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DOCUMENT RESUME ED 330 548 SE 052 058 TITLE The State of Mathematics Achievement in Arizona: 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, District of Columbia, Guam, and the virgin Islands, respectively; see SE 052 055-096. AVAILABLE FROM Individual state reports are available directly from the assessment division of the appropriate State Department of Education. PUB TYPE Statistical Data (110) -- Reports - Research/Technical (143) EDRS PRICE MF01/PC06 Plus Postage. DESCRIPTORS Academic Achievement; Calculators; *Educational Assessment; Family Environment; *Grade 8; Homework; Junior High Schools; *Mathematics Achievement; Mathematics Instruction; Mathematics Skills; Mathematics Tests; National Programs; Problem Solving; Public Schools; *State Programs; Student Attitudes; Teacher Attitudes; Teacher Qualificaions; Television Viewing IDENTIFIERS *Arizona; National Assessment of Educational Progress; *Numeracy; State Mathel..atics 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 Arizona, 2,558 students in 102 public schools were assessed. This report describes the mathematics proficiency of Arizona eighth-graders, compares their overall performance to students in the West region of the United States and the nation (using data from the NAEP national assessments), presents the average proficiency separately for the five content areas, and summarizes the performance of subpopulations (race/ethnicity, type of community, parents' educational level, and gender). To provide a context for the assessment data, participating students, their mathematics teachers, and principals completed questionnaires which focused on: instructioaal 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 tie NAEP math scale, Arizona students had an average proficiency of 259 compared to 261 nationwide. Many fewer students (Arizona-10%; U.S.-12%) appear to have acquired reasoning and problem solving skills. (JJK/CRW) NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics in ARIZONA The Trial State Assessment at Grade Eight THE NATION'S REPORT CARD BUST C71 AVLA.LE U S DEPARTMENT OF EDUCATION Orqr or f Ow atone; Pews,. n ann 'mpromero E 1 JCATIC)Nk. RE SOURCES INFORMATION CI NTE R tERtC1 Tfss elm ment na% Loorr, reUrPrjkaed as :med from (r)e person Or OrVilnZMion or.ypnetny 1 . Mmor crAryes Piavt been made to ,fileove reprodu(1101, cwat.b, -- Poms ot ,.e* 0, op,m,,,,s stated , n t h,i rtirni do rlot nr(essaril, reprOSP,It .Mtt,a1 Of R, GAIS.Iwn nr petr,, Prepared by Educational Testing Service under Contract wrth the National Center for Education Statistics Office of Educational Research and Improvement U.S. Department of Education What is The Nation's Report Card? THE NATION'S REPORT CARD. the National Asstssmcnt of Educational Progress tNAEP). is the only nationally representative and continuing assessment of what America's s. _ins know and can do in various subject areas. Since 19(9, assessments have been conducted periodically in reading. mathematics. science, writing. history/gtography. and other fields. By making objective information on student performance available to policymakers at the national. state, and local levels. NAEP is an integral part of our nation's evaluation of the condition and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of individual students and their families. NAEP is a congressionally mandated project of the National Center for Education Statistics, the U.S. Department of Education. The Commissioner of Education Statistics is responsible, by law. for carrying out the NAEP project through competitive awards to qualified organitations. NAEP reports directly to the Commissioner, who is also responsible for providing continuing reviews. including validation studies and solicitation of public comment, on NAEP's (=duct and usefulness. In 1988. Congress created the National Assessment Governing Board iNAGEtt to formulate policy guidelines for NAEP. The board is responsible for selecting the subject areas to he assessed, which may include adding to those specified by Congress: identifying apropriate achievement goals tor each age and grade: developing assessment objectives: developing test specifications: designing the assessment methodology: developing guidelines and standards for data analysis and for reporting and disseminating results: developing standards and procedures for interstate, regional, and national comparisons: improving the form and use of the National Assessment: and ensuring that all items selected for use iu the National Assessment are fret from racial, cultural, gender, or regional bias. The National Assessment Governing Board Richard A. Boyd. Chairman Executive Director Martha Holden Jennings Foundation Cleveland. Ohio Phyllis Williamson Aldrich Curriculum Coordinator Saratoga-Warren B.ac,E.S. Saratoga Springs, New York Francie Alexander Associate Superintendent Ca lifOrma Department of Education Sacramento. California David P. Battini High School History Teacher Cairo-Durham High School Cairo. New York Parris C. Battle Teacher Horace Mann Elementary' School Miami. Honda Mary R. Blanton Attorney Cromwell, Porter. Blanton & Salisbury, North Carolina Boyd W. Boehkie Attorney Ciaass. Klyn. & Boehlie PeN, Iowa Unda R. Bryant Teacher Greenway Middle School Teacher Center Pittsburgh, Pennsylvania Honorable Michael N. Castle Governor of Delaware Carve! State Office Building Wilmington. Delaware Honorable Naomi K. Cohen State of C'onnecticut House of Representatives Legislative Office Building Hartford, Connecticut Chester F. Finn, Jr. Professor of Education and Public Policy. Vanderbilt University Washington. DC. Michael S. Glode Wyoming State Board of Educiaion Saratoga, Wyoming Christine Johmon Principal Abraham Lincoln High School Denver. Colorado John Lindley P neipal South Colby. Elementary School Port Orchard, Washington Carl J. Maser Director of Scnook The 1.utheran Church International Center St. Loins, Missouri Missouri Synod Mark D. Musick President Southern Regional Education Board Atlanta. Georgia Honorable Carolyn Pollan Arkansas House of Representatives Fort Smith, Arkansas Matthew W. Prophet. Jr. Superintendent Portland Oregon School District Portland. Oregon Honorable William T. Randall Commissioner or Education State Department ot Educatil n Denver. Colorado Dorothy K. Rich President Home and School Institute Special Projects Office Washington, D.C. Honorable Richard W. Riley Attorney Nelson. Mullins. Riley and Scarborough Columbia, South Carulma Thotruo Toptues Attorney Law Offices of Frank Rogotienski Coronado, California Herbert J. Wa !berg Professor of Education University of Illinois Chicago. Illinois Assistant Secretary for Educational Research and mprov one nt I Es. Offic io S. Department of Education Washington, DC Roy Truby Executive Director, NAGB ...,lungton. D.C. NATIONAL CENTER FOR EDUCATION STATISTICS The STATE of Mathematics Achievement in ARIZONA The Trial State Assessment at Grade Eight Report No 21-ST-02 June 1991 Prepared by Educational Testing Service undel Contract with the National Center for Education Statistics Office ot Educational Resoarch 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 Secrttary National Center for Education Statistics Emerson J. Elliott Acting Congnissioner FOR MORE INFORMATION: Copies of the 1990 NAEP Trial State Assessment's individual State reports are available directly from the participating States. For ordering information, please contact the assessment division of your State Department of Education. Fcc ordering information on the composite report of results for the Nation and all State participants, or for single copies of the Executive Summary while supplies last, write: Education Information Blanch Office of Educational Research and Improvement U.S. Department of Education 555 New Jersey Avenue, NW Washington, D.C. 20208-5641 or call 1-800-424-1616 (in the Washington, D.C. metropolitan area call 202-119-i651). Library of Congress, Catalog Card Number 91-61478 ISBN: 0-88685-14-9 The work upon which this publication is based wu performed for the National Center fot Education Statistics. Office of Educational Research and heprovement, by Educational Testing Service. Educational lbsting Service is an equal opponunity/affumnive action employer. Educational Tea-tins Service, ETS, and are registered trademarks of Educational Testing Service» 5 Table of Contents EXECUTIVE SUMMARY INTRODUCTION 7 Overview of the 1990 Trial State Amessment 8 This Report 9 Guidelines for Analysis 12 Profile of Arizona 14 Eighth-Grade School and Student Characteristics 14 Schools and Students Assessed 15 PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Arizona Public Schools/ 17 Chapter 1. Students' Mathematics Performance 18 1.evels 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 Content Area Performance 33 THE 1990 NAEP TRIAL STATE ASSESSMENT PART TWO Finding a Context for Understanding Students' Mathematics Proficiency 37 Chapter 3. What Are Students Taught in Mathematics' 39 Curriculum Coverage 41 Mathematics Homework 42 Instructional Emphasis 45 Summary 48 Chapter 4. How Is Mathematics Instruction Derivered" 49 Availability of Resources 49 Patterns in Classroom Instruction 51 Collaborating in Small Groups 54 Using Mathematical Objec.s 55 Materials for Mathematics Instruction 56 Summary 59 Chapter 5. How Are Calculators Used" The Availaoility of Calculators 62 The Use of Calculators 63 When To Use a Calculator 64 Summary 66 Chapter 6. Who Is Teaching Eighth-Grade Mathematics" 67 Educational Background 68 Summary 71 Chapter 7. The Coaditions Beyond School that Facilitate Mathematics Learning and Teaching 73 Amount of Reading Materials in the Home 74 Ilours of Television Watched per Da:, 75 Student Absenteeism 76 Students' Perceptions of Mathematics 78 Summary 79 PROCEDURAL APPENDIX 81 DATA APPENDIX 97 7 iv THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona