.8) 19 ( 4.3) 253 ( 3.9)1 Persontage and Praidarto 74 2.9) 261 1,5) 09 3.9) 263 1.9) 75 ( 2.9) 264 ( 1.1) 72 ( 42) 2.1) 89 ( 7.0) 55 ( 7.3) 245 ( 3,6)f 06 ( 8.8) 240 ( 4.7)1 22 (34.6) ( *41 100 ( 0.0) 288 ( 2.7) 63 (11.5) 27$ ( 5.8)1 89 ( 7.1) 280 ( 3.1) 65 (14.8) 262 ( 2.8)I 73 ( 2$) 282 ( 1.7) 72 ( 5.0) 263 ( 2.2) Paroolags end Praildency 5 0.9) 4,41 9 2.6) 282 ( 5.9)1 5 ( 1.1) ( 10 ( 2.7) 288 ( 62); 5 ( 5.0) ( 0.*) 7 ( 2.6) 4.44, 0 ( 0.0) o ( 0.0) .") ( 0.0) *** ( 15 ( 9.3) *** ( ***) 2 ( 2.2) ..**) 8 ( 3.9) 7 ( 1.0) 9 ( 32) 281 ( 7,1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature at' 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 gut-lents). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A lOb I Teachers' Reports on the Use of Mathematical (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT _ At Least Once a weak Less Than Once a Week Kamer TOTAL Peroantige and Proliciona Parnerdago and Prolloionoy Poroaniaga and Proficiency State 21 ( 2.7) 279 ( 1.9) 74 ( 2.9) 281 ( 1.3) 5 ( 0.9) ( *el Nation 22 ( 3.7) 09 ( 3.9) 9 ( 2.6) 234 C 3.2) 263 ( 1.9) 282 ( 5.9)1 PARENTS EDUCATION KS non-graduate State 35 ( 7.5) 58 ( 6.0) rrr cowl ( 4.6) err ( rrr) Nation 25 ( 5.6) Oa ( 7 2) 9 ( 6.5) val 243 ( 22) NS graduate State 24 ( 4.6) 74 ( 4.7) 2 ( 1.0) 272 ( 2.1) 272 ( 2.9) Nation 23 ( 4.8) 246 ( 4.0)1 ( 5.3) 255 ( 2.2) 7 ( 2.8) rri $om. collar) State 20 ( 4.1) 284 ( 2.9)1 73 ( 4.4) 281 ( 2.4) ( 2,0) rr. ( Nation 18 ( 4.0) 73 ( 4.3) 9 ( 2.4) 261 ( 4.4)i 289 ( 2.3) College graduate State 18 ( 22) 78 ( 2.8) 6 ( 1.7) 287 ( 22) 289 ( 1.6) Nation 20 ( 3.9) 69 ( 3.7) 11 ( 2$) 266 ( 3.5)1 274 ( 2.2) 297 ( 4.2)1 GENDER Male State 21 ( 3.2) 279 ( 2.4) 75 ( 3.2) 285 ( 1.6) 4 ( 0.9) rpr «in Nation 22 ( 4.1) 69 ( 4.1) 8 ( 2.0) 265 ( 4.1) 265 ( 2.1) 267 ( 7.2)1 Female State 20 ( 2.9) 74 ( 3.1) 6 ( 1.2) 278 ( 2.6) 277 ( 2.1) 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 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 ; 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 113 North Dakota TABLE Alla Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 MEP TRIAL STATE ASSESSMENT Almost boy Day Savarai Times a Wm* About Once a Week or Lass TOTAL Pareantaa and Pra Salem 79 ( 33) 262 ( 1.1) 82 ( 3.4) 207 ( 1.8) 80 ( 3.2) 284 ( 1.0) 64 ( 3.7) 272 ( 1.9) 79 ( 7.4) 61 ( 6.8) 251 ( 3.1) 42 (10.6) 2413 ( 3.9)i 15 (25.9) 83 (15.9) 283 ( 7.3)1 77 ( 8.6) 281 ( 1.4) 50 (10.6) 288 ( 4.0)! 79 ( 1.4) 282 ( 1$) 63 ( 3.9) 2e1 ( 2.3) Peraente86 Poreentaga and and Prolkilancy Praidenq 18 ( 3.4) 5 ( 0.3) 260 ( 56)1 ipen 31 ( 3.1) 1.8) 254 ( 2.9) 260 ( 5.1$ 14 ( 3.3 6 ( 0.4) .44(4.4) 268 ( 3.5)1 28 ( 3.2) 8 ( 2.3) 264 ( 3.4) 284 ( 5.4)! 15 ( 8.0) ( 5.5) «hp 32 ( 5.3) 8 ( 2.3) 240 ( 4.3)1 44,1 5$ (10.6) 0 ( 0.0) .kik .4.9) 444 «al 83 (28.3) 2 ( 3.0) 0,4 44) ( 0 ( 0.0) 28 ( 1.7) 4) 4,1 23 ( 5.2) 14 (14.6) *V* ( IN* ) 23 ( $.8) 0 ( 0.0) 277 ( 9.4)1 40 (10.0) 10 ( 7.3) *** ) 247 ( 7.6)1 14 ( 1.2) 8 ( 0.4) 282 ( 4.2) 31 ( 3.5) ( 1.9) 255 ( 3.1) 257 ( 5,8)1 State Nation RACE/ETHNICITY White State Nation Hispanic State Nation American Imilan State Nation TYPE Of COMMUNITY Advantaged urban State Nation Extrema nral State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within * 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow awurate determination of the variability of this estimated mean proficiency. *** Sample 6i2e is insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE Al la I Tembers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 1,11EP TRIAL STATE ASSESSMENT Aknost EVary Day Several Times a Week About Ones a Mask or Loss TOTAL Perconteset and Prediciency Poroontego and Pronciency Percoatago and Proficiency State 79 ( 282 ( 3.3) 1.1) 16 ( 2$0 ( 34) 5.6)1 5 ( «h. 0.3) Nation 62 ( 3.4) 31 ( 3.1) ( 1.8) 267 ( 1.8) 264 ( 2.9) 200 ( 5.1)1 PAgENTS' EDUCATION NS not-graduate State 74 ( 6.2) 26 ( 62) 0 ( 0.0) 259 ( 4.1)1 ( ***) Nation 67 ( 245 ( 5.5) 3.2) 27 ( .44 ( 52) HS graduate State 75 ( 5.7) 22 ( 5.7) 3 ( 0.8) 272 ( 2.4) 275 ( 7.4)1 Nation 61 ( 4.4) 34 ( 3.7) ( 1.5) 257 ( 2.5) 250 ( 2.9) ( ***/ Some coilog. Ptate 84 ( 4.0) 12 ( 4.0) 5 ( 0.8) 284 ( 1.9) ( "") Nation 68 ( 42) 26 ( 3.7) 8 ( 1.9) 272 ( 2.7) 258 ( 52) ( "") Cottage graduate State 80 ( 3.1) 13 ( 3.1) ( 0.5) 289 ( 1.4) 290 ( 6.7)1 ( ***) Nation 61 ( 281 ( 4.0) 2.2) 31 ( 265 ( 3.9) 3.1) ( 3.1) *** ( ese) GENDER Male State 78 ( 3.8) 17 ( 3.9) 5 ( 0.7) 284 ( 1.4) 287 ( 5.1)1 Nation 60 ( 3.7) 33 ( 3.4) ( 1.9) 269 ( 2.1) 256 ( 3.6) 281 ( 0.7)1 Female State 60 ( 3.1) 15 ( 3.0) 6 ( 0.5) 280 ( 1.5) 270 ( 8.9)1 Nation 65 ( 3.8) 26 ( 3.3) ( 2.2) 266 ( 1.8) 253 ( 2.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population Of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample dots 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 North Dakota TABLE Al lb I Teachers' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Lust Several Tknes STATE ASSESSMENT a WM About Once a Wuk Lm than Weeny . _ TOTAL Percentage and Praldensy Perventage and Prellatency Percentage satil Prelkflancy State S7 ( 2.5) 34 ( 3.3) 20 ( 2.1) 279 ( 2.1) 201 1.5) 286 ( 2.3) Nation 34 ( 3.8) 256 ( 23) 33 ( $.4) 200 ( 2.3) 324 " 27 .71 2 RACE/ETHNICITY Mita State 38 ( 2.8) 33 ( 3.5) 31 ( 2.9) 283 ( 1.1) 285 ( 1.4) 239 ( 2.2) Nation 32 ( 4.1) 33 ( 3.5) ( 3E) 264 ( 2.7) 284 ( 22) 279 ( 2.9) Hispanic State 40 ( 9.1) HP* ( 4141 43 ( 7.8) WS* 1141 17 ( 1.4) a.