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DOCUMENT RESUME ED 330 551 SE 052 061 TITLE The State of Mathematics Achievement in Colorado: The Trial State Assessment at Grade Eight. INSTITUTION Educational Testing Service, Princeton, N.J.; National Assessment of Educational Progress, Princeton, NJ. SPONS AGENCY National Center for Education Statistics (ED), Washington, DC. REPORT NO ETS-21-ST-02; ISBN-0-88685-14-9 PUB DATE Jun 91 NOTE 146p.; The entire Report consists of a composite report, an executive summary, and 40 separate reports for 37 states, DC, Guam, and the Virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Juni,7r Hin Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualifications; Television Viewing IDENTIFIERS *Colorado; National Assessment of Educational Progress; *Numeracy; State Mathematics Assessments; Trial State Assessment (NAEP) ABSTRACT In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and probability; and algebra and functions). In Colorado, 2,576 students in 105 public schools were assessed. This report describes the mathematics proficiency of Colorado eighth-graders, compares their overall performance to students in the West region of the United States and the nation (using data from the MAE? national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, parents' educational level, and gender). To provide a context for '.he assessment data, participating students, their mathematics teachers, and primcipals 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, Colorado students_had an average proficiency of 267 compared to 261 nationwide. Many.fewer students (Colorado-14%; U.S.-I2%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics /Wee e e t in COLORADO The Trial State Assessment at Grade Eight 144)'rt7 tiPMI Ni AcliVLATI U 9 DEPARTMENT OF EOuCATIOW i. do- at.i-ma Nemparc ',Inc rrsrucmaornent ilE )0CATIONAL RI SOURCES iNfORMATION CE NTE R If RIC) Tr,s clocut.tont Play [pen reprodoced a% ,, e,,,,,e, tt or,, the person ,,f 0.gan,:aldr, 0,,,,pnat.rii ,r 1- iv.nor , nanyes nik.t. nee, ,,,ade IL, anprove ,Rtcr ok Lai tIon uua,,tt Porrts ot vrtor rod,ons slated .o th,s ddc "P' dC r,cd r,e( eSsa,,,r ^r.pce%Pni Ottit tat pds,tt,o, 0, polo v Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S RF,ORT CARD. the National Assessment of Educational Progress (NAEP), is the only nationally mpresentative and confirming assessment of what America's students know and can do in various subject umas. Since (969. assessments have been conducted pernxiically in reading. mathematics. science. writing. history/geography. and other fields. By making objeetive information on student performance available to policymakers at the national, state. and local NAEP is an integral part of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAM' guarantees the privacy of individual students and their families. NAEP is a congressionally mandated projeo cif the National Center for liducatitm Statistics. the U.S. Department of Edwation. The Commissioner of Education Statktics is responsible. by law. for carrying out the NAEP project through competitive awards to quahtled organitations. NAEP reports directly to the Commissioner. who is also responsible for providing continuing reviews. including vahdanon studies and solicitation of public comment. on NAEP's conduct and usefulness. In 198S. Congress created the National Assessment Governing Board (NAGBI to formulate policy guidelines for NAVY. The lxiard is respiinsible for selecting the subject areas to be assessed. which may mclude adding to those specified by Congress: idenufying appropriate achievement goals for each age and grade: developing assessment objectives; developing test specifications, designing the assessment methodology: developing guidehnes and standards for data analysis and for reporting and disseminating results; developing standards and procedures for interstate. regional, and national compansons, improving the form and use of the National Assessment: and ensuring that an 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 Directot Martha Holden knnings Eoundatitm Cleveland. Ohio Phyllis Williamson Aldrich Cunicutum Cmirdinator Saratoga-Warren BD.C.ES. Saratoga Springs. New York Francie Alexander Associate Superintendent California Department of Education Sacramenw. California David P. Battini High School History Teacher Cairo-Durham High School Cairo. New York Parris C. Battle Teacher Horace Mann Elementary School Miami. Florida Mary R. Blanton Attorney Cromwell. Porter. Blanton & Blanton Salisbury. North Carohna Boyd W. Boehije Attorney Gaass. Klyn. & Boehlie Pella, Iowa Linda R. Bryant Teacher rlieenway Middle School Teacher Center Pittsburgh. Pennsylvania Honorabk Mkhael N. Castle Governor of Delaware Camel State Office Budding Wilmingttm. De,laware Honorabk Naomi K. Cohen State or Conworcut House of Representatives Legislative Office Building if:afford. Connection Chester E. Finn. Jr. Professor of Education and PuNic Policy Vanderbilt Unisersity Washingum. D.C. Michael S. Glode Wytuning State Board of Educatnni Saratoga. Wyoming Christine Johnson Principal Abraham Lincoln High Schott! Denver. Colorado John Lindley Principal South Colby Elenwntary School Port Orchard. Washington .'arl J. Maser Dircoor of Schools The Lutheran Church -- Missour Synod International Center St. Linn.. Missouri Mark D. Musick President Southern Regional Education Board Atlimta. Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith, Arkansas Mstthew W. Prophet, Jr. Supenntendent Portland Oregon School District Pon land. Oregon Honorable William T. Randall Commissitmer of Education State Department of Education IN:nver. Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington. D.C. Honorabk Richard W. Riley Attorney Nelson. Mullins. Riley iind Scarborough Columbia. South Carolina Thomas Topuies Attorney Law Offices of Frank Rogoiamski Coronado. Califorma Herbert J. Walberg Professm of Education University of Illinois Chicago. Assistant Secrcuay tor Educational Research and Improvement (Ex-tHfieitti U.S. Depanment of- Education Washington. DC Roy Truhy Executive D:rc tot. NAGB Washington. D . NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Athievement in COLORADO The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD Report No. 21-ST-02 June 1991 Prepared by Educational Testing Service under Contract with the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education U.S. Department of Education Lamar Alexander Secretary Office of Educational Research and Improvement Bruno V. Manno Acting Assistant Secretary National Center for Education Statistics Emerson J. Elliott Acting Commissioner FOR MORE INFORMATION: Copies of the 1990 NAEF Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. For ordering information on the composite report of results for the Nation and all State participants, or for single copifu of the Executive Summary while supplies last, write: Education Information Branch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-4241616 (in the Washington, D.C. metii/politan drea call 202-219-1651) Library of Congress, Catalog Card Number: 91-61478 ISBN: G.88685-14-9 The work upon which this publication is based was performed for the NationalCenter for Education Statistics, Office of Educational Research and Improvement, by Educational Testing Service. Educational Testing Savice is an equal opponunity/affumative acsion employer. Educational Tegins Service, Ers, and are registered trademarks of Educational Testing Service. Table of Contents EXECUTIVE SUMMARY INTRODUCTION 7 Overview of the 1990 Trial State Assessment 8 This Report 9 Guidelines for Analysis 12 Profile of Colorado 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Colorado 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 11 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT III PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Arc Students Taught in Mathematics? 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Sununary 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 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 xi DATA APPENDIX 97 iv THE 2990 NAEP TRIAL STATE ASSESSMENT Colorado 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 as,cssments on a trial basis, in addition to continuing its primary mission, the national as,%isments that NAEP has conducted since its inception. As a result of the legislation, the 1990 NAFP progyam included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading. writing, and science were conducted simultaneoasly 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-gyade public-school population in a state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of 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 degyee of quality and uniformity across sessions. r THE 1990 NAEP TRIAL STATE ASSESSMENT 1 Colorado In Colorado, 105 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in Colorado. 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 9 percent had an Individualized Education Plan (IEP). An 1EP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and/or related services necesEary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in ekher case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an 1EP represented 1 percent and 4 percent of the population, respectively. In total, 2,675 eighth-grade Colorado public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligible eighth-grade public-school student population in Colorado. Students' Mathematics Performance Thc average proficiency of eighth-gade public-school students from Colorado on the NAEP mathematics scale is 267. This proficiency is higher than that of students across the nation (261). Average proficiency on the NALL/ 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, NAP P used the results from the 1990 national assessments of fourth-, eighth-, and twelfthgrade students to defme the skills, knowledge, and understandings that characterize four levels of mathematics performance -- levels 200, 250, 300, and 350 -- on the NAFP scale. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado In Colorado, 99 percent of t} e eighth gradeis, 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 Colorado (14 perant) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in Colorado performed higher than students in the nation in Measurement, Geometry, Data Analysis, Statistics, and Probability, and Algebra and Functions. Students in Colorado performed comparably to students in the nation in Numbers and Operations. Subpopulation Performance In addition to the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the Colorado eighth-grade student population defined by race, ethnicity, type of community, parents' education level, and gender. In Colorado: White students had higher average mathematics proficiency than did Black or Hispanic students. Further, a greater percentage of White students than Black or Hispanic students attained level 300. The results by type of community indicate that the average mathematics performance of the Colorado students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural areas, or areas classified as "other". In Colorado, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduawd from college was approximately 34 points higher than that of students whose parents did not graduate from high school. The results by gender show that eighth-grade males in Colorado had a higher average mathematics proficiency than did eighth-grade females in Colorado. In addition, there was no difference between the percentages of males and females in Colorado who attained level 300. Compared to the national results, females in Colorado performed higher than females across tie country; males ir Colorado performed higher than males across the country. AA/ THE 1990 NAEP TRIAL STATE ASSESSMENT 3 Colorado A Context for Understanding Students' Mathematics Proficiency Information en 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 Colorado are as follows: About half of the students in Colorado (45 percent) were in schools where mathematics was identified as a special prior4. This is a smaller percentage than that for the nation (63 percent). In Colorado, 82 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. About the same percentage of students in Colorado were taking eighth-grade mathematics (46 percent) as were taking a course in pre-algebra or algebra (50 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. According to their teachers, the greatest percentage of eighth-grade students in public schools in Colorado spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Across the netion, 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 and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 11 4 THE 1990 NAEP TRIAL STATE. ASSESSMENT Colorado In Colorado, 15 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 23 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Colorado, 18 percent of the students never used a calculator to work problems in class, while 49 percent almost always did. In Colorado, 50 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About half of the students (53 percent) had teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in Colorado 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-gade public-school students in Colorado (17 percent) watched one hour or less of television each day; 9 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 5 Colorado THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NALP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial St?..te Assessment was conducted in February 1990 with the following participalits: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas Louisiana Oregon California Maryland Pmnsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guam Indiana North Dakota Virgin Islands THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Colorado Tbis report describes the performance of the eighth-grade public-school students in Colorado and consists of ti ree 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 Colorado. Part One describes the mathematics performance of the eighth-grade public-school students in Colorado, the West region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Colorado, the West region, and the nation. Overview of the 1990 Trial State Assessment In 19S8, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survey instrument for the eighth grade cnd 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 representatiw data. (Section 406 (i)(2)(C)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(0.0 As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within eacn selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degee of quality and uniformity across sessions. 1,4 8 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and natterned 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 (NCLS). and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-grade public-school students in CA,lorado, in the West region, and for the nation. Results also are provided for groups of students defined by shared characteristics -- race ethnicity, type of community, parents' education level, and gender. Definitions of the subpopulations referred to in this report are presented below. The results for Colorado arc based only on the students included in the Trial State Assessment Program. However, ..he 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 v...:antary nature of the Trial State Assessment Program did not guarantee representative national or regional results, since not every stat.. participated in the program. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). TUE 1990 NAEP TRIAL STATE ASSESSMENT 1 9 Colorado 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 fullowing 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 Colorado. 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 i tetropolitan statistical areas, live in areas with a population below 10,000, and attend schools where many of the students' parents are farmers or farm workers. Other: Students in this category attend schools in areas other than those defined as advantaged urban, disadvantaged urban, or extreme rural. The reporting of results by each type of community was also subject to a minimum student sample size of 62. PARENTS' EDUCATION LEVEL Students were asked to indicate the extent of schooling for each of their parents -- did not finish high school, graduated high school, some education after high school, or graduated college. The response indicating the higher level of education was selected for reporting. 1. 10 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado GENDER Results are reported separately for males and females. REGION The United States has been divided into four regions: Northeast, Southeast, Central, and West. States included in each region are shown in Figure I. All 50 states and the District of Columbia are listed, with the participants in the Trial State Assessment highlighted in boldface type. Territories were not assigned to a region. Further, the part of Virginia that is included in the Washington, DC, metropolitan statistical area is included in the Northeast region; the remainder of the state is included in the Southeast region. Because most of the students are in the Southeast region, regional comparisons for Virginia will be to the Southeast. THE NATION'S REPORT CARD FIGURE 1 f Regions of the Country , NORTHEAST SOUTHEAST CENTRAL WEST _ Connecticut Alabama Illinois Alaska Delaware Arkansas Indiana Arizona District of Columbia Florida Iowa California Maine Georgia Kansas Colorado Maryland Kentucky Michigan Hawaii Massachusetts Louisiana Minnesota Idaho New Hampshire Mississippi Missouri Montana New Jersey North Carolina Nebraska Nevada New York South Carolina North Dakota New Mexico Pennsylvania Tennessee Ohio Oklahoma Rhode island Virginia South Dakota Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT 1 i II Colorado Guidelines for Analysis This report describes and compares the mathematics proficiency of various subpopulations of students -- for example, those who have certain demographic characteristics or who responded to a specific background question in a particular way. The report examines the results for individual subpopulations and individual background questions. It does not include an analysis of the relationships among combinations of these subpopulations or background questions. Because the proportions of students in these subpopulations and their average proficiency are based on samples -- rather than the entire population of eighth graders in public schools in the state or territory -- the numbers reported are necessarily estimates. As such, they are subject to a measure of uncertainty, reflected in the standard error of the estimate. When the proportions or average proficiency of certain subpopulations are compared, it is essential that the standard error be taken into account, rather than relying solely on observed similarities or differences. Therefore, the comparisons discussed in this report are based on statistical tests that consider both the magnitude of the difference between the means or proportions and the standard errors of those statistics. The statistical tests determine whether the evidence -- based on the data from the groups in the sample -- is strong enough to conclude that the means or proportions are really different for those 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 ma0tude of the difference between sample means or proponions -- 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 gioups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure are disc,-ssed in greater detail in the Procedural Appendix. 1c) 12 ME 1990 NAEP TRIAL STATE ASSESSMENT Colorado It is also important to note that the confidence intervals pictured in the figures in Part One of this report are approximate 95 percent confidence intervals about the mean of a particular population of interest. Comparing such confidence intervals for two populations is not equivalent to examining the 95 percent confidence interval for the difference between the means of the populations. If the individual confidence intervals for two populations do not overlap, it is true that there is a statistically significant difference between the populations. However, if the confidence intervals overlap, it is not always true that there is not a statistically significant difference between the populations. Finally, in several places in this report, results (mean proficiencies and proportions) are reported in the text for combined groups of students. For example, in the text, the percentage of students in the combined group taking either algebra or pre-algebra is 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 arc 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 a 1 the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). 1 07 THE 1990 NAEP TRIAL STATE ASSESSMENT 13 Colorado Profile of Colorado E1GHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in Colorado, the West region, and the nation. This profile is based on data collected from the students and schools participating in the Trial State Assessment. TABLE 1 I Profile of Colorado Eighth-Grade Public-School I Students PERCENTAGE OF STUDENTS _ 1990 NAEP TRIAL STATE ASSESSMENT Colorado West Nation ; DEMOGRAPHIC SUBGROUPS L Race/Ethnichy Percentage Percentage Percentage White 73 ( 1.3) 63 ( 1.9) 70 ( 0.5) Black 4 ( 1.0) ( 2.0) 16 ( 0.3) Hispanic 19 ( 1.6) 21 ( 1.5) 10 ( 0.4) Asian 2 ( 0.3) 4 ( 1.3) 2 ( 0.5) American Indian 2 ( 0.3) 4 ( 2.3) 2 ( 0.7) Type of Community Advantaged urban 29 ( 3.9) 14 ( 8.5) 10 ( 3.3) Disadvantaged urban 6 ( 2.4) 19 ( 7.5) 10 ( 2.8) Extreme rural 15 ( 3.0) 10 ( 3,8) 10 3.0) Other 50 ( 4.9) 58 (10.1) 70 ( 4.4) Parents' Education Did not finish high school 7 ( 0.7) 10 ( 1.3) 10 ( 0.8) Graduated high school 19 ( 0.9) 19 ( 2.5) 25 ( 1.2) Some education after high School 19 ( 0.9) 16 ( 1.2) 17 ( 0.9) Graduated college 47 ( 1.6) 42 ( 4.0) 39 ( 1.9) Gender Male 51 ( 1.0) 55 ( 2.1) 51 ( 1.1) Female 49 ( 1.0) 45( 2.1) 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 t 2 standard errors of the estimate for the sample, The percentages for Race Ethnicity may not add to 100 percent because some students categorized themselves as "Other." This may also be true of Parents' Education, for which some students responded "I don't know." Throughout this report, percentages less than 0.5 percent are reported as 0 percent. 14 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Colorado schools and students sampled for the 1990 Trial Statc. Assessment. In Colo-ado, 105 public schools participated in the assessment. The weighted school participation rate was 100 percent, which means that all of the eighth-grade students in this sample of schools were representative of 100 percent of the eighth-grade public-school students in Colorado. TABLE 2 I Profile of the Population Anessed in Colorado EIGHTH-GRADE PUBLIC SCHOOL PARTICIPATION Weighted school participation rate before substitution 100% 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 substitute schools participating Total number of participating schools 107 2 105 0 105 EIGHTH-GRADE PUBLIC-SCHOOL STUDENT PARTICIPATION Weighted student participation rate after make-ups 94% 3,177 Number of students Selected to participate in the assessment Number of students withdrawn trom the assessment 182 Percentage of students who were of Limited English Proficiency 1% Percentage of students excluded from the assessment due to Limited English Proficiency 1% Percentage of students who had an individualized Education Plan 9% Percentage of students excluded from the assessment due to Individualized Education Plan status Number of students to be assessed 2,843 Number of students assessed 2,675 4,0 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Colorado 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 9 percent had an Individualized Education Plan (IEP). An IEP is a plan, written for a student who has been determined to be eligible for special education, that typically sets forth goals and objectives for the student and describes a program of activities and,or related services necessary to achieve the goals and objectives. Schools were permitted to exclude certain students from the assessment. To be excluded from the assessment, a student had to be categorized as Limited English Proficient or had to have an Individualized Education Plan and (in either case) be judged incapable of participating in the assessment. The students who were excluded from the assessment because they were categorized as LEP or had an IEP represented 1 percent and 4 percent of the population, respectively. In total, 2,675 eighth-grade Colorado public-school students were assessed. The weighted student participation rate was 94 percent. This means that the sample of students who took part in the assessment was representative of 94 percent of the eligible eighth-grade public-school student population in Colorado. 