THE NATION'S REPORT CARD EXECUTIVE SUMMARY In 1985, Congress passed new legislation for the National Ass,Asment of Educational Progress (NAEP), which included -- for the first time in the project's history a provision authorizing voluntary statc-by-state assessments on a trial basis, in addition to continuing its primary mission, thY Lational assessments that NAFP has conducted since its inception. As a result of the legtslation, the 1990 NAEP program included a Trial State Assessment Program in eighth-gxade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-gxade public-school students were assessed in each of 37 states, the District of Columbia, and two territories in February 1990. The sample was carefully designed to represent the eighth-gxade 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 progam designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 8 1 1990 NAEP TRIAL STATE ASSESSMENT 1 Arizona In Arizona, 102 public schools participated in the assessment. The weighted school participation rate was 97 percent, which means that all of the eighth-grade studnnts ir. this sample of schools were representative of 97 percent of the eighth-grade public-school students in Ariz.ona. In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 6 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 7 percent had an Individualized FAucation 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 eatepprized as Limited English Proficient or had to have an Individualized Education Plan an, i (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 2 percent and 4 percent of the population, respectively. In total, 2,558 eighth-grade Arizona public-school students were assessed. The weighted student participation rate was 93 percent. This means that the sample of students who took part in the assessment was representative of 93 percent of the eligible eighth-gxade public-school student population in Arizona. Students' Mathematics Performance 'The average proficiency of eighth-grade public-school students from Arizona on the NMI' mathematics scale is 259. This proficiency is no different from that of students across the nation (261). Average proficiency on the NAEP scale provides a global view of eighth gaders' mathematics achievement; however, it does not reveal specifically what the students know and can do in the subject. To describe the nature of students' proficiency in greater detail, NAEP used the results from the 1990 national assessments of fourth-, eighth-, and twelfth-grade students to define the skills, knowledge, and understandings that characterize four levels of mathematics performance -- 200, 250, 300, and 350 -- on the NAEP scale. 2 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona In Arizona, 98 per;ent 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 Arizona (10 percent) and 12 percent in the nation appear to have acquired reasoning and problem-solving skills involving fractions, decimals, percents, elementary geometric properties, and simple algebraic manipulations (level 300). The Trial State Assessment included five content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students in Arizona performed comparably to students in the nation in all of these five content areas. Subpopulation Performance In addition td the overall results, the 1990 Trial State Assessment permits reporting on the performance of various subpopulations of the Arizona eighth-grade student population defined by race/ethnicity, type of community, parents' education level, and gender. In Arizona: White students had higher average mathematics proficiency than did Black, Hispanic, or American Indian students. Further, a greater percentage of White students than Black, Hispanic, Or America.n Indian students attained level 300. The results by type of community indicate that the average mathematics performance of the Arizona 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 Arizona, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 32 points higher than that of students whose parents did not graJuate from high school. The results by ge:Itler show that eighth-grade males in Arizona had a higher average mathematics proficiency than did eighth-grade females in Arizona. In addition, a greater percentage of males than females in Arizona attained level 300. Compared to the national results, females in Arizona performed lower than females across the country; males in Arizona performed no differently from males across the country. 1 0 THE 1990 NAEP TRJAL STATE ASSESSMENT 3 lb I Arizona A Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instruction and setting policy when supplemented with contextual information about schools, teachers, and students. To gather such information, the students participating in the 1990 Trial State Assessment, their mathematics teachers, and the principals or other administrators in their schools were asked to complete questionnaires on policies, instruction, and programs. Taken together, the student, teacher, and school data help to describe some of the current practices and emphases in mathematics education, illuminate some of the factors that appear to be related to eighth-grade public-school students' proficiency in the subject, and provide an educational context for understanding information about student achievement. Some of the salient results for the public-school students in Arizona are as follows: More than half of the students in Arizona (64 percent) were in schools where mathematics was identified as a special priority. This is about the same percentage as that for the nation (63 percent). In Arizona, 87 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 Arizona were taking eighth-grade mathematics (48 percent) as were taking a course in pre-algebra or algebra (47 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. According to their teachers, the greatest percentage of eighth-grade students in public schools in Arizona spent 30 minutes doing mathematics homework each day; according to the students, most of them spent 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, whi1,7 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. 4 THE 1990 NAEP TRIAL 6TATE ASSESSMENT Arizona In Arizona, 17 percent of the eighth-grade students had mathematics teachers who reported getting all of the resources they needed, while 31 percent of the students were taught by teachers who got only some of none of the resources they needed. Across the nation, these figures were 13 percent and 31 percent, respectively. In Arizona, 27 percent of the students never used a calculator to work problems in class, while 46 percent almost always did. In Arizona, 45 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (73 percent) had teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by teachers who were certified at the highest level available in their states. Students in Arizona who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of these materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. Some of the eighth-grade public-school students in Arizona (15 percent) watched one hour or less of television each day; 12 percent watched six hours or more. Average mathematics proficiency was lowest for students who spent six hours or more watching television each day. THE 1990 NAEP TRIAL STATE ASSESSMENT 5 Arizona THE NATION'S REPORT CARD INTRODUCTION As a result of legislation enacted in 1988, the 1990 National Assessment of Educational Progress (NAEP) included a Trial State Assessment Program in eighth-grade mathematics. The Trial State Assessment was conducted in February 1990 with the following participants: Alabama Iowa Ohio Arizona Kentucky Oklahoma Arkansas I,ouisiana Oregon California Maryland Pennsylvania Colorado Michigan Rhode Island Connecticut Minnesota Texas Delaware Montana Virginia District of Columbia Nebraska West Virginia Florida New Hampshire Wisconsin Georgia New Jersey Wyoming Hawaii New Mexico Idaho New York Illinois North Carolina Guain Indiana North Dakota Virgin Islands 3 THE 1990 NAEP TRIAL STATE ASSESSMENT 7 Arizona This report describes the performance of the eighth-grade public-school students in Arizona and consists of three sections: This Introduction provides background information about the Trial State Assessment and this report. It also provides a profile of the eighth-grade public-school students in Arizona. Part One describes the mathematics performance of the eighth-grade public-school students in Arizona, the West region, and the nation. Part Two relates students' mathematics performance to contextual information about the mathematics policies and instruction in schools in Arizona, the West region, and the nation. Overview 0f the 1990 Trial State Assessment In 1988, Congress passed new legislation for the National Assessment of Educational Progress (NAEP), which included -- for the first time in the project's history -- a provision authorizing voluntary state-by-state assessments on a trial basis, in addition to continuing its primary mission, the national assessments that NAEP has conducted since its inception: The National Assessment shall develop a trial mathematics assessment survey instrument for the eighth grade and shall conduct a demonstration of the instrument in 1990 in States which wish to participate, with the purpose of determining whether such an assessment yields valid, reliable State representative data. (Section 406 (i)( 2 )(C)(i) of the General Education Provisions Act, as amended by Pub. L. 100-297 (20 U.S.C. 1221e-1(i)(2)(C)(i))) As a result of the legislation, the 1990 NAEP program included a Trial State Assessment Program in eighth-grade mathematics. National assessments in mathematics, reading, writing, and science were conducted simultaneously in 1990 at grades four, eight, and twelve. For the Trial State Assessment, eighth-grade public-school students were assessed in each state or territory. The sample was carefully designed to represent the eighth-grade public-school population in the state or territory. Within each selected school, students were randomly chosen to participate in the program. Local school district personnel administered all assessment sessions, and the contractor's staff monitored 50 percent of the sessions as part of the quality assurance program designed to ensure that the sessions were being conducted uniformly. The results of the monitoring indicated a high degree of quality and uniformity across sessions. 