* Nation 41 7.7) 26 ( 5.3) 33 ( 7.5) 242 ( 3.2)I 244 ( 5.1)I 257 ( 2.3)1 &nods= Mien State 54 (11.3) 4.** ( 44 (10.8) *fir 2 ( 1.1) Nation 10 (18.8) 78 (362) .41 13 (18.5) OitT 14111 TYPE Of COMMUNITY Advantaged urban State 41 ( 1.9) .44 ( ...) 32 ( 5.6) ( 4 ) 28 ( 0.6) *** ( . ) Nation 59 (13.9) 20 ( 8.0) 21 ( 8.2) 273 ( 3.4)1 ....* ( 444.) 0*4 ( *** ) Extreme rural State 37 ( 5.8) 32 ( 6,0) 31 ( 5,6) 278 ( 5.3) 278 ( 3.0)1 286 ( 3.7)1 Nation 27 (14.3) ..... ( .t.g.) 49 (12.7) 258 ( 8.7)f 24 (10,1) . ( ,,,,,) Whirr State 39 ( 2.4) 36 ( 4.0) 24 ( 2.7) 279 ( 1.3) 283 ( 2.4) 285 ( 2.7) Nation 30 ( 4.4) 35 ( 4.3) 36 ( 4.2) 256 ( 3.3) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 116 THE 1990 NAEP TRIAL. STATE ASSESSMENT North Dakota TABLE Al lb I Teachers' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MU NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week About Once a Week Less than Weekly tom. Percentage and Proficiency Peroentage and Proidancy Percentage and Proficiency state 37 ( 34 ( 3.3) 29 ( 2.7) 279 ( 2.1 2$1.( 1.6) 288 ( 2.3) Nation 34 ( 3.11 32 ( 3.8) 2se 2.3) 200" 274 ( 2.7) PANBITS' EDDCATiOil NS non-graduate State 43 (( 8.1) «el 34 ( 8.8) 23 ( 7.4) ,.) Nation 35 239 ( 8.0) ( 3.5) 29 ( *N. ( 6.3) 30 ( 250 ( 8.9) 4.5)1 NS graduate State 33 ( 3.8) 39 ( 4.6) 27 ( 3.9) 270 ( 4.0) 273 ( 3.0) 278 ( 5.1) Nation 35 ( 5.3) 36 ( 4.5) 30 ( 4.8) 250 ( 3.6) 250 ( 2.7) 283 ( 3,4) $0.1141 college State 38 ( 3.9) 32 ( 4.2) 31 ( 3.8) 280 ( 2.6) 285 ( 3.8) 258 ( 3.2) Nation 33 ( 4.7) 32 ( 4.0) 35( 4.1) 200 ( 2.8) 286 ( 4.2) 278 ( 2.8) College graduate State 37 ( 2.5) 32 ( 3.1) 31 ( 2.9) 287 ( 2.2) 288 ( 2.2) 292 ( 2.0) Nation ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.8) 271 ( 2.4) 289 ( 2.9) GENDER M. State 38 ( 2.9) 33 ( 3.3) 20. ( 3.4) 283 ( 2.4) 284 ( 1.8) 288 ( 2.8) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 261 ( 2.8) 275 ( 3.2) Female State ( 3.0) 35 ( 4.0) 29 ( 2.8) 275 ( 3.1) 279 ( 2.1) 283 ( 2.6) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimateJ statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 rtandatd errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 22 THE 1990 NAEP TRIAL STATE ASSESSMENT 117 North Dakota TABLE Al2 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AWRAGE MATHEMATICS PROFICIENCY 1990 NAEP MAL STATE ASSESSMENT Al Lust Once a Week Less Than Once a Ws* Myer TOTAL Pewits., and Preflalana Pargeltaff and Pralidenty forgentelle and Proficiang State 19 ( 1.8) Si ( 1.2) SO ( 282 ( -1.7) 283 ( 1.6) 200 ( 1.5 Nation 28 ( 2.5) 28 ( 1.4) 44 ( 2.9 256 ( 2.7) 267 ( 2.0) 281 ( 1.8) RACE/ETHNICITY *bite State 19( 1.7) 32 ( 1.3) SO ( 2.1) 287 ( 1$) 285 ( 1.8) 283 ( 1.2) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3.5) 288 ( 3.1) 272 ( 1.9) 270 ( 1.7) Hispanic State 27 8.8) fere ( 21 ( 4.7) 04111 52 ( 8.7) ( .41 Nation 37 ( 5.2) 22 ( 3.8) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) American kulian State 24 ( 4.1) 30 ( 4.6) 48 ( 5.5) 239 ( 5.7)I Nation 31 ( 5.1) ..**) 35 ( 5.5) 33 ( 5.0) -0* ( TYPE OF COMMUNITY Advaniagad urban State 10 ( 2.9) 54 ( 2.8) ( 0.1 Nation 27 (13,9) 33 ( 4.5) 40 (13.4) 286 ( 5.4)1 279 ( 33)1 Extreme rural State 18 ( 22) 28 ( 1.9) 56 ( 3.1) 274 ( 3.7) 282 ( 3.1) 281 ( 2.8) Nation 34 (10.8) 27 ( 3.8) 39 (11.6) 249 ( 5.2)1 284 ( 3.5)1 256 ( 8.2)1 Other State 22 ( 2A) 33 ( 1.7) 45 ( 2.8) 288 ( 2.1) 282 ( 2.0) 279 ( 2.0) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 280 ( 3.3) 284 ( 2.11 262 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with sbout 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. 11 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 rt 1 t... j 1 18 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE Al2 I Students' Reports on the Frequency of Small (continued) I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMAT(CS PROFICIENCY 1500 NAEP MAL STATE ASSESSMENT 1 At Lead Once a Meek Lass Than Once a Week Never TOTAL Paramtap and PrelicioncY 10 1.6) 252 1.7) 23 2.5) 258(2.1) Percistage Prellthacy 31 1.2) 2113 1,8) 26 1.4) ( 2.0) State Nation PARENTS' ECUCAT1ON HS non-graduate State 19 ( 5.5) 1,,,, ( ..e.) 26 ( 5.4) 4.1) Nation 29 ( 43) 29 ( 3.0) 242 ( 3.4) 244 ( 3.0) NS graduate State 17 ( 2A) St ( 32) 276 ( 5.5) 272 2.5) Nation 23 ( 3.0) 26 14) 251 ( 3.7) 261 23) Some college State 20 ( 3.3) 30 ( 3.3) 283 ( 3.0) 264 ( 23) Nation 27 ( 3.9) 27 ( 2.4) 2t$ ( 33) 268 ( 3.3) College graduate State 19 ( 2.0) 31 ( 13) 289 ( 2.9) 291 ( 2.6) Nation 28 ( 3.0) 26 ( 1,9) 270 ( 2.7) 276 ( 23) SIENDE9 Mite State 20 ( 1.7) 31 ( 1,7) 287 ( 2.4) 287 ( 2.4) Nation 31 ( 2.9) 2$ ( 1.7) 250 ( 32) ( 23) AMMO State 18 ( 2.8) 31 ( 13) Nation 277 ( 2.8) 2e ( 24) 279 ( 2.3) 27 ( 13) 257 ( 2.8) 268 ( 1.7) 111109611010 end Ihrseekoliat SO 2.0) 200 14) 44 2,0) 201 13) SS 0.71 42 ( 43) 242 ( 2.7) 49 ( 4.0) 272 ( 43 ( 3.4 252 ( 13 50 ( 4.$) 283 ( 2.5) 46 ( 33) 255 ( 2.1) 50 ( 22) 2ee ( 1.5) 44 ( 34) 275 ( 22) 49 ( 22) 282 ( 1.7) 41 ( 2.9) 262 ( 1.8) Si ( 2.7) 278 ( 1.9) 47 ( 3.2) 260 ( 13) The standard errors of the estimated statisfics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the ,alue for the entire population is within * 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 student4). 1 2 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 119 North Dakota TABLE A13 I Students' Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week New TOTAL Pomade/to and Pre/dewy Percentage and Prelidency Percentoge and Proficiency State 24 ( 1.4) 45 ( 1.5) 1.4) 276 ( 1.7) 294 . 