24; 16 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Colorado Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAFP mathematics scale, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficiency of eighth-grade public-school students in Colorado. Chapter I compares the overall mathematics performance of the students in Colorado to students in the West region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 summarizes thc students' overall mathematics performance for subpopulations defined by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 17 Colorado CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from Colorado on the NAEP mathematics scale is 267. This proficiency is higher than that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School Mathematics Proficiency NAEP Mathematics Scale 0 200 225 250 275 300 500 CAM Average ProfIciency NI Colorado 267 ( 1.0) P.PO4 West 261 ( 2.6) 114 Nation 261 ( 1.4) Thc standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within .± standard crrors of the estimated mean (95 percent confidence interval, denoted by I-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of Interest. r IS TILE 1990 NAEP TRIAL STATE ASSESSMENT Colorado LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal the specifics of what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the 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 define the skills, knowledge, and understandings that characterize each proficiency level, mathematics specialists studied the questions that were typically answered correctly by most students at a particular level but answered incorrectly by a majority of students at the next lower level. They then summarized the kinds of abilities needed to answer each set of questions. While defining proficiency levels below 200 and above 350 is theoretically possible, so few students performed at the extreme ends of the scale that it was impractical to define meaningful levels of mathematics proficiency beyond the four presented here. Definitions of the four levels of mathematics proficiency are given in Figure 3. It is important to note that the definitions of these levels are based solely on student performance on the 1990 mathematics assessment. The levels are not judgmental standards of what ought to be achieved at a particular grade. Figure 4 provides the percentages of students at or above each of these proficiency levels. In Colorado, 99 percent of the eighth graders, compared to 97 percent in the nation, appear to have acquired skills involving simple additive reasoning and problem solving with whole numbers (level 200). However, many fewer students in Colorado (14 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 Colorado, West region, and national results for each content area. Students in Colorado performed higher than students in the nation in Measurement, Geometry, Data Ana lyfis, Statistics, and Probability, and Algebra and Functions. Students in Colorado performed comparably to students in the nation in Numbers and Operations. THE 1990 NAEP TRIAL STATE ASSESSMENT 19 Colorado FIGURE 3 1 Levels of Mathematics Proficiency LEVEL 200 Simple Additive Reasoning and Problem Solving with Whole Numbers Students at this level have some degree of understanding of simple quantitative relationships involving whole numbers. They can solve simple addition and Subtraction problems with and without regrouping. Using a calculator, they can extend theSe abilities to multiplication and division problems. These students can identify Solutions to one-step word problems and select the greatest four-digit number in a list. in measurement, these students can read a ruler as well as common weight and graduated Scales. They also can make volume comparisons based on visualization and determine the value of coins. In geometry, these students can recognize simple figures. In data analysis, they are able to read Simple bar graphs. In the algebra dimension, these students can recognize translations of word problems to numerical sentences and extend simple pattern sequences. LEVEL 250 Simple Multiplicative Reasoning and Two-Step Problem Solving Students at this level have extended their understanding of quantitative reasoning with whole numbers from additive to multiplicative settings. They can solve routine one-step multiplication and division problems involving remainders and two-step addition and subtraction problems involving money. Using a calculator, they can identify solutions to other elementary two-step word problems. In these basic problem-solving situations, they can identify missing or extraneous information and have some knowledge of when to use computational estimation. They have a rudimentary understanding of such concepts as whole number place value, "even," "factor," and "multiple." In measurement, these students can use a ruler to measure objects, convert units within a system when the conversions require multiplication, and recognize a numerical expression solving a measurement word problem. In geometry, they demonstrate an Initial understanding of basic terms and properties, such as parallelism and symmetry. In data analysis, they can complete a bar graph, sketch a circle graph, and use information from graphs to solve simple problems. They are beginning to understand the relationship between proportion and probability. In algebra, they are beginning to deal informally with a variable through numerical substitution in the evaluation of simple expressions. 20 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado FIGURE 3 Levels of Mathematics Proficiency (continued) 1 ME NATION'S REPORT CARD 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 frar.tions and decimals on number linos, simplify fractions, and recognize the equivalence between common fractions and decimals, including pictorial representations. They can interpret the meaning of percents less than and greater than 100 and apply the concepts of percentages to solve simple problems. These students demonstrate some evidence of using mathematical notation to interpret expressions, including those With exponents and negative integers. In measurement, these Students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the Solution to open linear sentences and inequalities by substitution, and checking and graphing an interval representing a compoune 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 transition between scientific notation and decimal notation. In measurement, they can apply their knowledge of area and perimeter of rectangles and triangles to Solve problems. They can find the circumferences of CirCAS and the surface areas of sr 'igures. In geometry, they can apply the Pythagorean theorem to solve problems involving indirec. .ileasurement. These students also can apply their knowledge of the properties of geometric figures to solve problems, such as determining the slope of a line. In data analysis, these students can compute means from frequency tables and determine the probability of a simple event In algebra, they can identify an equation describing a linear relation provided in a table and solve literal equations and a system of two linear equations. They are developing an understanding of linear functions and their graphs, as well as functional notation, including the composition of functions. They can determine the nth term of a sequence and give counterexamples to disprove an algebraic generalization. THE 1990 NAEP TRIAL STATE ASSESSMENT 21 Colorado FIGURE 4 I Levels of Eighth-Grade Public-School i Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation INIMP TN UPON'S CARD "1111P pamprall 1-10s1 Percentage 1-01 PIM 0 20 40 60 80 Amu& 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-+-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 22 THE 1990 NAEP TRIAL STATE ASSESSMENT 0 ( 0.0) 0 ( 0.4) o J.2) 14 ( 0.9) 12 ( 4) 12 ( 1.2) 72 ( 1.5) 63 ( 2.8) 64 ( 1.8) 99 ( 0.3) 97 ( 1 0) 97 ( 0.7) Colorado TIE NATION'S REPORT FIGURE 5 I Eighth-Grade Public-School Mathematics CARD I Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation NUMBERS APS OPERATIONS DATA ANALYSIS, STATISTICS, AND PROBABILITY ALGEBRA AND FUNCTIONS GEOMETRY .4 11 l'041 1..+""11 1.40111 1401 1004 401 04.4 P41 No. 1.406114 1=9". MEASUREMENT 0 200 225 250 275 300 Average Proficiency 269 ( 1.0) 264 ( 2.6) 268 ( 1.4) 265 ( 1.3) 258 ( 3.0) 258 ( 1.7) 266 ( 1.1) 260 ( 2.6) 259 ( 1.4) 269 ( 1.1) 262 ( 3.6) 262 ( 1.8) 266 ( 1.1) 259 ( 2.4) 260 ( 1.3) SOO 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 :t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-1). lf the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 4 :/' THE 1990 NAEP TRIAL STATE ASSESSMENT 23 Colorado 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/ETI-LNICITY The Trial State Assessment results can be compared according to the different raciat'ethnic goups 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, Black, and Hispanic students from Colorado are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black or Hispanic students. Figure 7 presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Black or Hispanic students attained level 300. 3 if 24 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado FIGURE 6 I Average Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity NAEP Mathematics Scale 0 200 225 250 275 300 500 Colorado WI wme re-1 Black Hispanic Proficiency ,11117 3.4)1 IN7 ( 1.5) We St White ( 3.2) Black W 41.9)1 Hispanic 2411 3.7) Nation White 21/0 14) te-4 Black 2.1) e-4-4 Hispanic hIS ( 2.1) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within ± 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 4-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. Si THE 1990 NAEP TRIAL STATE ASSESSMENT 25 Colorado DE NATION'S REPORT FIGURE 7 I Levels of Eighth-Grade Public-School CARD I Mathematics Proficiency by Race/Ethnicity LEVEL 300 State White Black Hispanic Region White Black Hispanic Nation White Black Hispanic LEVEL 250 State white Black Hispanic Region White Black Hispanic Nation White Black Hispanic LEVEL 200 State White Black Hispanic Region White Black Hispanic Nation White Black Hispanic fre-1 1.1.111OPPIMM1041 1/'41141 p4mosem.(1 P.1401 4 1111110mpowilmmi1 0 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by )-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level, f Interpret with caution -- the nature of the sample does not allow acurate determination of the variability of' this estimated mean proficiency. 100 3 4: 26 THE 1990 NAEP TRIAL STATE ASSESSMENT Percentage 18 ( 1.2) 1 ( 1.0)i 2 ( 0.8) 18 ( 3.2) 8 ( 5.0)1 3 ( 1.6) 16 ( 1.5) 2 ( 1.3) 3 ( 1.1) ( 1.3) 31 ( 7.0)1 48 ( 3.0) 74 ( 3.3) 44 (129)1 41 ( 5.4) 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) 100 ( 0,2) 95 ( 3.2)1 96 ( 1.1) 90 ( 0.8) 96 ( 3.0)1 93 ( 2.0) 99 ( 0.4) 89 ( 3.1) 93 ( 1.6) Colorado TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in advantaged urban areas, disadvantaged urban areas, extreme rural areas, and areas classified as "other". (These are the "type of community" groups in Colorado with student samples large enough to be reliably reported.) Theresults indicate that the average mathematics performance of the Colorado students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme rural areas, or areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community VIIMMIMIMI11.141=1=.11MINIMM., NAEP Mathematics Scal MEM Average sem 200 225 250 275 330 500 Proficiency 64 IP-01 Colorado Advantaged urban Disadvantaged urban Extreme rural Other no ( 1.7) 249 ( 4.4)1 20$ ( 2.6) 265 ( 1.7) West Advantaged urban 21M ( 3.1)! Disadvantaged urban 269 ( 5.8)I Extreme rural 263 ( 7.3)5 1-4-1 Other 250 ( le) Nation Advantaged urban 251 ( 3.8)1 t-+.01 Disadvantaged urban 249 ( 3.5)1 11-11 Extreme rural 265 ( 11-1 Other 251 ( 1.8) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidence interval, denoted by F4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. THE 1990 NAEP TRIAL STATE ASSESSMENT 27 Colorado FIGURE 9 LEVEL 300 Stat. Adv. urban ()--004 24 ( 1.8) Disadv. urban 3 ( 3.2)) Dot. rural p.........mil 10 ( 2.8) Other 11-4-4 12 ( 1.1) Region Adv. urban 1-..-.....,...pi 31 ( 3.1)1 Disadv. urban 11.....-4 9 ( 3.5)1 Ext. rural p. 4 8 ( 4.8)1 Other 1-4-11 10 ( 1.8) Nation Adv. urban 1.--1-m-No, ....4 28 ( 4.8)1 Disadv. urban 1---,-.4 7 ( 2.1)1 Ext. rural tii--.4 8 ( 2.3)1 Other 1..44 12 ( 1.2) LEVEL 250 Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community THE NATION'S REPORT CARD Percentage State Adv. urban SS ( 2.2) asadv. urban 47 ( 4.7)) Ext. rural Ipo.........4 73 ( 5.2) Other 5....mpl...4 70 ( 2.6) Region Adv. urban 83 ( 3.3)1 Disadv. urban I. I ! 57 ( 8.0)1 Ext. rural 52 (12.8)1 Other 52 ( 5.0) Nation Adv. urban 83 ( 4.6)1 Disadv. urban p........-.........,.....,...q 48 ( 5.0)1 Ext. rural o- 4 ( 8.2)1 Other I-4ft....4 94 ( 2.3) LEVEL 200 State Adv. urban 100 ( 0.2) Disadv. urban 97 ( 2.3)) Ext. rural Other 99 ( OS) Region Adv. urban 100 ( 0.0) Disadv. urban 96 ( 2.0)1 Ext. rural 98 ( 1.311 Other i. 98 ( 1.7) Nation Adv. urban 100 ( 0.0) Disadv. urban 1-4..4 95 ( 1.5)1 Ext. rural 97 ( 2.8)i Other P.I.4 97 ( 1.0) 0 20 40 60 BO 100 Percentage at or Above Proficiency Levels 'Plc 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 confidena interval, denoted by 544). 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 esumated mean proficiency. 3 4 28 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado 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 Colorado, the average mathematics proficiency of eighth-gade public-school students having at least one parent who graduated from college was approximately 34 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, a larger percentage of students in Colorado (47 percent) than in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 7 percent for Colorado and 10 percent for the nation. FIGURE 10 Average Eighth-Grade Public-School Mathematics Proficiency by Parents' Education 01114 NAEP Mathematics Scale 200 225 250 275 300 500 Average Proftchmcy Colorado P*1 HS non-graduate 243 ( 24) HS graduate 254 ( 1.4) F14 Some college 271 ( 1.2) 141 College graduate 277 ( 1.2) West HS non-graduate 246 ( 4.4) M-11 HS graduate 250 ( 2.2) Some college 21111 ( 3.0) 1-4-1 College graduate 233 ( 2.6) Nation HS non-graduate 283 ( 2.0) MI HS graduate 254 ( 1.5) 141 Some college 205 ( 1.7) College graduate 234 ( 1.6) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by/4-4), If the confidentx intervals for the populations do not overlap, there is a statistically significant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Colorado 11* MON% REPORT FIGURE 1 1 I Levels of Eighth-Grade Public-School CARD I Mathematics Proficiency by Parents' Education LEVEL 200 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 250 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. LEVEL 200 State HS non-grad. HS graduate Some college College grad. Region HS non-grad. HS graduate Some college College grad. Nation HS non-grad. HS graduate Some college College grad. 0-11*1 1-Pani iewinme 104E04 0,41,011.001.04 19.4 11-1004 1.11,04 111-11mon4 Iporrproirril pponwrof 11.=4 IIformose 0-404 treammoilIII P.41 Pel 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). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 2 ( 2.0) 4 ( 1.5) 14 ( 1.7) 21 ( 1.3) 2 ( 2.3) 2 ( 1.3) 15 ( 2.8) 21 ( 3.5) ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.9) 40 ( 4.7) 55 ( 2.8) 79 ( 2.0) 54 ( 1.7) 44 ( 6.8) 51 ( 4.4) 75 ( 4.1) 78 ( 3.6) 37 ( 4.6) 56 ( 2.7) 71 ( 2.6) 75 ( 2.0) 04 ( 1.3) 95 ( 0.8) 100 ( 0.2) 100 ( 0.2) 06 ( 3.2) 07 ( 1 .8) ea ( 0.7) ( 0.7) 96 ( 1.9) 07 ( 0.8) 00 ( 0.7) 00 ( 0.7) 100 3 0 30 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado GENDER As shown in Figure 12, eighth-grade males in Colorado had a higher average mathematics proficiency than did eighth-grade females in Colorado. Compared to the national results, females in Colorado performed higher than females across the country; males in Colorado performed higher than males across the country. FIGURE 12 I Average Eighth-Grade Public-School i Mathematics Proficiency by Gender 0 200 NAEP Mathematics Scale 225 250 275 300 SOO 116 WON CAN Average Proficiency NI Colorado Male INS ( 1.0) PM Female 285 ( 1.3) West Male 2.2 ( 3.5) 1-0,01 Female 21. ( 2.6) Nation 0+4 Male 282 ( 1.8) PM Female 260 ( 1.3) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 1-1-4). 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 Colorado who attained level 200. The percentage of females in Colorado who attained level 200 was similar to the percentage of females in the nation who attained level 200. However, the percentage of males in Colorado who attained level 200 was greater than the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASSESSMENT 31 Colorado 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 THE NATION'S REPORT Nam CARD 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within :! 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 1-4-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 ( 1.0) 13 ( 1.2) 13 ( 3.1) 11 ( 2.2) 14 ( 1.7) 10 ( 1.3) 73 ( 1.7) 71 ( 1.9) 65 ( 4.1) 61 ( 3.2) 64 ( 2.0) 64 ( 1.8) 99 ( 0.3) 98 ( 0.5) 97 1 1.2) 96 ( 1.0) 47 ( 0.9) ( 0.8) Colorado In addition, there was no difference between the percentages of males and females in Colorado who attained level 300. The percentage of females in Colorado who attained level 300 was similar to the percentage of females in the nation who attained leVel 300. Also, the percentage of males in Colorado who attained level 300 was similar to the percentage of males in the nation who attained level 300. CON'rENT AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. - LI 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Colorado TABLE 3 I Eighth-Grade Public-School Mathematics 1 Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measurement- Geometry Data Analysis, Statistics, and Probability ,,,,..,,... ..., 74;;;i0717 - TOTAL Proficiency Pnaficiency Proficiency Proficiency Proficiency State 269 ( 1.0) 265( 1.3) 266 ( 1.1) 269 ( 1.1) 266 ( 1.1) Region 264 ( 2.6) 258 ( 3.0) 280 ( 2.6) 2152 ( 3.6) 259 ( 24) Nation 266 ( 1.4) 258 ( 1.7) 259 ( 1.4) 262 ( 1.8) 260( 1.3) RACE/ETHNICITY White State 276 ( 1.0) 273 ( 1.4) 271 ( 1.2) 277 ( A) 273 ( 1.1) Region 271 ( 3.2) 267 ( 3.9) 267 ( 3.0) 272 ( 4.4) 267 ( 2.8) Nation 273 ( 1.6) 267 ( 2.0) 267 ( 1. 272 ( 1.8) 268 ( 1.4) Slack State 242 ( 3.8)1 229 ( 4.4)1 237 ( 3.6)1 237 ( 4.1)1 237 ( 3.9)1 Region 250 ( 6.8)1 240 (10.7)1 249 ( 5.7)1 244 ( 8.7)1 248 ( 7.4)1 Nation 244 ( 3.1) 227 ( 3.6) 234 ( 2.8) 231 ( 3.8) 237 ( 2.7) Hispanic State 249 ( 1.8) 243 ( 1.8) 250 ( 1.8) 247 ( 2.0) 242 ( 1.8) Region 248 ( 3.5) 239 ( 4.2) 245 ( 4.4) 240 ( 4.7) 243 ( 4.0) Nation 248 ( 2.7) 238 ( 3.4) 243 ( 3.2) 239 ( 3.4) 243 ( 3.1) TYPE OF COMMUNITY Advantaged urban State 281 ( 1.8) 278 ( 2.5) 278 ( 1.8) 281 ( 2.0) 278 ( 2.0) Region 284 ( 3.6)1 283 ( 2.7)1 279 ( 8.9)1 288 ( 4.1)1 279 ( 2.9)1 Nation 283 ( 3.2)1 281 ( 3.2)1 277 ( 5.2)1 285 ( 4.8)1 277 ( 4.8)1 Disadvantaged urban State 250 ( 4.8)1 245 ( 5.2)1 248 ( 4.6)1 248 ( 5.1)1 246 ( 4.6)1 Region 260 ( 5.4)1 250 ( 8.9)1 258 ( 4.5)1 255 ( 8.3)1 254 ( 4.6)1 Nation 255 ( 3.1)1 242 ( 4.9)1 248 ( 3.7)1 247 ( 4.6)1 247 ( 3.2)1 Extreme rural State 269 ( 2.4) 263 ( 2.9) 265 ( 3.0) 269 ( 3,4) 263 ( 3.1) Region 254 ( 8.6)1 254 ( 4.6)1 252 ( 9.4)1 253 ( 8.8)! 251 ( 8.5)1 Nation 258 ( 4.3)! 254 ( 4.2)1 253 ( 4.5)1 257 ( 5.0)1 256 ( 4.8)1 Other State 267 ( 1.7) 264 ( 2.0) 263 ( 1.7) 267 ( 2.0) 264 ( 16) Region 262 ( 3.5) 255 ( 4.2) 258 ( 3.4) 259 ( 4.2) 258 ( 3 5) Nation 266 ( 1.9) 257 ( 2.4) 259 ( 1.7) 261 ( 2.2) 261 ( 1.7) 'Die 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. U 34 THE 1990 NAEP TRIAL STATE ASSESSMENT tiorado TABLE 3 I Eighth-Grade Public-School Mathematics (continued) Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measurement Geometry Statistics, and Data Analysis, il Probabity Functions TOTAL Proficiency ikoficiency Proficiency Proficiency Proficiency State 269 ( 1.0) 265 ( 1.3) 260 ( 1.1) 26t? ( 1.1) 206 ( 1.1) Region 264 ( 2.6) 25$ ( 3.0) 260 ( 2.6) ( 3.0) 259 ( 2.4) Nation 266 ( 1.4) 25$ ( 1.7) 259 ( 1.4) 28; ( 1.8) 260 ( 1.3) PARENTS' EDUCATION NS non-graduate State 244 ( 3.4) 240 ( 3.6) 246 ( 2.2) 244 ( 3.4) 239 ( 2.9) Region 248 ( 42) 242 ( 62) 246 ( 4.9) 246 ( 6.2) 24$ ( 5.1) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 21) 240 ( 3.1) 242 ( 3.0) HS graduate State 257 ( 1.7) 250 ( 2.3) 254 ( 1.5) 256 ( 1.9) 253 ( 1.7) Region 254 ( 2$) 245 ( 3,0) 251 ( 3.6) 249 ( 32) 250 ( 2.4) Nation 259 ( 1.8) 246 ( 2.1) 252 ( 1.6) 253 ( 22) 253 ( 2.0) Some college State 274 ( 1.3) 270 ( 2.4) 268 ( 1.5) 274 ( 1.6) 269 ( 1.5) Region 272 ( 2.7) 268 ( 5.3) 264 ( 3.9) 271 ( 4.9) 264 ( 3.2) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 263 ( 2.2) College graduate State 279 ( 1.2) 276 ( 1.7) 275 ( 1.4) 280 ( 1.3) 276 ( 1.6) Region 275 ( 2.7) 271 ( 3.0) 271 ( 2.3) 278 ( 4.3) 272 ( 2.6) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 270 ( 2.2) 273 ( 1.7) GENDER Male State 271 ( 1,0) 269 ( 1,4) 268 ( 1.3) 271 ( 1.1) 2.8( 1.1) Region 284 ( 3,8) 263 ( 3$) 261 ( 3.4) 264 ( 4.1) 260 ( 3.3) Nation 286 ( 2.0) 262 ( 2.3) 260 ( 1.7) 262 ( 2.1) 260 ( 1.6) Female State 267 ( 1.3) 261 ( 1.6) 263 ( 1.5) 287 ( 1$) 266 ( 1.5) Region 263 ( 2$) 252 ( 2.9) 259 ( 2.9) 260 ( 4.0) 259 ( 2.8) Nation 266 ( 1.4) 253 ( 1.6) 258 ( 15) 281 ( 1.9) 260 ( 1.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, tlle value for the emir,: population is within ± 2 standard errors of the estimate for the rample. THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Colorado ME NATION'S REPORT CARO 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 a- 'ting policy when supplemented with contextual information about schools, teachers, t'idents. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information on student achievement. It is important to note that thc NAM' data cannot establish cause-and-effect links betwe.,..n various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. THE 1990 NAEP TRIAL STATE ASSESSMENT 44: 37 Colorado Through the questionnaires administered to students, teachers, and principals, NAEP is able to provide a broad picture of educational practices prevalent in American schools and classrooms. In many instances, however, these findings contradict our perceptions of what school is like or educational researchers' suggestions about what strategies work best to help students learn. For example, research has indicated new and more successful ways of teaching and learning, incorporating more hands-on activities and student-centered learning techniques; however, as described in Chapter 4, NAEP data indicate that classroom work is still dominated by textbooks or worksheets. Also, it is widely recognized that home environment has an enormous impact on future academic achievement. Yet, as shown in Chapters 3 and 7, large proportions of students report having spent much more time each day watching television than doing mathematics homework. Part Two consists of five chapters. Chapter 3 discusses instructional content and its relationship to students' mathematics proficiency. Chapter 4 focuses on instructional practices -- how instruction is delivered. Chapter 5 is devoted to calculator use. Chapter 6 provides information about teachers, and Chapter 7 examines students' home support for learning. 4 0 38 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado CHAPTER 3 What Are Students Taught in Mathematics? In response to the continuing swell of information about the poor mathematics achievement of American students, educators and policymakers have recommended widespread reforms that are changing the direction of mathematics education. Recent reports have called for fundamental revisions in curriculum, a reexamination of tracking practices, improved textbooks, better assessment, and an increase in the proportions of students in high-school mathematics programs.' This chapter focuses on curricular and instructional content issues in Colorado public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and staffing. Some of the salient results are as follows: About half of the eighth-grade students in Colorado (45 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 Nai,er- .1 Report on the Second International Mathematics Study (Champaign, IL: itipes Pubhshmg Company, 1987). 