7 4 8 THE 1990 NAEP TRIAL STATE ASSFSSM ENT Arizona The Trial State Assessment was based on a set of mathematics objectives newly developed for the program and patterned after the consensus process described in Public Law 98-511, Section 405 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 FAucation Statistics (NCES), and the Assessment Policy Committee (APC), a panel that advised on NAEP policy at that time. The objectives were further refined by NAEP's Item Development Panel, reviewed by the Task Force on State Comparisons, and resubmitted to NCES for peer review. Because the objectives needed to be coordinated across all the grades for the national program, the final objectives provided specifications for the 1990 mathematics assessment at the fourth, eighth, and twelfth grades rather than solely for the Trial State Assessment in grade eight. An overview of the mathematics objectives is provided in the Procedural Appendix. This Report This is a computer-generated report that describes the performance of eighth-grade public-school students in Arizona, in the West region, and for the nation. Results also are provided for groups of students defined by shared characteristics -- race/ethnicity, type of community, parents' education level, and gender. Defmitions of the subpopulations referred to in this report are presented below. The results for Arizona are based only on the students included in the Trial State Assessment Program. However, the results for the nation and the region of the country are based on the nat;onally and regionally representative samples of public-school students who were assessed in January or February as part of the 1990 national NAEP program. Use of the regional and national results from the 1990 national NAEP program was necessary because the voluntary nature of the Tiial State Assessment Program did not guarantee representative national or regional results, since not every state participated in the program. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School MaMematics (Reston, VA: National Council of Teachers of Mathematics, 1989), THE 1990 NAEP TRIAL STATE ASSESSMENT 9 Arizona RACE/ETHNICITY Results are presented for students of different racial/ethnic groups based on the students' self-identification of their race/ethnicity according to the following mutually exclusive categories: White, Black, Hispanic, Asian (including Pacific Islander), and American Indian (including Alaskan Native). Based on criteria described in the Procedural Appendix, there must be at least 62 students in a particular subpopulation in order for the results for that subpopulation to be considered reliable. Thus, results for racial/ethnic groups with fewer than 62 students are not reported. However, the data for all students, regardless of whether their racial/ethnic group was reported separately, were included in computing overall results for Arizona. 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. Disadvantgged 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 ovLside metropolitan statistical areas, live in areas with a population below l0,0t.", 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 a.,,I(ed to indicate the extent of schooling for each of their paren/s -- 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. 6 10 THE 1990 NAM' TRIAL STATE ASSESSMEN1 Arizona GENDER Results are reported separately for males and females. REGION The United States has been divided into four regions: Northeast, Southeast, Central, and West. States included in each region are shown in Figure 1. All 50 states and the District of Columbia are r sted, with the participants in the Trial State Assessment highlighted in boldface type. Tenitories 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. NE NATION'S REPORT CARD FIGURE 1 I 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 Dakoth Oregon Vermont West Virginia Wisconsin Texas Virginia Utah Washington Wyoming THE 1990 NAEP TRIAL STATE ASSESSMENT I) Arizona 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 tor those goups in the population. If the evidence is strong (i.e., the difference is statistically significant), the report describes the group means or proportions as being different (e.g., one goup 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 he about the same or widely discrepant. The reader is cautioned to rely on the results of the statistical tests -- rather than on the apparent magnitude of the difference between sample means or proportions -- to determine whether those sample differences are likely to represent actual differences between the groups in the population. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second goup, 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 goups, the confidence interval included zero, and thus no difference could be assumed between the gxoups. When three or more groups are being compared, a Bonferroni procedure is also used. The statistical tests and Bonferroni procedure arc discussed in greater detail in the Procedural Appendix. 12 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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 3 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 are based on unrounded estimates (i.e., estimates calculated to several decimal places) of the percentages in each group. The percentages shown in the tables are rounded to integers. Hence, the pementage for a combined group (reported in the text) may differ slightly from the sum of the separate percentages (presented in the tables) for each of the groups that were combined. Similarly, if statistical tests were to be conducted based on the rounded numbers in the tables, the results might not be consonant with the results of the statistical tests that are reported in the text (based on unrounded numbers). THE 1990 NAEP TRIAL STATE ASSESSMENT 13 Arizona Profile of Arizona EIGHTH-GRADE SCHOOL AND STUDENT CHARACTERISTICS Table 1 provides a profile of the demographic characteristics of the eighth-grade public-school students in Arizona, the West region, and the nation. This profile is based on data collected from the studenis and schools participating in the Trial State Assessment. TABLE 1 I Profile of Arizona Eighth-Grade Public-School I Students PERCENTAGE OF STUDENTS MO NAEP TRIAL STATE ASSESSMENT Arizona West Nation DEMOGRAPHIC SUBGROUPS Race/Ethnicity Percentage Percentage Percentage White 59 ( 1.8) 63 ( 1.9) 70 ( 05) Black 3 ( 0.4) 7 ( 2.0) 16 ( 0.3) Hispanic 29 ( 1.3) 21 ( 1.5) 10 ( 0.4) Asian 2 ( 0.3) 4 ( 1.3) 2 ( 0.5) American Indian 7 ( 1.5) 4 ( 2.3) 2 ( 0,7) Type of Community Advantaged urban 13 ( 2.7) 14 ( 8.5) 10 ( 3.3) Disadvantaged urban 16 ( 4,0) 19 ( 7.5) 10 ( 2.8) Extreme rural 8 ( 3.0) 10 ( 3.8) 10 ( 3.0) Other 63 ( 4.7) 58 (10.1) 70 ( 4.4) Parents' Education Did not finish high school 9 ( 0.6) 10 ( 1.3) 10 0.8) Graduated high school 22 ( 0.9) 19 ( 2.5) 25 ( 1.2) Some education after high school 20 ( 0.9) 16 ( 1.2) 17 ( 0.9) Graduated college 37 ( 1.2) 42 ( 4.0) 39 ( 1.9) Gender Male 50 ( 0.9) 55 ( 2.1) 51 ( 1,1) Female 50 ( 0.9) 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 ± 2 standard errors of the estimate for the sample. The percentages for Rau! 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." Throughcut this report, percentages less than 0.5 percent arc reported as 0 percvnt. 14 2 0 HE 1990 NAEP TRIAL STATE ASSESSMENT Arizona SCHOOLS AND STUDENTS ASSESSED Table 2 provides a profile summarizing participation data for Arizona schools and studerts sampled for the 1990 Trial State Assessment. In Arizona, 102 public schools participated in the assessment. The weighted school participation rate was 97 percent, which means that all of the eighth-grade students in this sample of schools were representative of 97 percent of the e tth-grade public-school students in Arizona. TABLE 2 I Profile of the Population Assessed in Arizona EIGHTH-ORADE PUBUC SCHOOL PARTICiPATION Weighted sCh001 participation rate before substitution Weighted school participation rate after substitution Number ot schools originally Sampled Number of schools not eigible Number of schools in original sample participating Number of substitute schools provided Number of substitute schools participating Total number ot participating schools 97% 97% 110 7 102 0 0 102 EIGHTH-GRADE PUBUC-SCHCOL STUDENT PARTICIPATION Weighted student participation rate after make-ups Number of students selected to participate in the assessment Number of students withdrawn from the assessment Percentage of students who were of Limited English Proficiency Percentage of students excluded from the assessment due to Limited English Proficiency Percentage of students who had an Individualized Education Plan Percentage of students excluded from the assessment due to Individuahzed Education Plan status Number of students to be assessed Number of students assessed 93% 3,106 206 6% 2% 7% 4% 2,742 2.558 For two schools in Arizona, assessments were conducted, but the materials were destroyed in shipping via the 1:.S. Postal Service. These schools were included in the counts of participating schools, both before and after substitution. However, in the weighted results, these schools were treated in the same manner as a nonparticipating school because no student responses were available for analysis and reporting. THE 1990 NAEP TRIAL STATE ASSESSMENT 15 Arizona In each school, a random sample of students was selected to participate in the assessment. As estimated by the sample, 6 percent of the eighth-grade public-school population was classified as Limited English Proficient (LEP), while 7 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 progam of activities andlor related services necessary to achieve the goals and objectives. Schools were permitted to exclude cenain students frcm 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 (n 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 2 pereen and 4 percent of the populatim, respectively. In total, 2,558 eighth-grade Arizona public-school students were assessed. The weighted student participation rate was 93 percent. This means that the sample of students who took part in the assessment was representative of 93 percent of the eligible eighth-grade public-school student population in Arizona. 