1 AI) 280 1.9) Nation 28 ( 1.8) 31 ( .1.2) 41 2.2) 258 ( 2.0) 209 ( 1.5) 259 ( 1.6) RACE/ETHNICITY Whits State 24 ( 13) 47 ( 1.6) 30 ( 1.5) 281 ( 1.4) 286 ( 1.6) 284 ( 1.9) Nation 27 ( 1.0) 33 ( 1.6) 40 ( 2.5) 266 ( 2.6) 275 ( 1.6) 268 ( 1.8) Hispanic State 34 ( INT* ( 7.8) *el 41 ( 7.2) ..04) Nation 33 ( 4.2) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) American Indian State 38 ( 3.5) 34 ( 3.7) ( "") *fib 238 ( 4.5)1 Nation 35 ( 3.4) 37 ( 8.2) 28 ( 8.8) ( ***/ ( TYPE OF COMMUNITY Advantaged urban State 16 ( 3.8) ) 50 ( 2.3) 34 ov ( 3.1) «I») Nation 36 (10.3) 33 ( 4.8) 32 (11.1) 278 ( 6.1)1 284 ( 3.2)1 281 ( 5.9)1 Extreme rural State 25 ( 2.3) 47 ( 2.3) 28 ( 2.9) 276 ( 2.6) 284 ( 2.9) 277 ( 3.8) Nation 21 ( 3.1 ) 37 ( 4.7) 43 ( 5.0) 262 ( 4.7)1 251 ( 5.2)1 Other State 25 ( 2.2) 42 ( 2.4) 33( 1.9) 279 ( 2.6) 286 ( 2.3) 279 ( 2.4) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 258 ( 2.9) 270 ( 1.8) 260 ( 2.2) =11..' The standard errors of the estimated statistics appear in parentheses. It car 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 North Dakota TABLE A13 I Students' Reports on the Use of Mathematics (ccetinued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY IMO NAEP TRIAL STATE ASSESSMENT At Least Once a Week Lass Than Once a Week Now TOTAL Parandain and Paranoias* and Pnaliciancy Peranealle and Profideray State 24 ( 45 1.5) 30(14 ) 27$ ( 1.7) 264 1.6) 280 ( 1.9) Nation 26 ( 16) 31 1.2) 41 ( 2.2) 258 ( 2.6) 209 ( 1.5) 250 ( 1.6) PARENTS EDUCATION HS non-graduate State 31 ( 6.1) 37 ( 62) 31 ( 6.0) Of* ( Nation 27 ( 42) 26 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) 14S graduate State 23 ( 3.2) 45 ( 3.8) 32 ( 33) 267 ( 3.4) 278 ( 3.0) 270 ( 32) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 33) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some college State 24 ( 3.0) 43 ( 3.4) 33 ( 32) 280 ( 3.1) 285 ( 2.4) 283 ( 3.4) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.6) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) College graduate State 24 ( 1.8) 43 ( 2.1) 29 ( 1.5) 285 ( 2.1) 290 ( 1.8) 289 ( 2.2) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.6) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Make State 29 ( 2.0) 44 ( 2.2) 27 ( 1.9) 280 ( 1.9) 287 ( 1.9) 284 ( 3.0) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 19 ( 1.5) 47 ( 1.8) 34 ( 1.8) 274 ( 2.6) 282 ( 2.0) 276 ( 2.0) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 268 ( 1$) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). iG THE 1990 NAEP TRIAL STATE ASSESSMENT 121 North Dakota TABLE A14 I Students' Reports on the Frequency of 1 Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1950 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Lass TOTAL a841 Proadwav 60 ( 1.2) 264 ( 1.1) 74 ( 1.9) 287 ( 1.2) 82 ( 1.0) 268 ( 1.0) 78 ( 2.5) 274 ( 1.3) 58 ( 9.3) «..t) 61 ( 3.7) 249 ( 2.3) 49 ( 7.3) 249 ( 3.4) 61 ( 4.4) Imo ( 0.*) 711( 0.5) 267 ( 2.1) 73(11.1) 286 ( 4.6)1 84 ( 2.7) 264 ( 1.8) 68 (11.3) 263 ( 4.2)1 76 ( 1.0) 284 ( 1.3) 75 ( 2.2) 267 ( 1.6) Illeventwe ind Proicionqf 11 0.9) 28$ 3.7) 14 0.$) 252 1.7) 9 ( 0.9) 277 ( 22) 13 ( 0.8) 258 ( 2.2) 25 ( 7.5) 41,1* ( 21 ( 2.9) 242 ( 5.1) 39 ( 5.6) 22 ( 3.6) 11 ( 3.0) *44) 13 ( 1.7) ( 12 ( 1.7) 257 ( 7.5) is ( 3.6) *4* ( 11 ( 1.2) 272 ( 3.2) 14 ( 1.0) 252 ( 2.6) Percerdage and !radon 9 ( 0.6) 275 ( 2.5) 12 ( 1.11) 242 ( 4.5) 9 ( 0.9) 260 ( 2.4) 11 ( 22) 252 ( 17 ( 7.7) 17 ( 2.7) 224 ( 3.4) 12 ( 2.3) ( It** ) 17 ( 4.0) l* 444 ( 14 (10.4) ( 5 ( 1.5) IP* 11-11 +Mt 13 ( 1.0) Imp* 10 ( 1.9) 239 ( 4.3)1 State Nation BASNEWfflly White State Nation Htspante State Nation American Main State Nation TYPE OF COMMUNITY Advantaged urban State Nation Extreme rural State Nation Other State Nation The standard esrors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A14 I Students' Reports on the Frequency of (continued) i Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 12110 NAEP TRULL STATE ASSESSMENT Almost Every Day Several Times a Week About Once a Week or Lass TOTAL Percertiose and Proficiency PsrooNaige mid Prelialeivar Percentage and Preedency State 80 ( 12) 11 ( 0.9) 9 ( OA) 284 ( 1.1) 266 ( 3.7) 275 ( 2.5) Nation 74 ( 1.9) 14 ( 0.6) 12 ( 1.6) 287 ( 1.2) 252 ( 13) 242 ( 4.5) PARENTS' EDUCATION HS non-graduate State 73 ( 260 ( 7.1) 42) 14 ( «oft 5.8) 12 ( 5.1) tHigt) Nation 64 ( 245 ( 34) 2.3) 16 ( 2.0) 18 ( 3.1) 441 ItS graduate State 80 ( 2.7) 10( 1.6) 10 ( 1.9) 270 ( 2.3) 258 ( 7.4) Nation 71 ( 3.6) 10 ( 1.8) 13 ( 2.8) 256 ( 1 .6) 249 ( 32) 239 ( 3.4)l Some colter State 79 ( 286 ( 3.1) 2.0) 18 ( 2.6) .41 Nation college graduate 80 ( 270 ( 2.0) 1.9) 11 ( ( 1.2) 441 9 ( ( 1.7) Statd 81 ( 1.5) 9 ( 0.9) 290 ( 1.3) 279 ( 4.7) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.8) ( 2.8) 257 ( 6.4)1 GENDER Male State 78 ( 1.5) 13 ( 1.3) 9 ( 1.0) 287 ( 1.3) 273 ( 3.2) 278 ( 7.1) Nation 72 ( 2.4) 16 ( 1.2) 12 ( 2.1) 268 ( 1.8) 252 ( 23) 242 ( 8.1) Female State $2 ( 1.4) 9 ( 1.1) 10 ( 1.2) 2$1 ( 1.4) 259 4.9) 274 ( 5.8) Nation 78 ( 1.8) 13 ( 1.0) 11 ( 1.8) 265 ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 78 THE 1990 NAEP TRIAL STATE ASSESSMENT 123 North Dakota TABLE A 15 I Students' Reports on the Frequency of 1 Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 100 NAEP TRIAL STATE ASSESSMENT , At Lust Suomi Thus a Moak About Ones a Wook Lass Than Weakly TOTAL 80ventap and Pirsialancy Perosidass and finsidency