1.ynn Steen, Ld. Lverybody Counts A Report to the Nation on the Iuture cy Mathematics Education (Washington, DC: National Academy Press. 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 39 Colorado In Colorado, 82 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Many of the students in Colorado (84 percent) were taught mathematics by teachers who teach only one subject. More than half (66 percent) of the students in Colorado were typically taught mathematics in a class that was grouped by mathematics ability. Ability grouping was equally prevalent across the nation (63 percent). TABLE 4 I Mathematics Policies and Practices in Colorado 1 Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1900 NAP TRIAL STATE ASSESSMENT Colorado West Nation Percentage of eighth-grade students in public schools that identified mathematics as receiving special emphasis in school-wide goals and objectives, instruction, in-service training, etc. Percentage of eighth-grade public-school students who are offered a course in algebra for high school course placement or credit Percentage of eighth-grade students in public schools who are taught by teachers who teach only mathematics Percentage of eighth-grade students in public schools who are assigned to a mathematics class by their ability in mathematics Percentage of eighth-grade students in public schools who receive four or more hours of mathematics instruction per week Percentage Percentage Percentage 45 ( 3.9) 61 ( 8.6) 63 ( 5.9) 82 ( 3.3) 92 ( 4.7) 78 ( 4.6) 84 ( 3.3) 98 ( 1.8) Si ( 3.3) 66 ( 2.9) 64 ( 8.3) 63 ( 4.0) 23 ( 2.9) 25 ( 5.9) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 t.tandard errors of the estimate for the sample. e` 4 0 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in Colorado are taking mathematics courses. Based on their responses, shown in Table 5: About the same percentage of students in Colorado were taking eighth-grade mathematics (46 percent) as were taking a course in pre-algebra or algebra (50 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in Colorado who were enrolled in pre-algebra or algebra courses exhibited higher average mathematics proficiency than did those who were in eighth-grade mathematics courses. This result is not unexpected since it is assumed that students enrolled in pre-algebra and algebra courses may be the more able students who have already mastered the general eighth-grade mathematics curriculum. TABLE 5 I Students' Reports on the Mathematics Class They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Colorado West Nation What kind of mathematics class are you taking this year, Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Eighth-grade mathematics 46 ( 2.5) 63 ( 2.7) 62 ( 2.1) 255 ( 1.4) 252 ( 2.4) 251 ( 1.4) Pro-algebra 32 ( 2.1) 15 ( 2.7) 19 ( 1.9) 270 ( 1.2) 266 ( 3.6) 272 ( 2.4) Algebra 18 ( 1.1) 17 ( 1.8) 15 ( 12) 295 ( 2.0) 299 ( 4.5) 296 ( 2.4) The standard errors of thu 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 thc estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Colorado Further, from Table A5 in the Data Appendix:4 About the same percentage of females (51 percent) and males (49 percent) in Colorado were enrolled in pre-algebra or algebra courses. In Colorado, 53 percent of White students, 53 percent of Black students, and 38 percent of Hispanic students were enrolled in pre-algebra or algebra courses. Similarly, 63 percent of students attending schools in advantaged urban areas, 60 percent in schools in disadvantaged urban areas, 36 percent in schools in extreme rural areas, and 45 percent in schools in areas classified as "other" were enrolled in pre-algebra or algebra courses. MATHEMATICS HOMEWORK To illuminate the relationship between homework and proficiency in mathematics, the assessed students and their teachers were asked to report the amount of time the students spent on mathematics homework each day. Tables 6 and 7 report the teachers' and students' responses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in Colorado spent either 15 or 30 minutes doing mathematics homework each day; according to the students, the greatest percentage spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, according to their teachers, the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported spending either 15 or 30 minutes daily. Further, as reported by their teachers (Table 6 and Table A6 in the Data Appendix): In Colorado, 1 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 3 percent of the students in Colorado 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 mrresponding table presenting the results for the four subpopulations -- race ethnicity, type of community, parents' education level, arid gender. 42 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado The results by race/ethnicity show that 4 percent of White students, 2 percent of Black students, and 2 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 1 percent of White students, 6 percent of Black students, and 2 percent of Hispanic students spent no time doing mathematics homework. In addition, 4 percent of students attending schools in advantaged urban areas, 7 percent in schools in disadvantaged urban areas, 5 percent in schools in extreme rural areas, and 3 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 1 percent of students attending schools in advantaged urban areas, 0 percent in schools in disadvantaged urban areas, 2 percent in schools in extreme rural areas, and 1 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT I Colorado 1 West Nation Percentage and Proficiency Permits** and Proficiency Paramtage and Profidency [About how much time do students spend 1 on mathematics homework each day? 1 None 1 ( 0.5) 1 ( 0.3) 1 ( 0.3) 15 minutes 40 ( 3.5) 42 ( 6.7) 43 ( 4.2) 281 ( 1.8) 258 ( 4.2) 256 ( 2.3) 30 minutes 45 ( 3.3) 43 ( 6.2) 43 ( 4.3) 267 ( 1.6) 264 ( 4.7) 266 ( 2.6) 45 minutes 10 ( 1.8) 9 ( 2.3) 10 ( 1.9) 288 ( 3.3) 270 ( 6.5)1 272 ( 5.7)1 An hour or more 3 ( 1.1) 4 ( 0.9) 286 ( 6.1)1 278 ( 5.1)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within t 2 standard errors of the estimate for the sample. l 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 THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Colorado 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 MO NAEP TRIAL STATE ASSESSMENT Colorado West Nation 1 About how much time do you usually spend each day on mathematics t homework? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency None 9 ( 0.8) 12 ( 1.7) 9 ( 0.8) 265 ( 2.8) 254 ( 4.2) 251 ( 2.8) 15 minutes 28 ( 1.1) 31 ( 4.5) 31 ( 2.0) 269 ( 1.3) 263 ( 3.8) 264 ( 1.9) 30 minutes 31 ( 0.9) 28 ( 1.7) 32 ( 12) 268 ( 1.3) 261 ( 2.9) 263 ( 1.9) 46 minutes 16 ( 0.9) 15 ( 1.6) 16 ( 1.0) 267 ( 1.7) 267 ( 4.2) 266 ( 1.9) An hour or more 16 ( 1.1) 14 ( 1.7) 12 ( 1.1) 266 ( 1.9) 261 ( 4.3) 258 ( 3.1) WIMMI1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within r 2 standard errors of the estimate for the sample. And, according to the students (Table 7 and Table A7 in the Data Appendix): In Colorado, 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, 16 percent of the students in Colorado 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 15 percent of White students, 23 percent of Black students, and 18 percent of Hispanic students spent an hour or more on mathematics homework each day. In comparison, 9 percent of White students, 4 percent of Black students, and 11 percent of Hispanic students spent no time doing mathematics homework. 4t; 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado In addition, 14 percent of students attending schools in advantaged urban areas, 15 percent in schools in disadvantaged urban areas, 17 percent in schools in extreme rural areas, and 17 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 5 percent of students attending schools in advantaged urban areas, 6 percent in schools in disadvantaged urban areas, 15 percent in schools in extreme rural areas, and 10 percent in schools in areas classified as "other" spent no time doing mathematics homework. ENSTRUCTIONAL EMPHASIS According to the approach of the National Council of Teachers of Mathematics (NCTM), students should be taught a broad range of mathematics topics, including number concepts, computation, estimation, functions, algebra, statistics, probability, geometry, and measurement. Because the Trial State Assessment questions were designed to measure students' knowledge, skills, and understandings in these various content areas -- regardless of the type of mathematics class in which they were enrolled -- the teachers of the assessed students were asked a series of questions about the emphasis they planned to give specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn the various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent, Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. 5 \ ati on al Council of Teachers of Mathematics. Curriculum and Evaluation Standar& for School Mathematics (Reston, VA: !National Council of Teachers of Mathematics, 1989). THE 1990 NAEP TRIAL STATE ASSESSMENT 45 Colorado 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 piovides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instnictional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 46 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Colorado West Nation Percentage End Proficiency Percentage and Proficiency Penantage and Proficiency Teacher -emphasts" categones by content areas Numbers and Operations Heavy emphasis 37 ( 3.0) 42 ( 7.4) 49 ( 3.8) 262 ( 1.7) 257 ( 3.6) 260 ( 1i) Little or no emphasis 14 ( 1.8) 13 ( 2.1) 15 ( 2.1) 288 ( 3.7) 291 ( 6.6) 287 ( 3.4) Meastrement Heavy emphasis 7 ( 1.2) 11 ( 2.8) 17 ( 3.0) 259 ( 4,5) 251 ( 7.7)1 250 ( 5.6) Little or no emphasis 43 ( 3.5) 36 ( 5.3) 33 ( 4.0) 272 ( 2.4) 275 ( 6.3) 272 ( 4.0) Geometry Heavy emphasis 20 ( 3.1) 24 ( 6.3) 28 ( 3.8) 269 ( 2.4) 260 ( 2.8)1 260 ( 3.2) Little or no emphasis 31 ( 2.8) 16 ( 4.5) 21 ( 3.3) 263 ( 1.9) 277 (11.4)1 294 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 15 ( 2.0) 14 ( 3.7) 14 ( 2.2) 271 ( 2.8) 264 (10.6)1 269 ( 4.3) Little or no emphasis 63 ( 3.5) 54 ( 6.3) 53 ( 4.4) 270 ( 1.5) 262 ( 4.9) 261 ( 2.9) Algebra and Functions Heavy emphasis 51 ( 3.5) 43 ( 5.6) 46 ( 3.6) 276 ( 1.7) 277 ( 5.2) 275 ( 2,5) Little or no emphasis 14 ( 2.6) 23 ( 5.1) 20 ( 3.0) 242 ( 3.5) 243 ( 4.2)1 243 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Interest, the value for the enure population is within t 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 4. THE 1990 NAEP TRIAL STATE ASSESSMENT 47 Colorado SUMMARY Although many types of mathematics learning can take place outside of the school environment, there are some topic areas that students are unlikely to study unless they are covered in school. Thus, what students are taught in school becomes an important determinant of their achievement. The information on curriculum coverage, mathematics homework, and instructional emphasis has revealed the following: About half of the eighth-grade students in Colorado (45 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Colorado, 82 percent of the students could take an algebra course in eighth grade for high-school course placement or credit. About the same percentage of students in Colorado were taking eighth-grade mathematics (46 percent) as were taking a course in pre-algebra or algebra (50 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. According to their teachers, the greatest percentage of eighth-grade students in public schools in Colorado spent either 15 or 30 minutes doing mathematics homework each day; according to the students, most of them spent either 15 or 30 minutes doing mathematics homework each day. Across the nation, teachers reported that the largest percentage of students spent either 15 or 30 minutes doing mathematics homework each day, while students reported either 15 or 30 minutes daily. In Colorado, 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, 16 percent of the students in Colorado and 12 percent of students in the nation spent an hour or more each day on mathematics homework. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 5 0 48 THE 1990 NAEi TRIAL STATE ASSESSMENT Colorado CHAPTER 4 1111111111111BIIIII II 1111181111111M11 11111811i8MOIIII 11811111111111111111111 I11111.1111111111riall 11111111111111111111Th MUNN :..111/.11111 .751111111111,4111 1 %IMMO .1111NOMJUsge IIIIME11181111M1111 ,1111112111O111116 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 learnine activities in their mathematics classrooms. AVA1LAB1LIIN OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. ° National Council of Teachers of Mathematics, Profeccinnal Standards for the Tewhing cu Mathernatks (Reston, VA: NatIonal Council of Teachers of Mathematics. )991). THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Colorado From Table 9 and Table A9 in the Data Appendix: In Colorado, 15 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 23 percent of the students were taught by teachers who got only some or none of the resources they needed. Across the nation, these figures were 13 percent and 31 perctnt, respectively. In Colorado, 10 percent of students attending schools in advantaged urban areas, 19 percent in schools in disadvantaged urban areas, 26 percent in schools in extreme rural areas, and 15 percent in schools in areas classified as "other" had mathematics teachers who got all the resources they needed. By comparison, in Colorado, 18 percent of students attending schools in advantaged urban areas, 27 percent in schools in disadvantaged urban areas, 17 percent in schools in extreme rural areas, and 29 percent in schools in areas classified as "other" were in classrooms where only some or no resources were available. Students whose teachers got all the resources they needed had 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 _ IWO NAEP TRIAL STATE ASSESSMENT Colorado West Net Ion Which of the following statements is true about how well supplied you are by your Porcontap Percentage Percentage school system with the instructional and and and materials and other resources you need to teach your class, get all the resources I need. Proficiency 15 C 2.4) Proficiency 15 ( 5.2) PrOficiency 13 ( 2.4) 266 ( 2.8) 281 ( 5.9)1 265 ( 4.2) I get most of the resources I ni 61 ( 3.6) 62 ( 3,8) 56 ( 4.0) 268 ( 1,4) 266 1 4.1) 265 ( 2.0) I get some or nonr- of the resowcos I mod. 23 ( 3.2) 23 ( 6.1) 31 ( 4.2) 263 ( 2.5) 257 ( 3.7) 1 261 ( 2,9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that. for each population of interest, the value for the entire population is within ± 2 standard errors of tin estimate for the sample. ! interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 50 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado PATTERNS IN CLASSROOM INSTRUCTION Research in education and cognitive psychology has yieldtxl many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers; More than half of the students in Colorado (69 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics problems in small groups (6 percent). The largest percentage of the students (57 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; relatively few never used such objects (9 percent). In Colorado, 59 percent of the students were assilmed problems from a mathematics textbook almost every day; 10 percent worked textbook problems about once a week or less. Less than half of the students (40 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (31 percent). Thomas Romberg, "A Common Curriculum for Mathematics," Individual Differences and the Common Curriculum Eighty-second Yearbook of the National' Society for the Snia), of Education (Chicago, University of Chicago Press, 1983). THE 1990 NAEP TRIAL STATE ASSESSMENT 51 Colorado TABLE 10 I Teachers' Reports on Patterns of Mathematics I Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT Colorado West Nation Percentage and Pro Money Percentage and Proficiency Percentage and Proadency About how often do students work problems in small groups? At least once a week 69 ( 3.0) 57 ( 8.9) ( 4.4) 266 ( 1.4) 262 ( 4.2)t 230 ( 22) Less than once a week 25 ( 2.9) 39 ( 7.6) 43 ( 4.1) 26.5 ( 23) 266 ( 4.5) 264 ( 2.3) Never 6 ( 1.6) 3 ( 2.2) 8 ( 2.0) 276 ( 4.5)1 "" ( 4") 277 ( 5.4)1 About how often do students use objects Percentage Percentage Percentage like rulers, counting blocks, or geometric and and ar solids? Proficiency Proficiency Proficiency At least wee a week 34 ( 2.9) 34 ( 8.2) 22 ( 3.7) 264 ( 2.0) 256 ( 4.9)1 254 ( 32) Less than once a week 57 ( 2.7) 57 ( 6.4) 69 ( 3.9) 267 ( 1.3) 265 ( 4.0) 263 ( 1.9) Never 9 ( 1.6) 276 ( 3.5) 8 ( 3.0). 9 ( 2.6) 282 ( 5.9)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r - J 52 1 HE 1990 NAEP 'MAL STATE ASSESSMENT Colorado TABLE Ii Teachers' Reports on Materials for i Mathematics instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19110 NAEP TRIAL STATE ASSESSMENT Colorado West Nation _ Percentage Percentage Percentage About how often do students do problems and and and from textbooks? Proficiency ProNcieney Proficiency Almost every dey 59 ( 3.6) 55 ( 6.0) 62 ( 3.4) 271 ( 1.2) 270 ( 3.3) 267 ( 1.8) Several times a week 31 ( 2.7) 36 ( 5.1) 31 ( 3.1) 263 ( 2,1) 256 ( 52) 254 ( 2.9) About once a week or less 10 ( 2.4) 9 ( 4.9) ( 1.8) 253 ( 3.2)1 260 ( 5.1)1 About how often do students do problems on worksheets? Percentage and Percentage and Percentage and Proficiency Proliciemy Proficiency Al least several times a week 40 ( 3.6) 25 ( 5.2) 34 ( 3.8) 259 ( 1.8) 258 ( 4.3)1 256 ( 2.3) About once a week 29 ( 2.7) 34 ( 4.6) 33 ( 3.4) 270 ( 2.2) 258 ( 4.1) 260 ( 2.3) Less than weekly 31 ( 3.3) 41 ( 5.6) 32 ( 3.6) 274 ( 2.3) 274 ( 4 2) 274 ( 2:7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ' Sample size is insufficient to permit a reliable 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 Colorado COLLABORATING IN SMALL GROUPS In Colorado, 32 percent of the students reported never working mathematics problems in small groups (see Table 12); 38 percent of the students worked mathematics problems in small groups at least once a week. TABLE 12 I Students' Repots on the Frequency of Small i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL STATE ASSESSMENT Colorado West Nation Percentage and Proficiency Percentage and Proficiency Percentage and Pre& Ism How often cla you work in small groups in your mathematics class? At least once a week 38 ( 2.3) 35 ( 4.8) 28 ( 2.5) 266 ( 1.5) 258 ( 4.2) 258 ( 2.7) Less than once a week 30 ( 1.4) 29 ( 2.8) 28 ( 1.4) 270 ( 1.6) 271 ( 3,1) 267 ( 2.0) Never 32 ( 2,1) 36 ( 4.8) 44 2.9) 265 ( 1.6) 258 ( 2.0) 261 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. Examining the subpopulations (Table Al2 in the Data Appendix): In Colorado, 40 percent of students attending schools in advantaged urban areas, 47 percent in schools in disadvantaged urban areas, 28 percent in schools in extreme rural areas, and 41 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 38 percent of White students, 43 percent of Black students, and 38 percent of Hispanic students worked mathematics problems in small groups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (39 percent and 37 percent, respectively). rJ 54 THE 1990 NAEP TRIAL STATE ASSFSSMENT Colorado USING MATHEMATICAL OBJECTS Students were asked to report on the frequency with which they used mathematical objects such as rulers, counting blocks, or geometric solids. Table 13 below and Table A 13 in the Data Appendix summarize these data: Less than half of the students in Colorado (43 percent) never used mathematical objects; 26 percent used these objects at least once a week. Mathematical objects were used at least once a week by 34 percent of students attending schools in advantaged urban areas, 33 percent in schools in disadvantaged urban areas, 35 percent in schools in extreme rural areas, and 19 percent in schools in areas classified as "other". Males were as likely as females to use mathematical objects in their mathematics classes at least once a week (28 percent and 23 percent, respectively). In addition, 25 percent of White students, 31 percent of Black students, and 26 percent of Hispanic students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Colorado west Nation I How often do you work with objects like rulers, counting blocks, or geometric solids in your mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency At least once a week 26 ( 1.9) 36 ( 3.5) 28 ( 1.8) 264 ( 1.7) 260 ( 4.0) 258 ( 2.6) Less than once a week 32 ( 12) 28 ( 1.8) 31 ( 1.2) 271 ( 1.3) 269 ( 2.7) 269 ( 1.5) Never 43 ( 1.9) 36 ( 3.3) 41 ( 2.2) 266 ( 1.4) 256 ( 2.8) 259 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent ivrtainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ctJ THE 1990 NAEP TRIAL STATE ASSESSMENT 55 Colorado MATERIALS FOR MATHEMATICS INSTRUCTION The percentages of eighth-grade public-school students in Colorado who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table A14 in the Data Appendix): About three-quarters of the students in Colorado (73 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of the students in the nation. Textbooks were used almost every day by 77 percent of students attending schools in advantaged urban areas, 64 percent in schools in disadvantaged urban areas, 74 percent in schools in extreme rural areas, and 74 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 MI NAEP TRIAL STATE ASSESSMENT Catered* West Nation How often do you do maMematics problems from textbooks in your mathematics class? Percentage and Proficiency Percentage and Pretty:fancy Percentage and Proficiency Almost evefy day 73 ( 2.1) 71 ( 3.5) 74 ( 1.9) 272 ( 1.0) 267 ( 2.4) 267 ( 1.2) Several times a week 15 ( 1.0) 15 ( 1.5) 14 ( 0.8) 256 ( 1.9) 251 ( 2.4) 252 ( 1.7) About once a week or less 12 ( 1.6) 14 ( 3.1) 12 ( 1.8) 250 ( 2.2) 242 (11.2)1 242 ( 4.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the vample. ! Interpret with caution -- the nature of the sample does not allow accurate determinauon of the variability of this estimated mean proficiency. 56 THE 1990 NAP FRIAL STATE ASSESSMENT Colorado And, for the frequency of worksheet usage (Table 15 and Table A I S in the Data Appendix): Less than half of the students in Colorado (36 percent) used worksheets at least several times a week, compared to 38 percent in the natiqn. Worksheets were used at least several times a week by 39 percent of students attending schools in advantaged urban areas, 40 percent in schools in disadvantaged urban areas, 26 percent in schools in extreme rural areas, and 34 percent in schools in areas classified as "other". TABLE 15 I Students' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1960 NAEP TRIAL STATE ASSESSMENT Colorado West Nation How often do you do Mathematics problems on worksheets in your Mathematics class? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency At least several times a week 36 ( 2.3) 35 ( 4.0) 38 ( 2.4) 259 ( 1.5) 250 ( 4,2) 253 ( 2.2) About once a week 28 ( 1.4) 23 ( 2.6) 25 ( 1.2) 270 ( 1.3) 262 ( 2.1) 261 ( 1.4) Lass than weekly 37 ( 2.2) 41 ( 4.1) 37 ( 2.5) 274 ( 1.3) 27') ( 3.4) 272 ( 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 stan errors of the estimate for the sample. Table 16 compares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. , THE 1990 NAEP TRIAL STATE ASSESSMENT 57 Colorado TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1900 PIMP TRIAL STATE ASSESSMENT Colorado West Nation Patterns of classroom instruction Percentage Students Teachers Percustage Students Teachers Percentage Students Teachers Percentage of students who work mathematics problems In small groups At least once a week 38 ( 2.3) 69 ( 3.0) 35 ( 4.8) 57 ( 8.9) 28 ( 2.5) 50 ( 4.4) Less than once a week 30 ( 1.4) 25 ( 2.9) 29 ( 2.8) 39 ( 7.6) 28 ( 1.4) 43 ( 4.1) Never 32 ( 2.1) 6 ( 1.6) 36 ( 4.8) 3 ( 2.2) 44 ( 2.9) 8 ( 2.0) Percentage of students who use objects like rulers, count blocks, or geometric solids At least once a week 26 ( 1.9) 34 ( 2.9) 36 ( 3.5) 34 ( 82) 28 ( 1.8) 22 ( 3.7) Less than once a week 32 ( 12) 57 ( 2.7) 28 ( 1.8) 57 ( 6.4) 31 ( 1.2) 69 ( 3.9) Never 43 ( 1.9) 9 ( 1.6) 36 ( 3.3) 8 ( 3.0) 41 ( 22) 9 ( 2.6) , Materials for mathematics 1 Percentage Percentage Percentage instruction Students Teachers Students Teachers Students Teachers L. Percentage of students who use a mathematics textbook Almost every day 73 ( 2.1) 59 ( 3.6) 71 ( 3.5) 55 ( 6.0) 74 ( 1.9) 62 ( 3.4) Several times a week 15 ( 1.0) 31 ( 2.7) 15 ( 1.5) 36 ( 5.1) 14 ( 0.8) 31 ( 3.1) About once a week or less 12 ( 1.6) 10 ( 2.4) 14 ( 3.1) 9 ( 4.9) 12 ( 1.8) 7 ( 1.8) Percentage of students who use a mathematics worksheet At least several times a week 36 ( 2.3) 40 ( 3.6) 35 ( 4.0) 25 ( 5.2) 38 ( 2.4) 34 ( 3.8) About onCe a week 28 ( 1.4) 29 ( 2.7) 23 ( 2.6) 34 ( 4.6) 25 ( 1.2) 33 ( 3.4) Less than weekly 37 ( 2.2) 31 ( 3.3) 41 ( 4.1) 41 ( 5.6) 37 ( 2.5) 32 ( 3.