36 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona THE NATION'S REPORT CARD PART ONE How Proficient in Mathematics Are Eighth-Grade Students in Arizona Public Schools? The 1990 Trial State Assessment covered five mathematics content areas -- Numbers and Operations; Measurement; Geometry; Data Analysis, Statistics, and Probability; and Algebra and Functions. Students' overall performance in these content areas was summarized on the NAEP mathematics scale, which ranges from 0 to 500. This part of the report contains two chapters that describe the mathematics proficiency of eighth-gade public-school students in Arizona. Chapter 1 compares the overall r,:athematics performance of the students in Arizona to students in the West region and the nation. It also presents the students' average proficiency separately for the five mathematics content areas. Chapter 2 summarizes the students' overall mathematics performance for subpopulations defined by race/ethnicity, type of community, parents' education level, and gender, as well as their mathematics performance in the five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT 17 Arizona CHAPTER 1 Students' Mathematics Performance As shown in Figure 2, the average proficiency of eighth-grade public-school students from Arizona on the NAEP mathematics scale is 259. This proficiency is no different from that of students across the nation (261).2 FIGURE 2 I Average Eighth-Grade Public-School I Mathematics Proficiency it* moon NAEP Mathematics Scale won Average CA40 200 225 250 275 300 500 Proficiency 144 Arizona 259 ( 1.2) 1-4-4 West 261 ( 2.6) pts Nation 261 ( 1.4) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within z 2 standard errors of the estimated mean (95 percent confidence interval, denoted by t-H). if the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. 2 Differences reported are statistically different at about the 95 percent certainty level. This means that with about 95 percent certainty there is a real difference in the average mathematics proficiency between the two populations of interest. 4 18 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona LEVELS OF MATHEMATICS PROFICIENCY Average proficiency on the NAEP scale provides a global view of eighth graders' mathematics achievement; however, it does not reveal tne 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 sudents 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 Arizona, 98 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 Arizona (10 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 Arizona, West region, and national results for each content area. Students in Arizona performed comparably to student; in the nation in all of these five content areas. THE 1990 NAEP TRIAL STATE ASSESSMENT t.J 19 Arizona FIGURE 3 I Levels of Mathematics Proficiency KATION'S REPORT mop CARO 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. The Se 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 1 Simple Multiplicative Reasoning and Two-Step Problem SoMng 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 Arizona FIGURE 3 I Levels of Mathematics Proficiency (continued) I LEVEL 300 Reasoning and Problem Solving Involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations Students at this level are able to represent, interpret, and perform simple operations with fractions and decimal numbers. They are able to locate fractions and decimals on number lines, simplify fractions, and recognize the equivalence between 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 us,ng mathematical notation to interpret expressions, inCluding those with exponents and negative integers. In measurement, these students can find the perimeters and areas of rectangles, recognize relationships among common units of measure, and use proportional relationships to solve routine problems involving similar triangles and scale drawings. In geometry, they have some mastery of the definitions and properties of geometric figures and solids. In data analysis, these students can calculate averages, select and interpret data from tabular displays, pictographs, and line graphs, compute relative frequency distributions, and have a beginning understanding of sample bias. In algebra, they can graph points in the Cartesian plane and perform simple algebraic manipulations such as simplifying an expression by collecting like terms, identifying the solution to open linear sentences and inequalities by substitution, and checking and graphing an interval representing a compound inequality when It is described in words. They can determine and apply a rule for simple lunctional 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 circleS and the surface areas of solid figures. In geometry, they can apply the Pythagorean theorem to solve problems frivol, ndirect measurement. These students also can ..oply their knowledge of the properties of geometric fi..ires 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. 1-1 THE 1990 NAEP TRIAL STATE ASSESSMENT 21 Arizona FIGURE 4 I Levels of Eighth-Grade Public-School 1 Mathematics Proficiency LEVEL 350 State Region Nation LEVEL 300 State Region Nation LEVEL 250 State Region Nation LEVEL 200 State Region Nation IN 11-.1 Ph 0 20 40 60 80 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within i 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. S 22 THE 1990 NAEP TRIAL STATE ASSESSMENT Parcentage ( 0.1) 0 ( 0.4) 0 ( 0.2) 10 ( 1.0) 12 ( 2.4) 12 ( 1.2) 61 ( 1.9) 63 ( 2,8) 64 ( 1.6) 98 ( 0.3) 97 ( 1.0) 97 ( 0.7) Arizona FIGURE 5 I Eighth-Grade Public-School Mathematics Content Area Performance State Region Nation State Region Nation State Region Nation State Region Nation State Region Nation mom NW OPERATIONS MEASUMENT GEOMETRY DATA ANALYSIS, STA11STICS, AND PROBABILITY ALGEBRA AND FUNCTIONS 1-1-1 0 200 225 250 275 Average Pronclency . 264 ( 1.2) 264 ( 2.6) 266 ( 1.4) 257 ( 1.4) 2156 ( 3.0) 2158 ( 1.7) 2156 ( 1.1) 260 ( 2.6) 2159 ( 1.4) 258 ( 1.4) 262 ( 3.6) 262 ( 1.8) 258 ( 1.3) 259 ( 2.4) 260 ( 1.3) 300 500 Mathematics Subscale Proficiency The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 23 Arizona CHAPTER 2 Mathematics Performance by Subpopulations In addition to the overall state results, the 1990 Trial State Assessment included reporting on the performance of various subgroups of the student population defined by race/ethnicity, type of community, parents' education level, and gender. RACE/ETHNICITY The Trial State Assessment results can be compared according to the different racial/ethnic groups when the number of students in a racial/ethnic group is sufficient in size to be reliably reported (at least 62 students). Average mathematics performance results for White, Black, Hispanic, and American Indian students from Arizona are presented in Figure 6. As shown in Figure 6, White students demonstrated higher average mathematics proficiency than did Black, Hisp;inic, or American Indian students. Figure presents mathematics performance by proficiency levels. The figure shows that a greater percentage of White students than Black, Hispanic, or American Indian students atuined level 300. 3 0 24 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona HGURE b I Average Eighth-Grade Public-School I Mathematics Proficiency by Race/Ethnicity MEP Mathematics Scal 0 200 225 250 275 300 500 Average Proficiency Arizona MS White t 1.1) res Black $40) KI Hispanic 142 11.4) 1+5 American Indian 111311(.1Z$ West White $.2) 1--Foo4 Black -40117 4, &VI Hispanic SO 4 $.7) American Indian "lir 4 Nation .1.1 White 20 ( 1.5) r-e-e Black 23, ( 2.0) I-1 Hispanic IND ( 2.0) American Indian 24$ ( 5.3)1 i--...-.0.4 'lite standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within + 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 25 Arizona FIGURE 7 LEVEL 300 State White Black Hispanic Amer. Indian Region White Black Hispanic Amer. Indian Nation White Black Hispanic Amer. Indian LEVEL 250 State White Black Hispanic Amer. Indian Raglan White Black Hispanic Amer. Indian Nation White Black Hispanic Amer. Indian LEVEL 200 State White Black Hispanic Amer. Indian Region White Black Hispanic Amer. Indian Nation White Black Hispanic Amer. Indian NE RATION'S REPORT Levels of Eighth-Grade Public-School CARD Mathematics Proficiency by Race/Ethnicity 1...