State 36 1.9) 24 ( 1.4) 275 2.0) 2.0 ( 1.8) Nation 38 24) 25 ( 1.2) 253 ( 2.2) 201 ( 1.4) RACE/ETHNICITY White State 35 ( 2.1) 24 ( 14) 283 ( 1.5) 293 ( 14) Nation 35 ( 2.9) 24 ( 1.3) tiltbank 262 ( 2.5) zee ( 1.5) State 35 $44, ( 8.4) .44) 27 (( 8.0) Nation 44 ( 4.1) 25 ( 3.4) 238 ( 31) 247 ( 3.3) American Indian State 59 ( 8.5) 23 ( 7.2) 241 ( 3.3)1 **It ( Nation 41 ( 4.2) 30 (11.3) *el TYPE OF COMMUNITY Advantaged trban State 25 ( ( 1.3) *44 ) 19 ( et, 2.6) Nat1on 50 ( 271 ( 9.0) 3.3)1 19 ( 4.9) .1.4) Exfrsene rural State ( 3.9) 25 ( 3.4) 277 ( 4.1) 260 ( 2.3) Nation 42 (10.1) 30 ( 4.4) 249 ( 4.0)1 250 ( 3.4)1 Other State 37 ( 2.4) 24 ( 1.9) 279 ( 2.1) 281 ( 2.7) Natioct 30 ( 2.9) 28 ( 1.2) 252 ( 3.0) 261 ( 2.1) Paressise ProRdway 40 ( 24) 21g 2 7 2 ( Ti 41 ( 24) iA) 41 ( 3.0) 277 ( 2.0) 38 ( 9.0) dim ( .41 32( 4.3) 248 ( 3.3) 18 ( 3.6).) 28 (12.5) ilP** 58 ( 1.8) ( 441 31 ( 9.3) 299 ( 5.3)1 36 ( 49) 283 ( 3.6) 25 ( 7.5) 267 ( 7.3)1 39 ( 3.3) 265 ( 1.7) 38 ( 24) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). I 2 124 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A15 I Students' Reports on the Frequency of (continUed) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAB' TRIAL STATE ASSESSMENT At Least Several Tknes a Weak About Once &Weak Lest Than *Reidy Perosntage and Prs idiocy Pmentage mW Pradencll percapiap and PnAdency state 38 ( 1.9) 24 ( 1.8) 40 ( 2.4) 278 ( 2.0) 260 ( 1.8) 284 ( 1$) Nation 38 ( 2.4) 25 ( 12) 37 ( 24) 253 ( 2.2) 261.( 1A) 272 ( 1.9) PARENTS' EDUCATION le non-graduate State 43 ft** (8.9) ***) 17 ( 4.4)) 35 ( Mgr T.?) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) HS graduate State 35 ( 3.4) 24 ( 3.2) 41 ( 4.0) 270 ( 3.2) 274 ( 3.0) 275 ( 3.1) Nation 40 ( 32) 29 ( 2.2) 32 ( 3.5) 247 ( 2.7) 256 ( 2.5) 262 ( 2.2) Saw college State 38 ( 3-3) 25 ( 34) 38 ( 4.0) 280 ( 2.0) 285 ( 34) 284 ( 3.0) Nation 34 ( 3.4) 20 ( 22) 40 ( 3.5) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) College graduate State 35 ( 2.3) 24 ( 1.9) 41 ( 2.5) 287 ( 2.1) 285 ( 2.8) 292 ( 1.8) Nation 38 ( 2.8) 22 ( 1.6) 41 ( 2.6) 264 ( 2.6) 273 ( 2.5) 285 ( 2.3) 5IENDER Male State 37 ( 2.5) 25 ( 2.2) 3$ ( 3.0) 281 ( 2.1) 284 ( 2.4) 287 ( 2.1) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 203 ( 2.3) 274 ( 2.4) Female State 34 ( 2.5) 24 ( 1.9) 42 ( 2.7) 275 ( 2.7) 277 ( 2.3) 282 ( 1.6) Nation 37 ( 2-5) 2S ( 14) 38 ( 2.6) 253 ( 2.1) 259 ( 1.8) 269 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 30 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 North Dakota 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 18110 PIMP TRIAL STATE ASSESSMENT Calculator Teacher Explains Calculator the Yes No _ , Yes No TOTAL Poraantaga and Praidancy Paroantap and Preadancy Portantap and Preficiency Parcentage and Proficiency State 100 ( 0.1) 1 ( 0.1) 49 ( 1.7) 51 ( 1.7) 281 ( 1.2) 279 1.7) 264 ( 1.3) Nation 97 ( 0.4) 3 ( 0.4) 49 2.3) 51 ( 2.3) 263 ( 1.3) 234 ( 3.8) 2511 ( 1.7) 206 ( 1.5) RACFATHNICITY White State 100 ( 0.1) 284 ( 0.9) 0 ( 0.1) ( 441 48 ( 1.7) 262 ( 1.1) 52 ( 1.7) 286 ( 1.3) Nation 98 ( 0.3) 2 ( 0.3) 4$ ( 2.6) 54 ( 2.6) 270 ( 1.5) 266 ( 1.8) 273 ( 1.8) Hispanic State 99 ( 0.7) 251 ( 4.9) ( 0.7) ( "") 64 ( 8.4) 4,1 37 ( 8.4) 41 Nation 92 ( 1.2) 8 ( 1.2) 63 ( 4.3) 37 ( 4.3) 245 ( 2.7) 243 ( 3.4) 245 ( 2.9) Arnorican Indian State R2 ( 3.1) ( 3.1) 01 ( 7.0) 39 ( 7.0) 243 ( 3.8)1 241 ( 4.4)1 244 ( 4.2) Nation 94 ( 3.1) 6 ( 3.1) ( ***) 71 (16.7) 29 (16.7) .p** «on TYPE OF COMMUNITY Advargagod urban State 100 ( 0.0) 0 ( 0.0) 49 ( 3.0) 51 ( 3.0) 285 ( 1.8) 1144, ( 0-.11 4,-«* 44.* Nation 99 ( 1.0) 1 ( 1 ) 45 (12.2) 55 (12.2) 281 ( 3.8)1 *44 ( 276 ( 2$)! 285 ( 8.4)1 Extreme rural State 99 ( 0.3) 1 ( 0.3) 47 ( 3.3) 53 ( 3.3) 280 ( 2.5) 278 ( 4.1) 283 ( 2.2) Nation 96 ( 1.3) 4 ( 1.3) 42 ( 8.7) 58 ( 13.7) 257 ( 3.9)1 251 ( 4.8)1 261 ( 4.4)1 Other State 99 ( 0.2) ( 0,2) 49( 2.2) 51 ( 2.2) 282 ( 1.3) 280( 1.3) 283 ( 1.9) Nation 97 ( 0,5) 3 ( 0.5) 50 ( 2.7) 50 ( 2.7) 283 ( 1.7) 233 ( 5.4) 258 ( 2.1) 266 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution - the nature of the sample does not allow accurate determMation of the variability of this estimated mean proficiency *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 131 126 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE Al8 (continued) Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How'To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Own a Calculator - Teacher Dv lens Caktiattor Use a Yes No Ye3 No TOTAL Percentage and Prt &dew 100 ( 0.1) 2111 ( 1.2) 97 ( 0.4) 263( 1.3) State Nation PARENTS' EDUCATION 1111 non-graduate State 98 ( 1.3) 256 ( 3.6) Nation 92 ( 1.6) 243 ( 2.0) 1111 graduate State 99 ( 0.4) 273 ( 2.4) Nation 97 ( 0.8) 255 ( 1.5) Nom college State 100 ( 02) 263 ( 1.9) Nation 96 ( 0.9) 26$ ( 1.8) College graduate State 100 ( 0.0) 288 ( 1.3) Nation 09 ( 0.2) 275 ( 1.6) GENDER State 100 ( 0.1) 264 ( 1.4) Nation 97 ( 0.5) 264 ( 1.7) Ferrol. State 99 ( 0.2) 279 ( 1.5) Nation 97 ( 0.5) 262 ( 1.3) Percentage and Prot Money 1 0.1) 3 0.4) 234 3.8) 2 ( 1.3) 8 ( 1.6) 444 ( ( 0.4) 3 ( 0.6) ( 0 ( 0.2) ( 4 ( 0.9) 44 ( ) 0 ( 0.0) ( 02) P* ( *41 Percentage and Pro *ism Percentage and Pnolicionev 49 ( 1.7) 51 ( 1.7) 279 1.7) 254 ( 1.3) 49 2.3) 51 ( 2.3) 25$ ( 1.7) 206 ( 1.5) 43 ( 8.4) ..