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within :t. 2 standard errors of the estimate for the sample. 6 58 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado SUMMARY Because classroom instructional time is typically limited, teachers need to make the best possible use of what is known about effective instructional delivery practices and resources. It appears that mathematics textbooks and worksheets continue to play a major role in mataematics 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: More than half of the students in Colorado (69 percent) worked mathematics problems in small groups at least once a week; relatively few never worked in small goups (6 percent). The largest percentage of the students (57 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and relatively few never used such objects (9 percent). In Colorado, 59 percent of the students were assigned problems from a mathematics textbook almost every day; 10 percent worked textbook problems about once a week or less. Less than half of the students (40 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (31 percent). And, according to the students: In Colorado, 32 percent of the students never worked mathematics problems in small groups; 38 percent of the students worked mathematics problems in small groups at least once a week. Less than half of the students in Colorado (43 percent) never used mathematical objects; 26 percent used these objects at least once a week. About three-quarters of the students in Colorado (73 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 Colorado (36 percent) Lsed worksheets at least several times a wPck, compared to 38 percent in the nation. 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Colorado CHAPTER 5 How Are Calculators Used? Although computation skills are vital, calculators -- and, to a lesser extent, computers have drastically changed the methods that can be used to perform calculations. Calculators are important tools for mathematics and students need to be able to use them wisely. The National Council of Teachers of Mathematics and many other educators believe that mathematics teachers should help students become proficient in the use of calculators to free them from time-consuming computations and to permit them to focus on more challenging tasks.' The increasiniavailability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. 8 National Assessment of Educational ProgressWathentatics 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 I eachers of Mathematics, 1989). ru 60 THE 1990 N 4,EP TRIAL STATE ASSESSMENT Colorado Table 17 provides a profile of Coloradi eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 45 percent of the students in Colorado had teachers who allowed calculators to be used for tests. A greater percentage of students in Colorado than in the nation had teachers who permitted unrestricted use of calculators (30 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of Colorado Policies on i Calculator Use PERCENTAGE OF STUDENTS 11/S0 NAEP TRIAL. STATE ASSESSMENT Colorado West Nation Percentage of eghth-grade students in puChc schools whose teachers permit the unrestricted use of calculators Percentage of eighth-grade students in public schools whose teachers permit the use of calculators tor tests Percentage of eighth-grade students in public schools whose teachers report that students have access to calcsiators owned by the school Percentage Percentage Paraintage 30 ( 2.9) 20 ( 4.9) 18 ( 3.4) 45 ( 2.9) 48 ( 8.8) 33 ( 4.5) 62 ( 4.0) 72 ( 7.4) 56 ( 4.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within / 2 standard errors of the estimate for the sample. 6 u- THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Colorado THE AVAILABILITY OF CALCULATORS In Colorado, most students or their families (98 percent) owned calculators (Table 18); however, fewer students (52 percent) had teachers who explained the use of calculators to them. From Table A 18 in the Data Appendix: In Colorado, 51 percent of White students, 58 percent of Black students, and 55 percent of Hispanic students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (50 percent and 54 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Colorado West Nation Percentage and Proficiency 98 ( 0.3) 268 ( 1.0) 2 ( 0.3) Percentage and Proficiency Percentage and Proficiency 96 ( 0.6) 263 ( 2.6) 4 ( 0.6) Percentage and Proficiency Percentage and Proficiency 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( 3.8) Percentage and Proficiency Do you or your family own a Calculator? I Yes No Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes 52 ( 2.0) 59 ( 3.4) 49 ( 2.3) 263 ( 1.2) 260 ( 2.7) 258 ( 1.7) No 48 ( 2.0) 41 ( 3.4) Si ( 2.3) 272 ( 1.4) 265 ( 3.0) 266 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that. for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 62 6 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado 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, stu .s were asked how frequently (never, sometimes, almost always) they used cakuiaLors for working problems in class, doing problems at home, and taking quizzes or tests. As reported in Table 19: In Colorado, 18 percent of the students never used a calculator to work problems in class, while 49 percent almost always did. Some of the students (13 percent) never used a calculator to work problems at home, compared to 33 percent who almost always used one. Ak^.ut one-quarter of the students (29 percent) never used a calculator to take quizzes or tests, while 24 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL. STATE ASSESSMENT Colorado West Nation . _ Now often do you use a calculator for the , following tasks? Percentage and Proficiency Percentage and Proficiency Percentage and Prolidency, Working problems in class Almost always 49 ( 1.4) 53 ( 2.1) 48 ( 14) 262 ( 1.2) 255 ( 2.6) 254 ( 1.5) Never 18 ( 1.3) 14 ( 2.4) 23 ( 1.9) 277 ( 1.7) 265 ( 3.0) 272 ( 1.4) Doing problems at holm Almost always 33 ( 1.4) 29 ( 1.7) 30 ( 1.3) 269 ( 1.3) 263 ( 3.3) 261 ( 1.8) Never 13 ( 0.9) 19 ( 1.6) 19 ( 0.9) 270 ( 2.1) 258 ( 3.7) 263 1.8) Taking Wu*: or tests Almost always 24 ( 1.3) 25 ( 1.6) 27 ( 1.4) 263 ( 2.1) 259 ( 3.9) 253 ( 2.4) Never 29 ( 1.5) 22 ( 3.0) 30 ( 2.0) 277 ( 1.3) 270 ( 3.3) 274 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population or interest, the value for the entire population is skithin I 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. THE 1990 NAEP TRIAL STATE ASSESSMENT 63 Colorado WHEN TO USE A CALCULATOR Part of the Trial State Assessment was designed to investigate whether students know when the use of a calculator is helpful and when it is not. There were seven sections of mathematics questions in the assessment; however, each student took only three of those sections. For two of the seven sections, students were given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested tbe 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 tilc 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 v tio 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 calcteator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 64 THE 1990 NAEP TRIAL STATE ASSESSMENT 4a Colorado The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: About the same percentage of students in Colorado were in the High group as were in the Other group. A smaller percentage of males than females were in the High group. In addition, 51 percent of White students, 50 percent of Black students, and 43 percent of Hispanic students were in the High group. TABLE 20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Colorado Wost Nation -Calculator-use" group Parcantage and Proadancy Parcentaga and Prnedancy Parcentaga and Profkloncy High 49 ( 1.1) 38 ( 2.8) 42 ( 1,3) 274 ( 1.2) 273 ( 2.7) 272 ( 1.6) Other 51(1.1) 62 ( 2.6) 58 ( 13) 261 ( 1.3) 253 ( 2.8) 255 ( 14) The standard errors of the estimated statistics appear in parentheses. It. can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within ±. 2 standard errors of the estimate 4'or the sample. 1 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 Colorado SUAMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of instructional time to teaching students how to perform routine calculations by hand. Using calculators to replace this time-consuming process would create more instructional time for other mathematical skill topics, such as problem solving, to be emphasized. The data related to calculators and their use show that: In comparison to 33 percent across the nation, 45 percent of the students in Colorado had teachers who allowed calculators to be used for tests. A greater percentage of students in Colorado than in the nation had teachers who permitted unrestricted use of calculators (30 percent and 18 percent, respectively). In Colorado, most students or their families (98 percent) owned calculators; however, fewer students (52 percent) had teachers who explained the use of calculators to them. In Colorado, 18 percent of the students neva used a calculator to work problems in class, while 49 percent almost always did. Some of the students (13 percent) never used a calculator to work problems at home, compared to 33 percent who almost always used one. About one-quarter of the students (29 percent) never used a calculator to take quizzes or tests, while 24 percent almost always did. 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado 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 Colorado, 50 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About half of the students (53 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states, About three-quarters of the students (79 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 I eachers of Mathematics, Professional Standards for the Teaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). i THE 1990 NAEP TRIAL STATE ASSESSMENT 67 Colorado TABLE 21 1 Profile of Eighth-Grade Public-School Mathematics Teachers PERCENTAGE OF STUDENTS 1990 NAEP TRIAL STATE ASSESSMENT Colorado West Nation Percentage of students whose mathematics teachers reported having the following degrees Percentage Percentage Percentage Bachelor's degree SO ( 3.3) 68 ( 52) 56 ( 4.2) Master's or specialist's degree 49 ( 3.4) 32 ( 52) 42 ( 42) Doctorate or professional degree 1 ( 0.7) 0 ( 0.0) 2 ( 1.4) Percentage of students whose mathematics teachers have Me following types of teaching certificates that are roc:prized by Colorado No regular certification 6 ( 1.7) 6 ( 2.4) 4 ( 1.2) Regular certification but less than the highest available 41 ( 2.9) 20 ( 3.3) 29 ( 4.3) Highest certification available (permanent or long-term) 53 ( 3.4) 74 ( 3.3) 66 ( 4.3) Percentage of students whose mathematics teachers have the following types of teaching certificates that are recognized by Colorado Mathematics (middle school or secondary) 79 ( 2.5) 88 ( 3.0) 84 ( 2.2) Education (elementary or middle school) 17 ( 1.9) 9 ( 2.8) 12 ( 2.6) Other 4 ( 1.6) 2 ( 1.3) 4 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Interest, the value for the entire population is within i 2 standard errors of the estimate for the sample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. 68 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado Teachers' responses to questions concerning their undergraduate and graduate fields of study (Table 22) show that: In Colorado, 57 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergxaduate 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 st adents in Colorado (20 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. TABLE 22 I Teachers' Reports on Their Undergraduate and i Graduate Fields of Study PERCENTAGE OF STUDENTS WOO NAEP TRIAL. STATE ASSESSMENT Colorado West Nation , What was your undergraduate major? Percentage Percentage Percentage Mathematics 57 ( 2.9) 31 ( 5.9) 43 ( 3.9) Education 27 ( 2.4) 34 ( 6.6) 35 ( 3.8) Other r 16 ( 2.4) 35 ( 8.6) 22 ( 3.3) What was your graduate major, Percentage Percentage Percentage Mathematics 20 ( 3.0) 19 ( 4.7) 22 ( 3.4) Education 35 ( 3.4) 38 ( 4,5) 38 ( 3$) Other or no graduate level study 45 ( 3.1) 45 ( 5.4) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within :t 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 69 Colorado Teachers' responses to questions concerning their in-serviee training for the year up to the Trial State Assessment (Table 23) show that: In Colorado, 37 percent of the eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teaching of mathematics. Across the nation, 39 percent of the students had teachers who spent at least that much time on similar types of in-service training. Some of the students in Colorado (14 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. TABLE 23 I Teachers' Reports on Their In-Service Training PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT Colorado West Nation , During the last year, how much time in total have you spent on in-service education in mathematics or the teaching of mathematics? Nona One to 15 hours 18 hours or more Percentage Percentage Percentage 14 ( 2.1) 11 ( 3.0) 11 ( 2.1) 49 ( 3.3) 45( 7.0) Si ( 4.1) 37 ( 3.3) 44 ( 6.9) 39 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado SUMMARY Recent results from international studies have shown that students from the United States do not compare favorably with students from other nations in mathematics and science achievement." Further, results from NAEP assessments have indicated that students' achievement in mathematics and science is much lower than educators and the public would like it to be." In curriculum areas requiring special attention and improvement, such as mathematics, it is particularly important to have well-qualified teachers. When performance differences across states and territories are described, variations in teacher qualifications and practices may point to areas worth further exploration. There is no guarantee that individuals with a specific set of credentials will be effective teachers; however, it is likely that relevant training and experience do contribute to better teaching. The information about teachers' educational backgrounds and experience reveals that: In Colorado, 50 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44. percent for students across the nation. About half of the students (53 percent) had mathematics teachers who had the highest level of teaching certification available. This is different from the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In Colorado, 57 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 Colorado (20 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. '° Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Differences An international Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). 11 Ina V.S. Mullis, John A. Dossey, Eugene H Owen, and Gary W. Phillips, The State of Mathematics Achievement NAEP's MO Assessment of the Nation and the Thal Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 71 Colorado In Colorado, 37 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 simihn types of in-service training. Some of the students in Colorado (14 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of the students had mathematics teachers who spent no time on similar in-service training. 72 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado 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 Colorado 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 Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Colorado West Nation .. Does your family have, or receive on a i regular basis, any of the following items: more than 25 books, an encyclopedia, newspapers, magazines? Zero to two types Three types Four types Percentage Normally Percentage and and and Proficiency Proficiency Proficiency 15 ( 0.7) 24 ( 1.6) 21 ( 1.0) 250 ( 1.7) 245 ( 4.1) 244 ( 2.0) 32 ( 0.8) 31 ( 1.4) 30 ( 1.0) 264 ( 1.2) 258 ( 2.4) 258 ( 1.7) 53 ( 1.0) 45 ( 1.9) 4.8 ( 1.3) 274 ( 1.1) 273 ( 3.2) 272 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. The data for Colorado reveal that: Students in Colorado 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 Colorado A smaller percentage of Black and Hispanic students had all four types of these reading materials in their homes than did White students. A greater percentage of students attending schools in advantaged urban areas than in disadvantaged urban areas, extreme rural areas, or 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 se as detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Colorado West Nation _ How much television do you usually watch each day? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency One how or Ins 17 ( 0.8) 14 ( 1.8) 12 ( 0.8) 276 ( 1.7) 269 ( 3.6) 269 ( 22) Two hours 25 ( 0.9) 20 ( 1.6) 21 ( 0.9) 273 ( 1.4) 265 ( 3.6) 268 ( 1.8) Three hours 24 ( 0.7) 20 ( 12) 22 ( 0.8) 267 ( 1.3) 202 ( 32) 265 ( 1.7) Four to five hours 25 ( 0.9) 29 ( 1.7) 23 ( 1.1) 262 ( 1.4) 263 ( 2.9) 260 ( 1.7) Six hours or more 0 ( 0.7) 16 ( 2.0) 16 ( 1.0) 249 ( 2.2) 246 ( 2.6) 245 ( 1.7) AD The standard errors of the estimated statistics appear in parentheses. It can be said wah 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 1990 NAEP TRIAL STATE ASSESSMENT 75 Colorado From Table 25 and Table A25 in the Data Appendix: In Colorado, 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 Colorado (17 percent) watched one hour or less of television each day; 9 percent watched six hours or more. A greater percentage of males than females tended to watch six or more hours of television daily. However, a smaller percentage of males than females watched one hour or less per day. In addition, 7 percent of White students, 24 percent of Black students, and 12 percent of Hispanic students watched six hours or more of television each day. In comparison, 19 percent of White students, 11 percent of Black students, and 14 percent of Hispanic 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 Colorado, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in Colorado (40 percent) did not miss any school days in the month prior to the assessment, while 25 percent missed three days or more. In addition, 22 percent of White students, 27 percent of Black students, and 33 percent of Hispanic students missed three or more days of school. 6 I 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado Similarly, 22 percent of students attending schools in advantaged urban areas, 35 percent in schools in disadvantaged urban areas, 15 percent in schools in extreme rural areas, and 27 percent in schools in areas classified as "other" missed three or more days of school. TABLE 26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL t '.. AI '. ,119ESSILIENT Colorado West Nation 1 How many days of school did you miss last month? Percentage and Prolidoncy Percentage and Proficiency Percentage and Proficiency None 40 ( 0.9) 43 ( 2.7) 45 ( 1.1) 272 ( 1.1) 266 ( 3.5) 265 ( 1.8) One or two days 35 ( 1.0) 30 ( 1.4) 32 ( 0.9) 269 ( 1.3) 265 ( 3.0) 266 ( 1.5) Three days or more 25 ( 0.9) 27 ( 1.8) 23 ( 1.1) 258 ( 14) 250 ( 3.1) 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 Colorado STUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require studens not only to master essential skills and concepts but also fo develop confidence in their mathematical abilities and to value mathematics as a discipline. 1 2 Students were asked if they agreed or disagreed with five statements designed to elicit their perceptions of mathematics. These included statements about: Personal experience with mathematics, including students' enjoyment of mathematics and level of confidence in their mathematics abilities: like mathematics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevar.x to future work and life requirements: Almost all people use mathematics in their jobs; mathematics is not more for boys than for girls. The nature of mathematics, including students' ability to identify the salient features of the discipline: Mathematics is useful for solving everyday problems. A student "perception index" was developed to examine students' perceptions of and attitudes toward mathematics. For each of the five statements, students who responded "strongt. agree" were given a value of 1 (indicating very positive attitudes about the subject;, those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's responses were averaged over the five statements. The students were then assigned a perception index according to whether they tended to strongly agree with the statements (an index of I), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the statements (an index of 3). Table 27 provides the data for the students' attitudes toward mathemaiics as defined by their perception index. The following results were observed for Colorado: Averar mathematics proficiency was highest for students who were in the "strongly avec" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. About one-quarter of the students (27 percent) NV ere in the "strongly agree" category (perception index of I). This compares to 27 percent aeross the nation. About one-quarter of the students in Colorado (23 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. 0 it'ulum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mauiematics. 1989), s 78 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE 27 f Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1910 NAEP TRIAL STATE ASSESSMENT Colorado West Nation _ Student "perception index" groups Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Strongly agree 27 ( 1.0) 27 ( 1.9) 27 ( 1.3) ("perception index" of 1) 277 ( 12) 273 ( 3.9) 271 ( 1.9) Agree 50 ( 1.0) 48 ( 1$) 49 ( 1.0) ("perception index" of 2) 268 ( 1.1) 262 ( 2.4) 262 ( 1.7) Undecided, disagree, strongly disagree 23 ( 0.8) 25 ( 2.1) 24 ( 1.2) ("perception index" of 3) 255 ( 1.5) 249 ( 2.9) 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 t 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 Colorado who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. b THE 1990 NAEP TRIAL STATE ASSESSMENT 79 Colorado Some of the eighth-grade public-school students in Colorado (17 percent) watched one hour or less of television each day; 9 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. Less than half of the students in Colorado (40 percent) did not miss any school days in the month prior to the assessment, while 25 percent missed three days or more. Average mathematics proficiency was lowest for students who missed three or more days of school. About one-quarter of the students (27 percent) were in the "strongly agree" category relating to students' perceptions of mathematics. Average mathematics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. b 80 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado 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 assess.nent were developed through a consensus process managed by the Council of Chief State School Officers, and the items were developed through a similar process managed by Educational Testing Service. The development of the Trial State Assessment Program benefitted from the involvement of hundreds of representatives from State Education Agencies who attended numerous NETWORK meetings, served on committees, reviewed the framework, objectives, and questions, and, in general, provided important suggestions on all aspects of the program. Assessment Design The 1990 Trial State Assessment was based on a focused balanced incomplete block (BIB) spiral matrix design -- a design that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The first step in impIenunting the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. THE 1990 NAEP TRIAL STATE ASSESSMENT 81 Colorado The blocks were then assembled into assessment booklets so that each booklet contained two background questionnaires -- the first consisting of general background questions and the second consisting of mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minutes to complete the three 15-minute blocks of mathematics items. Thus, the entire assessment required approximately 55 minutes of student time. In accordance with the BIB design, the blocks were assigned to the assessment booklets so that each block appeared in exactly three booklets and each block appeared with every other block in one booklet. Seven assessment booklets were used in the Trial State Assessment Program. The booklets were spiraled or interleaved in a systematic sequence so that each booklet appeared an appropriate number of times in the sample. The students within an assessment session were assigned booklets in the order in which the booklets were spiraled. Thus, students in any given session received a variety of different booklets and only a small number of students in the session received the same booklet. Assessment Content The framework and objectives for the Trial State Assessment Program were developed using a broad-based consensus process, as described in the introduction to this report.' The assessment framework consisted of two dimensions: mathematical content areas and abilities. The five content areas assessed were Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions (see Figure A I). The three mathematical ability areas assessed were Conceptual Undei standing, Procedural Knowledge, and Problem Solving (see Figure A2). Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (IRT) was used to estimate average mathematics proficiency for each jurisdiction and for various subpopulations, based on students' performance on the set of mathematics items they received. IRT provides a common scale on which performance can be reported for the nation, each jurisdiction, and subpopulations, even when all students do not answer the same set of questions. This common scale makes it possible to report on relationships between students' characteristics (based on their responses to the background questions) and the;r overall performance in the assessment. National Assessment of Educational Progress, Mathematks Objectives 1990 Assessment (Princeton, NJ: Educational Testing Service, 1988). 82 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado FIGURE Al I Content Areas Assessed TIE NATION'S REPORT CARO 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, time, money, temperature, nass/weight, area, volume, capacity, and angles are also included in this content area. Geometry This content area focuses on students' knowledge of geometric figureS and relationships and on their skills in working with this knowledge. These skills are important at all levels of Schooling as well as in practical applications. Students need to be able to model and visualize geometric figures in one, two, and three dimensions and to communicate geometric ideas. In addition, students should be able to use informal reasoning to establish geometric relationships. IData Analysis, Statistics, and Probability This content area focuses on data representation and analysis across all disciplines and reflects the importance and prevalence of these activities in our society. Statistical knowledge and the ability to interpret data are necessary skills in the contemporary world. Questions emphasize appropriate methods for gathering data, the visual exploration of data, and the development and evaluation of arguments based on data analysis. Algebra and Functions This content area is broad in scope, covering algebraic and functional concepts in more informal, exploratory ways for the eighth-grade Trial State Assessment. Proficiency in this concept area requires both manipulative facility and conceptual understanding: it involves the ability to use algebra as a means of representation and algebraic processing as a problem-solving tool. Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descriptions, tables of values, and graphs. THE 1990 NAEP TRIAL STATE ASSESSMENT 83 Colorado FIGURE A2 I Mathematical Abilities The following three categories of mathematical abilities are not to be const d as hierarchical. For example, problem solving involves interactions between conceptual knowledge and procedural skills, but what is Considered complex problem salving at one grade level may be considered conceptual understanding or procedural knowledge at another. Conceptual Understanding Students demonstrate conceptual understanding in mathematicS whtin 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 proOedures correctly, verify and justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors inherent in problem settings. Procedural knowledge includes the various numerical algorithms in Mathematics that have been created as tools to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncomputational skills Such as rounding and ordering. Problem Solving In problem solving, students are required to use their reasoning and analyticabilwes when they encounter new situations: Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, data, models, and relevant mathematics: generate, extend, and modify procedures: use reasoning (Le., spatial. inductive, deductive, statistical, and proportional): and judge the reasonableness and correctness of solutions. 84 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado A scale ranging from 0 to 500 was created to report performance for each content area. Each content-area scale was based on the distribution of student performance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. ln contrast, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 0-to-500 scale. Although proficiency levels below 200 and above 350 could theoretically have been defined, they were not because so few students performed at the extreme ends of the scale. Any attempts to define levels at the extremes would thettfore have been highly speculative. To define perfon ,ance at each of the four levels on the scale, NAEP analyzed sets of mathematics item, from the 1990 assessment that discriminated well between adjacent levels. The criteria for selecting these "benchmark" items were as follows: To defme perfbrmance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To define performance at each of the higher levels on the scale, items were chosen that were: a) answered correctly by at least 65 percent of students whose proficiency was at or near that level; and b) answered incorrectly by a majority (at least 50 percent) of the students performing at or near the next lower level. The percentage of students at a level who answered the item correctly had to be at least 30 points higher than the percentage of students at the next lower level who answered it correctly. THE 1990 NAEP TRIAL STATE ASSESSMENT 85 Colorado Once these empirically selected sets of questions had been identified, mathematics educators analyzed the questions and used their expert judgment to characterize the knowledge, skills, and understandings of students performing at each level. Each of the four proficiency levels was defined by describing the types of mathematics questions that most students attaining that proficiency level would be able to perform successfully. Figure 3 in Chapter 1 provides a summary of the levels and their characteristic skills. Example questions for each level are provided in Figure A3, together with data on the estimated proportion of students at or above each of the four proficiency levels who correctly answered each question.' 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 out&ide of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared through an iterative process that involved extensive development, field testing, and review by external advisory groups. MATHEMATICS TEACHER QUESTIONNAIRE The questionnaire for eighth-grade mathematics teachers consisted of two parts. The first requested information about the teacher, such as race/ethnicity and gender, as well as academic degrees held, teaching certification, training in mathematics, and ability to get instructional resources. In the second part, teachers were asked to provide information on each class they taught that included one or more students who participated in the Trial State Assessment Program. The information included, among other things, the amount of time spent on mathematics instruction and homework, the extent to which textbooks or worksheets were used, the instructional emphasis placed on different mathematical topics, and the use of various instructional approaches. Because of the nature of the sampling for the Trial State Assessment, the responses to the mathematics teacher questionnaire do not necessarily represent all eighth-grade mathematics teachers in a state or territory. Rather, they represent the teachers of the particular students being assessed. 2 Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 91 86 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado FIGURE A3 I Example Items for Mathematics Proficiency Levels ..11.1111 Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 Teams Iniss Golf lab 0 Robber gala 7. Linda had Aso laras boas. aLl elia lama also sad sham &limns kinds of balk as shows Aosta U she fills mob hos with she bad of balls shown whacks boa will Ism tha kwass belle la Se CD no has wish Sha man balk OD Tlut boa wish ast sal balls CID Tha baa wish she NM., hallo CII6 Toss can's adt. EXAMPLE 2 1100.1C0 OF MIT PK= AT FARAWAY FARM Drps Or110 Isloa 081.4= Onipsforn C. How many kiss of mays woe packed os Tbussdayr CD 65 CD 60 CO 70 CD SO CD 90 a) don't know. THE 1990 NAEP TRIAL STATE ASSESSMENT Grads 4 Overall Percentage Correct: 73% Percentage Correct for Anchor Levels: 2912 222 es 91 loo Grade 4 Overall Percentage Cv,t,,- 80% Percentage Correct for Anchor Levels: ZISI 22Q aN 75 91 100 Grade 8 Overall Percentage Correct: 89% Percentage Correct for Anchor Levels: a§g 222 78 87 96 87 Colorado FIGURE 4 3 I Example Items for Mathematics Proficiency Levels (continued) 1 Level 250: Simple Multiplicative Reasoning and Two-Step Problem Solving I EXAMPLE 1 7. What is thc value of a + 5 when n 3 Answes: EXAMPLE 2 34.437t MCI RIMY WILTS Psseensiat. cur trot Stows Twit The tat* Om Aetna* multi el a stsres7 a Mix coke. O tbt draft kbw. make a arcie ;mph to illustrate Ike dau du sable. Label escb pan ol ase ellsbe wag lira she matt bale as*. D4 yOu use the calculate/ an this ovesticiai O Yes 0 No EXAMPLE 3 6. Kasklexa is mama basebells into boxes. Each box holds 6 baseballs She has 24 Wis. Whicb number 'menet will help bes find out bow many boxes she will nee& CD 24 6 El cp 24 + 6 0 OD 24 6 0 CID 24 6 0 OP I don't know. 88 Grad* 8 Overall Percentag Percentage Correct at42 211/ 23 69 Grade 8 Overall Percentage Percentage Correct acc raQ 21 68 Correct 76% for Anchor Levels: 222 11Q es vs Correct 73% for Anchor Levels: &22 92 92 Grade 8 Overall Percentage Percentage Correct g2Q 37 71 9 Correct 77% for Anchor Levels: 95 100 ME 1990 NAE1' TRIAL STATE ASSESSMENT Colorado FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 300: Reasoning and Problem SoMng involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE 1 ICI. Which ot the following shows the leak Isf flipping the above t ranee over the line 2 t w EXAMPLE 2 In the needel sew, that class it bending. a car IS ken Mfg represented e nate mawk) 3 inches long. J be ewe sale a via, a bouts 33 fess high weuid he repreettneeei by e sae model Iowans, niches Ugh/ Dti you nu the cekisktet on thie guestinsit O Yee O No Grade 8 Overall Percentage Correct: 60% Percentage Correct for Mchor Levels: ZQQ ZffQ ZSIQ 222 33 49 77 90 Grade 12 Overall Percentage Correct: 75% Percentage Correct for Anchor Levels: 222 Z§D Ng 46 79 95 Grade 8 Overall Percentage Correct: 59% Percentage Correct for Anchor Levels: ni/ gffgi agg 17 46 86 99 Colorado FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) Level 350: Reasoning and Problem Solving Involving Geometric Relationships, Algebraic Equations, and Beginning Statistics and Probability EXAMPLE 1 10. Questives 16-17 reia the roam. paltem ot Joe t,pres a I 2 a 16. 11 Ow pattem of dot (Awes 11 continued bow many dou welt Iv in the 100-1 ("sure CS) luO tai 101 0199 OD 200 CD 201 EXAMPLE 2 17. I splaan bow you found your answer co question 16 Annwm Grade 8 Overall Percentage Correct 34% Percentage Correct for Anchor Levels: 222 /IQ 13 19 53 88 Grade 12 Overall Percentage Correct 49% Percentage Correct for Anchor Levels: ng aQ2 222 22 48 90 Grade 8 Overall Percentage Correct; 15% Percentage Correct for Anchor Levels: 204 ZEI NQ 1 4 28 74 Grade 12 Overall Percentage Correct: 27% Percentage Correct for Anchor Levels: a5g a§i/ 3 22 74 5 0- 90 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado SCHOOL CHARACTERISTICS AND POLICIES QUESTIONNAIRE An extensive school questionnaire was completed by principals or other administrators in the schools participating in the Trial State Assessment. In addition to questions about the individuals who completed the questionnaires, there were questions about school policies, course offerings, and special priority areas, among other topics. It is important to note that in this report, as in all NAEP reports, the student is always the unit of analysis, even when information from the teacher or school questionnaire is being reported. Having the student as the unit of analysis makes it possible to describe the instruction received by representative samples of eighth-grade students in public schools. Although this approach may provide a different perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEll's goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or territory. If a different representative sample of students were selected and the assessment repeated, it is likely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school studtnt in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAEP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like almost all estimates based on assessment measures, NAFP's total group and subgroup proficiency estimates are subject to a second source lf uncertainty, in addition to sampling error. As previously noted, each student who participated in the Trial State Assessment was administered a subset of questions from the to al 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 ofuncertainty arises because each student was administered a subset of the total pool of questions. J 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 Colorado In addition to reporting estimates of average proficiencies, proportions of students at or above particular scale-score levels, and proportions of students giving various responses to background questions, this report also provides estimates of the magnitude of the uncertainty associated with these statistics. These measures of the uncertainty are called standard errors and are given in parentheses in each of the tables in the report. The standard errors of the estimates of mathematics proficiency statistics reflect both sources of uncertainty discussed above. The standard errors of the other statistics (such as the proportion of students answering a background question in a certain way or the proportion of students in certain racial/ethnic groups) reflect only sampling error. NAEP uses a methodology called the jackknife procedure to estimate these standard errors. Drawing Inferences from the Results One of the goals of the Trial State Assessment Program is to make inferences about the overall population of eighth-grade students in public schools in each participating state and territory based on the particular sample of students assessed. One uses the results from the sample -- taking into account the uncertainty associated with all samples -- to make inferences about the population. The use of confidence intervals, based on the standard errors, provides a way to make inferences about the population means and proportions in a manner that reflects the uncertainty associated with the sample estimates. An estimated sample mean proficiency ± 2 standard errors represents a 95 percent confidence interval for the corresponding population quantity. This means that with approximately 95 percent certainty, the average performance of the entire population of interest (e.g., all eighth-grade students in public schools in a state or territory) is within ± 2 standard errors of the sample mean. As an example, suppose that the average mathematics proficiency of the students in a particular state's sample were 256 with a standard error of 1.2. A 95 percent confidence interval for the population quantity would be as follows: Mean ± 2 standard errors = 256 ± 2 (1.2) = 256 ± 2.4 = 256 - 2.4 and 256 + 2.4 = 253.6, 258.4 Thus, one can conclude with 95 percent certainty that the average proficiency for the entire population of eighth-grade students in public schools in that state is between 25:3.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small ( less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. 92 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado Analyzing Subgroup Differences in Proficiencies and Proportions In addition to the overall results, this report presents outcomes separately for a variety of important subgroups. Many of these subgroups are defmed by shared characteristics of students, such as their gender, race/ethnicity, and the type of community in which their school is located. Other subgroups are defined by students' responses to background questions such as About how much time do you usually spend each day on mathematics homework? Still other subgroups are defmed by the responses of the assessed students' mathematics teachers to questions in the mathematics teacher questionnaire. As an example, one might be interested in answering the question: Do students who reported spending 45 minutes or more doing mathematics homework each day exhibit higher average mathematics proficiency than students who reported spending 15 minutes or less? To answer the question posed above, one begins by comparing the average mathematics proficiency for the two groups being analyzed. If the mean for the group who reported spending 45 minutes or more on mathematics homework is higher, one may be tempted to conclude that that group does have higher achievement than the group who reported spending 15 minutes or less on homework. However, even though the means differ, there may be no real difference in performance between the two groups in the population because of the uncertainty associated with the estimated average proficiency of the groups in the sample. Remember that the intent is to make 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 sty 'ents in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalent, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the &gee of uncertainty -- called the standard error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the manner in which the standard error for an individual group mean or proportion is used, the standard error of the difference can be used to help determine whether differences between groups in the population are real. The difference between the mean proficiency or proportion of the two groups ± 2 standard errors of the difference represents an approximate 95 percent confidence interval. If the resulting interval includes zero, one should conclude that there is insufficient evidence to claim a real difference between goups in the population. If the interval does not contain zero, the difference between groups is statistically significant (different) at the .05 level. THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Colorado As an example, suppose that one were interested in determining whether the average mathematics proficiency of eighth-grade females is higher than that of eighth-grade males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard errors for females and males were as follows: Group Average Proficiency Standard Error Female 259 4 2.0 Male 255 2.1 The difference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of !his difference is Ni 2.02 + 2.12 = 2.9 Thus, an approximate 95 percent confidence interval for this difference is Mean difference ± 2 standard errors of the difference = 4 ± 2 . (2.9) = 4 ± 5.8 = 4 - 5.8 and 4 + 5.8 = -1.8, 9.8 The value zero is within this confidence interval, which extends from -1.8 to 9.8 (i.e., zero is between -1.8 and 9.8). Thus, one should conclude that there is insufficient evidence to claim a difference in average mathematics proficiency between the population of eighth-grade females and males in public schools in the state.' Throughout this report, when the mean proficiency or proportions for two groups were compared, procedures like the one described above were used to draw the conclusions that are presented. If a statement appears,in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. When a itatement indicates that the average proficiency or proportion of some attribute was 6ou1 the same for two gjoups, 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. F'7 certain comparisons in the report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used. 94 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado 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. Ifone wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this report to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions mported by NAEP are statistics and therefore are subject to a certain degree of uncertainty. In certain cases, typically when the standard error is based on a small number of students, or when the group of students is enrolled in a small number of schools, the amount of uncertainty associated with the standard errors may be quite large. Throughout this report, estimates of standard errors subject to a large degree of uncertainty are followed by the symbol "!". In such cases, the standard errors -- and any confidence intervals or significance tests involving these standard errors -- should be interpreted cautiously. Further details concerning procedures for identifying such standard errors are discussed in the Trial State Assessment technical report. Minimum Subgroup Sample Sizes Results for mathematics proficiency and backgound variables were tabulated and reported for croups defmed by race/ethnicity and type of school community, as well as by gender and parents' education level. NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and/or background variable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probability of .8 or greater. Ou THE 1990 NAEP TRIAL STATE ASSESSMENT 95 Colorado The effect size of .2 pertains to the true difference between the average proficiency of the subgroup in question and the average proficiency for the total eighth-grade public-school population in the state or territory, divided by the standard deviation of the proficiency in the total population. If the true difforence between subgroup and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is required to detect such a difference with a probability of .8. Further details about the procedure for determining minimum sample size appear in the Trial State Assessment technical report. Describing the Size of Percentages Some of the percentages reported in the text of the report are given quantitative descriptions. For example, the number of students being taught by teachers with master's degrees in mathematics might be described as "relatively few" or "ahnost 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 repon and the rules used to select them are shown below. Percentage Description 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 halt 69 < p 5 79 About three-quarters 79 < p 5_ 89 Many 89 < p < 100 Almost all p = 100 All , 101 96 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado 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 racejethricy, type of community, parents education level, and gender. THE 1990 NAEP TRIAL STATE ASSESSMENT 97 Colorado TABLE AS I Students' Reports on the Mathematics Clan 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Eighth-grade Mathematics Pre-algebra Algebra TOTAL Percentage and Proficiency Percentage and Proficiency Percantitge and Proficiency State 46 ( 2.5) 32 ( 2.1) 18 ( 1.1) 255 ( 1.4) 270 ( 1.2) 295 ( 2.0) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 296 ( 2.4) RACE/ETHNICITY White State 43 ( 2.6) 33 ( 2.2) 20 ( 12) 282 ( 1,3) 275 ( 1.1) 300 ( 1,5) Nation 59 ( 23) 21 ( 2.4) 17 ( 1.5) 259 ( 1.6) 277 ( 22) 300 ( 2.3) Black State 44 -... ( 8.1) ( ...) 