-11001 h41 104 1111110141 20 40 SO 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 i 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by I-1-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). Percentage 100 3 2 26 THE 1990 NAEP TRIAL STATE ASSESSMENT 15 ( 1.4) 3 ( 1,5) 2 ( 0.7) ( 0.0) 16 ( 3.2) 6 ( 5.0)1 3 ( 1.6) ( ) 15 ( 1.5) 2 ( 1.3) 3 ( 1.1) 1 ( 2.3)1 77 ( 1.5) 41 ( 6.1) 37 ( 2.5) 27 ( 3.6)1 74 ( 3.3) 44 (12.9)1 41 ( 5.4) PM ( *) 74 ( 1.8) 30 ( 3.4) 41 ( 4.5) 46 (16.0)I 100 ( 0.1 ) 98 ( 2.1) 94 ( 1.1) 93 ( 2.1)1 99 ( 0.8) 95 ( 3.0)1 93 ( 2.0) It II / ) ge ( 0 .4 ) ( 3,1) 93 ( 1.6) 97 ( 6,7)1 Arizona TYPE OF COMMUNITY Figure 8 and Figure 9 present the mathematics proficiency results for eighth-grade students attending public schools in idvantaged urban areas, disadvantaged urban areas, extreme rural areas, and areas classified as "other". (These are the "type of community" groups in Arizona with student samples large enough to be reliably reported.) The results indicate that the average mathematics performance of the Arizona students attending schools in advantaged urban areas was higher than that of students attending schools in disadvantaged urban areas, extreme niral areas, or areas classified as "other". FIGURE 8 Average Eighth-Grade Public-School Mathematics Proficiency by Type of Community p.mA NAEP Mathematics Scal WORT Averate 200 225 250 275 300 500 Proficiency psi Arizona Advantaged urban Disadvantaged urban 27$ 24111 ( 1.9)4 3.13)1 Extreme rural 24$ ( 5.3)4 1-4"-.04 141 Other 200 ( 2.0) West 11P011 Advantaged urban 212 ( 3.1)i Disadvantaged urban 20$ ( 5.8)! Extreme rural 263 ( 7.3)1 Other 2101 3.8) Iti Nation Advantaged urban 201 ( 3.3)1 Disadvantaged urban 249 ( 3.5)! 1-1."4 Extreme rural 2615 4.1)! 041 Other 201 ( 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 t 2 standard errors of the estimated mean (95 percent confidence interval, denoted by I4-1). If the confidence Mtervals 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. 3 THE 1990 NAEP MAL STATE ASSESSMENT 27 Arizona FIGURE 9 LEVEL 300 State Adv. urban DIsadv. urban Ext. rural Other MOM Adv. urban Disadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other LEVEL 250 State Adv. urban Disadv. urban Ext. rural Other Region Mv. urban Disadv. urban Ext. rural Other Nation Adv. urban Disadv. urban Ext. rural Other LEVEL 200 State Adv. urban Disadv. urban Ext. rural Other Region Mv. urban Disadv. urban Ext. rural Other Nation Adv. urban DIsadv. urban Ext. rural Other Levels of Eighth-Grade Public-School Mathematics Proficiency by Type of Community 20 40 60 80 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within t 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by i-1-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ! Interpret with caution -- the nature of the sample does not allow accurate deterrmnation of the variability of this estimated mean proficiency. 100 " 4 28 THE 3990 NAEP TRIAL STATE ASSESSMENT Percentage 18 ( 3.5)1 4 ( 1.8)1 3 ( 1.7)1 9 ( 1.4) 31 ( 3.1)1 9 ( 3.5)1 8 ( 4.8)1 10 ( 1.8) 26 ( 4.6)1 7 ( 2.1)1 6 ( 2.3)1 12 ( 1.2) 80 ( 2.3)1 46 ( 5.7)1 46 ( 8.3)1 61 ( 3.0) 03 ( 3.3)1 57 ( 8.0)1 52 (12.8)1 62 ( 5.0) 83 ( 4.6)1 48 ( 5.0)1 58 ( 8.2)1 64 ( 2.3) 99 0.4)1 95 1.7)1 95 3.0)1 98 0.7) 100 0.0) 98 2.0)1 96 1.3)1 96 (1.7) 100 0.0) 96 1.5)1 97 2.8)1 97 ( 1.0) Arizona 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 Arizona, the average mathematics proficiency of eighth-grade public-school students having at least one parent who graduated from college was approximately 32 points higher than that of students who reported that neither parent graduated from high school. As shown in Table 1 in the Introduction, about the same percentage of students in Arizona (37 percent) and in the nation (39 percent) had at least one parent who graduated from college. In comparison, the percentage of students who reported that neither parent graduated from high school was 9 percent for Arizona and .10 percent for the nation. FIGURE 10 I Average Eighth-Grade Public-School I Mathematics Proficiency by Parents' Education NAEP Mathematics Scale 200 225 250 275 300 500 IVO ST CANS =zA =.Z Average Proficiency Arizona H S non-graduate 2410 ( 1.9) HS graduate 250 ( 1.5) 1+1 Some college 2110 ( 1.7) PIM College graduate 272 ( 14) West HS non-graduate 248 ( 4.4) 1-14 H S graduate 250 ( 21) Some college 21PS ( 3.0) College graduate 273 ( 2.6) Nation P-P1 H S non-graduate 243 2.0) hts HS graduate 244 ( 14) Some college 268 1.7) 1+0 College graduate 274 ( 1.6) The standard errors are presented in parentheses. With about 95 percent certainty, the average mathematics proficiency for each population of interest is within 2 standard errors of the estimated mean (95 percent confidemx interval, denoted by II-1). lf the confidence intervals for the populations do not overlap, there Is a statistically significant difference between the populations. THE 1990 NAEP TRIAL STATE ASSESSMENT 29 Arizona 111E won REPORT FIGURE I 1 I Levels of Eighth-Grade Public-School CARD I Mathematics Proficiency by Parents' Education LEVEL 300 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 Soma 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, 9. I-404 1--PP*4 14000.11 10..411=411 1101...mgolimmipm41 44 1."424 111611 4110111111M111111V 14 10=f1=1.1MINIIIIMI.; psommilimm..11 Immmmillomme 2 ( 2.3) 2 ( 1.3) 15 ( 2,8) 21 ( 3.5) 1 ( 0.9) 5 ( 1.5) 12 ( 1.4) 21 ( 1.9) 35 ( 3.6) 49 ( 3.5) 72 ( 2.6) 77 ( 2.0) 44 ( 6,8) 51 ( 4.4) 75 ( 4.1) 75 ( 3.6) 37 ( 4.6) 543 ( 2.7) e1141011 71 ( 2,6) 144 ( 2.0) 0 20 40 60 BO Percentage at or Above Proficiency Levels he standard errors are presented in parentheses. With aboust 95 percent certainty, the value for each population of interest is within z 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by 144). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. ( 1.8) ( 0.8) ( 0,6) ( 0.3) ( 3.2) ( 1,6) ( 0.7) ( 0.7) 96 ( 1.9) 11,01 97 ( 0,8) 99 ( 0.7) 99 ( 0.7) 100 30 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona GENDER As shown in Figure 12, eighth-grade males in Arizona had a higher average mathematics proficiency than did eighth-grade females in Arizona. Compared to the national results, females in Arizona performed lower than females across the country; males in Arizona performed no differently from males across the country. FIGURE 12 I Average Eighth-Grade Public-School Mathematics Proficiency by Gender MEP Mathimatics Scala 200 22S 250 275 300 ME IIIPCP1 CAM 500 Average Proficlancy Arizona 111 Male 263 ( 1.4) Female ( 1.2) West t-4.4 Male 262 ( 3.5) Female 2110 ( 2.8) Nation Male 262 ( 1.8) 1+1 Female 2110 ( 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 :4: 2 standard errors of the estimated mean (95 percent confidence interval, denoted by 14-1). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. As shown in Figure 13, there was no difference between the percentages of males and females in Arizona who attained level 200. The percentage of females in Arizona who attained level 200 was similar to the percentage of females in the nation who attained level 200. Also, the percentage of males in Arizona who attained level 200 was similar to the percentage of males in the nation who attained level 200. THE 1990 NAEP TRIAL STATE ASSESSMENT 31 Arizona FIGURE 13 I Levels of Eighth-Grade Public-School Mathematics Proficiency by Gender LEVEL 300 State Male Female Region Male Female Nation Male Female LEVEL 250 State Male Female Region Male Female Nation Male Female LEVEL 200 State Male Female Region Male Female Nation Male Female 0 20 40 BO Percentage 100 Percentage at or Above Proficiency Levels The standard errors are presented in parentheses. With about 95 percent certainty, the value for each population of interest is within -_ 2 standard errors of the estimated percentage (95 percent confidence interval, denoted by I-0-4). If the confidence intervals for the populations do not overlap, there is a statistically significant difference between the populations. Proficiency level 350 is not presented in this figure because so few students attained that level. 32 THE 1990 NAEP TRIAL STATE ASSESSMENT 12 ( 1,2) ( 1.0) 13 ( 3,1) 11 ( 2.2) 14 ( 1.7) 10 ( 1.3) 84 ( 2.2) 58 ( 2.0) 65 ( 4.1) 81 ( 3.2) 84 ( 2.0) 84 ( 1.8) 98 ( 0.4) 97 ( 0.6) 97 ( 1.2) 98 ( 1.0) 97 ( 0.9) 97 ( 0.8) Arizona In addition, a greater percentage of males than females in Arizona attained level 300. The percentage of females in Arizona who attained level 300 was similar to the percentage of females in the nation who attained level 300. Also, the percentage of males in Arizona who attained level 300 was similar to the percentage of males in the nation who attained level 300. CONTEN'T AREA PERFORMANCE Table 3 provides a summary of content area performance by race/ethnicity, type of community, parents' education level, and gender. THE 1990 NAEP TRIAL STATE ASSESSMENT 33 Arizona TABLE 3 I Eighth-Grade Public-School Mathematics 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 ,,,..,.,... ..,., ruirm74701.7 TOTAL Proficiency Proficiency Proficiency Pnificiency Proficiency State 264 ( 1.2) 257 ( 1.4) 258 ( 1.1) 258 ( 1.4) 258 ( 1.3) Region Nation 264 ( 266 ( 2.6) 1.4) 258 ( 258 ( 3.0) 1.7) 260 ( 2sa 2.8) 1.4) 262 ( 262 ( 3.6) 1.8) 259 ( 260 ( 2.4) 1.3) RACE/ETHNICITY White State 275 ( 1.2) 268 ( 1.6) 266 ( 1.2) 273 ( 1.4) 269 ( 1.2) Region 271 ( 3,2) 267 ( 3.9) 767 ( 3,0) 272 ( 4.4) 267 ( 2.8) Nation 273 ( 1.6) 287 ( 2.0) '67 ( 1.5) 272 ( 1.8) 268 ( 1.4) Slack State 250 ( 3.7) 241 ( 4.6) 246 ( 3.8) 238 ( 4.5) 247 ( 3.3) 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 248 ( 1.4) 239 ( 2.0) 240 ( 1.5) 238 ( 1.7) 241 ( 1.9) 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) American Indian State 237 ( 1.9)1 238 ( 3.3)1 241 ( 2 8)1 223 ( 2.7)1 232 ( 2.1)1 Region *44 ( *I* ) **4 ) IN* *** Nation 249 ( 7.8)1 247 ( 6.8)1 248 ( 8.6)1 242 ( 5.2)1 242 ( 4.9)1 TYPE OF COMMUNITY Advantaged urban State 279 ( 2.4)1 276 ( 3.8)1 268 ( 2.0)1 278 ( 2.1)1 27.; , 2.2), 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 ( 48)1 277 ( 4.8)1 Disadvantaged urban State 252 ( 3.4)1 246 ( 3.9)1 248 ( 3.5)1 247 ( 4,8)1 245 ( 41)1 Region 260 ( 5.4)1 250 ( 8.9)1 256 ( 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 249 ( 5.8)1 24.6 ( 4.5)1 247 ( 5.1)1 240 ( 7.5)1 245 ( 6.4)1 Region 254 ( 8.6)1 254 ( 4.631 252 1 9.4)1 253 ( 8.8)i 251 ( 8.5)1 Nation 258 ( 4.3)1 254 ( 4.2)1 253 ( 4.5)1 257 ( 5.0)1 256 ( 4,8)1 Other State 264 ( 2.0) 256 ( 2.2) 256 ( 1.9) 256 ( 2.4) 258 ( 2.1) 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) l'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 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 sire is insufricient to permit a reliable esumate (fewer than 62 studems). 