**) 52 ( 8.4) 53 ( 4.6) 47 ( 4.6) 242 ( 2.9) 243 ( 2.5) 49 ( 2.5) 51 ( 2.5) 270 ( 3.5) 275 ( 2.6) 54 ( 3.0) 46 ( 3.0) 252 ( 1.9) 258 ( 2.0) 52 ( 4.2) 48 ( 42) 281 ( 2.0) 285 ( 2.9) 48 ( 3.2) 52 ( 3.2) 265 ( 2.4) 268 ( 22) 47 ( 2.0) 53 ( 2.0) 287 ( 1.7) 290 ( 1.6) 46 ( 2.6) 54 ( 2.6) 266 ( 2.2) 280 ( 1.9) 50 ( 2.1) 50 ( 2.1) 282 ( 2.0) 286 ( 1.8) 51 ( 2.6) 49 ( 2.6) 256 ( 2.1) 269 ( 2.1) 47 ( 2.3) 531 2.3) 275 ( 2.4) 281 ( 1.5) 47 ( 2.5) 53 ( 2.5) 258 ( 1.7) 263 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within I 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 North Dakota TABLE A19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY I 1900 NAEP TRIAL STATE ASSESSMENT Worldng Problems in ClasS Doing Problems at Nome Taking Quizz or Tests Almost Always Ne if Almost Always Never Almost Always Never . TOTAL Paramiage and Pralidency Percentage and Proficiency State 415 23 ( 277 1.5 238 ( 1.4 Nation 48 1.5 23 ( 1.9 254, ( 1.5) 272 ( 1.4) RACE/ETHNICITY White State 46( 1.8) 23 ( 1.7) 2$0 ( 1.2) 290 ( 1.4) Nation 46 ( 1.7) 24 ( 2.2) 262 ( 1.7) 278 ( 1.3) Hispanic State 4$ ( 1, ( 7.0) 11 ( 4.3) ( **el Nation 51 ( 2.9) 18 ( 3.5) 239 ( 2.8) 252 ( 3.3)1 Ametican Indian State 42 ( *4,4 ( 4.5) 141 24 ( *** 5.5) Nation 33 ( 9.8) 23 ( 4.9) *b. ( Mel *4110 4* ) TYPE OF COMMUNITY Advantaged urban State 48 ( 4.2) .1,4) 20 ( 2.1) 4.4.) Nation 51 ( 5.4) 23 (10.7) 270 ( 4.7)1 Extreme rural State 42 2.7) 29 ( 2.8) 275 ( 3.5) 287 ( 2.1) Nation 46 ( 7.4) 29 ( 8.5) 248 ( 4,3)1 268 ( 8.1)1 Other State 46 ( 2.0) 20 ( 2.1) 278 ( 1.8) 290 ( 2.0) Nation 48 ( 1.9) 22 ( 2.0) 254 ( 2.1) 272 ( 1.8) Pawning, Percentage Penology Penentage and end and and Proficiency Psi:114mm Pre Scam linliciency 31 ( 231 ( 1.5 30 ( 1.3 261 ( 1.8) 32 ( 1.4) 263 ( 1.5) 31 ( 1.5) 270 ( 1.7) 40 ( 7.8) ( «it.) 26 ( 3.2) 238 ( 4.8) 21 ( 3.3) 15 ( 4.9) *14 ( MN) 39 ( 2.7) 32 ( 6.1) 274 ( 4.9)1 26 ( 2.4) 277 ( 2.9) 20 ( 2.5) 34 (. 1.9) 282 ( 2.2) 32 ( 1.7) 263 ( 2.3) 12 ( 0.9) 23 ( 1.2) 34 1.7) 282 ( 1.9) 277 ( 1.9) 20 1.2) 19 ( 0.9) 27 ( 1.4) 30 2.0) 263 ( 1.11) 253 ( 2.4) 274 ( 1.3) 12 ( 0.9) 23 ( 1.3) 35 ( 1.8) 237 ( 1.7) 260 ( 2.1) 291 ( 1.2) 18 ( 1.2) 25 ( 1.5) 32 ( 2.3) 289 ( 2.3) 263 ( 2,8) 279 ( 1.2) 18 ( 0.8) 24 (( 7.2) 20 ( 414se 7.0) ***) 21 ( 2.1) 26 ( 2.7) 22 ( 3.1) 244 ( 3.1) 237 ( 3.2) 258 ( 4.2) 24 ( 444 3.9) 28 ( ( 2.0) 441 31 ( *44 ( 4.9) 32 (10.1) 20 ( 6.2) 21 ( 7.8) *Mb ( **111 IMP1 *NI ( 1111.1 4 ( 1.7) 27 ( 3.4) 29 ( 4.5) ***) 15 ( 24) 31 ( 3.8) 28 ( 9.8) 281 ( 7.6)r 285 ( 4.2)1 16 ( 1.8) 23 ( 1.7) 38 ( 2.7) 280 ( 2.7) 275 ( 3.7) 288 ( 2.0) 23 ( 3.9) 24 ( 8.6) 37 ( 8.3) 283 ( 4.4)1 270 ( 4.0)1 12 ( 1.3) 22 ( 1.8) 32 ( 2.2) 283 ( 3.0) 277 ( 2.5) 289 ( 1.7) 18 ( 1.1) 27 ( 1,8) 29 ( 2.1) 283 ( 2.8) 253 ( 2.7) 276 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. ! Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). L'; 3 328 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A 19 I Students' Reports on the Use of a alkillator (continued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 MEP TRIAL. STATE ASSESSMENT "icing Prciaiams in am . Doing Problems at Homo . Taking Quizzes or Testa Almost Always . Never Almost Always Never _ , Almost Alwa ys , I Never TOTAL State Nation PARENTS EDUCATION NS non-graduate State Nation NS graduate State NatiOn Some college State Nation College graduate State Nation GENDER Male State NatiOn Female State Nation Porimeass Pommies* Pereeniese Pereeniase Poraniese Perosegese and and am6 and me Preiloionos Madam Peoliciemy Prelicioncy Maoism Preeoliner 48 ( 1.6) 23 ( 1.6) 31 ( 1.4) 12 0.9 23 34 1.1 277 ( 2111( 14) 291 ( 252 1.9 277 1.9 MS 1.2 46 ( 1.5 23 ( 1.9) 90 ( 1.3 19 0.9 27 1.4 so 2.0 254 ( 1.5 272 ( 1.4) 261 ( 13 263 13 253 2.4) 274 13 00 ( 6.0) 15 ( 4.5) 25 ( 5.9) 15 ( 4.8) *IN ( *e) *** 114. ) CINNI ( '141 54 ( 3.3) 19 ( 3.8) 26 ( 3.1) 22 ( 2.0) 240 ( 2.3) *** ( ') 244 ( 3.8) 244 ( 4.2) 45 ( 2.9) 19 ( 2.2) 33 ( 2.9) 10 ( 1.5) 260 ( 3.1) 281 ( 2.8) 275 ( 3.2) 271 ( 4.2) 52 ( 2.5) 20 ( 2.4) 29 ( 1.9) 18 ( 1.5) 248 ( 1.4) 206 ( 2.7) 250 ( 2.4) 256 ( 2.4) 45 ( 2.8) 21 ( 2.6) 29 ( 3.5) 17 ( 2.4) 281 ( 2.2) 286 ( 3.8) 281 ( 2.4) 285 ( 3.3) 46 ( 2.8) 26 ( 2.8) 28 ( 2.0) 20 ( 1.9) 258 ( 2.1) 272 ( 2.5) 267 ( 3.0) 268 ( 3.2) 45 ( 2.2) 25 ( 2.1) 32 ( 2.2) 11 ( 1.2) 284 ( 1.8) 295 ( 1.7) 287 ( 2.0) 289 ( 3.2) 45 ( 1.9) 25 ( 2.4) 33 ( 2.0) 16 ( 1.4) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 48 ( 2.2) 280 ( 1.7) 50 ( 1.7) 255 ( 1.9) 43 ( 2.1) 273 ( 2.2) 46 ( 2.0) 252 ( 1.7) 21 ( 1.8) 293 ( 2.0) 20 ( 2.0) 275 ( 2.2) 24 ( 2.2) 285 ( 1.7) 26 ( 2.1) 269 ( 1$) 31 ( 2.0) 284 ( 2.1) 29 ( 1.6) 264 ( 2.8) 31 ( 2.3) 278 ( 1.8) 32 ( 1.6) 259 ( 1.7) 14 ( 1.3) 2b4 ( 2.5) 19 ( 1.3) 263 ( 23) 11 ( 1.3) 278 ( 3.1) 18 ( 1.2) 263 ( 2.1) 24 ( 6.4) 21 ( 5.3) AM. 1144, IN* 32 ( 3.6) 24 3.2 237 ( 2.3) 251 4.6 24 ( 2.3) 30 ( 2.6) 209 ( 4.1) 261 ( 2.5) 26 ( 1.5) 27 ( 2.2) 246 ( 2.6) 265 ( 2.0) 22 ( 2.7) 35 ( 2.8) 233 ( 3.0) 286 ( 3$) 26 ( 2.4) 35 ( 2.5) 255 ( 3.6) 275 ( 2.0) 23 ( 1.7) 36 ( 2.1) 263 ( 2.6) 296 ( 1.7) 26 ( 1.8) 33 ( 2.7) 268 ( 2.6) 285 ( 2.0) 23 ( 1.3) 31 ( 2.0) 281 ( 2.7) 293 ( 1.5) 27 ( 1$ ) 26 ( 2.1) 256 ( 3.0) 277 ( 1.9) 23 ( 2.1) 37 ( 2.4) 273 ( 3.0) 285 ( 1.5) 27 ( 1.8) 33 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sontetimes" category is not included. *1* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT 129 North Dakota TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY ISS0 NAEP TRIAL "Calculator-Use" "CMculator-Use" STATE ASSESSMENT High Group Ot Mr Grow , TOTAL Parcantap Pareantat and and Paoli Idiocy Madam State 56 ( 1.5) 44 ( 1.5) 286 ( 1.8 275 ( 1.8) Nation 42 ( 1.3 Set 1.3) 272 ( 12) 255 ( 1.5) RACE/ETWOCITY M. State 57 ( 1.6) 43 ( 1.6) 288 ( 1.6) 279 ( 1.5) Nation 44 ( 1.4) 56 ( 1.4) 277 ( 1.7) 263 ( 1.7) Hispank Sts.e 54 ( 8.9) 46 ( 6.9) IMO ( CM/ Nation 38 ( 42) 84 ( 42) 254 ( 4.8) 238 ( 3.0) American Indian State 32 ( 7.3) 88 ( 7.3) 240 ( 3.9)1 Nation 29 (12.0) *** 71 (12.0) TYPE OF COMMUNITY Advantaged urban State 50 ( 5.6) 44-.) 