39 ( ....., ( 7.1) - ) 14 ( ( 4.9) .41 Nation 72 ( 4.7) 16 ( 3.0) 9 ( 2.2) 232 ( 3.4) 246 ( 6.4) ( ,..,) Hispanic State 59 ( 3.6) 25 ( 3.0) 10 ( 1.7) 238 ( 1.9) 254 ( 2.7) +0. ( .1) Nation 75 ( 4.4) 13 ( 3.9) 6 ( 1.5) 240 ( 2.4) -- ( .4) 4... ( .-.,.) TYPE OF COMMUNITY Advantaged urban State 311 4.1) 43 ( 4.0) 21 ( 1.6) 266 ( 2.8)1 277 ( 2.2) 308 ( 1.9) Nation 55 269 ( 9.4) ( 2.5)1 22 ( 7,9) 21 4.4) Disadvantaged urban State 39 (11,0).) 35 (- 8.0) ..) Nation 65 240 ( 6.0) ( 4.0)1 16 ( 4.1) ) 14 ( 287 ( 3.3) 4.2)1 Extreme rural State 60 ( 8.7) 27 ( 8.1) 9 ( 3.0) 258 ( 2.4)1 277 ( 4.1)1 **4 Nation 74 249 ( 4.5) ( 3.1)1 *** 7 ( .. 2.2) Other State 52 ( 3.8) 26 ( 2.8) 18 ( 1.9) 255 ( 2.0) 284 ( 2.0) 296 ( 1.9) Nation 61 ( 2.2) 20 ( 2,1) 16 ( 1.4) 251 ( 2.0) 272 ( 2.8) 294 ( 2.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within i 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 allcm accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 00 98 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE AS I Students' Reports on the Mathematics Clan ("mtinued) I They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Elghthirade Mathematics Pro-algabra _ Algobra TOTAL rod Proficiency Percentage and Prone fancy Percentage and Proficiency State 40 ( 2.5) 32 ( 2.1) 18 ( 1.1) 255 ( 1.4) 270 ( 1.2) 295 ( 2.0) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 298 ( 2.4) PARENTS EDUCATION NS non-graduate State 63 ( 238 ( 5.2) 2.7) ( ( 3.8) «4) 8 ( 4.4* 2.3) Nation 77 ( 241 ( 3.7) 2.1) 13 ( Mr* ( 3.4) 3 ( 1.1) 4$4) HS graduate State 56 ( 4.0) 29 ( 2.8) 11 ( 12) 247 ( 2.0) 260 ( 2.4) ( *el Nation 70 ( 2.6) 18 ( 2.4) 8 ( 1.1) 249 ( 1.9) 286 ( 3.5) 277 ( 52) Some college State 47 ( 3.0) 33 ( 2.9) 17 ( 1.9) 261 ( 1.91 274 ( 2.0) 295 ( 2.7) Nation 60 ( 21 ( 2.9) 15 ( 1.9) 257 ( 276 ( 2.8) 295 ( 3.2) College graduate State ( 2.6) 35 ( 2.2) 24 ( 1.3) 261i ( 1.7) 275 ( 1.5) 302 ( 1.6) Nation 53 ( 2.7) 21 ( 2.3) 24 ( 1.7) 259 ( 1.5) 278 ( 2.8) 303 ( 2.3) GENDER Male State 48 ( 2.8) 32 ( 2.4) 18 ( 1.5) 258 ( 1.4) 271 ( 1.3) 298 ( 2.7) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 2.5) Female State 44 ( 2.7) 33 ( 2.2) 19 ( 1.3) 251 ( 1.8) 268 ( 1.7) 293 ( 2.0) Nation 61 ( 2.6) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interett, the value for the entire population is within rt 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. a* * Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 10 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Colorado TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT None 15 'Mutes 30 Minutes 45 Minutes An Hour or More TOTAL Percentage and Proficiency 1 ( 0.5) 1 ( 0.3) 1 ( 0.3) ..) 1 0.3) 6 (5.1) 1 0,7) 2 (1.2) 1 0.8) 1 ( 1.1) 44-4 ( 4") 1 ( 0.9) 0 ( 0.0) 4" 1 444) 2 ( 1.2) 444 ( 444) 0 1 0.0) ". ** ) 1 ( 0.4) Percentage and Proficiency 40 ( 3.5) 261 ( 1.8) 43 ( 4.2) 266 ( 2.3) 39 ( 3.7) 268 ( 1.6) 39 ( 6..7) 266 ( 22) 55 ( 7.6) 232 ( 3.1) 43 ( 52) 242 ( 2.6) 46 ( 7.8) 245 ( 3.0)1 33 ( 5.1) 274 I 2.8) 61 (11.3) 273 ( 3.1)1 39 (12.5) ...) 41 (12.6) 236 ( 2.1)i 47 (15.6) 265 ( 3.4)1 68 (14.9) 253 1 5,4)1 42 ( 5.6) 256 ( 3.0) 37 ( 4.3) 256 ( 3.1) Percentage and Proficiency 45 ( 3.3) 267 ( 1.6) 43 ( 4.3) 266 ( 2.6) 45 ( 3.4) 274 ( 1.5) 45 ( 5.1) 270 ( 2.7) 41 ( 6.5) ...) 40 ( 6.7) 248 ( 5.3) 47 ( 5.2) 247 ( 2.2) 34 ( 6.8) 251 ( 4.2)1 48 ( 4.6) 275 2.3) 32 ( 8.6) .. ...) 54 ( 9.8) 249 ( 6.7)1 36 ( 9.4) 253 ( 9.0)1 44 (14.9) 268 ( 3.8)1 14 (10.9) 43 ( 53) 266 ( 3.1) 49 ( 5.1) 265 ( 2.$) Percentage and Proficiency 10 ( 1.8) 288 ( 3.3) 10 ( 1.9) 272 ( 5.7)1 11 ( 2.0) 291 ( 3.6) 11 ( 2.4) 277 ( 7.8)1 6 ( 3.8) ) 3 ( 12) ( 1,5) 444 ( 444) 13 ( 2,9) 444 ( 444) 141 2.6) 334 ( 3.5)1 5 ( 3.4) ...) 0 ( 0.0) 44" ( "4) 12 ( 5.9) ...) 2 ( 1.5) 444 ( 444) 8 ( 5.6) 444 ( 444) 12 ( 3.3) 277 ( 3.9)1 10 ( 2.4) 276 ( 8.6)1 Parcentage and Proficiency 3 ( 1.1) 286 ( 6.1)) 4 ( 0.9) 278 ( 5.1)1 4 ( 1.3) ...) 4 ( 0.9) 279 ( 5.8)1 2 ( 1.4) ( 2 ( 0.8) ...) 2 ( 1.2) ...) 7 ( 2.1) 444 ( 4") 41 1.7) "4 ( "*) 0 ) 0.0) *4 * ( 441 7 ( 5.7) 4" ( 444) 10 ( 6.2) ...) 5 ( 4.7) .4* ( - 10 7.3) **1. ( ** 3 ( 1.6) 4 ( 1.1) 282 (11.6)' State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- thc nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "6 Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 o THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A6 (continued) 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 - None _ 15 Minutes 30 Minutes 4$ Minutes An Hour or Mere TOTAL Percer*age and Preaciency 1 ( 0.5) ( 0.3) IN" ( 2 ( 12) 1 ( 0.8) 2 ( 0.7) 1 ( 0.5) ( 1 ( 0.9) ( ne) 1 ( 0.9) *IN ( 4e4 0 ( 0.3) 1 ( 0.5) ( en) 1 ( 0.3) ( en) 1 ( 0.5) en ( net 1 ( 0.4) en ( en) Percentage and Prolicianw 40 ( 3.5) 261 ( 1.8) 43 ( 42) 258 ( 2.3) 52 ( 6.3) 242 ( 3.3) 49 ( 6.3) 240 ( 2.8) 44 ( 4.5) 249 ( 2.0) 43 ( 5.2) 249 ( 3.1) 36 ( 4.6) 269 ( 22) 44 ( 5.4) 265 ( 2.6) 38 ( 3.5) 270 ( 1.9) 40 ( 4.7) 265 ( 2.5) 42 ( 4.1) 263 ( 1.9) 44 ( 4.4) 257 ( 2.9) 37 ( 3.4) 258 ( 2.3) 41 ( 4.4) 255 ( 2.3) Percentage end Preficiancy 45 ( 3.3) 267 ( 1.6) 43 ( 4.3) 286 ( 2.6) 9-1- 40 ( 6.1) 246 ( 3.7) 44 ( 4.1) 255 ( 2.1) 44 ( 5.8) 258 ( 2.7) 49 ( 4.2) 269 ( 2.4) 43 ( 5.8) 270 ( 3.8) 46 ( 3.4) 276 ( 1.7) 44 ( 4.1) 277 ( 3.0) 43 ( 3.6) 269 ( 1.9) 43 ( 4.3) 268 ( 2.9) 48 ( 3.4) 264 ( 1.8) 43 ( 4,7) 264 ( 2.8) Percentage and Proficiency 10 ( 1.8) 288 ( 3.3) 10 ( 1.9) 272 ( 5.7)1 ( 3.6) ***) 6 ( 1.7) *sit wo.) 7 ( 2.0) ( 9 ( 3.1) .11 7 ( 2.1) 12 ( 1,9) 295 ( 3.0) 11 ( 2.3) 287 ( 6.1)1 9 ( 1.6) 289 ( 4.1) 9 ( 1.9) 273 ( 7.3)1 11 ( 2.1) 287 ( 3.7) 11 ( 2.0) 272 ( 5.7)1 Percentage and Pratt:hew 3 ( 1.1) 286 ( 6.1)1 4 ( 0.9) 278 ( 5.1)1 ( en) 4 ( 1.3) ( ) 3 ( 1.8) ( en) 3 ( 1.0) ( en) 3 ( 15) 4 ( 1.0) 4 ( 1.3) ( en) 5 ( 1,3) ". ( ```) 5 ( 1.3) 279 ( 7.7)1 3 ( 1.3) en ( en) 4 ( 0.9) 6** ( C") State Nation PARENTS EDUCATION KS non-graduate State Nation HS graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated Stat,StiCS appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within i 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 202 Colorado TABLE A7 I Students' Reports on the Amount of Time They I Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1 990 NAEP TRIAL. STATE ASSESSMENT None 10 Minutes 30 Minutes 40 Minutes - An Hour or More vm14ImmillimmmnompmEmswi TOTAL Percentage and Pro &gem Percentage and Proficiency Percentago and Proficiency Pereentage and Pro fidgety Percentage and Pmficiency State 9 ( 0.8) 28 ( 1.1) 31 ( 0.9) 16 ( 0.9) 1tI ( 1.1) 205 ( 2.8) 209 ( 1.3) 288 ( 1.3) 267 ( 1.7) 266 ( 1.9) Nation 6 ( 0.8) 31 ( 2.0) 32 ( 1.2) 18 ( 1.0) 12 ( 1.1) 251 ( 2.8) 204 (.1.9) 263 ( 1.9) 201( 1.9) 268 ( 3.1) RACE/ETHNICITY White State 9 ( 0.9) 25 ( 1.3) 30 ( 1.1) 17 ( 0.9) 15 ( 1,1) 271 ( 2.7) 276 ( 1.4) 275 ( 1.4) 271 ( 1.9) 275 ( 1.9) Nation 10 ( 1.0) 33 ( 2.4) 32 ( 1.3) 15 ( 0.9) 11 ( 1.3) 258 ( 3.4) 270 ( 1.9) 270 ( 2.1) 277 ( 2.2) 268 ( 3.3) Slack State 4 ( 1.3) 4.4) ( .4) 30 ( 4.3) ...) 19 2.9) 23 ( .44 ( 4.9) ...) Nation ( 1.5) 26 ( 2.5) 33 ( 2.7) 18 ( 2.3) 16 ( 1.9) 241 ( 3.8) 237 ( 3.5) 240 ( 3.6) 232 ( 3.7) Hispanic State 11 ( 44. ( 1.8) .4) 27 ( 246 ( 2.3) 2.5) 32 ( 248 ( 2.2) 2.2) 12 ( 4.4 ( 1.6) 4.4) 18 ( 244 ( 2.1) 4.4) Nation 12 ( 1.8) ) 27 ( 248 ( 3.0) 3.6) 30 ( 248 ( 2.6) 3.4) 17 ( 241 ( 2.1) 4.3) 14 ( .44 ( 1.7) .4. ) TYPE OF COMMUNITY Advantaged urban State 30 ( 2.3) 32 ( 1.7) 19 ( 1.8) 14 ( 2.1) 278 ( 2.5) 283 ( 1.9) 279 ( 3.0) 230 ( 3.1)1 Nation 8 ( 2.5) 41 (12.5) 278 ( 3.0)1 31 ( 280 ( 6.6) 4.6)1 12 ( 3.3) .4) 7 I, 4.4 ( 3,4) .44) Disadvantaged urban State ( 4.4 ( 2.7) '") 30 ( 0.4 ( 5.5) .4) 39 f 4.5) .4. 444) 10 ( 4. ( 2.9) .44) 15 ( ( 4.6) .4) Nation 12 ( ( 3.7) 4.4) 24 ( 253 ( 3.3) 4.9)1 31 ( 247 ( 3.0) 4.7)1 20 ( 250 ( 1.9) 4.8)1 14 ( ( 2.2) 4") Extreme rural State 15 ( 3.3) 4.) 28 ( 270 ( 4.3) 2.8)1 25 ( 264 ( 3.2) 3.3)1 15 ( 2.5) 444) 17 ( 5,1) Nation 8 ( ( 2.3) 36 ( 260 ( 4.6) 3.5)1 31 ( 255 ( 2.9) 5.1y 18 ( 3.8) .44) ft ( IN* ) Other State 10 ( 1.7) 27 ( 1.7) 30 ( 1.4) 16 ( 1.5) 17 ( 1.3) 263 ( 4.7)1 267 ( 2.1) 266 ( 2.3) 265 ( 2.1) 283 ( 3.0) Nation 9 ( 1.0) 30 ( 1.8) 32) 1.3) 15 ( 1.1) 13 ( 1.1) 250 ( 3.8) 203 ( 2.3) 264 ( 2.3) 267 ( 2.1) 258 ( 3,6) The standard errors of the estimawd 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 thc variability of this estimated mean proficiency. us Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 0 102 THE 1990 NAEP TRIAL MATE ASSESSMENT Colorado 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 MO NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 46 Minutes An Mow or Moro TOTAL Porcintat. Proficiency Partontaffe and Proficiency Percentage and Profidency Percentage and Proficiwcy Percentage and Proficiency State 8 ( 0.8) 2$ ( 1.1) 31 ( 0.9) 16 ( 0.9? 16 ( 1.1) 205 ( 2.8) 269 ( 1.3) 268 ( 1.3) 267 ( 1.7) 266 ( 1.9) Nation 9 ( 0.8) 31 ( 2.0) 32 ( 1.2) 16 ( 1.0) 12 ( 1.1) 251 ( 2.8) 264 ( 1,9) 263 ( 1.9) 266 ( 1.9) 258 ( 3.1) PARENTS' EDUCATION NS non-graduate State 15 ( ( 3.3) ***) 29 ( 18) ...) 26 ( 3.6) r ) 4.. 15 ( 2,6) Nation 17 ( ( 3.0) ***) 26 ( 246 ( 3.3) 4.0) 34 ( 246 ( 4.4) 2.6) .4.) 10 ( 2.2) .44) NS graduate State 11 ( .4. ( 1.6) 44.) 24 ( 258 ( 2.0) 2.6) 33 ( 257 ( 2.3) 2.4) 16 ( 250 ( 1.9) 4.0) 16 ( 250 ( 1.9) 2.9) Nation 10 ( 1.7) 33 ( 22) 31 ( 1.9) 16 ( 1.4) 11 ( 1.5) 246 ( 42) 259 ( 3.2) 254 ( 2.4) 256 ( 22) 244 ( 3.4) Some college State 8 ( 1.2) 31 ( 2.2) 32 ( 2.2) 13 ( 1.5) 16 ( 2.0) 273 ( 1.9) 269 ( 1.9) 270 ( 3.3) 270 ( 3$) Nation 9 ( .4 1.2) ...) 30 ( 266 ( 2,7) 3.0) 36 ( 266 ( 2.1) 2.6) 14 ( 274 ( 1,8) 3$) 11 ( 4. 1.5).) College gradLate State 7 ( 0.9) 28 ( 1.4) 31 ( 1.1) 18 ( 1.4) 16 ( 1.4) 273 ( 3.7) 277 ( 1.6) 278 ( 1.8) 277 ( 1,8) 277 ( 22? Nation 7 ( 0,9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1.9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3.2) 271 ( 2.8) GENDER Melo State 11 ( 1.2) 30 ( 1.4) 29 ( 1.3) 14 ( 1.0) 15 ( 1.3) 267 ( 2.9) 272 ( 1.5) 269 ( 1.7) 269 ( 2.4) 267 ( 2,9) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.8) 266 ( 2.4) 265 ( 3,0) 258 ( 4.1) Female State 7 ( 0.9) 25 ( 1.5) 32 ( 1.4) 19 ( 1.4) 17 ( 1.3) 261 ( 4.6) 264 ( 2,0) 268 ( 2.1) 265 ( 2.3) 265 ( 2.3) Nation 7 ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 246 ( 4.1) 263 ( 1,5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The s;.andard errors of the estimated statist= appear in parentheses. a can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer tha.1 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 103 Colorado TABLE A8 I Teachers' Reports on the Emphasis Given To I Specific Mathematics Content Areas PERCENTACE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT L Numbers and Operations Measurement Omenetty Heavy Emphasis Latta or No Emphasis Heavy I Little or No EmphasIs 1 Emphasis Heavy Emphasis Little or No Emphasis TOTAL Percentage and Proficiency 37 ( 3,0) 262 ( 1.7) 49 ( 3.8) 260 ( 1.8) 33 ( 32) 289 ( 1.9) 48 ( 3.7) 287 ( 2.2) 29 ( 7.1) 54 ( 7.9) 243 ( 4.3) 53 ( 4.5) 248 ( 2.5) 47 ( 8.7) 248 ( 4.6) 31 ( 4.4) 276 ( 3.5) 28 (13.0) ) 54 (12.6)) 48 (12.1) 255 ( 6.3)1 34 (12.3) 265 ( 4.5)1 53 (12.4) 257 ( 7.1)1 40 ( 4.5) 259 ( 3,0) 52 ( 4.1) 260 ( 2.3) Percentage mot Prattokincy 14 ( 1.8) 288 ( 3.7) 15 ( 2.1) 287 ( 3.4) 16 ( 2.0) 205 ( 2.8) 16 ( 2.4) 289 ( 3.5) 16 ( 7.2) 4r44*) 11 ( 3.3) 9 ( 2.4) *44 ( *1111 ) 8 ( 2.2) 19 ( 3.2) 299 ( 3.8)1 16 ( 4.2) 30 (12.1) 9 ( 4.0) *4 6 ( 3.6) 12 ( 2.6) 291 ( 3.9)1 16 ( 2.7) 286 ( 3.6) Percentage and Pmeciency 7 ( 1.2) 259 ( 4.5) 17 ( 3.0) 250 ( 5.8) 7 ( 1.3) 206 ( 4.7) 14 ( 3.4) 259 ( 6.9)1 7 ( 3.2) 4+9 25 ( 7.4) 228 ( 2.8)1 8 ( )) 23 ( 4.1) *** ( 9 ( 7.0) " . ( 4 ( 4.8) 39 (10.3) 238 ( 8.4)1 8 ( 5.5) 6 ( 4.9) ( 7 ( 1.9) 256 ( 6.3)1 16 ( 3.9) 253 ( 71)1 Pimento. and Proaciency 4$. ( 3,5) 272 ( 2.4) 33 ( 4.0) 272 ( 4.0) 45 ( 3.4) 280 ( 2$) 36 ( 4.7) 277 ( 4.3) 30 ( 9.5) 4.411 23 ( 5.7) 238 ( 8.1)1 40 ( 5.9) 246 ( 3.9) 34 ( 5.8) 255 ( 4.4)1 58 ( 3.5) 283 ( 3.8) 40 ( 8$) ( 49 48 (14.1)) 21 ( 6.5) 42 (15.4) 261 ( 6.3)1 32 (11.7) 265 ( 9.1)1 34 ( 5.2) 273 ( 3.2) 34 ( 5.3) 270 ( 4.6) Pimiento. and Proticieniy 20( 3.1) 269 ( 2.4) 28 ( 3.8) 280 ( 3.2) 22 ( 3.4) 272 ( 2.4) 27 ( 4.4) 265 ( 3.3) 18 ( 7.4) .44 33 ( 7.9) 242 ( 5.8)1 15 ( 3.4) 254 ( 4.4)1 27 ( 61).) 28 ( 5.3) 278 ( 3.8)1 38 ( 9.4) 267 ( 4.9)1 11 ( 7.6) 33 (11.8) 248 ( 8.2)1 26 (11.9) 270 ( 5.8)1 9 ( 6.1) 11.4. 011) 17 ( 4$) 285 ( 3.9)1 28 ( 4.8) 260 ( 3.9) Percentage and Preiciency 31 2.8) 263 1.9) 21 3.3) 264 ( 5.4) 31 ( 3.0) 270 ( 2.3) 22 ( 3.4) 273 ( 5.8) 27 ( 5.4) 1.4.4. 4.4..) 24 ( 7.3) 233 ( 4.7)1 35 ( 5.0) 243 ( 2.8) 18 ( 5.5) ( 01 30 ( 3.61 279 ( 2.9) 13 ( 3.2) 4. 27 (10.1) ( *eV ) 18 ( 7.6) ( 0 28 ( 9.2) 254 ( 4.3)1 16 ( 7.9) 33 ( 4.8) 282 ( 3.0) 24 ( 4.3) 285 ( 5.7) State Nation RACUETHNICITY White State Nation Black State Nation Hispanic State Nation TYPE OF COMMUNITY Advantapd urban State Nation Diudvantaged urban State Nation Extract* 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 withm 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). 10 104 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A8 I Teachers' Reports on the Emphasis Given to (ccetinued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Numbers and Operations Measurement - Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis . Little or No Emphasis TOTAL Percentage and Proficiency 37 ( 3.0) 262 ( 1.7) 49 ( 3.8) 2 60 ( 1.8) 51 ( 8.0) 237 ( 4.7) 60 ( 6.9) 251 ( 3.4) 42 ( 4.3) 256 ( 2.4) 55 ( 4.8) 259 ( 2.9) 37 ( 3.6) 268 ( 2.3) 47' ( 4.4) 265 ( 2.6) 33 ( 3.1) 271 ( 1.9) 44 ( 4.1) 289 ( 2.6) 38 ( 3.2) 283 ( 1.8) 48 ( 4.1) 261 ( 2.5) 37 ( 3.3) 260 1 2.2) 51 ( 3.9) 260 ( 2.0) Percentage and Proficiency 14 ( 1,$) 288 ( 3.7) 15 ( 2.1) 287 ( 3.4) 8 ( 2.8) ( .41 7 ( 2.3) ( 4.1 8 ( 1.7) *44(4*4) 11 ( 2.8) 11.44 ( 444 ) 13 ( 2.5) 044 ( 444) 17 ( 3.3) 284 ( 4.1)1 18 ( 2.2) 295 ( 2.8) 19 ( 2.4) 298 ( 3.4) 14 ( 1.9) 290 ( 4.1) 14 ( 2.1) 287 ( 4.4) 13 ( 2.0) 286 ( 4.2) 15 ( 2.4) 286 ( 3.3) Percentage and Proficiency 7 ( 1.2) 259 ( 4.5) 17 ( 3.0) 250 ( 5.8) 5 ( 3.0) ( 04.) 22 ( 5.3) 4.) 9 ( 2.1) **4, ( 4.) 17 ( 3.9) 251 ( 6.1)1 8 ( 1.1) *44 ( 444) 12 ( 2.7) ( *44 ) 7 ( 1.3) 270 ( 8.4) 16 ( 3.3) 264 ( 7.2)1 8 ( 1.4) 259 ( 5.4) 17 ( 3.3) 258 ( 6.7) 7 ( 1.1) 259 ( 6.0) 17 ( 3.2) 241 ( 5.4) Percentage old Proficiency 43 ( 3.5) 272 ( 24) 33 ( 4.0) 272 ( 4.0) 42 ( 6.8) ) 25 ( 5.3) (444444) 36 ( 4.3) 255 ( 5.0) 27 ( 5.0) 253 ( 4.7)1 42 ( 4,5) 277 ( 3.3) 39 ( 5$) 279 ( 4.5) 47 ( 3.1) 282 ( 3.0) 37 ( 3.8) 283 ( 3.8) 44 ( 4.0) 277 ( 2.7) 32 ( 3.9) 275 ( 4.8) 42 ( 3.4) 268 ( 2.8) 35 ( 4.3) 268 ( 4.1) Percentage and Proficiency 20 ( 3 1) 289 ( 2.4) 28 ( 3.8) 260 ( 3.2) 19 ( 5.0) 44) *** 18 ( 3.8) 283 ( 36)1 27 ( 4.5) 255 ( 4.2) 22 ( 3.9) 278 ( 3.9) 27 ( 5.0) 262 ( 4.8)1 21 ( 3.3) 274 ( 2.6) 26 ( 3.4) 270 ( 3.8) 21 ( 3.2) 270 ( 2.8) 29 ( 4.1) 283 ( 3.8) 19 ( 3.2) 287 ( 3.2) 27 ( 3.9) 256 ( 3.3) Percentage and Proficiency 31 ( 2.8) 263 ( 1.9) 21 ( 3.3) 264 ( 5.4) 29 ( 5,9) 20 ( 6.7) 15 ( 3.7) 250 ( 2.8) 24 ( 5.1) 248 ( 4.8)1 29 ( 3.7) 266 ( 3.5) 23 ( 4.1) 270 ( 4.7) 31 ( 2.8) 274 ( 2.4) 21 ( 2.9) 280 ( 6.4) 32 ( 3.2) 264 ( 2.3) 20 ( 3.3) 266 ( 6.8) 30 ( 2.7) 261 ( 2.5) 23 ( 3.5) 263 ( 5.0) State Nation PARENTS EDUCATION HS non-graduate State Nation liS graduate State Nation Same collage State Nation College graduate State Nation GENDER Male State Nation Ferial. State Nation 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 erro... of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Colorado TABLE AS I Teachers' Reports on the Emphasis Given To ("mtinued) Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT r :ta Analysis, Statistics, and Probabilty Algebra and Functions Heavy Emphasis LIttle or No Emphasis Heavy Emphasis Utt le or No Emphasis TOTAL Percentage and Proficiency Percentage and Pro fickocy Percentage and Pro Wesley Percentage and Proficiency State 15 ( 2.0) 63 ( 3.5) 61 ( 3.5) 14 ( 2.6) 271 ( 2.8) 270 ( 1.5) 276 ( 1.7) 242 ( 3.5) Nation 14 ( 2.2) 53 ( 4.4) 48 ( 3.8) 20 ( 3.0) 259 ( 4,3) 251 ( 2.9) 275 ( 2.5) 243 ( 3.0) RACE/ETHNICITY White State 15 ( 2.3) 63 ( 3.7) $4 ( 3.7) 12 ( 2.7) 277 ( 3.0) 27$ ( 1.4) 282 ( 1.3) 252 ( 3.5)1 Nation 14 ( 2.4) 53 ( 5.0) 43 ( 4.2) 18 ( 2.8) 276 ( 4.1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) Slack State 11 ( 4.7) *** ( ***) 52 ( 7.6) *44(4*) 35 ( 6.9) ( 411 17 ip4.4 Nation 14 ( 3A) 53 ( 82) 39 ( 7.1) 27 ( 6.9) ( 225 ( 4.3) 253 ( 6.3) 226 ( 2.2)1 Hispanic State 12 ( 2.6) 65 ( 5.0) 43 ( 5.1) 19 ( 32) ( ***) 246 ( 2.6) 253 ( 3.8) 223 ( 5.5) Nation 56 ( 6.3) 246 ( 4.4) 46 ( 5.9) 257 ( 4.0)1 18 ( 4.2) ( ..4) TYPE OF COMMUNITY Advantaged urban State 21 ( 5.1) 63 ( 5.6) 64 ( 4.3) 4 ( 1.4) 281 ( 4.5)1 283 ( 2.6) 283 ( 1.8) Nation 65 (19.4) 41 ( 8.9) 284 ( 7.4)1 296 ( 7.9)1 Disadvantaged urban State 17 ( 9.3) 67 ( 8.8) 255 ( 6.2)1 1 ( 0.9) *. Nation 19 ( 9.4) ft* 11.1He 34 (11.4) 236 ( 8.2)1 53 (11.8) 254 ( 6.3)1 20 ( 9.4) ( 4*. Extreme rural State 18 ( 7.5) 277 ( 7.8)1 67 (13.7) 268 ( 45)1 29 (10.1) 264 ( 8.6)1 17 (10.9) 4.. ( .4.) Nation ( 5.4) 65 (16.9) 33 ( 8.1) 42 (16.0) 254 ( 6.7)1 241 ( 5.9)1 Other State 10 ( 2.5) 54 ( 5.7) 49 ( 5.1) 15 ( 3$) 267 ( 6.1)7 207 ( 2.8) 276 ( 2.6) 243 ( 6.C1)1 Nation 15 ( 2.9) 53 ( 5.2) 47 ( 4.3) 17 ( 33) 267 ( 4.7) 260 ( 3.4) 276 ( 2.8) 245 ( 4.4)1 The standard errors of the estimated statistics appear in parentheses. It can be saw with about 95 percent certainty that, for each population of interest, the value for the entire population is within .1: 2 standard errors of 'Ile estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included, ! Interpret with caution -- the nature or the sample does not allow accurate determination of the variability of this estimated mean proficiency, *"" Sample size is insufficient to permit a reliable estimate (fewer than 62 students), lii 106 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A8 I Teachers' Reports on the Emphasis Given To (wntinued) Specific Matirmatics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability . Algebra Slid Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Perceniage and Proficiency Ponsentage and Proficiency Percentage and Proficiency Percerdage and Proficioncy State 15 ( 2.0) 63 ( 34) 51 ( 3.5) 14 ( 2.6) 271 ( 2.8) 270 ( 1$) 278 ( 1.7) 242 ( 3.5) Nation 14 ( 2.2) 53 ( 4.4) 46 ( 3.6) 20 ( 3.0) 269 ( 4.3) 261 ( 2.9) 275 ( 2.5) 243( 3.0) PARENTS' EDUCATiON HS non-graduate State 10 ( «Hp ( 3.C) 62 ( 241 ( 6.7) 4.1) 40 ( ( 5.7) wfril 21 ( 4«, ( 5.8) Nation 9 ( 3.0) 53 ( 7.7) 28 ( 5.2) &PO ( 240 ( 6.2) *TR ( HI graduat State 14 ( 2.5) 64 ( 4.5) 41 ( 4.4) 18 ( 3.6) 259 ( 4.4) 254 ( 2.9) 281 ( 24) 237 ( 4.7)1 Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 261 ( 6.0)1 247 ( 2.9) 265 ( 34) 239 ( 3.4) Scow college State 14 ( 2.4) 03 ( 3) 51 ( 3.9) 14 ( 3.0) 276 ( 4.9) 275 ( .1) 278 ( 2.5) Olt* *We) Nation 13 ( 2.5) 57 ( 5.8) 48 ( 4.8) 17 ( 3.1) I* ( 4,1tfr 270 ( 3.7) 278 ( 3.0) *iv ( College graduate State 15 ( 2.3) 64 ( 3.4) 58 ( 3.7) 9 ( 2.1) 282 ( 3.0) 281 ( 1.9) 284 ( 1.8) 251 ( 3.8)1. Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 18 ( 2.4) 282 ( 4.5) 275 ( 3.8) 286 ( 3.0) 249 ( 4.0) GENDER Mal. State 16 ( 2.4) 62 ( 3.8) 48 ( 3.9) 14 ( 2.7) 273 ( 3.0) 272 ( 1.8) 276 ( 2.1) 246 ( 3.6) Nation 13 ( 22) 54 ( 4.7) 44 4.1) 22 ( 3.6) 275 ( 5.8) 260 ( 3$) 276 ( 3.2) 243 ( 3.0) Female State 13 ( 1.9) 64 ( 3$) 54 ( 3.4) 13 ( 2.6) 269 ( 3.8) 268 ( 1.9) 276 ( 1.8) 239 ( 4.7)i Nation 16 ( 2.4) 53 ( 4.5) 48 ( 3.6) 16 ( 2.9) 263 ( 4.4) 262 ( 2.8) 274 ( 2 7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each populauon 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 bevause the "Moderate emphasis" category is not included. ! Interpret with caution the nature of the sample does not a:low 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 11 4, 107 Colorado TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STL,DENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL I Ot AU the Resources I I Oot Most of the I Get Some or None of STATE ASSESSMENT Need Resources I Need the Resources I Need TOTAL Percentage and ProRelency Percentage and Proficiency Percentage and Proficiency State 15 2.4) 61 ( 3.6) 23 3.2) 268 ( 2.8) 268 ( 1.4) 263 ( 2.5) Nation 13 ( 2.4) 56 ( 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 261 ( 2.9) RACE/ETHNICITY White State 15 ( 2.5) 64 ( 3.5) 21 ( 2.9) 274 ( 2.4) 274 ( 1.4) 273 ( 1.9) Nation 11 ( 2.5) 58 ( 4.6) 30 ( 4.6) 275 ( 3.5)1 270 ( 2.3) 267 ( 3.3) Black State 11 ( 5.3) 63 (11.0) 26 (12.0) ( 239 ( 4.2)1 Nation 15 ( 4.2) 52 ( 6.8) 33 ( 7.2) 241 ( 5.3)1 242 ( 2.4) 238 ( 4.9) Hispanic State 19 ( 4.8) 50 ( 6.3) 31 ( 6.6) 247 ( 3.7)1 249 ( 1.8) 241 ( 3.2)1 Nation 23 ( 7.6) 44 ( 4.9) 34 ( 7.7) 246 ( 7.7)1 250 1 2.9) 244 ( 3.0)1 TYPE OF COMMUNITY Advantaged urban State 10 ( 4.6) 72 ( 4.6) 18 ( 3.6) 275 ( 6.0)1 280 ( 2.1) 277 ( 5.0)1 Nation 38 ( 9.2) 272 ( 83)1 59 ( 8.9) 286 ( 1.3)1 3 ( 3.1)) Disadvantaged urban State 19 (13.0) 54 (15.4) 27 (19.8) "" ( ...) 247 ( 3.9)' Nation 10 ( 6.8) 40 (13.1) 251 ( 5.4)1 SO (14.5) 253 ( 53)1 Extreme rural State 26 (13.4) 266 ( 7.4)1 57 (16.2) 266 ( 1.9)1 17 ( 8.9)) Nation 2 ( 2.6)) 54 (10.4) 260 ( 8.8)1 43 (10.3) 257 ( 5.0)1 Other State 15 ( 3.1) 56 ( 5.0) 29 ( 5.3) 265 ( 4.1)1 265 ( 2.1) 262 ( 3.6)1 Nation 11 ( 2.9) 58 ( 5.4) 31 ( 5.6) 265 ( 3.9)1 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear m parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within 1. 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample 517C is insufficient to permit a reliable estimate (fewer than 62 students). 11, 108 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado T: 3LE A9 Teachers' Reports on the Availability of (continued) 1 Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL I Get All the Resources I I Oft Most of the I Oct Some or None of STATE ASSESSMENT Need Resources I Need the Resources I Need TOTAL Percentage and Proficiency Percentage and Pretlelency Percentage and Proadency State 15 ( 2.4) 81 ( 3.6) 23 ( 3.2) 266 ( 2.8) 268 ( 1.4) 203 ( 2.5) Nation 13 ( 2.4) 50 ( 4.0) 31 ( 4.2) 265 ( 4.2) 265 ( 2.0) 281 ( 2.9) PARENTS' EDUCATION NS non-graduate State 8 ( 3.6) 59 ( 6.5) 33 ( 6.0) 247 ( 2.9) file 1-1.1 Nation 8 ( 2.6) 54 ( 5.7) 3$ ( 6.3) 244 ( 2.7) 243 ( 3.5)1 NS graduate State 19 ( 3.3) 25 ( 4.4) 253 ( 3.1) 255 ( 1.9) 252 ( 2.8) Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.9) 253 ( 4.8)f 256 ( 1.9) 2S6 ( 2.8) Some college State 18 ( 3.4) 59 ( 4.3) 23 ( 3.8) 274 ( 2.7) 273 ( 1.9) 267 ( 3.4) Natio 13 ( 3.3) 62 ( 4.3) 25( 4.1) 269 ( 2.5) 267 ( 3.8) College graduate State 13 ( 2.5) 66 ( 3.1) 21 ( 2.6) 276 ( 2.91 276 ( 1.6) 277 ( 2.6) Nation 15 2.9) 56 ( 4.9) 30 ( 5.1) ,( 276 ( 5.4)1 276 ( 2.2) 273 ( 3.7) GENDER Male State 16 ( 2.7) 60 ( 3.9) 24 ( 3.4) 267 ( 3,1) 270 ( 1.4) 266 ( 3.1) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4.0) 264 ( 5.0)i 265 ( 2.6) 264 ( 3.3) Female State 14 ( 2.2) 63 ( 3.7) 22 ( 3.2) 265 ( 3.2) 267 ( 1.9) 259 ( 3.0) Nation 13 ( 2.4) 55 4.4) 32 ( 4.7) 266 ( 3.9) 264 ( 2.0) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It ran 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 determmation of the variability or this estimated mean proficiency. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). in THE 1990 NAEP TRIAL STATE ASSESSMENT 109 Colorado TABLE Al Oa I Teachers' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1000 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency 69 ( 3.0) 268 ( 1.4) 50 ( 4.4) 260 ( 2.2) 69 ( 3.3) 273 ( 1.4) 49 ( 4.8) 265 ( 2.7) SS ( 5,9) 239 ( 4.4)' 47 ( 8.1) 240 ( 3.4) 72 ( 4.3) 247 ( 1.6) 64 ( 72) 246 ( 2.5) 64 ( 5.6) 280 ( 2.1) 39 (22.9) ** ( 4,1 72 (11.8) 248 ( 3.3)1 70 (11.7) 248 ( 4.8)1 79 (11.7) 267 ( 3.4) 35 (14.6) 255 ( 5.5)1 72 ( 5.1) 263 ( 2.2) 50 ( 4.4) 260 ( 2.4) Percentage and Proficiency 25 ( 2.9) 265 ( 2.5) 43 ( 4.1) 264 ( 2.3) 25 ( 3.2) 274 ( 2.3) 43 ( 4.5) 271 ( 2.2) 31 ( 6.0) .44 45 ( 7.0) 238 ( 4.0) 23 ( 4.0) 242 ( 4.3)1 32 ( 6.9) 247 ( 6.3)1 32 ( 5.8) 275 ( 4.1)1 41 (17.9) 273 ( 6.0)1 22 ( 7.5) 21 ( 9.0) 249 ( 8.7)! 20 (11.1) 4-114. ( ) 56 (17.1) 258 ( 5.9)1 20 ( 4.3) 264 ( 4.7)1 44 ( 4.5) 264 ( 2.8) Percentage and Proftdancy 8 ( 1.8) 278 ( 4.8)1 8 ( 2.0) 277 ( 5.4)1 7 ( 2.0) 280 ( 4.5)1 8 ( 2.3) 285 ( 4.9)1 ( 12) 9 ( 4.1) 5 ( 1.8) 41411, ) 4 ( 1.4) ..) 4 ( 1.6) *..) 20 (12.2) *" ( *44) ( 6.9) Mr, 41-0 ) 9 ( 8.5) ...) 