4 0 34 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE 3 I Eighth-Grade Public-School Mathematics (continued) I Content Area Performance by Subpopulations AVERAGE MATHEMATICS PROFICIENCY OF STUDENT., 1990 NAEP TRIAL Numbers and Measurement Geometry Data Analysis, Statistics, and .,...., "sZ4701;" STATE ASSESSMENT Operations Probability TOTAL Proficiency Proficiency Proficiency Proficiency Proficiency State 264 ( 1.2) 257 ( 1.4) 250 ( 1.1) 258 ( 1.4) 258 ( 1.3) Region 264 ( 2.6) 258 ( 3.0) 260 ( 2 6) 282 ( 3.8) 259 ( 2.4) Notion 286 ( 1.4) 258 ( 1.7) 259 1 4 4) 262 ( 1.8) 20.) ( 1.3) PARENTS EDUCATION HS non-graduate State 246 ( 2.1) 234 ( 3.4) 241 ( 2.1) 235 ( 2.8) 238 ( 3.6) Region 248 ( 42) 242 ( 62) 246 ( 4.9) 248 ( 8.2) 245 ( 5.1) Nation 247 ( 2.4) 237 ( 3.6) 242 ( 2.2) 240 ( 3.1) 242 ( 3.0) HS graduate State 255 ( 1.7) 247 ( 2.0) 249 ( 1.5) 248 ( 2.2) 250 ( 1.9) Region 254 ( 2.5) 245 ( 3.0) 251 ( 3.6) 249 ( 32) 250 ( 2.4) Nation 259 ( 1.8) 248 ( 2.1) 252 ( 1.8) 253 ( 22) 253 ( 2.0) Some college State 271 ( 2.0) 262 ( 2.3) 260 ( 2.0) 266 ( 2.4) 285 ( 2.0) Region 272 ( 2.7) 268 ( 5.3) 264 ( '3.9) 271 ( 4.9) 284 ( 32) Nation 270 ( 1.5) 264 ( 2.7) 262 ( 2.0) 269 ( 2.4) 283 ( 2.2) College graduate State 276 ( 1.6) 271 ( 1.9) 267 ( 1.5) 273 ( 1.8) 271 ( 1.7) Region 275 ( 2.7) 271 ( 3.0) 271 ( 2.3) 276 ( 4.3) 272 ( 2.0) Nation 278 ( 1.8) 272 ( 2.0) 270 ( 1.6) 276 ( 2.2) 273 ( 1.7) GENDER Male State 267 ( 1.5) 263 ( 1.5) 260 ( 1.4) 262 ( 1.8) 259 ( 1.6) Region 264 ( 3.8) 263 ( 35) 261 ( 3.4) 264 ( 4.1) 260 ( 3.3) Nation 266 ( 2.0) . 262 ( 2.3) 260 ( 1.7) 262 ( 2.1) 260 ( 1.6) Female State 262 ( 1.3) 251 ( 1.7) 253 ( 1.2) 254 ( 1.5) 257 ( 1.4) Region 263 ( 2.5) 252 ( 2.9) 259 ( 2.9) 260 ( 4.0) 259 ( 2.8) Nation 286 ( 1.4) 253 ( 1.6) 258 ( 1.5) 261 ( 1.9) 260 ( 1.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 9$ percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 35 Arizona THE NATION'S REPORT CARD PART TWO Finding a Context for Understanding Students' Mathematics Proficiency Information on students' mathematics proficiency is valuable in and of itself, but it becomes more useful for improving instmetion and setting policy when supplemented with contextual information about schools, *. i, 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 thc subject, and provide an educational context for understanding information on student achievement. It is important to note that the NALP data cannot establish cause-and-effect links between various contextual factors and students' mathematics proficiency. However, the results do provide information about important relationships between the contextual factors and proficiency. The contextual information provided in Part Two of this report focuses on four major areas: instructional content, instructional practices, teacher qualifications, and conditions beyond school that facilitate learning and instruction -- fundamental aspects of the educational process in the country. 4 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 37 Arizona 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 enomious impact on future academic achievement. Yet, as shown in Chapters 3 and 7, large proportions of students report ha,ing 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. 3 38 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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 Arizona public schools and their relationship to students' proficiency. Table 4 provides a profile of the eighth-grade public schools' policies and stalling. Some of the salient results are as follows: More than half of the eighth-grade students in Arizona (64 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. Curtis McKnight, et al., The Underachieving Curriculum Assessing U.S. School Mathematics from an International Perspective. A National Report on the Second International Mathematics Study (Champaign, IL: Stipes PublishmE, "--,mpany. 1987). Lynn Steen, Ed. Everybody Counts A Report to the Nation on the Future of Mathematk. Education (Washington, DC: National Academy Press, 1989). Al 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 39 A ri zona In Arizona, 87 percent of the students could take an algebra course in eighth grade for high school course placement or credit. Many of the students in Arizona (84 percent) were taught mathematics by teachers who teach only one subject. About three-quarters (71 percent) of the students in Arizona 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 Arizona I Eighth-Grade Public Schools PERCENTAGE OF STUDENTS 1990 MAEP TRIAL STATE ASSESSMENT Arizona 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 64 ( 3,9) 61 ( $.6) 63 ( 5.9) 87 ( 3.1) 92 ( 4.7) 78 ( 4.6) 84 ( 3.3) 98 ( 1.6) 91 ( 33) 71 ( 2.5) 64 ( 8.3) 53 ( 4.0) 33 ( 3.8) 25 ( 5,9) 30 ( 4.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 40 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona CURRICULUM COVERAGE To place students' mathematics proficiency in a curriculum-related context, it is necessary to examine the extent to which eighth graders in Arizona are taking mathematics courses. Based on their responses, shown in Table 5: About the same percentage of students in Arizona were taking eighth-grade mathematics (48 percent) as were taking a course in pre-a/gebra or algebra (47 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. Students in Arizona 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 MO NAEP TRIAL STATE ASSESSMENT Arizona West Nation What kind of mathematics class are you taking this year", Pen:engage and Proficiency Percentage and Proficiency Percentage and Proficiency EiOath-grado mathematics 48 ( 1.5) 63 ( 2.7) 62 ( 2.1) 246 ( 1.3) 252 2.4) 251 ( 1.4) Pre-algebra 29 ( 1.5) 15 ( 2.7) 19 ( 1.9) 266 ( 1.8) 266 ( 3.6) 272 ( 2.4) Algebra 18 ( 1.3) 17 ( 1.8) 15 ( 1.2) 289 ( 2.4) 299 ( 4.5) 296 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 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. G THE 1990 NAEP TRIAL STATE ASSESSMENT 41 Arizona Further, from Table A5 in the Data Appendi :4 About the same percentage of females (49 percent) and males (45 percent) in Arizona were enrolled in pre-algebra or algebra courses. In Arizona, 52 percent of White students, 40 percent of Black students, 39 percent of Hispanic students, and 38 percent of American Indian students were enrolled in pre-algebra or algebra courses. Similarly, 60 percent of students attending schools in advantaged urban areas, 55 percent in schools in disadvantaged urban areas, 45 percent in schools in extreme rural areas, and 44 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' rtsponses, respectively. According to their teachers, the greatest percentage of eighth-grade students in public schools in Arizona spent 30 minutcs doing mathematics homework each day; according to the students, the greatest percentage spent 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 Arizona, 3 percent of the students spent no time each day on mathematics homework, compared to 1 percent for the nation. Moreover, 5 percent of the students in Arizona and 4 percent of the students in the nation spent an hour or more on mathematics homework each day. For every table in the body of the report that includes estimates of average proficiency, the Data Appendix provides a corresponding table presenting the results for the four subpopulations -- race ethnicity, type of community, parents education level, and gender. 7 42 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona The results by race/ethnicity show that 6 percent of White students, 2 percent of Black students, 5 percent of Hispanic students, and 1 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 2 percent of White students; 3 percent of Black students, 3 percent of Hispanic students, and 6 percent of American Indian students spent no time doing mathematics homework. In addition, 10 percent of students attending schools in advantaged urban areas, 15 percent in schools in disadvantaged urban areas, 0 percent in schools in extreme rural areas, and 4 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 1 percent of students attending schools in advantaged urban areas, 1 percent in schools in disadvantaged urban areas, 4 percent in schools in extreme rural areas, and 2 percent in schools in areas classified as "other" spent no time doing mathematics homework. TABLE 6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Eact Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Arizona West Nation _ 1 About how much time do students spend on mathematics homework each day? None 16 minutu 30 minutes 45 minutes An hour or more Percentage and Proficiency Percentage and Proficiency Percentage and Proaciancy 3 ( 0.5) ( 0.3) 1 ( 0.3) 36 ( 2.5) 42 ( 6.7) 43 ( 4.2) 253 ( 1.8) 258 ( 4.2) 256 ( 23) 46 ( 2.6) 43 ( 6.2) 43 ( 4.3) 261 ( 1,7) 264 ( 4.7) 266 ( 2.6) 10 ( 15) 9 ( 2.3) 10 ( 1.9) 271 ( 3.7) 270 ( 5.5)1 272 ( 5.7)i 5 ( 0.8) 5 ( 1.9) 4 ( 0.9) 276 ( 4.8) 278 ( 5.1)1 The standard errors or the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within i 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 43 Arizona TABLE 7 1 Students' Reports on the Amount of Time They Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Arizona West Nation ._ About how much bme do you usually spend each day on rnathemabc$ homework? Percentage end Proficiency Percentage and Proliciancy Percentage end Pro lidency None 9 ( 0.9) 12 ( 1.7) 9 ( 0.6) 257 ( 2.2) 254 ( 4.2) 251 ( 2.8) 15 minutes 24 ( 0.8) 31 ( 4.5) 31 ( 2.0) 280 ( 1.6) 263 ( 3.8) 284 ( 1.9) 30 minutes 32 ( 0.9) 28 ( 1.7) 32 ( 12) 261 ( 1.5) 261 ( 2.9) 263 ( 1.9) 45 minutes 17 ( 06) 15 ( 1.6) 16 ( 1.0) 281 ( 1,8) 267 ( 4.2) 268 ( 1.9) An hour or more 18 ( 1.0) 14 ( 4.7) 12 ( 1.1) 258 ( 1.9) 261 ( 4.3) 258 ( 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 z 2 standard errors of the estimate for the sample. And, according to the students (Table 7 and Table A7 in the Data Appendix): In Arizona, 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, 18 percent of the students in Arizona 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, 20 percent of Hispanic students, and 25 percent of American Indian students spent an hour or more on mathematics homework each day. In comparison, 9 percent of White students, 6 percent of Black students, 9 percent of Hispanic students, and 10 percent of American Indian students spent no time doing mathematics homework. 