50 ( 5.6) Nation 50 ( 3.8) 50 ( 3.8) 288 ( 4.9)1 275 ( 4.4)1 Extreme rural State 55 ( 2.3) 45 ( 2.3) 286 ( 2.5) 272 ( 3.6) Nation 39 ( 5.6) 81 ( 5.8) 289 ( 4.4)1 248 ( 4.3)1 Other State 57 ( 1.7) 43 ( 1.7) 286 ( 2.3) 275 ( 1.9) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) The sti ndard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "1* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). t L.) 130 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1800 MEP TRW. STATE MOSESSMENT High "Cidadator-Use" Group Other "Caiculattw-Uee" OANIP TOTAL Per4Nolele 8811 Praid01441, 208 1.6 42 1.3 272 1.6 State Nation PA/MI5' EpLICATION 146 non-graduate State 34 ( 8.6) ***) oistion 34 ( 3.3) 248 ( 4.4) 149 graduate State 56 ( 3.2) 277 ( 2.6) Nation 40 ( 22) 263 ( 2.0) Some colkoge State SS ( 3.4) 290 ( 2.7) Nation 48 ( 22) 277 ( 2.6) CeRege graduate State 57 ( 2.1) 292 ( 1.8) Nation 48 ( 2.0) 282 ( 2.1) GENDER Male State 53 ( 2.5) 288 ( 2.0) Nation 39 ( 2.0) 274 ( 2.0) Female State 59 ( 2.3) 284 ( 2.1) Nation 45 ( 1.8) 269 ( 1.7) awl direlkisicy 44 ( 1.5) 275 ( 14) 58 ( 1.3) 255 ( 1.5) 66 ( 8.8) ( ***) ea ( 3.3) 242 ( 2.4) 44 ( 3.2) 207 ( 3.2) 00 ( 2.2) 249 ( 1.8) 42 ( 3.4) 276 ( 2.3) 52 ( 2.2) 258 ( 2.5) 43 ( 2.1) 283 ( 2.5) 54 ( 2.0) 208 ( 1.9) 47 ( 2.5) 270 ( 2.5) ( 2.0) 255 ( 2.3) 4? ( 2.3) 273 ( 1.9) 55 ( 1.8) 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 ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 136 THE 1990 NAEP TRIAL STATE ASSESSMENT 131 North 2. ia TABLE A24 I Students' Reports on Types of Reading I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Zero to Two Typos Pow Typos TOTAL Pernantage and Skolicialoy Persentage and Prolledency Potvonlogo owl Proildoncy State 10 ( 1.0) 30 ( 12) ex 1.3) 261 ( 3.5) ( 1.8) ( 0.9) Nation 21 ( 1.0) 90 ( 1.0) ( 41.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) NMI/IMO. %Mita State ( 0.0) 30 ( 1.3) 63 ( 1.3) 269 ( 2.8) 284 ( 1.6) 288 ( 1.0) Nation 16 ( 1.1) 29 ( 1.3) 58 ( 13) 251 ( 22) 268 ( 1.5) 278 ( 13) Hispank State 25 ( 6.8) 35 ( .44 ( 8.2) 041 40(( 1.0) fen Nation 44 ( 3.0) 30 ( 2.4) 26 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) American When State 32 ( .4* 2.8) 44 ( 4.3) 24 ( 4.2) Vi Nation 29 (11.1) ***) 40 ( 4.9) 31 ( 4* 9.21 *41 ( TYPE OF COMMUNITY Advantaged urban State 8 ( 28) 29 ( 6.4) 63 ( 6.1) *00 ( 269 ( 1.5) Nation 13 ( 4.* ( 3.8) 26 ( 4*. ( 2.1) .41 61 ( 287 ( 4.9) 3.6)! Extreme rural State 9 ( 1.4) 30 ( 1.7) 51 ( 1.7) 253 ( 6.4) 277 ( 4.1) 2135 ( 1.0) Nation 17 ( 4.9) 33 ( 3.2) 50 ( 5.1) 253 ( 4.3)i 263 ( 5.6)1 Other State 10 ( 1.6) 30 ( 1.8) 60 ( 2.0) 263 ( 4.8) 232 ( 2.2) 265 ( 1.3) Nation 22 ( 1.5) 30 ( 1.3) 46 ( 1.5) 244 ( 2.8) 259 ( 2.2) 272 ( 1.7) The standard errors of the estiolated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each populatie.1 of :rest, the value for the entire population is within * 2 standard errors of the estimate for the sample. Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "8 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 137 132 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A24 I Students' Reports on Types of Reading (continued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MAEP TRIAL STATE ASSESSMENT Zero to Two Types Trims Types Four Types TOTAL Percentage and Prolidency Plavantage and Proficiency Percentage and Proficiency State 10 ( 1.0) 30 ( 12) CO ( 1.3) 261 ( 3.5) 280 ( 1.8) 285 ( 0.9) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) PARENTS EDUCATION HO nors-graduate State Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 246 ( 3.3) HS graduate State 14 ( 2.2) a* ( 2.5) 54 ( 2.3) 253 ( 4.8) 272 ( 3.4) 278 ( 2.1) Nation 26 ( 2.2) 33 ( 1.9) 40 ( 1.7) 246 ( 2.2) 253 ( 2.7) 260 ( 2.1) Some college State 8 ( 1.8) 30 ( 2.8) 62 ( 3.0) ( 282 ( 2.5) 285 ( 2.2) Nation 17 ( 14) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College gracluate State 6 ( 1.2) 28 ' : ' 65 ( 1.9) 281 290 ( 1-3) Nation 10 ( 0.8) 26. , " 62 ( 2.0) 254 ( 2.8) 269 ( :e....41 280 ( 1.8) GENDER Male State 10 ( 1.2) 29 ( 1.6) 61 ( 1.9) 264 ( 3.6) 282 ( 32) 288 ( 1.3) Nation 21 ( 244 ( 1.5) 2.3) 31 ( 259 ( 14) 2.1) 48 ( 273 ( 1.4) 2.0) Female State 9 ( 1.3) 31 ( 1.8) 59 ( 1.7) 257 ( 5.9) 278 ( 1.8) 282 ( 1.6) 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 atm:, 95 percent certainty that, for each population of interest, the value for the ritire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 18 THE 1990 NAEP TRIAL STATE ASSESSM EN , 133 North Dakota TABLE A25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1 11790 NAEP TRIAL One Hour or Four to Five Six Hours or STATE ASSESSMENT Less T wo Hours Three Hours Hours More TOTAL Peramtage and Pro *Maw 14 ( 0.9) Porcentaga and Wolk Macy 27 ( 1.2) illeroantags and Pro Many 24 ( 1.2) Pannuntaga and Pro edam 24 ( 13) Parcsata Pr8081808W ( 81) * te 289 ( 2.0) 263 ( 1.3) 2$2 ( 279 2.3) 284 ( 3.1) volition 12 ( 0.8) 21 ( 0.9) 22 ( 0.6 28 1.1) 15 ( 1.0) 209 ( 24) 205 ( 1.8) 206 ( 1.7 200 1.7) 245 ( 1.7) RACE/ETHNICITY White State 15 ( 0.9) 28 ( 1.3) 24 ( 1.3) 25 ( 1.4) ( 290 ( 2.0) 255 ( 1.5) 255 ( 1.4) 283 ( 2.1) 270 ( 2.4 Nation 13 ( 1.0) 23 ( 1.2) 24 ( 1.1) 27 ( 1.4) 12 ( 1.2 278 ( 2.5) 275 ( 2.2) 272 ( 14) 1.7) 253 ( 2.4 Hispanic State 10 ( 42) ipos ( *61 32 t a 0)) 21 ( 0.1) 29 ( 8.3) 440 ( .441 8 ( 42) 1P 11.1 Nation 14 ( 2.4) :0 ( 2.5) 19 ( 2.1) 31 ( 3.1) 17 ( 1.7) *SIP ( WO* ) 245 ( 3.2) 242 ( 5.6) 247 ( 3.5) 235 ( 3.5) American Indian State 9 ( 3.0) vs.) 14 ( 2.1) felt ( 11 27 ( 4.7) es. ( 36 ( 4.6) ***) 14 ( 4.1) «he ( Nation 13 ( "ir 44 ) 21 (10.5) .0**) 25 ( 5.7) *4* ( 22 ( 5.4) «04. ( «el TYPE Of COMMUNITY Advantaged urban State 21 ( 4.3) 24 ( 5.4) 25 ( 8.5) ( 22 ( 2.1) te ( *4-1 3 ( 1.9) 1014fr ) Nation 18 ( 1.4) svs) 25 ( 4.3) ( 21 ( 1.8) s,H,) 30 ( 4.3) ( 2.0) ( Extreme rural State 14 ( 1.3) 24 ( 1.7) 25 ( 1.2) 31 ( 1.7) 8 ( 1.1) 285 ( 2.3) 285 ( 1.0) 278 ( 2.5) 279 ( 3.8) 253 ( 8.8) Nation 14 ( 3.3) ( .41 26 ( 2.7) 256 ( 3.6)1 Other State 13 ( 12) 29 ( 1.6) 27 ( 1.7) 24 ( 2.2) 7 ( 1.1) 290 ( 3.3) 282 ( 1.7) 283 ( 2.4) 279 ( 3.3) 271 ( 2.5) Nation 12 ( 1.0) 21 ( 1.0) 23 ( 1.2) 27 ( 1.2) 17 ( 1.4) 268 ( 2.6) 289 ( 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). ()t t 134 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A25 I Students' Reports on the Amount of Time Spent (continued) I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT Ono Hour or 'Pau Loss Nom { 1 n Hours Tar . Four' to Fivo Hours SIx Hours or Mons TOTAL Percentage and Pradancy 14 ( 0.9) 289 ( 2.0) 12 ( 0.8) 269 2.2) 13 ( 4.9) .41 12 ( 22) a* ( el 1 0 ( 1.8) 282 ( 3.6) 8 ( 1.0) 249 ( 4.7) 15 ( 2.4) 283 ( 3.6) 10 ( 1.4) ***) 17 ( 1.4) 295 ( 2.8) 17 ( 1.3) 282 ( 2.6) 11 ( 1.1) 290 ( 2.8) 11 ( 0.9) 269 ( 3.3) 18 ( 1.5) 288 ( 25) 14 ( 1.1) 269 ( 2.8) Paroantags and Prollidency 27 ( 1.2) 263 ( 1.3) 21 ( 0.9) 268 ( 1.8) 25 ( 6.9) 1144 ( *41 24 ( 2.3) 274 ( 3.4) 17 ( 1.4) 257 ( 2.8) 26 ( 2.8) 285 ( 2.5) 25 ( 2.4) 275 ( 2.7) 30 ( 2.0) 289 ( 1.9) 22 ( 1.6) 280 ( 2,5) 25 ( 1.9) 287 ( 1.8) 22 ( 1.2) 267 ( 2.6) 30 ( 1.6) 280 ( 2.0) 20 ( 1.3) 269 ( 22) Parcantaga and Prolidency 26( 1.2) 282 ( 1.6) 22 ( 0.8) 2es ( 1.7) 30 ( 6.3) 21 ( 2.8) 25 ( 2.6) 275 ( 3.0) 23 ( 2.0) 259 ( 3.2) 25 ( 2.4) 281 ( 4.1) 23 ( 2.6) 269 ( 3.5) 26 ( 1.8) 289 ( 2.4) 23 ( 1.1) 277 ( 2.2) 30 ( 1.5) 285 ( 2.1) 22 ( 1.0) 267 ( 2.2) 21 ( 1.8) 277 ( 2.5) 23 ( 1.4) 264 ( 1.8) Psroantaga and PM/dem 20 ( 1.3) 279 ( 2.3) 26 ( 1.1) 260 ( 1.7) 20 ( 5.3) ( «al 28 ( 2.9) 244 ( 3.2) 32 ( 2.8) 270 ( 4.1) 32 ( 2.3) 253 ( 2.5) 31 ( 3.2) 284 ( 3.6) 28 ( 22) 267 ( 2.5) 22 ( 1.8) 286 ( 2.8) 25 ( 1.5) 270 ( 2.4) 27 ( 1.6) 282 ( 2.8) 28 ( 1.3) 252 ( 2.1) 25 ( 1.7) 275 ( 2.4) 28 ( 1.6) 258 ( 1.9) Parcantaga and !madam ( 0.7) 264 ( 3.1) 16 ( 1.0) 245 ( 1.7) 12 ( 4.3) «Hi ( fin 20 ( 2.4) ( 441 9 ( 1.3) ( .41 19 ( 1.6) 248 ( 3.0) 3 ( 1.0) Mr* ( 441 14 ( 1.5) 242 ( 3,4) 5 ( 0.9) 12 ( 1.1) 255 ( 3.2) ( 1.1) 269 ( 2.6) 17 ( 1.5) 248 ( 2.5) 5 ( 1.0) 256 ( 5.3)1 15 ( 1.2) 241 ( 2.2) State Nation PARENTS EDUCATION H5 nonipraduate State Nation HS oraduato State Nation Som college State Nation College graduate State Nation GENDER Male State Nation Fsmale 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 withM ± 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 est& .ed mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 40 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 North Dakota TABLE A26 I Students' Reports on the Number of Days of 1 School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY rSag NAEP TRIAL TATE ASSESSMENT None One or TWO Days Three Dalt* re' Mere TOTAL PlifoRlais and Prolidatcy Parambige sad Palidency Paraddige aid Prellaamt State 50 ( 1.2) 30 ( 1.2) 14 ( 1.0) 285 1.2) 281 1.3) 289 ( 2.9) Nation 45 1.1) 32 0.9) 23 ( 1.1) twojrnimictry 205 51 ( 1.8) 1.1) ne 35 ( 1.5) 12) 250 ( 13 ( 1.9) 1.0) write state 287 ( 1.1) 284 ( 1.3) 275 ( 2.3) Nation 43 ( 1.2) 34 ( 12) 23 ( 1.2) 273 ( 1.8) 272 ( 1.7) 258 ( 2.1) Hispank State 37 (( 7.3) 4.1 43 ( 8.4) 20 ( 5.9) Natlon 41 ( 3.3) 32 ( 22) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) Modem Indian State 26 ( 2.5) 41 ( 3.4) 33 ( 4.3) Nation 23 ( 8.8) gpie.) 39 ( et* 5.1) **) 38 ( *** 5.2) ***) TYPE OF COMMUNITY Advantaged urban State 48 ( Mr* ( 4.7) 38 ( 5.6) *el 14 ( 2.0) Nation 47 ( 2.3) 38 ( 2.6) 284 ( 4.4)1 279 ( 4,5)1 4-4H1 Extreme rural State 51 ( 1.7) 34 ( 1.7) 15 ( 1.7) 284 ( 1.8) 281 ( 2.5) 284 ( 5.8) Nation 43 ( 4.4) 32 ( 4.2) 25 ( 3.8) 257 ( 4.1)1 264 ( 5.8)1 Other State 48 ( 1.8) 37 ( 1.5) 15 ( 1.7) 285 ( 1.6) 282 ( 1.8) 272 ( 3.0) Nation 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 266 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution - the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 141 136 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A26 I Students' Reports on the Number of Days of (mntinued) I School Nlissed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1880 NAEP TRIAL STATE ASSESSMENT Mona 1_ One or Two Days Three Days or More TOTAL State Nation PARENTS goucAroN NS non-graduate State Nation HS graduate State Nation Some college State Nation College graduate State Nation OENDER M. State Nation Female State Nation losrosetage and Pridlaisacy 50 1.2) 265 1.2) 45 1.1) 285 1.6) 29 ( 5$) 38 ( 3.2) 245 ( 3.0) 49 ( 3.1) 275 ( 2.9) 43 ( 2.1) 255 ( 2.0) 47 ( 3.7) 265 ( 2.2) 40 ( 1.6) 270 ( 3.0) 54 ( 1.9) 291 ( 1.3) 51 ( 1.8) 275 ( 2.1) 55 ( 1.8) 288 ( 1.7) 47 ( 1.8) 288 ( 2.0) 45 ( 2.0) 283 ( 1.9) 43 ( 1.4) 264 ( 2.3) Pomade. tad Prelikkincy 38 ( 1.2 261 ( 1,31 32 ( 0.9 208 ( 1.5) 43 ( 8.4) *Mt ( fen Poremelp ami Pralkienay 14(1.9) 209 2.91 23 1.1) 250 1.9) 28 ( 5.9) .414. 