9 ( 9.6) .4» dro 8 ( 3.5) 273 ( 6.2)1 6 ( 1.8) 277 ( 8.3)1 State Nation RACE/ETHNICITY White State Nation Slack State Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -I 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 110 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE AI0a I Teachers' Reports on the Frequency of Small (continued) i Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MD NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency Percentage and Prodciancy Percentage and Proficiency State 89 ( 3.0) 25 ( 2.9) 8 ( 1.6) 268 ( 1.4) 265 ( 25) 276 ( 4.5)) Nation 50 ( 4.4) 43 ( 4.1) ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 5.4)1 PARENTS EDUCATION HS non-graduate State 65 ( 6.2) 29 ( 5.8) 6 ( 2.5) 242 ( 3.1) ( wri Nation 60 ( 6.4) 39 ( 6.5) 1 ( 1,4) 244 ( 32) 244 ( 3.2)1 NS grackiate State 72 ( 3.7) 23 ( 3.4) 5 ( 1,6) 253 ( 1.8) 254 ( 3.6) Nation 49 ( 4.8) 45 ( 5.1) 6 ( 2$) 252 ( 2.8) 257 ( 2.7) ( Sane college State ( 3.7) 24 ( 3.4) 8 ( 2.3) 271 ( 1.7) 270 ( 3$) ( ) Nation 5/ ( 266 ( 5.2) 3.1) 42 ( 268 ( 5.1) 3.2) 7 ( 4. 2.3).) College graduate State 68 ( 277 ( 3.4) 1.5) 26 ( 275 ( 3.3) 2.9) 6 ( 1.6) 4.4) Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 276 ( 3.0) 285 ( 4.9)1 GENDER Mate State 69 ( 3.0) 25 1 2.9) 6 ( 2,0) 266 ( 1.4) 268 ( 2.8) 278 ( 5.5)1 Nation 50 ( 4.5) 42 ( 4.0) ( 2.1) 261 ( 3.0) 265 ( 3.1) 278 ( 5.3)1 Female State 69 ( 3,4) 25 ( 3.2) 6 ( 1.4) 265 ( 1.8) 263 ( 2.9) 4" ( *) Nation 50 ( 43 ( 4.7) 7 ( 2.1) 259 ( 2.2) 263 ( 2.1) 275 ( 6.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT I 11 Colorado TABLE MOb I Teachers' Reports on the Use of Mathematical Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO MEP TRIAL STATE ASSESSMENT Al Least Once a Week _ Less Than Once a Week Never TOTAL Percentage and Proficiency Percentage and Profit:ferny Percentage and Proficiency State 34 ( 2.9) 57 ( 2.7) 9 ( 1.6) 264 ( 2.0) 267 ( 1.3) 276 ( 35) Nation 22 ( 3.7) 69 ( 3.9) 9 ( 2.6) 254 ( 3.2) 263 ( 1.9) 282 ( 5.9)1 RACE/ETHNICITY White State 33 ( 3.2) 58 ( 3.2) 9 ( 1.6) 272 ( 1.9) 273 ( 1.3) 285 ( 3.0) Nation 17 ( 4.0) 72 ( 4.2) 10 ( 2.7) 261 ( 3.8)1 269 ( 2.1) 288 ( 6.2)1 Black State 37 ( 6.6) 58 ( 6.3) 5 ( 2.3) Mit ( 11`11-11) Nation 22 233 ( 5.9) ( 5.9)1 70 241 ( 6.3) ( 2.9) 8 ( *. 3.9) 4,-*) Hispanic State 36 ( 5.2) 55 ( 4.8) ( 2.4) 245 ( 2.1)1 247 ( 2.6) ( "4) Nation 39 247 ( 7.5) ( 3.8) 55 245 ( 7.3) ( 3.8)1 7 ( 2.6) **) TYPE OF COMMUNITY Advantaged urban State 38 ( 5.9) 52 ( 5.7) 10 ( 3.5) 277 ( 3.1)1 278 ( 2.3) ". ( 4 " ) Nation 23 (14.4) 63 (11.5) 15 ( 9.3) 278 ( 5.6)1 "` Disadvantaged urban State 50 (13.1) ( *40) 44 (17.2) 6 ( ". ( 6.9) 4") Nation 39 (11.4) 59 (12.1) 2 ( 1.8) 247 ( 7.5)1 253 ( 7.0)1 Extreme rural State 52 ( 7.6) 48 ( 7.6) 0 ( 0.0) 268 ( 5.0) 264 ( 2.9)1 **4 ( "4) Nation 27 *4, (14.9) 65 262 (14.8) ( 2.8)1 8 ( 3.9) Other State 27 ( 5.1) 65 ( 4.6) 9 ( 2.9) 260 ( 3.0)1 265 ( 2.4) 267 ( 6.3)1 Nation 19 ( 4.3) 72 ( 5.0) 9 ( 3.3) 253 ( 3.9)1 263 ( 2.2) 281 ( 7.1)t The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of merest, the value for the entire population is within I 2 standard errors of the estimate for the sample. Interpret with caution the nature of the sample does not allow accurate determmation of the variability of this estimated mean proficiency. *4* Sample size is insufficient to permit a reliable estimate (fewe.r than 62 students). 112 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A lOb I Teachers' Reports on the Use of Mathematical (continued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 34 ( 2.9) 57 ( 2.7) 9 ( 1.6) 264 ( 2.0) 207 ( 1.3) 276 ( 3.5) Nation 22 ( 3.7) 69 ( 3.9) 9 ( 2.6) 254 ( 3.2) 263 ( 1.9) 282 ( 5.9)1 PARENTS' EDUCATION HS non-graduate State 41 ( 7.0) 52 ( 62) ( 411 ) 246 ( 3.7) Nation 25 ( 5.6) 66 ( 2) 9 ( 6.5) 11** ( ) 243 ( 2.2) ( tiS graduate State 36 ( 3.9) 57 ( 3.4) ( 2.2) 252 ( 2.4) 254 ( 2.1) Nation 23 ( 4.8) 70 ( 5.3) 246 ( 4.0)1 255 ( 22) ( ".) Some college State 34 ( 3.6) 56 ( 3.4) 9 ( 2.4) 269 ( 2.3) 270 ( 2.0) Nation 18 ( 4.0) 73 ( 4,3) 9 ( 2.4) 261 ( 4.4)1 289 ( 2.3) ( College graduate State 32 ( 3.1) 59 ( 3.2) 10 ( 1.7) 274 ( 2.2) 276 ( 1.7) 288 ( 3.5) Nation 20 ( 3.9) 69 ( 3.7) 11 ( 2.5) 266 ( 3.5)1 274 ( 2.2) 297 ( 4.2)1 GENDER Male State 35 ( 3.0) 57 ( 2.8) 8 ( 1.6) 266 ( 2.2) 268 ( 1.4) 280 ( 4.1) Nation 22 ( 4.1) 69 ( 4.1) 8 ( 2.0) 255 ( 4.1) 265 ( 2.1) 287 ( 7.2)1 Female State 33 ( 3.2) 58 ( 3.1) 9 ( 1.7) 262 ( 2.6) 265 ( 1.8) 272 1 4.6) Nation 21 ( 3.6) ( 4.2) 10 ( 3.3) 254 ( 3.3) 262 ( 1.9) 278 ( 8.0)1 The standard errors of the estimated staustics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within i 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 11 THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Colorado TABLE Al la I Teachers' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Weak Mout Once a Week or Less TOTAL Percentage and Proficiency Percentage and Pinficiency Percentage and Proficiency State 59 ( 3.6) 31 ( 2.7) 10 ( 2.4) 291 ( 1.2) 283 ( 2.1) 253 ( 3.2)1 Nation 62 ( 3.4) 31 ( 3.1) 7 ( 1.8) 267 ( 1.8) 254 ( 2.9) 260 ( 5.1)1 RACE/ETHNICITY White State 61 ( 3.7) 29 ( 2.5) 10 ( 2.7) 277 ( 1.2) 271 ( 2.1) 282 ( 2.8)1 Nation 64 ( 3.7) 28 ( 3.2) 8 ( 2.3) 272 ( 1.9) 264 ( 3.4) 284 ( 5.4)1 Black State 88 ( 6.2) 16 ( 4.8) 239 ( 4.8)1 *41 Nation 56 244 ( 7.7) ( 4.0) 41 ( 233 ( 7.9) 3.9)1 2 ( 1.4) ( 0+1 Hispanic State 49 ( 5.3) 40 ( 5.5) 252 ( 2.3) 243 ( 2.0)1 Nation 61 ( 6.8) 32 ( 5.3) ( 2.3) 251 ( 3.1) 240 ( 4.3)1 TYPE OF COMMUNITY Advantaged urban State 57 (' 5.6) 39 ( 5.3) 280 ( 1.9) 281 ( 2.4) Nation 03 283 (15.9) ( 7.3)1 23 ( «a.* ( 5.2) 14 (14.6) ( Disadvantaged urban State 52 (18.3) ( 38 (17.4) 4*. Nation 06 (10.7) 31 (11.1) 4 ( 2.2) 252 ( 4.7)1 243 ( 8.0)1 Extreme rural State 61 (15.3) 11 ( 8.2) 28 (14.2) 268 ( 2,4)1 264 ( 2.9)1 Nation 50 (10.6) 40 (10.0) ( 7.3) 268 ( 4.0)) 247 ( 7.6)1 Other State 02 ( 4.9) 30 ( 4.5) 8 ( 1.6) 270 ( 2.0) 256 ( 3.0) 250 ( 4.3) Nat.on 63 ( 3.9) 31 ( 3.5) 6 ( 1.9) 207 ( 2.3) 255 ( 3.1) 257 ( 5,8), 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 valur for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 IL THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE Al la I Teachers' Reports on the Frequency of (continued) Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Times a Week . , About Once a Week or Less TOTAL Pane Meg* and Proficiency Percentage and Proficiency Percentage and Proficiency State 59 ( 3.6) 31 ( 2.7) 10 ( 2.4) 271 ( 1.2) 283 ( 2.1) 253 ( 3.2)1 Nation 62 ( 3.4) 31 ( 3.1) ( 1.8) 267 ( 1.8) 254 I 2.9) 260 ( 5.1)1 PARENTS' EDUCATION HS non-graduate State 52 ( 247 ( 8.4) 3.3) 35 4. 6.2) .4,4) 13 ( 4.7) Nation 67 ( 5.5) 27 ( 5.2) 245 ( 3.2) 41.* HS graduate State 53 ( 5.1) 33 ( 4.1) 14 ( 3.2) 256 ( 2.1) 252 ( 2.3) 247 ( 3.8)1 Nation 61 ( 4.4) 34 ( 3.7) 6 ( 1.5) 257 ( 2.5) 250 ( 2.9) ( ".) Some college State 60 ( 4.4) 29 ( 3.4) 11 ( 3.4) 275 ( 1.7) 288 ( 2.8) Nation 68 ( 42) 26 ( 3.7) 6 ( 1.9) 272 ( 2.7) 258 ( 5.2) College graduate State 63 ( 3.2) 29 ( 2.5) 8 ( 1.8) 280 ( 1.5) 274 ( 2.2) 259 ( 3.8)1 Nation 81 ( 281 ( 4.0) 2.2) 31 ( 265 ( 3.9) 3.1) 8 ( .s. 3.1) GENDER Male State 60 ( 3.8) 29 ( 2.8) 11 ( 2.8) 273 ( 1.21 265 ( 2.2) 258 ( 4.1)1 Nation 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2.1) 256 ( 3.6) 261 ( 8.7)1 Female State 58 ( 3.7) 32 ( 3.1) 9 ( 2.1) 269 ( 1.8) 261 ( 2.6) 248 ( 3.4)1 Nation 65 ( 266 ( 3.6) 1.8) 28 ( 253 ( 3.3) 2.5) 7 ( .. 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 erroi of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurat4. determination of the variability of this estranged mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 THE 1990 NAEP TRIAL STATE ASSESSMENT 115 Colorado TABLE Al lb I Teachers' Reports on the Frequency of Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY - 1090 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Weak About Once a Week Less than Weekly TOTAL Percentage and endogamy earcantage and Pradonsy Percentage and Praddency State 40 ( 3.6) 29 ( 2.7) 31 ( 3.3) 269 ( 11) 270 ( 2.2) 274 ( 2.3) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 260 ( 2.3) 274 ( 2.7) RACE/ETHNICITY Whit. State 39 ( 3.7) 30 ( 3.1) 32 ( 3.4) 267 ( 1.8) 276 ( 1.9) 281 ( 1.6) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Bieck State 36 (11.1) 21 (10.3) 42 ( 8.5) .44 v.) ( ft* ( RI* ) Nation 45 ( 7$) 31 ( 7.6) 23 ( 6.3) 232 ( 3.1)1 243 ( 2.3)1 248 ( 7.0)1 Hispanic State 47 ( 6.4) 27 ( 3.7) 26 ( 5.8) 238 ( 1.9) 251 ( 3.2) 256 ( 3.1)1 Nation 41 ( 7.7) 26 ( 5.3) 33 ( 7.5) 242 ( 3.2)i 244 ( 5.1)' 257 ( 2.3)1 TYPE OF COMMUNITY Advantaged urban State 34 ( 7.3) 37 ( 4.6) 29 ( 6.2) 271 ( 4.4)! 282 ( 2.4) 236 ( 2.8)1 Nation 59 (13.9) 20 ( 6.0) 21 ( 8.2) 273 ( 3.4)1 ". ( '4') ( Disadvantaged urban State 32 (16.9) ..) 17 (10.1) ( .") SI (17.4) ( ) Nation 50 (13.9) 22 (11.2) 28 (10.7) 237 ( 2.4)1 258 ( 8.3)1 263 ( 4.1)! Extreme rural State 28 (14.0) 26 (11.0) 46 (13.9) 264 ( 2.6)1 268 ( 5.3)1 266 ( 4.9)1 Nation 27 (14.3) .. ) 49 (12.7) 258 ( 6.7)I 24 (10,1) Other State 47 ( 4.4) 27 ( 3.5) 26 ( 3.8) 256 ( 2.8) 265 ( 2.8) 277 ( 3.3) Nation 30 ( 4.4) 36 ( 4.3) 36 ( 4.2) 256 ( 3.3) 259 ( 2.8) 272 ( 2.9) A 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 srze is insufficient to permit a reliable estimate (fewer than 62 students). 116 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A 1 lb I Teachers' Reports on the Frequency of (continued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Less than Weekly TOTAL Percentage and Pro6ciency Percentage and Proficiency Percentage and Proficiency State 40 ( 3.6) 29 ( 2.7) 31 ( 3.3) 259 ( 1.8) 270 ( 22) 274 ( 2.3) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 256 ( 2.3) 260 ( 2.3) 274 ( 2.7) PARENTS' EDUCATION HS non-graduate State 48 ( 235 ( 6.0) 3.4) 25 ( .44 5.0) 27 ( 4.9) "4) Nation 35 ( 239 ( 0.0) 3.5) 29 ( Am. 6.3) 36 ( 250 ( 6.9) 4.5)1 HS graduate State 48 ( 5.1) 27 ( 3.6) 25 ( 4.1) 249 ( 2.2) 255 ( 2.9) 260 ( 3.1) Nation 35 ( 5.3) 36 ( 4.5) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 263 ( 3.4) Some college State 38 ( 4.1) 31 ( 3.4) 31 ( 3.6) 265 ( 2.5) 274 ( 3.1) 277 ( 2.8) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 266 ( 4.2) 278 ( 2.6) College graduate State 35 ( 3.5) 30 ( 3.1) 35 ( 3.6) 270 ( 2.1) 279 ( 2.3) 282 ( 2.1) Nation 35 ( 3.8) 32 ( 3.4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Male State 39 ( 3.8) 30 ( 3.0) 31 ( 3.5) 261 ( 2.0) 270 ( 2.3) 277 ( 2.7) Nation 35 ( 4.1) 35 ( 3.6) 31 ( 3.5) 257 ( 3.2) 261 1 2.8) 275 ( 3.2) Female State 41 ( 3.8) 27 ( 2.8) 31 ( 3 3) 256 ( 2.2) 270 ( 2.6) 271 ( 2.5) Nation 34 ( 4.1) 32 ( 3.7) 34 ( 4.1) 254 ( 2.1) 258 ( 2.3) 273 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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 a this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 117 Colorado TABLE A 12 I Students' Reports on the Frequency of Small 1 Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL percentage and Proficiency Permits** and Proficiency Percentage and Proficiency State 38 ( 2.3) 30 ( 1.4) 32 ( 2.1) 288 ( 1$) 270 ( 1.6) 285 ( 1.8) Nation 28 ( 2.5) 28 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 281 ( 1.8) RACE/ETHNICITY White State 38 ( 2$) 31 ( 1.5) 32 ( 22) 274 ( 1$) 277 ( 1$) 272 ( 1.5) Nation 27 ( 2.9) 29 ( .7 ) 44 ( 3.5) 288 ( 3.1) 272 ( 1.9) 270 ( 1.7) Black State ( *** 23 ( 3.7) se. ( Nation 28 ( 3.0) 24 ( 3.6) 48 ( 4.7) 234 ( 3.0) 245 ( 4.6) 234 ( 3.1) Hispanic State 38 ( 3.4) 28 ( 2.3) 33 ( 3.8) 245 ( 2.4) 250 ( 2.8) 245 ( 2.8) Nation 37 ( 5.2) 22 ( 3.6) 41 ( 5.0) 242 ( 3.9) 250 ( 3.4) 240 ( 2.8) TYPE OF COMMUNITY Advantaged viban State 40 ( 3.9) 29 ( 2.3) 31 ( 2.8) 280 ( 2.7) 282 ( 2.7) 277 ( 2,9) Nation 27 (13.9) 33 ( 4$) 40 (13.4) 286 ( 5.4p 279 ( 3.5)1 Disadvantaged urban state 47 ( 6.8) 31 I 7.3) ht* Nation 31 ( 5.7) 20 ( 2.8) 49 ( 6.3) 24 ( 4.0)1 287 ( 6.4)) 245 ( 3,7)1 Extreme rural State 28 ( 7$) 34 ( 5.6) 37 ( 8,5) 265 ( 42)1 268 ( 3.2)1 265 ( 3.1)1 Nation 34 (10.8) 27 ( 3.8) 39 (11.6) 249 ( 5.2)1 264 ( 35)1 256 ( 6.2)1 Other State 41 ( 4.1) 30 ( 2.4) 29 ( 3$) 263 ( 2.3) 2P0 ( 2,4) 263 ( 3.0) Nation 27 ( 2.6) 1,7) 45 ( 3.3) 260 ( 3.3) , 2.1) 262 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, 8" Sample sin is insufficient to permit a reliable estimate (fewer than 62 students). 4 118 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A 12 Students' Reports on the Frequency of Small (continued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY _ 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never _ AMR TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Praddency State 38 ( 2.3) 30 ( 1.4) 32 ( 2.1) 280 ( 1$) 270 ( 1.0) 285 ( 1.8) Nation 28 ( 2.5) 26 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 281 ( 1.8) PARENTS' EDUCATION HS non-graduate State 31 ( 3.4) ,Hm.) .**) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4.5) liS graduate state 242 ( 41 ( 3.4) 3.0) 244 ( 28 ( 3.0) 2.5) 242 ( 32 ( 2.7) 3.2) 251 ( 1.8) 258 ( 2.8) 25$ ( 2.6) Nation 28 ( 3.0) 28 ( 1.8) 43 ( 34) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some college State 36 ( 3.2) 33 ( 2.6) 32 ( 3.2) 270 ( 2.2) 273 ( 2.4) 270 ( 2$) Nation 27 ( 3.9) 27 ( 2.4) 46 ( 3.8) 265 ( 3.6) 268 ( 3.3) 266 ( 2.1) College graduate State 39 ( 2.7) 31 ( 1.7) 30 ( 2.0) 277 ( 1/) 280 ( 2.0) 274 ( 1.9) Nation 28 ( 3.0) 28 ( 1.9) 44 ( 3.6) 270 ( 2.7) 278 ( 2.8) 275 ( 2.2) GENDER Male State 37 ( 25) 30 ( 1.7) 32 ( 2.3) 267 ( 1.8) 272 ( 1.9) 269 ( 1.9) Nation 31 ( 2.9) 28 ( 1.7) 41 ( 2.9) 259 ( 3.3) 268 ( 2.6) 262 ( 1.8) Female State 39 ( 2.6) 31 ( 1.8) 31 ( 2.3) 266 ( 1.9) 268 ( 1.9) 262 ( 2.0) Nation 26 ( 2.4) 27 ( 1.8) 47 ( 32) 257 ( 2.8) 266 ( 1.7) 260 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Colorado TABLE A 13 I Students' Reports on the Use of Mathematics 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 28 ( 1.9) ( 1 .2 ) 43 ( 1.9) 264 ( 1.7) 271 ( 1.3) 266 ( 1.4) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.6) 269 ( 1$) 259 ( 1.6) RACE/ETHNIC1TY White State 25 ( 2.1) 33 ( 1.2) 411 2.0) 271 ( 1.6) 277 ( 1.4) 274 ( 1.3) Nation 27 ( 1.9) 33 ( 1.6) 40 ( 2.5) 266 ( 2.6) 275 ( 1.6) 268 ( 1.8) Black State 27 ( 3.8) ...) 42 ( 4.2) *4* Nation 27 ( 3.3) 27 ( 3.2) 46 ( 4.5) 234 ( 3.7) 248 ( 4.5) 232 ( 2,6) Hispanic State 26 ( 3.6) 29 ( 2.7) 45 ( 3.9) 243 ( 3.3) 252 ( 2.5) 245 ( 1.6) Nation 38 ( 4.2) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) TYPE OF COMMUNITY Advantaged urban State 34 ( 4.3) 31 ( 2.3) 36 ( 3.4) 273 ( 2.8) 287 ( 1.8) 279 ( 2.4) Nation 35 (10.3) 33 ( 4.8) 32 (11.1) 278 ( 8.1)1 284 ( 3.2)! 281 ( 5.9)1 Disadvantaged urban State 33 ( 5,1) 33 ( 7.1) 4.. I 4.4) 34 ( 3.2) Nation 35 ( 6.6) 19 ( 2.1) 46 ( 6.4) 249 ( 5.3)1 258 ( 5.7)1 246 ( 4.8)1 Extreme rural State 35 ( 6.7) 36 ( 3.8) 29 ( 4.3) 285 ( 4.7)1 267 ( 2.5)1 267 ( 4.0)1 Nation 21 ( 3.1) 37 ( 4.7) 43 ( 5.0) 411 ( 44 282 ( 4.7)1 251 ( 5.2)1 Other State 19 ( 2.4) 32 ( 1.7) 49 ( 2.7) 261 ( 3.2) 268 ( 2.1) 285 ( 2.2) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2,4) 256 ( 2.9) 270 ( 1.8) 260 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 1. 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 4.; 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A 13 Students' Reports on the Use of Mathematics (cmitinued) Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Al Least Once a Week Less Than Once a Week Never TOTAL Penmintage and Proficiency Percentage and PrOcloncy Percentage and PrOdency State 26 ( 1.9) 32 ( 1.2) 43 ( 1.9) 264 ( 1.7) 271 ( 1.3) 266 ( 1.4) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.6) 269 ( 1.5) 259 ( 1.6) PARENTS' EDUCATION HS non-graduate State 24 ( 4.4) 47 ( 5.0) ( 242 ( 2.7) Nation 27 ( 4.2) 26 ( 2.7) 47 ( 5.01 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) HS graduate State 26 ( 2.5) 30 ( 2.6) 43 ( 2.9) 251 ( 2.9) 257 ( 2.1) 254 ( 2.4) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some college State 21 ( 2.5) 35 ( 2.3) 44 ( 2.7) 264 ( 2.6) 275 ( 1.9) 272 ( 2.2) Nation 29 ( 2.6) 36 ( 2.3) 35 ( 2.6) 261 ( 3.5) 274 ( 2.2) 263 ( 2.1) College graduate State 26 ( 2.1) 33 ( 1.4) 40 ( 2.0) 274 ( 1.9) 279 ( 1.7) 278 ( 1.5) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2.6) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Male State 28 ( 2.2) 32 ( 1.3) 39 ( 2.0) 265 ( 2.0) 272 ( 1.6) 270 ( 1.3) Nation 32 ( 2.0) 30 ( 1.5) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 23 ( 2.0) 31 ( 1.7) 46 ( 2.1) 263 ( 2.2) 270 ( 263 ( 1.8) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3.0) 268 ( 1.5) 257 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. " Sample size is insufficient to permit a reliable estinlaw (fewer than 62 students). c' u THE 1990 NAEP TRIAL STATE ASSESSMENr 121 Colorado TABLE A14 1 Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Almost Every Day Saw& Times a Wart( - About Once a Week or Less TOTAL Pawning. and Proficiency Percentage and Proficiency Percentage and Proficiency State 73 ( 2.1) 15 ( 1.0) 12 ( 1.6) 272 ( 1.0) 256 ( 1.9) 250 ( 2.2) Nation 74 ( 1.9) 14 ( 0,8) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 4$) RACE/ETHNICITY White State 76 ( 2.2) 14 ( 1.2) 10 ( 1.5) 278 ( 1.1) 265 ( 1.6) 258 ( 2.2) Nation 76 ( 2$) 13 ( 0.8) 11 ( 2.2) 274 ( 1.3) 258 ( 22) 252 ( 5.1)1 Black State 62 ( 9.1) 15 ( 5.3) 241 ( 4.6)1 Irlt *** Nation 71 ( 2.8) 15 ( 1.7) 14 ( 3.2) 240 ( 2.9) 232 ( 3.1) 223 ( 6.1)i Hispanic State 65 ( 3.4) 17 ( 1,4) 17 ( 2.7) 252 ( 1.9) 237 ( 3.4) 236 ( 2.6) Nation 61 ( 3.7) 21 ( 2.9) 17 ( 2.7) 249 ( 2.3) 242 ( 5.1) 224 ( 3.4) TYPE OF COMMUNITY Advantaged urban State 77 ( 3.3) 16 ( 2.2) 7 ( 1.6) 284 ( 1.6) 267 ( 4.0) t .41 ) Nation 73 286 (11.1) ( 4.6)1 13 ( 1.7).) 14 (10.4) .44 ..) Disadvantaged urban State 64 ( 4.0) 22 2.9) 14 ( 2.2) 251 ( 5.5)1 .) Nation 69 ( 2.8) 15 ( 2.5) 15 ( 2.2) 253 ( 3.7)1 243 ( 4.4)1 235 ( 64)1 Extreme rural State 74 268 (10.2) ( 2.3)1 9. 17 ( 8.9) ..) Nation 68 263 (11.3) ( 4.2)1 17 ( 8 2) ..) Other State 74 ( 2.6) 15 ( 1.6) 12 ( 1.8) 270 ( 1.6) 255 ( 3.0) 247 ( 3.0) Nation 75 ( 22) 14 ( 1.0) 10 ( 1.9) 267 ( 1.6) 252 ( 2.6) 239 ( 4.3)1 The standard errors of the estimated statistics appear in parentheses. 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. ! 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 Colorado TABLE A14 I Students' Reports on the Frequency of (continued) I Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL About Once a Week or STATE ASSESSMENT Almost Every Day Several Times a Week Less _ 11. TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 73 ( 2.1) 15 ( 1.0) 12 ( 1.6) 272 ( 1.0) 256 ( 1.9) 250 ( 2.2) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) 267 ( 1.2) 252 ( 1.7) 242 ( 4.5) PARENTS EDUCATION HS noniraduate State 63 ( 247 ( 5.1) 3.2) 22 ( 3,4) 4..) 15 ( 3.5) Nation 64 ( 245 ( 3,4) 2,3) 18 ( ( 2.0) .4.4) 18 ( 4*44*4) 3.1) PIS graduate State 68 ( 3.2) 14 ( 1.4) 18 ( 2.9) 258 ( 1.7) 246 ( 2.9) 245 ( 3.4) Nation 71 1 3.6) 16 ( 1.8) 13 ( 2.8) 258 ( 1.6) 249 ( 3.2) 239 ( 3.4)1 Some college State 72 ( 275 ( 3.4) 1.4) 17 ( 263 1 2.2) 3.4) 11 ( 2.0) 0-4.) Nation BO ( 270 ( 2,0) 1,9) 11 ( 1.2) 9 ( ( 1.7).) College graduate State 79 ( 1.8) 13 ( 1.3) 8 ( 1.0) 281 ( 1.2) 265 ( 2.4) 258 ( 2.9) Nation 77 1 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 260 ( 2.8) 257 ( 6.4)1 GENDER Male State 72 2.4) 15 ( 1.1) 13 ( 1.9) 274 ( 1.1) 260 ( 2.2) 252 ( 2.9) Nation 72 1 2.4) 16 ( 1.2) 12 ( 2,1) .268 ( 1.6) 252 I 2.5) 242 ( 6.1) Female State 75 ( 2.3) 15 ( 1.4) 11 ( 1.5) 270 ( 1.4) 253 ( 2.9) 249 ( 2.5) Nation 76 ( 1.8) 13 ( 1.0) 11 ( 1.6) 265 ( 1.3) 250 1 2.5) 242 1 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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 profkiency. *I" Sample stze is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Colorado TABLE A 15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Several Times a Week About Once a Week Less Than Weekly TOTAL Poundage and Prone:Wm Percentage and Proildancy Parcentage and Proficiency State 36(2.3) 26 ( 1.4) 37 ( 21) 259 ( 1.5) 270 ( 1.3) 274 ( 1.3) Nation 38 ( 24) 25 ( 1.2) 37 ( 2.5) 253 ( 22) 261 ( 1.4) 272 ( 1.9) RACE/ETHNICITY White State 34 ( 2.6) 28 ( 1.6) 38 ( 2.4) 267 ( 1.4) 278 ( 1.5) 280 ( 1.3) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 282 ( 2.5) 260 ( 1 4) 277 ( 2.0) Slack State ( 52) 4.**) 29 ( ft* ( 5.0) Nation 48 ( 3.8) 32 ( 2.7) 20 ( 3.1) 232 ( 4.3) 241 ( 2.9) 241 ( 4.4) Hispanic State 40 ( 3.4) 27 ( 2.4) 33 ( 3.5) 238 ( 2.2) 252 ( 2.1) 253 ( 2.3) Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 238 ( 3.9) 247 ( 3.3) 248 ( 3.3) TYPE OF COMMUNITY Advantaged urban State 39 ( 4.7) 28 ( 2.5) 33 ( 4.0) 273 ( 2.6) 280 ( 1.8) 287 ( 2.7) Nation 50 ( 9.0) 19 ( 4.9) 31 ( 9.3) 271 ( 3.3)1 299 ( 5.3)1 Disadvantaged urban State ( 26 ( *4,0 6.3) ) 35 ( 8.8) Nation 37 ( 5.8) 23 ( 3.6) 41 ( 8.7) 240 ( 4.8)1 253 ( 4.1)1 255 ( 4.2)1 Extreme rural State 26 ( 9.2) 28 ( 4.2) 46 ( 9.2) 263 ( 3.1)1 267 ( 3.1)1 287 ( 3.7)1 Nation 42 (10.1) 30 ( 4.4) 28 ( 7.5) 249 ( 4.0)1 256 ( 3.4)1 287 ( 7.3)1 Other State 34 ( 3.1) 28 ( 2.2) 38 ( 3.2) 254 ( 2.5) 267 ( 2.2) 273 ( 1.7) Nation 36 ( 2.9) 26 ( 1.2) 36 ( 2.9) 252 ( 3.0) 261 ( 2.1) 272 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 124 1 2 THE 1990 NAEP TRIAL STATE ASSESSMEN1 Colorado TABLE AlS I Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 MEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Once a Week Less Than Weekly TOTAL Percentage and Prodding/ Percentage and Proficiency Percentage and Proficiency State 3e ( 2.3) 28 ( 1.4) 37 ( 2.2) " ( 1.5) 270 ( 1.3) 274 ( 1.3) Nation 38 ( 2.4) 25 ( 12) 37 ( 2.5) 253 ( 2.2) 261 ( 1.4) 272 ( 1.9) PARENTS' EDUCATION HS non.graduate State 41 ( 3.9) 21 ( 3.0) 38 ( 3.7) 238 ( 3.2) ( 247 ( 4.4) Nation 41 ( 4.5) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) liS graduate State ( 3.4) 30 ( 2.3) 32 ( 3.4) 245 ( 22) 259 ( 22) 281 ( 2.2) Nation 40 ( 3.2) 29 ( 22) 32 ( 3.6) 247 ( 2.7) 258 ( 2$) 262 ( 2.2) Some college State 38 ( 3.3) 28 ( 2.3) 34 ( 2.8) 264 ( 2.3) 271 ( 2.6) 279 ( 2.0) Nation 34 ( 3.4) 26 ( 22) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) College graduate State 33 ( 2.4) 28 ( 1.8) 40 ( 2.5) 269 ( 1.8) 2T9 ( 1.9) 282 ( 1.6) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 273 ( 2$) 285 ( 2.3) GENDER Male State 38 ( 2.5) 28 ( 1.8) 34 ( 2.4) 260 ( 1.7) 271 ( 1.6) 277 ( 1.6) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 283 ( 2.3) 274 ( 2.4) Female State 34 ( 2.6) 27 ( 1.7) 39 ( 2.5) 257 ( 2.1) 268 ( 2.1) 271 ( 1.4) Nation 37 ( 2.5) 25 ( 1.5) 38 ( 2.6) 253 ( 2.1) 259 ( 1.8) 289 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 125 Colorado TABLE A 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 _ Ovon a Calculator Teacher Explains Calculator Use Yes No Yes _ No TOTAL Percentage and Pronciency 98 ( 0.3) 268 ( 1.0) 97 ( OA) 263 ( 1.3) 99 ( 0.2) 274 ( 1.0) 98 ( 0.3) 270 ( 1.5) 98 ( 1.9) 237 ( 3S)! 93 ( 13) 237 ( 2.8) 95( 0.8) 248 ( 1.5) 92 ( 1.2) 245 ( 2.7) 99 ( 0.5) 280 ( 1.7) 99 ( 1.0) 281 ( 3.8)1 97 ( 2.0) 248 ( 4.5)1 94 ( 1.2) 250 ( 3.5)1 99 ( 0.6) 267 ( 2.6) se 1.3) 257 ( 3.9)1 98 ( 0.5) 265 ( 1.7) 97 ( 0.5) 263 ( 1.7) Percentage and Proficiency 2 ( 0.3) .44(444) 3 ( 0.4) 234 ( 3.8) ( ) 2 ( 0.3) 2 ( 1.9) ( ".) 7 ( 1.5) ( .44) ( ) 8 ( 12) ( ) 1 1.0)") 3 2.0) ) 41 1.3) 4*. .) 3 ( 0.5) 233 i 5.4) Percentage and Proficiency 52 ( 2.0) 263 ( 12) 49 ( 2.3) 258 ( 1.7) 51 ( 2.3) 270 ( 1.3) 46 ( 2.6) 266 ( 1.8) 58 ( 4.7) 232 ( 3.9)1 53 ( 4.9) 235 ( 3.6) 55 ( 3.2) 245 ( 1.9) 63 ( 4.3) 243 ( 3.4) 55 ( 4.0) 276 ( 2.0) 45 (12.2) 276 ( 25)1 68 ( 8.5) 243 ( 4.2)1 53 ( 7$) 247 ( 4.1)1 53 ( 7.7) 264 ( 2.3)1 42 ( 8.7) 251 ( 4.8)1 50 ( 2.8) 259 ( 2.3) 50 ( 2.7) 258 ( 2.1) Percentage and Prondency 48 ( 2.0) 272 ( 1.4) 51 ( 2.3) 266 ( 1.5) 49 ( 2.3) 279 ( 1.3) 54 ( 2.6) 273 ( 1.8) 47 ( 4.9) 239 ( 2.7) 45 ( 3.2) 249 ( 2.2) 37 ( 4.3) 245 ( 2.9) 45 ( 4.0) 284 I 2.2) 55 (12.2) 285 ( 6.4)1 32 ( 8$) ii) 47 ( 7.5) 251 ( 3.6)1 47 ( 7.7) 268 ( 3.7)1 58 ( 8.7) 261 ( 4.4)1 50 ( 2.8) 271 ( 2.0) 50 ( 2.7) 266 ( 2.0) State Nation RACE/ETHNICITY Whit. State Nation Slack State Nation Hispanic State Nation TYPE Or COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation he standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to perrnit a reliable estimate (fewer than 62 students). 126 131 Th E 1990 NAEP TRIAL STATE ASSESSMENT Colorado 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 1000 NAEP TRIAL STATE ASSESSMENT Own a Calculator Teacher Explains Calculator Use Yes No Yes 1 No TOTAL Percentage and Proficiency Per tentage and Proficiency Percentage and ProlicienCy Percentage and Proficiency State 98 ( 0.3) 52 ( 2.0) 48 ( 2.0) 268 ( 1.0) 263 ( 1.2) 272 ( 1.4) Nation 97 ( 0.4) 3 ( 0.4) 49 ( 2.3) 51 ( 2.3) 203 ( 1.3) 234 ( 3.8) 258 ( 1.7) 266 ( 1.5) PARENTS EDUCATION HS non-graduate State 91 ( 2.0) 9 ( 2.0) 57 ( 4.5) 43 ( 4$) 243 ( 2.6) 242 ( 2.8) 245 ( 4.0) Nation 92 ( 1.6) 8 ( 1.6) 53 ( 4.6) 47 ( 4.6) 243 ( 2.0) 242 ( 2.9) 243 ( 23) HS graduate State 97 ( 0.7) 3 ( 0.7) 53 ( 3.4) 47 ( 3.4) 254 ( 1.4) 251 ( 1.8) 254 ( 2.0) Nation 97 ( 0.6) 3 ( 0.6) 54 ( 3.0) 48 ( 3.0) 255 ( 1.5) 2.52 ( 1.9) 258 ( 2.0) Sane college State 99 ( 272 ( 0.6) 1.2) **-.) 