44 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona In addition, 16 percent of students attending schools in advantaged urban areas, 21 percent in schools in disadvantaged urban areas, 20 percent in schools in extreme rural areas, and 18 percent in schools in areas classified as "other" spent an hour or more on mathematics homework daily. In comparison, 8 percent of students attending schools in advantaged urban areas, 8 percent in schools in disadvantaged urban areas, 7 percent in schools in extreme rural areas, and 10 percent in schools in arms classified as "other" spent no time doing mathematics homework. INSTRUCTIONAL EMPHASIS According to the approach of the National Council of TeRchers 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, &kith, 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 Ove specific mathematics topics during the school year. Their responses provide an indication of the students' opportunity to learn thc various topics covered in the assessment. For each of 10 topics, the teachers were asked whether they planned to place "heavy," "moderate," or "little or no" emphasis on the topic. Each of the topics corresponded to skills that were measured in one of the five mathematics content areas included in the Trial State Assessment: Numbers and Operations. Teachers were asked about emphasis placed on five topics: whole number operations, common fractions, decimal fractions, ratio or proportion, and percent. Measurement. Teachers were asked about emphasis placed on one topic: measurement. Geometry. Teachers were asked about emphasis placed on one topic: geometry. Data Analysis, Statistics, and Probability. Teachers were asked about emphasis placed on two topics: tables and graphs, and probability and statistics. Algebra and Functions. Teachers were asked about emphasis placed on one topic: algebra and functions. National Council of Teachers of Mathematics, Currifulwn and Erahdation Standards for School Mathematics (Reston, VA; National Council of Teachers of Mathematics, 1989). t) THE 1990 NAEP TRIAL STATE ASSESSMENT 45 Arizona The responses of the assessed students' teachers to the topic emphasis questions for each content area were combined to create a new variable. For each question in a particular content area, a value of 3 was given to "heavy emphasis" responses, 2 to "moderate emphasis" responses, and 1 to "little or no emphasis" responses. Each teacher's responses were then averaged over all questions related to the particular content area. Table 8 provides the results for the extreme categories -- "heavy emphasis" and "little or no emphasis" -- and the average student proficiency in each content area. For the emphasis questions about numbers and operations, for example, the proficiency reported is the average student performance in the Numbers and Operations content area. Students whose teachers placed heavy instructional emphasis on Algebra and Functions had higher proficiency in this content area than students whose teachers placed little or no emphasis on Algebra and Functions. Students whose teachers placed heavy instructional emphasis on Numbers and Operations and Measurement had lower proficiency in these content areas than students whose teachers placed little or no emphasis on the same areas. 445 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE 8 I Teachers' Reports on the Emphasis Given to I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Arizona West Nation Percentage and Preedency Percentage and Preadoncy Percentage and Prolkiency Teacher 'emphasis" categor es by content areas Numbers and Operations Heavy emphasis 52 ( 3.3) 42 ( 7.4) 49 ( 3.8) 250 ( 1.9) 257 ( 3.6) 260 ( 1.8) Little or no emphasis 12 ( 1.6) 13 ( 2.1) 15 ( 2.1) 286 ( 4.3) 291 ( 6.6) 287 ( 3.4) Measurement Heavy emphasis 10 ( 1.6) 11 ( 2.8) 17 ( 3.0) 250 ( 4.5) 251 ( 7.7)1 250 ( 5.6) Little or no emphasis 43 ( 2e8 ( 2.7) 2.1) 36 275 ( 5.3) ( 6.3) 33 ( 272 ( 4.0) 4.0) Geometry Heavy emphasis 14 ( 1.8) 24 ( 6.3) 28 ( 3.8) 260 ( 3.7) 260 ( 2.8)1 260 ( 3.2) Little or no emphasis 33 ( 2.3) 16 ( 4.5) 21 ( 3.3) 256 ( 2.1) 277 (11.4)1 264 ( 5.4) Data Analysis, Statistics, and Probability Heavy emphasis 7 ( 1.3) 14 ( 3.7) 14 ( 2.2) 252 ( 3.9) 264 (10.6)1 269 ( 4.3) Little or no emphasis 67 ( 3.1) 54 ( 6.3) 53 ( 4.4) 257 ( 1.8) 262 ( 4.9) 261 ( 2.9) Algebra and Functions Heavy emphasis 51 ( 2.8) 43 ( 5.6) 46 ( 3.6) 271 ( 2.0) 277 ( 5.2) 275 ( 2.5) Little or no emphasis 17 ( 1.9) 23 1 5.1) 20 ( 3.0) 234 ( 2.5) 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 entire population is within 7t- 2 standard errors of the esUmate 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 Arizona 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 cuniculum coverage, mathematics homework, and instructional emphasis has revealed the following: More than half of the eighth-grade students in Arizona (64 percent) were in public schools where mathematics was identified as a special priority. This compares to 63 percent for the nation. In Arizona, 87 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 Arizona were taking eighth-grade mathematics (48 percent) as were taking a course in pre-algebra or algebra (47 percent). Across the nation, 62 percent were taking eighth-grade mathematics and 34 percent were taking a course in pre-algebra or algebra. According to their teachers, the greatest percentage of eighth-grade students in public schools in Arizona spent 30 minutes doing mathematics homework each day; according to the students, most of them spent 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 Arizona, 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, 18 percent of the students in Arizona 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 3 48 THE 11,',O NAEP TRIAL STATE ASSESSMENT Arizona CHAPTER 4 111111111 MM. CO 111111111111811111111111111 OMEN 111111111111 MO 1151111111111111111111111,1111111 1111111111111101111111141111111 111111111111111111111111111111 1111111111111 -.1111111/,11111M 1111111111 SWAM 11111111.11111111111111111 ABIOS 1111111111011 How Is Mathematics Instruction Delivered? Teachers facilitate learning through a variety of instructional practices. Because a particular teaching method may not be equally effective with all types of students, selecting and tailoring methods for students with different styles of learning or for those who come from different cultural backgrounds is an important aspect of teaching!' An inspection of the availability and use of resources for mathematics education can provide insight into how and what students are learning in mathematics. To provide information about how instruction is delivered, students and teachers participating in the Trial State Assessment were asked to report on the use of various teaching and learning activities in their mathematics classrooms. AVAILABILITY OF RESOURCES Teachers' use of resources is obviously constrained by the availability of those resources. Thus, the assessed students' teachers were asked to what extent they were able to obtain all of the instructional materials and other resources they needed. e' National Council of Teachers of Mathematics. Professional Standards for the Thaching of Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1991). THE 1990 NAEP TRIAL STATE ASSESSMENT 49 Arizona From Table 9 and Table A9 in the Data Appendix: In Arizona, 17 percent of the eighth-grade studr :its had mathematics teachers who reported getting all of the resources they needed, while 31 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 Arizona, S percent of students attending schools in advantaged urban areas, 14 percent in schools in disadvantaged urban areas, 8 percent in schools in extreme rural areas, and 20 percent in schools in areas classified as "other" had mathematics teachers who got all the resourcesthey needed. By comparison, in Arizona, 34 percent of students attending schools in advantaged urban areas, 32 percent in schools in disadvantaged urban areas, 18 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 _ 1900 NAEP TRIAL STATE ASSESSMENT Arizona West Nation _ Which of the following statements is true about how well supplied you are by your Parentage Percentar Percentage school system with the instructional and and and materials and other resources you need to teach your class? get all the rnources I nee0 . Proncioncy 17 ( 2.6) ProlkdoncY 15 ( 5.2) PraciancV 13 ( 2.4) 261 ( 2.4) 261 ( 5.9)1 265 ( 42) get most of the resoer 'es I need. 53 ( 2.8) 62 ( 3,8) 56 ( 4.0) 281 ( 1.7) 266 ( 4.1) 265 ( 2.0) I get some or none of the resources I need. 31 ( 2.8) 23 ( 6.1) 31 ( 42) 257 ( 2.3) 257 ( 3.7)1 261 ( 2.9) The standard errors of the esfimated 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 4 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variab,lity of this estimated mean proficiency. 