26 ( 3.1) 3.5) 249 ( 3.3) 237 ( 3.1) 32 ( 2.9) 19 278 ( 2.8) 262 5.1 31 ( 1.9) 27 1.9 257 ( 2.8) 249 ( 24) 44 ( 3A) 10 (IA) 263 ( 2.7) IN* 1441) 37 ( 1.8) 23 1.8) 271 ( 2.5) 253 ( 3.1) 33 ( 1.9) 13 ( 1.3) 286 ( 2.0) 278 ( 4.1) 33 ( 1.2) 18 ( 1.3) 277 ( 1.7) 285 ( 3.1) 33 ( 1.9) 12 ( 1.4) 234 ( 2.1) 276 ( 3.8) 31 ( 1A) 22 ( 1.4) 267 ( 2.1) 250 ( 2.6) 38 ( 1.7) 17 ( 1.6) 279 ( 1.9) 265 ( 3.3) 32 ( 1.1) 25 ( 1.3) 208 ( 1.7) 250 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 72 THE 1990 NAEP TRIAL STATE ASSESSMENT 137 North Dakota TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Sir/m*441m Agin Undecided. Disagree, Wrongly Disagree TOTAL. Percentage and Pr Cadency Percentage and Proficiency Percentage and PreNdency State 29 ( 1.5) 50 ( 1.4) 20 ( 1.1) 293 ( 1.5) 2S0 ( 1.5) 268 ( 2.2) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.6) RACE/ETHNICITY WO, State 30 ( 1.5) 51 ( 1.5) 20 ( 1.1) 296 ( 1.3) 283 ( 1.4) 272 ( 1.9) Nation 26 ( 1.6) 4$ ( 1.3) 26 ( 1.5) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Hispanic State 23 IMP ( 7.4) ( 37 ( *** 8.2) *44 ) 40 (. 7.4) 41 Nation 24 ( 2.5) 48 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 236 ( 3.8) American Indian State 17 ( 3.3) f.e.) 50 ( 248 ( 7.5) 3.8)1 34 ( ( 52) Nation 23 ( 7.4) ( 48 (14.9) SIM ( 41.1111) 29 ( *** 9.5) **) TYPE OF COMMUNITY Aidvantaged urban State 36 ( 4.7) 49 ( 5.2) 15 ( 1.5) ( **It) 0,11* 41.44 ( *TR ) Nation 17 ( 3.2) 55 ( 280 ( 2.4) 4.1)1 28 ( 4.2) *44) Extreme rural State 28 ( 2.1) 50 ( 1.9) 22 ( 1.7) 202 ( 2.8) 280 ( 2.5) 266 ( 3.6) Nation 34 ( 2.8) 49 ( 2.2) 270 ( 3.9)1 252 ( 4.1)1 Other State 28 ( 2.3) 50 ( 2.3) 22 ( 1.8) 295 ( 2.2) 281 ( 2.0) 269 ( 2.9) Nation 27 ( 1.4) 4$ ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 250 ( 1.9) 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. 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). 138 THE 1990 NAEP TRIAL STATE ASSESSMENT North Dakota TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP MAL STATE ASSESSMENT Wan* Airs* AM* Undecided, Disagree, Strongly Disagree TOTAl, Percentage and Pre Odom Pireatille and Proficiency Peramenie and Prolkdency State 29 ( 14) 50 ( 14) 20 ( 1.1) 293 ( 1.5) 280 ( 1.5) 2S8 ( 22) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 2112 ( 1.7) 251 ( 14) PARENTS EDUCATION NS non-graduate State 16 ( 5.0) *41 54 ( 82) 29 7.5) Nation 50 ( 3.3) 30 ( 3.6) 243 ( 2.6) 238 ( 4.3) Id graduate State 26 ( 2.3) 51 ( 2.8) 23 ( 2.4) 284 ( 3.9) 273 ( 2.6) 200 ( 3.5) Nation 27 ( 2.1) 47 ( 2.3) 26 ( 2.0) 262 ( 2.7) 255 ( 2.3) 245 ( 2.4) Some college State 27 ( 2.5) 53 ( 2.9) 20 ( 2.4) 292 ( 2.3) 283 ( 2.3) 272 ( 4.3) Nation 28 ( 2.5) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 258 ( 32) Coi lege graduate State 34 ( 2.3) 50 ( 1.7) 17 ( 1.4) 300 ( 1.9) 285 ( 1.8) 277 ( 2.3) Nation 30 ( 2.3) 51 ( 1S) 19 ( 1.8) 280 ( 2.4) 274 ( 2.2) 206 ( 2.5) GENDER State 31 ( 1.9) 50 ( 1.9) 19 ( 1.5) 298 ( 2.2) 262 ( 1.5) 271 ( 2.6) Nation 28 ( 1.5) 48 ( 1.2) 24 ( 1.4) 273 ( 2.3) 283 ( 2.0) 251 ( 2.4) Femal State 28 ( 1.9) 50 ( 2.0) 22 ( 1.7) 289 ( 2.0) 278 ( 2.0) 265 ( 2.7) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 269 ( 2.1) 2EG ( 1.8) 252 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is muff-icier to permit a reliable estimate (fewer than 62 students). 144 THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and repotting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing Service (ETS), Westat, and National Computer Systems (NCS). The program benefitted from the contributions of hundreds of individuals at the state and local levels Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators who tirelessly provided their wisdom, experience, and hard work. Fmally, and most importantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Offirers (CCSSO) for its considerable contributions to the program, especially its management of the National Assessment Planning Project. That project resulted in the mathematics framework and objectives for the assessment and recommendations about reporting the results of the program. In particular, we note the significant contributions of Ramsay Selden, Director of the State Education Assessment Center for the CCSSO and the members of the Steering Mathematics Objectives, and Analysis and Reports Committees of the National Assessment Planning Project. The Trial State Assessment was funded through NCES, in the Office of Educational Research and Improvement of the US. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff alsodeserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people from school districts, colleges and universities, and State Education Agencies worked tirelessly to help ETS staff develop the assessment and a framework for interpreting the results. Under the NAEP contract to ETS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mazza, with consultation from Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffler, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zaback. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its charactesistics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koffier wrote the text for the report. Kent Ashworth was responale for coordinating thc 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 5 146