53 ( 266 ( 2.9) 1.5) 47 ( 277 ( 2.9) 2.0) Nation 96 ( 268 ( 0.9) 1.8) 4 ( 0.9) ***) 48 ( 285( 3.2) 2.4) 52 ( 268 ( 3.2) 2.2) College graduate State 99 ( 0.2) ( 02) 51 ( 25) 49 ( 2$) 277 ( 12) ( '+') 273 ( 1.5) 282 ( 1.6) Nation 99 ( 0.2) 1 ( 0.2) 46 ( 2.6) 54 ( 2.6) 275 ( 1.6) ( **) 268 ( 2,2) 280 ( 1.9) GENDER Male State 98 ( 0.4) 54 ( 2.2) 46 ( 2.2) 269 ( 1.0) 265 ( 1,5) 274 ( 1.4) Nation 97 ( 264 ( 0.5) 1.7) 3 ( *.. 0.5) 51 ( 258 ( 2.6) 2.1) 49 ( 289 ( 2.6) 2.1) Female state 98 ( 0.4) 2 ( 0.4) 50 ( 2.2) 50 ( 2.2) 266 ( 1.3) ( '") 261 ( 1.5) 270 ( 1.8) Nation 97 ( 0.5) 3 ( 0.5) 47 ( 2$) 53 ( 2$) 262 ( 1.3) `" ( a.) 258 ( 1.7) 283 ( 1.6) NIL 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 sire is insufficient to permit a reliable estimate (fewer than 62 students), 134; THE 1990 NAEP TRIAL STATE ASSESSMENT 127 Colorado TABLE A19 I Students' Reports on the Use of a Calculator 1 for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT "'king Probims in Class Doing Problems at Home Taking Quizzes or Tests Almost 1 Always Never . Almost Always Never Almost Always Never TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 49 ( 1.4) 18 ( 1.3) 33 ( 1.4) 13 ( 0.9) 24 ( 1.3) 29 ( 1.5) 282 ( 1.2) 277 ( 1.7) 269 ( 1.3) 270 ( 2.1) 283 ( 2.1) 277 ( 1.3) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 1.4 19 ( 0.9) 27 ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 201 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) RACE/ETHNICITY White State 47 ( 1.7) 19 ( 1.5) 35 ( 1.4) 13 ( 1.0) 24 ( 1.4) 31 ( 1.7) 269 ( 1.3) 282 ( 1.8) 275 ( 1.4) 278 ( 2.1) 211 ( 2.2) 281 ; 1.4) Nation 46 ( 1.7) 24 ( 2.2) 31 ( 1.5) 18 ( 1.2) 25 ( 1.6) 32 ( 202 ( 1.7) 278 ( 1.3) 270 ( 1.7) 269 ( 2.3) 263 ( 2.8) 279 ( 1.2) Rick State 56 ( 235 ( 4.3) 3,8)1 *4 ( 444 ) 32 ( 4*. ( 4.1) 16 ( *4 4 ( 3.7) 4** ) Nation 57 ( 3.2) 20 ( 3.9) 31 ( 2.9) 18 ( 1.9) 38 ( 3.3) 24 ( 3.1) 232 ( 2.4) 249 ( 4.0) 233 ( 3.3) 24.8 ( 5.5) 230 ( 3.6) 251 ( 4.1) Hispanic State 52 ( 2.5) 16 ( 1.9) 25 ( 2.5) 15 ( 1.5) 25 ( 2.4) 23 ( 2.2) 244 ( 2.1) 255 ( 3.5) 249 ( 2.6) 246 ( 3.3) 243 ( 2.9) 259 ( 2.6) Nation 51 ( 2.9) 16 ( 3.5) 26 ( 3.2) 21 ( 2.1) 26 ( 2.7) 22 ( 3,1) 239 ( 2.8) 252 ( 3.3)1 238 ( 4.8) 244 ( 3.1) 237 ( 32) 256 ( 4.2) TYPE OF COMMUNITY Advantaged urban State SO ( 3.2) 12 ( 1.9) 43 ( 2.7) 9 ( 1.6) 31 ( 2.9) 23 ( 2.9) 277 ( 2.0) 289 ( 3.0)1 281 2,3) 283 ( 5.6)1 279 ( 3.0) 287 ( 2.5) Nation 51 ( 5.4) 23 (10.7) 32 ( 6.1) 15 ( 24) 31 ( 3,8) 28 ( 8.8) 270 ( 4.1)1 ( i 274 ( 4.9)1 ( 281 ( 7.6)1 285 ( 4.2)1 Disadvantaged urban State 48 ( 3.3) 15 ( 1.8) 26 ( 4.6) 14 ( 3.8) 29 ( 5.1) 28 ( 3.1) 244 ( 8.0)1 ( ) Nation 52 ( 3.1) 22 ( 4.5) 30 ( 3.3) 24 ( 2.3) 27 ( 2.9) 27 ( 4.8) 241 ( 3.8)1 259 ( 5.4)1 246 ( 5.2)1 254 ( 4.6)1 240 ( 4.9)1 263 ( 5.0)1 Extreme rural State 46 ( 5.6) 20 ( 6,7) 31 ( 3.7) 9 ( 2.0) 22 ( 4.5) 30 ( 6.3) 262 ( 3.1)1 274 ( 2.8)1 265 ( 2.7)1 m '") 263 ( 3.8)1 277 ( 3.3)1 Nation 46 ( 7.4) 29 ( 6.5) 20 ( 2.5) 23 ( 3.9) 24 ( 6,6) 37 ( 8.3) 246 ( 4.3)1 268 ( 6.1)1 ( "") 263 ( 4.4)1 270 ( 4.0)1 Other State 41 ( 2.0) 22 ( 2.3) 28 ( 2.0) 16 ( 1.4) 19 ( 1.5) 331 2.4) 258 ( 1.9) 276 ( 2.6) 265 ( 2.0) 269 ( 2.7) 258 ( 3.9) 276 ( 2.0) Nation 48 ( 1.9) 22 ( 2.0) 32 ( 1.7) 18 ( 1.1) 27 ( 1,8) 29 ( 2.1) 254 ( 2.1) 272 ( 1.8) 263 ( 2.3) 263 ( 2.8) 253 ( 2,7) 275 ( 1.9) The standard errors of the estimated statistics appear in parentheses. 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 pervnt because the "Sometimes" categmy is not included. ! interpret with caution the nature of the sample does not allow accurate determination of the variability or this estimated mean proficiency. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 128 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A19 I Students' Reports on the Use of a Calculator (continued) I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT . - Working Problems hi Clan _ Doing Problems at Home Taking Quinn or Tests Almost Always i Never Almost Always Never Almost Always Never .11=O11 TOTAL Percentage and Proficiency Percentege and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage aid Proficiency Paventage and Proficiency State 49 ( 1.4) 18 ( 1.3) 33 ( 1.4) 13 ( 0.9) 24 ( 1.3) 29 ( 1.5) 262 ( 1.2) 277 ( 1.7) 289 ( 1.3) 270( 2.1) 263 ( 2.1) 277 ( 1.3) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 13) 19 ( 0.9) 27 ( 1.4) 30 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) PARENTS EDUCATION HS non-graduate State 56 ( 238 ( 3.6) 3.3) 12 ( 2.7) 23 ( 3.1) ...) 18 ( INN ( 2.8) 27 ( 3.7) ...) 23 ( 3.5) Nation 54 ( 240 ( 3.3) 2.3) 19 ( 3.8) ...) 26 ( 244 ( 3.1) 3,8) 22 ( 244 ( 2.8) 4.2) 32 ( 237 ( 3.6) 2.3) 24 ( 251 ( 3.2) 4.15) HS graduate State 51 ( 3.1) 17 ( 1.9) 32 ( 2.4) 15 ( 1.7) 22 ( 2.1) 24 ( 2.5) 250 ( 1.8) 265 ( 3.9) 255 ( 2.7) 258 ( 3.4) 248 ( 3.5) 266 ( 3.0) Nation 52 ( 2.5) 20 ( 2.4) 29 ( 1,9) 18 ( 1.5) 26 ( 1.5) 27 ( 2.2) 249 ( 1.4) 265 ( 2.7) 250 ( 2.4) 250 ( 2.4) 246 ( 2.8) 265 ( 2.0) Some college State 45 ( 2.3) 20 ( 2.2) 31 ( 2.2) 14 ( 1.5) 23 ( 2.1) 34 ( 2.8) 266 ( 1.8) 276 ( 3.2) 272 ( 1.7) 276 ( 3.2) 266 ( 2.5) 278 ( 2.1) Nation 46 ( 2.8) 26 ( 2.8) 2$ ( 2.0) 20 ( 1.9) 26 ( 2.4) 35 ( 2.5) 258 ( 2.1) 272 ( 25) 267 ( 3.0) 268 ( 3.2) 255 ( 3.6) 275 ( 2.0) College "'actuate State 48 ( 1,9) 19 ( 1.6) 37 ( 1,$) 11 ( 1.1) 26 ( 1.8) 30 ( 1.7) 273 ( 1.6). 286 ( 2.1) 277 ( 1.6) 281 31) 275 ( 2.4) 284 ( 1.7) Nation 45 ( 1.9) 25 ( 2.4) 33 ( 2.0) 16 ( 1.4) 26 ( 1.6) 33 ( 2.7) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 268 ( 2.6) 285 ( 2.0) ()ENDER Male State 50 ( 1.6) 17 ( 1.3) 33 ( 1.7) 15 ( 1.5) 24 ( 1.3) 2t 1.5) 264 ( 1.3) 281 ( 2.1) 271 ( 1.5) 272 ( 2.7) 286 ( 2.1) 28t. , 1.6) Nation 50 ( 1.7) 20 ( 2.0) 23 ( 1.8) 19 ( 1,3) 27 ( 1.5) 26 ( 2.1) 255 ( 1.9) 275 ( 2.2) 264 ( 2.8) 263 ( 2.5) 256 ( 3,0) 277 ( 1.9) Female State 47 ( 1.9) 19 ( 1.8) 34 ( 1.7) 11 ( 1.0) 25 ( 1.6) 29 ( 2.0) 260 ( 1.7) 272 ( 2.0) 267 ( 1.8) 267 ( 2.8) 261 ( 2.8) 274 ( 1.6) Nation 46 ( 2.0) 26 ( 2.1) 32 ( 1.6) 18 ( 1.2) 27 ( 1.8) 33 ( 2.1) 252 ( 1.7) 269 ( 1,8) 259 ( 1.7) 263 ( 2.1) 251 ( 2.4) 271 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of Interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 13, THE 1990 NAEP TRIAL STATE ASSESSMENT 129 Colorado TABLE A20 J Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 199O MEP TRIAL "Calculator-Use" "Calculator-Use" STATE ASSESSMENT High Group Other Group TOTAL Pententage and Pro Ildency Percentage and Proficiency State 49 ( 1.1) 51 ( 1..1) 274 ( 1.2) 261 ( 1.3) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACEJETNNICITY Wit Ns State 51 ( 1.3) 49 ( 1.3) 279 ( 1.3) 268 ( 1.3) Nation 44 ( 1.4) 56 ( 1.4) 277 ( 1.7) 283 ( 1.7) Slack State 50 ( 0+. ( 5.8) 50 ( 5.6) 4.4 ( Imre) Nation 37 ( 3.4) 63 ( 3.4) 248 ( 3.9) 231 ( 3.0) Hispanic State 43 ( 2.0) 57 ( 2.0) 252 ( 22) 242 ( 2.3) Nation 36 ( 4.2) 64 ( 4.2) 254 ( 4.6) 238 ( 3.0) TYPE OF COMMUNITY Advantaged urban State 51 ( 2.4) 49 2.4) 285 1 22) 273 ( 2.0) Nation 50 ( 3.8) 50 ( 3.8) 288 ( 4.9)1 275 ( 4.4)1 Disadvantaged urban State ...) 62 ( 4.5) Nation 38 ( 4.2) 821 4.2) 262 ( 5.6)1 244 ( 3.9)1 Extreme rural State 51 3.0) 49 ( 3.0) 270 ( 3.2) 264 ( 3.1)1 Nation 39 5.6) 61 ( 5.6) 269 ( 4.4)1 248 ( 4.3)1 Other State 50 ( 1.2) 50 ( 12) 272 ( 1.8) 258 ( 2.1) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value 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). 130 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1500 NAEP TRIAL "Calculator-Use" STATE ASSESSMENT High Group Other "Calculator-Use" Group TOTAL Percentage and Proficiency peraIrliage and Proficiency State 49 ( 1.1) 51 ( 1.1) 274 ( 1.2) 2131 ( 1.3) Nation 42 ( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) PARENTS EDUCATION HS nen-graduate State 42 ( 4.2) 58 ( 4.2) 237 ( 3.6) Nation 34 ( 3.3) 66 ( 3.3) 248 ( 4.4) 242 ( 2.4) liS graduate State 45 ( 2.5) 55 ( 2.5) 258 ( 4.8) 252 ( 2.5) Nation 4r* t, 22) 60 ( 2.2) 263 ( 2.0) 249 ( 1.8) Some college State 47 ( 2.4) 53 ( 2.4) 276 ( 1.9) 266 ( 2.0) Nation 48 ( 2.2) 52 ( 22) 277 ( 2.6) 258 ( 2.5) College graduate State 53 ( 1.6) 47 ( 1.6) 283 ( 1,4) 270 ( 1.6) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER Male State 46 ( 1.4) 54 ( 1.4) 275 ( 1.5) 263 ( 1.6) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 255 ( 2.3) Female State 52 ( 1.7) 48 ( 1.7) 272 ( 1.6) 258 ( 1.6) Nation 45 ( 1.8) 55 ( 1.8) 269 ( 1.7) 254 ( 1.3) 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 i 2 standard errors of the estimate for the sample. ''" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 13u THE 1990 NAEP TRIAL STATE ASSESSMENT 131 'mad° TABLE A24 1 Students' Reports on Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY . _ 1000 NAEP TRIAL STATE ASSSISMENT Zero to Two Types Throe Types Four Types TOTAL Porcontage and Proficiency Percentage and Proficiency Percentage end Proliciency State 15 ( 0.7) 32 ( 0.8) 53 ( 1.0) 250 ( 1.7) 264 ( 1.2) 274 ( 1,1) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 25$ ( 1.7) 272 ( 1.5) RACE/ETHNICITY White State 10 ( 0.6) 31 ( 1.0) 59 ( 1.1) 282 ( 2.3) 270 ( 1.4) 278 ( 1.1) Nation 16 ( 1.1) 29 ( 1.3) 56 ( 1$) 251 ( 2.2) 268 ( 1.5) 278 ( 1.7) Mad( State 29 ( 04* ( 3.2) 32 ( 3.7) ***) 40 ( 4.4) Nation 31 ( 1.9) 36 ( 22) 33 ( 2.4) 232 ( 3.2) 233 ( 3.9) 245 ( 3.3) H:spanic State 30 ( 2.1) 34 ( 2.0) 36 ( 2.3) 236 ( 2.2) 245 ( 22) 256 ( 2.1) Nation 44 ( 3.0) 30 ( 2.4) 28 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) TYPE OF COMMUNITY Advantaged urban State 8 ( 1.1) ..) 28 ( 276 ( 1.4) 2.4) 63 ( 284 ( 1.7) 1.7) Nation 13 ( 3.8) 26 ( 2.1) 61 ( 4.9) 287 ( 3.6)1 Disadvantaged urban State 28 ( *. 4.8)) 37 ( 1.8) ..) 35 ( 4.0) Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.6) 243 ( 2.9)1 247 ( 3.7)1 257 ( 4.9)1 Extreme rural State 17 ( 2.7) 32 ( 3.?.) 51 ( 4.0) 252 ( 8.7)1 264 ( 3.7)1 272 ( 1.5) Nation 17 ( 4.9) 33 ( 3.2) 50 ( 5.1) 253 ( 4,3)1 283 ( 5.6)1 Other State 17 ( 1.2) 32 ( 1.4) 51 ( 1.7) 253 ( 2.7) 262 ( 2.0) 271 ( 1.8) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 1.5) 244 ( 2.6) 259 ( 2.2) 272 ( 1.7) The standard errors o 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 thc sample does not allow accurate determination of the variability of this estimated mean proficiency. "1* Sample size is insufficient to permit a reliable esUmate (fewer than 62 students). 13 's 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A24 I Students' Reports OD Types of Reading (continued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Fote Types _ TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 15 ( 0.7) 32 ( 0.8) 53 ( 1.0) 250 ( 1.7) 264 ( 1.2) 274 ( 1.1) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) PARENTS' EDUCATION HS non-graduate State 39 ( 3.5) 38 ( 32) 23 ( 3.0) 232 ( 2.8) 247 ( 3.2) Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 246 ( 3.3) FiS graduate State 23 ( 1.8) 38 ( 1.9) 41 ( 2.0) 250 ( 2.7) 252 ( 1.9) 259 ( 2.4) Nation 26 ( 2.2) 33 ( 1.9) 40 ( 1.7) 246 ( 2.2) 253 ( 2.7) 260 ( 2.1) Some college State 13 ( 1.6) 32 ( 1.9) 55 ( 2.4) 265 ( 3.1) 267 ( 2.1) 275 ( 1.6) Nation 17 ( 1.5) 32 ( 1,7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduate State ( 0.8) 28 ( 1.2) 65 ( 1.3) 262 ( 3.1) 273 ( 1.9) 281 ( 1.3) Nation 10 ( 0.8) 28 ( 1.8) 62 ( 2.0) 254 ( 2.8) '4;9 ( 2.5) 280 ( 1.8) GENDER Male State 15 ( 0.9) 31 ( 1.2) 54 ( 1.2) 253 ( 2.3) 285 ( 1.4) 276 ( 1.4) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Female State 15 ( 1.0) 32 ( 1.2) 53 ( 1.5) 246 ( 2.2) 262 ( 1.7) 273 ( 1,5) Nation 22 ( 1.2) 29 ( 1.4) 49) 1.9) 244 ( 2.2) 258 ( 1.9) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than ('2 students). 13,) THE 1990 NAEP TRIAL STATE SSESSMENT 133 Colorado TABLE A25 I Students' Reports on the Amount of Time Spent 1 Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY , 1900 NAEP TRIAL One Hour or Two Hours Three Hours Four to Fivii Six Hours or STATE ASSESSMENT Less MOWS More _ TOTAL State Nation RACE/ETHNICITY Percentage and Proficiency 17 ( 0.8) 276 ( 1.7) 12 ( 0.8) 269 ( 2.2) 19 ( 1.0) 283 ( 1.7) 13 ( 1.0) 276 ( 2.5) 11 ( 2.8) 6 ( 0.8) Mit ( 4011 14 ( 1.9) 248 ( 3.5) 14 ( 2.4) f. ) 23 ( IS) 288 ( 2.3) 18 ( 1.4)) 15 ( 39) "` ( ) 9 ( 1.2))) 14 ( 3.3),) 16 ( 1.4) 275 ( 2.5) 12 ( 1.0) 268 ( 2.6) Percentage and Prceldency 25 ( 0.9) 273 ( 1,4) 21 ( 0.9) 268 ( 1.8) 27 ( 1.0) 277 ( 1.3) 23 ( 1.2) 275 ( 2.2) 13 ( 2.8)) 13 ( 1.7) 239 ( 7.0) 18 ( 1.7) 251 ( 3.7) 20 ( 2.5) 245 ( 3.2) 27 ( 1.7) 284 ( 2.4) 25 ( 4.3) ref 17 ( 3.1) 250 ( 4.C)1 25 ( 2.5) 271 ( 2.9)1 19 ( 2.6)) 25 ( 1.2) 270 ( 2.2) 21 ( 1.0) 269 ( 2.3) Percentage and Proticienew 24 ( 0.7) 267 ( 1.3) 22 ( 0.8) 285 ( 1.7) 24 ( 0.9) 273 ( 1.6) 24 ( 1.1) 272 ( 1.9) . 18 ( 3.0)) 17 ( 2.1) 239 ( 5.0) 24 ( 1.9) 249 ( 2.3) 19 ( 2.1) 242 ( 5.6) 22 ( 1.4) 277 ( 2.6) 21 ( 1.8) ) 19 ( 2.1) 255 ( 5.0)1 29 ( 2.6) 265 ( 4.1) 23 ( 2.0) 4.1 23 ( 1.1) 264 ( 2.0) 23 ( 1.2) 265 ( 2.1) Percentage and Proficiency 25 ( 0.9) 262 ( 1.4) 28 ( 1.1) 260 ( 1.7) 23 ( 1.0) 270 ( 1.4) 27 ( 1.4) 287 ( 1.7) 32 ( 1.8) 239 ( 4.0) 32 ( 2.0) 246 ( 2.2) 31 ( 3.1) 247 ( 3.5) 20 ( 1.4) 272 ( 2.0) 30 ( 4.3) ( 34 ( 2.4) 251 ( 4.7)1 24 ( 1.3) 262 ( 2.7)1 26 ( 2.7) 256 ( 3.6)1 27 ( 1.4) 262 ( 2.5) 27 ( 12) 259 ( 22) Percentage and Mildew ( 0.7) 249 ( 2,2) 16 ( 1.0) 245 ( 1.7) 7 ( 0.7) 259 ( 2.7) 12 ( 12) 253 ( 2.6) 24 ( 4.6) 32 ( 2.2) 233 ( 2.5) 12 ( 1.8)) 17 ( 1.7) 236 ( 3.6) 8 ( 1.4) ( )) 13 ( 62)) 20 ( 32) 238 ( 4.5)1 1144 () 19 ( 3.8) ( 4) 9 ( 0.8) 246 ( 2.7) 17 ( 1.4) 246 ( 2.5) WIdte State Nation Bieck State Nation Hispanic State Nation TYPE OF COMMUNITY Advantaged urban State Nation Disadvantaged urban State Nation Extreme rural State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 stsindard 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). 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A25 I Students' Reports on the Amount of Time Spent (ccetinued) Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MA) HEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One Hour or Less Two Hours The Hours Four to Five Hours Six Hours or More TOTAL Percentage and Proficiency Percantage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 17 ( 0.8) 25 ( 0.9) 24 ( 0.7) 25 ( 0.9) 9 ( 0.7) 276 ( 1.7) 273 ( 1.4) 267 ( 1.3) 202 ( 1.4) 249 ( 2.2) Nation 12 ( 0.8) 21 ( 0.9) 22 ( 0.8) 28 ( 1.1) 16 ( 1.0) 269 ( 2.2) 268 ( 1.8) 266 ( 1.7) 260 ( 1.7) 245 ( 1.7) PARENTS' EDUCATION HS non-graduate State 9 ( 2.7) 22 ( 3.7) 23 ( 2.8) ( ./eft Nation 12 ( 2.2) -«*) 20 ( 3.1) ) 21 ( 2.8) ..) 28 ( 244 ( 2.9) 3.2) 20 ( 2.4) HS graduate State 9 ( 1.4) 21 ( 1.6) 28 ( 2.0) 29 ( 2.1) 13 ( 1.6) 257 ( 3.0) 258 ( 2.5) 253 ( 2.2) 240 ( 3.6) Nation 8 ( 1.0) 17 ( 1.4) 23 ( 2.0) 32 ( 2.3) 19 ( 1.6) 249 ( 4.7) 257 ( 2.8) 259 ( 3.2) 253 ( 2.5) 248 ( 3.0) Some college State 17 ( 275 ( 1.6) 2.8) 23 ( 275 ( 1.5) 2.3) 25 ( 271 ( 1.9) 2.2) 28 ( 269 ( 2.1) 2.2) ...) Nation 10 ( 1.4) ...) 25 ( 275 ( 2.4) 2.7) 23 ( 269 ( 2.6) 3.5) 28 ( 267 ( 2.2) 2.5) 14 ( 242 ( 1.5) 3.4) College graduate State 23 ( 1.5) 28 ( 1.3) 22 ( 1.2) 21 ( 1.2) 6 ( 0.8) 284 ( 1.8) 281 ( 1.7) 276 ( 2.0) 269 ( 1,7) 263 ( 4.4) Nation 17 ( 1.3) 22 ( 1.6) 23 ( 1.1) 25 ( 1.5) 12( 1.1) 282 ( 2.6) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 3.2) GENDER Male State 15 ( 0.9) 24 ( 1.1) 24 ( 1.1) 27 ( 1.2) 11 ( 1.0) 277 ( 2.5) 274 ( 1.9) 269 ( 1.7) 265 ( 1.5) 256 ( 2.5) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 28 ( 1.3) 17 ( 1.5) 269 ( 3.3) 267 ( 2.8) 267 ( 2.2) 262 ( 2.1) 248 2.5) Female State 20 ( 1.4) 28 ( 1.6) 23 ( 1.1) 23 ( 1.3) 8 ( 0,7) 276 ( 1.9) 272 ( 2.0) 264 ( 1.8) 259 ( 1-9) 238 ( 3.1) Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 1.6) 15 ( 1.2) 269 ( 2.8) 269 ( 2.2) 264 ( 1.8) 258 ( 1-9) 241 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within r 2 standard errors of the estimate for the sample. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Colorado TABLE A26 I Students' Reports on the Number of Days of School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Nom Ono or Two Days Throe Days or Mom 1M. 11=1111111... TOTAL Percentage and Proficiency Penaintage and Praddency Percentage and Proficiency State 40 ( 0.9) 35 ( 1.0) 25 ( 0.9) 272 ( 1.1) 209 ( 1.3) 258 ( 14) Nation 45 ( 32 ( 0.9) 23 ( 1.1) 285 ( 1.8) 266 ( 14) 250 ( 1.9) RACE/ETHNICITY While State 41 ( 1.0) 37 ( 1.1) 22 ( 1.1) 278 1.2) 274 ( 1.3) 267 ( 1.5) Nation 43 ( 1.2) 34 ( 12) 23 ( 1.2) 273 ( 1.8) 272 ( 11) 258 ( 2.1) Bunk State 40 ( .4* 6.9)) 33 ( 5.0)) 27 ( 5.4)) Nation 56 ( 3.1) 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 34) Hispanic State 34 ( 2.1) 32 ( 2.1) 33 ( 1.7) 251 ( 2.4) 250 ( 1.7) 239 ( 24) Nation 41 ( 3.3) 32 ( 2.2) 27 ( 2.8) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) TYPE OF COMMUNITY Advantaged urban State 42 ( 1.3) 36 ( 14) 22 ( 1.2) 284 ( 2.4) 279 ( 1.9) 273 ( 2.3) Nation 47 ( 2.3) 38 ( 2.6) 15 ( 3.7) 284 ( 4.4)1 279 ( 4.5)1 Disadvantaged urban State 25 ( 1.1)) 40 ( 5.5)) 35 ( *44 4.9) ".) Nation 42 ( 3.3) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 256 ( 4.2)1 238 ( 6.3)1 Extreme rural State 49 ( 2.2) 38 ( 2.0) 15 ( 2.0) 268 ( 3.5) 268 ( 3.5)1 Nation 43 ( 257 ( 4.4) 4.1)1 32 ( 264 ( 4.2) 5.8)1 25 ( 3.6) 41.) 00w State 38 ( 1.6) 35 ( 1.6) 27 ( 1.4) 270 ( 1.9) 267 ( 1.7) 255 ( 2.3) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 2135 ( 2.2) 286 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is msufTicient to permit a reliable estimate (fewer than 62 students). 1 4 136 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A26 I Students' Reports on the Number of Days of (WntinUed) I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL. STATE ASSESSMENT None One or Two Days Three Days or More TOTAL Percentage and Prolidency Wonting, and Proectency Percentage and Proficiency State 40 ( 0.9) 35 ( 1A) 25 ( 0.9) 272 ( 1.1) 289 ( 1.3) 258 ( 1.4) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 285 ( 1.8) 286 ( 1.5) 250 ( 1.9) PARENTS' EDUCATION NS non-graduate State 29 ( 3.5) 32 ( 2.9) 38 ( 3.4) ( 238 ( 33) Nation 38 ( 32) 26 ( 3.1) 38 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) NS graduate State 37 ( 2.1) 38 ( 22) 27 ( 1.8) 259 ( 2.2) 255 ( 2.6) 248 ( 2.5) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.6) 249 ( 2.4) Some college State 39 ( 22) 38 ( 2.3) 23 ( 2.1) 277 ( 2.0) 271 ( 1.9) 282 ( 2.4) Nation 40 ( 1.8) 37 ( 1.8) 23 ( 1.8) 270 ( 3.0) 271 ( 23) 253 ( 3.1) College graduate State 43 ( 1.3) 36 ( 12) 21 ( 1.3) 280 ( 12) 277 ( 2.0) 271 ( 2.3) Nation 51 ( 1.8) 33 ( 12) 16 ( 1.3) 275 ( 2.1) 277 ( 1.7) 285 ( 3.1) GENDER Male State 44 ( 1.2) 35 ( 1.6) 21 ( 1.1) 272 ( 1.2) 270 ( 1.4) 281 ( 1.9) Nation 47 ( 1.8) 31 ( 1.4) 22 ( 1.4) 288 ( 2.0) 267 ( 2.1) 250 ( 2.8) Female State 38 ( 1.3) 36 ( 1.2) 28 ( 1.3) 273 ( 1.8) 267 ( 1.6) 255 ( 2.0) Nation 43 ( 1.4) 32 ( 1.1) 25 ( 1.3) 284 ( 2.3) 288 ( 1.7) 250 ( 1.8) The standard errors of the esUmated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 137 Colorado TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT Strongly Agree Agree Undecided, Disagret Strongly Disagree TOTAL Percentage and Pro Money Pereentag. and Proficiency Percentage and Profit:NNW State 27 ( 1.0) 50 ( 1.0) 23 ( 0.8) 277 ( 1.2) 268 ( 1.1) 255 ( 1.5) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) RACE/ETHNICITY Whit. State 28 ( 1.1) 50 ( 1.1) 22 ( 1.0) 283 ( 1.3) 275 ( 1.1) 263 ( 1.5) Nation 26 ( 1.8) 48 ( 1.3) 26 ( 1.5) 279 ( 2.0) 272 ( 1.8) 257 ( 2.0) Black State 46 ( 3.9) Nation 32 ( 2.5) 52 ( 2.3) 16 ( 1.9) 247 ( 4.1) 233 ( 3.3) 227 ( 4.2) Hispanic State 21 ( 2.1) 52 ( 2.7) 27 ( 2.1) 258 ( 3.4) 249 ( 1.7) 234 ( 2.8) Nation 24 ( 2.5) 48 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 236 ( 3.8) TYPE OF COMMUNITY Advantaged urban State 29 ( 2.1) 52 ( 2.0) 20 ( 1.9) 288 ( 2.1) 280 ( 2.4) 267 ( 2.3) Nation .. 4.) 55 ( 280 ( 2.4) 4.1)1 28 ( *. 4.2) Disadvantaged urban State 20 ( 3.5)) 56 ( 249 ( 5.4) 4.7)1 24 ( ( 2.9) Nation 26 ( 2.9) 48 ( 2.9) 28 ( 3.2) 260 ( 5.6)1 249 ( 4.6)1 240 ( 4.5)1 Extreme rural State 27 ( 3.4) 52 ( 2.8) 21 ( 2.8) 280 ( 2.7p 285 ( 3.2) 253 ( 4.8)1 Nation 34 ( 2.8) 49 ( 2.2) 17 ( 1.4) 270 ( 3.9)1 252 ( 4.1)1 Mho,' State 26 ( 1.4) 51 ( 1.3) 23 ( 1.2) 276 ( 2.0) 266 ( 1.8) 252 ( 2.4) Nation 27 ( 1.4) 45 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -r. 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 138 THE 1990 NAEP TRIAL STATE ASSESSMENT Colorado TABLE A27 Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT Strongly Agree Agree Undecided, Dlugree, Strongly Disagree TOTAL. Percentage and Proficiency Percentage and Proficiency Percentage and Proacioncy State 27 ( 1.0) 50 ( 1.0) 23 ( 0.8) 277 ( 1.2) 258 ( 1.1) 255 ( 1.5) Nation 27 ( 1.3) 48 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) PARENTS EDUCATION HS non-graduate State 22 ( 3.4) 46 ( 4.5) 32 ( 4.3) ) 244 ( 2.8) Nation 20 ( 2.6) 50 ( 3.3) 30 ( 3.6) 243 ( 2.6) 238 ( 4.3) HS graduate State 24 ( 2.2) 54 ( 2.6) 23 ( 2.0) 254 ( 2.7) 254 ( 1.9) 245 ( 2.7) Nation 2/ ( 2.1) 47 ( 2.3) 26 ( 2.0) 262 ( 2.7) 255 ( 2.3) 245 ( 2.4) Some college State 28 ( 2.1) 49 ( 2.0) 23 ( 1.6) 277 ( 2.1) 272 ( 1.8) 262 ( 2.5) Nation 28 ( 2$) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 258 ( 3.2) College graduate State 31 ( 1.4) 51 ( 14) 19 ( 1.0) 284 ( 1.6) 278 ( 1.5) 265 ( 2.1) Nation 30 ( 2.3) 51 ( 1.6) 19 ( 1.8) 280 ( 2.4) 274 ( 2.2) 266 ( 2.5) GENDER Male State 28 ( 1.4) 51 ( 1.3) 21 ( 1.1) 278 ( 1.6) 270 ( 1.4) 257 ( 2.1) Nation 28 1.5) 48 ( 12) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Female State 26 ( 1.4) 50 ( 1.2) 24 ( 1.2) 277 ( 1.9) 266 ( 1.6) 252 ( 1.8) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 269 ( 2.1) 262 ( 1.8) 252 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within r 2 standard errors of the estimate for the sample. *5* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 139 Acknowledgments The design, development, analysis, and reporting of the first Trial State Assessment was truly a collaborative effort among staff from State Education Agencies, the National Center for Education Statistics (NCES), Educational Testing Service (ETS), Westat, and National Computer Systems (NCS). The program benefitted from the contributions of hundreds of individuals at the state and local levels Governors, Chief State School Officers, State and District Test Directors, State Coordinators, and district administrators -- who tirelessly provided their wisdom, experience, and hard work. Finally, and most importantly, NAEP is grateful to the students and school staff who participated in the Trial State Assessment. Special recognition is due the Council of Chief State School Officers (CCSSO) for its 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 U.S. Department of Education. Emerson Elliott, NCES Acting Commissioner, provided consistent support and guidance. The staff -- particularly Gary Phillips, Eugene Owen, Stephen Gorman, Maureen Treacy, and Raul Garza -- worked closely and collegially with ETS, Westat, and NCS staff and played a crucial role in all aspects of the program. The members of the National Assessment Governing Board (NAGB) and NAGB staff also deserve credit for their advice and guidance. We owe a great deal to the Mathematics Item Development and Mathematics Scale Anchoring Panels. These people -- from school districts, colleges and universities, and State Education Agencies -- worked tirelessly to help ETS staff develop the assessment and a framework for interpreting the results. Under the NAEP contract to ETS, Archie Lapointe served as the project director and Ina Mullis as the deputy director. Statistical and psychometric activities were led by John Mazzeo, with consultation from Eugme 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 KoMer, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zaback. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesetting environments. Jennifer Nelson created the system and led the computer-based development of the report. John Mazzeo oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Kulick, and Phillip Leung collaborated to generate the data and perform analyses. They were asgisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koffler wrote the text for the report. Kent Ashworth was responsible for coordinating the cover design and final printing of this report. Special thanks are also due to many individuals for their invaluable assistance in reviewing the reports, especially the editors who improved the text and the analysts who checked the data. US. GOVERNMENT PRINTING OFFICE 1991 0 293-ZIE, QL S CEK. to 146