50 THE 1990 NAEP TRIAL STATE ASSFSSMENT Arizona PATFERNS IN CLASSROOM ESSTRUCTION Research in education and cognitive psychology has yielded many insights into the types of instructional activities that facilitate students' mathematics learning. Increasing the use of "hands-on" examples with concrete materials and placing problems in real-world contexts to help children construct useful meanings for mathematical concepts are among the recommended approaches.' Students' responses to a series of questions on their mathematics instruction provide an indication of the extent to which teachers are making use of the types of student-centered activities suggested by researchers. Table 10 presents data on patterns of classroom practice and Table 11 provides information on materials used for classroom instruction by the mathematics teachers of the assessed students. According to their teachers: More than half of the students in Arizona (61 percent) worked mathematics problems in small groups at least once a week; relatively few never worked mathematics problems in small groups (8 percent). The largest percentage of the students (63 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week; some never used such objects (17 percent) In Arizona, 72 percent of the students were assigned problems from a mathematics textbook almost every day; 5 percent worked textbook problems about once a week or less. Less than half of the students (32 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (36 percent). ' Thomas Romberg, "A Common Curnculum for Mathematics," Individual Differences and the Common Currkulum Eighty-second Yearbook of the National Society for the Study of Education (Chicago, IL: University of Chicago Ptess, 1983). THE 1990 NAEP TRIAL STATE ASSESSMENT 51 Arizona TABLE 10 I Teachers' Reports on Patterns of Mathematics 1 Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Arizona West Nation , About how often do students work I problems in small groups? At least once a week Less than once a week Never About how often do students use objects like rulers, counting blocks, or geometric solids? At lout once a week Less than once a week Never Percentage and Piolkiency Pementage Percentage and and Proliciancy Proficiency 61 ( 2.8) 57 ( 8.9) 50 ( 4.4) 257 ( 1.6) 262 ( 42)i 260 ( 2.2) 31 ( 2.6) 39 ( 7.6) 43 ( 4.1) 264 ( 1.9) 266 ( 4.5) 264 ( 2.3) 8 ( 1.2) 3 ( 22) 8 ( 2.0) 264 ( 3.3) ... ( ***) 277 ( 5.4)I Percentage mid Proliciency Percentage Percentage and and Proficiency Preticiency 21 ( 2.8) 34 ( 8.2) 22 ( 3.7) 256 ( 2.4) 256 ( 4.9)I 254 ( 3.2) 63 ( 3.1) 57 ( 6.4) 69 ( 3.9) 259 ( 1.7) 265 ( 4.0) 263 ( 1.9) 17 ( 2.3) 9 ( 2.6) 266 ( 3.4) 282 ( 5.9)i The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 52 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE 11 I Teachers' Reports on Materials for Mathematics Instruction PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 MEP TRIAL STATE ASSESSMENT Arizona West Nation About how often do students do problems from textbooks? Almost every day Several times a week About once a week or hiss About how often do students do problems Lon worksheets? Al least several times a week About once a week Less than *middy Percentage and Pn AidencY Perventage and Proficiency Percentage and Proficiency 72 ( 2.5) 56 ( tO) 82 ( 3.4) 262 ( 1.5) 270 ( 3.3) 267 ( 1.8) 23 ( 2.3) 38 ( 5.1) 31 ( 3.1) 257 ( 2.4) 258 ( 5.2) 254 ( 2.9) 5 ( 238 ( 1.3) 4.6)I 9 ( 4.9) ***) 7 ( 260 ( 1.8) 5.1)! Percentage and Proficiency Percentage and Prolidency Percentage and Proficiency 32 ( 32) 25 ( 5.2) 34 ( 3.8) 253 ( 1.9) 258 ( 4.3)1 256 ( 2.3) 32 ( 2.5) 34 ( 4.8) 33 ( 3.4) 258 ( 2.3) 258 ( 4.1) 260 ( 2.3) 36 ( 2.8) 41 ( 5.6) 32 ( 3.8) 266 ( 22) 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. '1" 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 thei- responses to their mathematics proficiency. It also compares the responses of the students to those of their teachers. S THE 1990 NAEP TRIAL STATE ASSESSMENT 53 Arizona COLLABORATING Di SMALL GROUPS In Arizona, 42 percent of the students reported never working mathematics problems in small groups (see Table 12); 33 percent of the students worked mathematics problems in small goups at least once a week. TABLE 12 I Student-4' Reports on the Frequency of Small I Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Adam& West Nation _ Percentage end Proficiency Percentage and Proficiency Percentage and Proficiency How often do you work in small groups in your mathematics class? At least once a week 33 ( 1.9) 35 ( 4.8) 28 ( 2.5) 256 ( 2.1) 258 ( 4.2) 258 ( 2.7) Less than once a week 26 ( 1.1) 29 ( 2.8) 28 ( 1.4) 264 ( 1.6) 271 ( 3.1) 267 ( 2.0) New 42 ( 1.3) 36 ( 4,8) 44 ( 2.9) 261 ( 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 t 2 standard errors of the estimate for the sample. Examining the subpopulations (Table Al2 in the Data Appendix): In Arizona, 25 percent of students attending schools in advantaged urban areas, 23 percent in schools in disadvantaged urban areas, 25 percent in schools in extreme rural areas, and 38 percent in schools in areas classified as "other" worked in small groups at least once a week. Further, 29 percent of White students, 27 percent of Black students, 40 percent of Hispanic students, and 41 percent of American Indian students worked mathematics problems in small goups at least once a week. Females were as likely as males to work mathematics problems in small groups at least once a week (34 percent and 31 percent, respectively). 54 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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 A13 in the Data Appendix summarize these data: About half of the students in Arizona (53 percent) never used mathematical objects; 21 percent used these objects at least once a week. Mathematical objects were used at least once a week by 17 percent of students attending schools in advantaged urban areas, 27 percent in schools in disadvantaged urban areas, 31 percent in schools in extreme rural areas, and 21 percent in schools in areas classified as "other". Males were more likely than females to use mathematical objects in their mathematics classes at least once a week (24 percent and 18 percent, respectively). In addition, 19 percent of White students, 23 percent of Black students, 24 percent of Hispanic students, and 29 percent of American Indian students used mathematical objects at least once a week. TABLE 13 I Students' Reports on the Use of Mathematics 1 Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT ArL na west Nation -1 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 ProliciancY At least once a weak 21 ( 1.4) 38 ( 3.5) 23 ( 1.8) 254 ( 1.8) 280 ( 4,0) 258 ( 2.6) Less than once a week 25 ( 1.2) 28 ( 1.8) 31 ( 1.2) 264 ( 1.9) 289 ( 2.7) 269 ( 1.5) Never 53 ( 1.7) 38 ( 3.3) 41 ( 2.2) 260 ( 1.3) 258 ( 2.8) 259 ( 1.6) 7he 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 55 Arizona MATERIALS FOR MATHEMATICS LNSTRUCTION The percentages of eighth-grade public-school students in Arizona who frequently worked mathematics problems from textbooks (Table 14) or worksheets (Table 15) indicate that these materials play a major role in mathematics teaching and learning. Regarding the frequency of textbook usage (Table 14 and Table A 14 in the Data Appendix): About three-quarters of the students in Arizona (79 percent) worked mathematics problems from textbooks almost every day, compared to 74 percent of the students in the nation. Textbooks were used almost every day by 92 percent of students attending schools in advantaged urban areas, 72 percent in schools in disadvantaged urban areas, 76 percent in schools in extreme rural areas, and 79 percent in schools in areas classified as "other" TABLE 14 I Students' Reports on the Frequency of Mathematics Textbook Use PERCENTAGE Cr- STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY r1900 NAEP TRIAL STATE ASSESSMENT Arizona Worst Nation -1 1 How often do you do mathematics problems from textbooks in your mathematics class? Almost every day Several times a week About once a week or less Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency 79 ( 1.4) 71 ( 3.5) 74 ( 1.9) 254 ( 1A) 267 ( 2.4) 267 ( 1.2) 13 ( 0.7) 15 ( 1.5) 14 ( 0.8) 247 ( 1.9) 251 ( 2.4) 252 ( 1.7) 8 ( 1.1) 14 ( 3.1) 12 ( 1.8) 241 ( 2.8) 242 (112)1 242 ( 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 determinatim, of the variability of this estimated mean proficiency. c 56 THE 190:', NAEP TRIAL STATE ASSESSMENT Arizona And, for the frequency of worksheet usage (Table 15 and Table Al5 in the Data Appendix): Less than half of the students in Arizona (31 percent) used worksheets at least several times a week, compared to 38 percent in the nation. Worksheets were used at least several times a week by 17 percent of students attending schools in advantaged urban areas, 34 percent in schools in disadvantaged urban areas, 37 percent in schools in extreme rural areas, and 32 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 _ IMO KAEP TRIAL STATE ASSESSMENT Arizona West Nation Percentage and Proficiency Percentage and Proltdency Percentage and ProficAtncy rHow often do you do mathematics problems on worksheets in your mathematics class? At least several times a week 31 ( 1.9) ( 4.0) 38 ( 2.4) 250 ( 1.8) 250 ( 42) 253 ( 2.2) About once a week 29 ( 12) 23 ( 2.8) 25 ( 1.2) 259 ( 1.5) 262 ( 2.1) 281 ( 1.4) Less than weekly 40 ( 1.5) 41 ( 4.1) 37 ( 2.5) 287 ( 1.8) 270 ( 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 -t 2 standard errors of the estimate for the sample. Table 16 conwares students' and teachers' responses to questions about the patterns of classroom instruction and materials for mathematics instruction. THE 1990 NAEP TRIAL STATE ASSESSMENT 57 Arizona TABLE 16 Comparison of Students' and Teachers' Reports on Patterns of and Materials for Mathematics Instruction PERCENTAGE OF STUDENTS 1900 NAEP TRIAL STATE ASSESSMENT West Nation Patterns of classroom Instruction Percentage of students who work mathematics problems In small groups At least once a week Less than once a week Never Percentage of students who us* objects like rulers, counting bigacks, or geometric solids At least once a week Less than once a week Never Materials for mathematics Instruction Percentage of studnts who use a mathematics textbook Almost every day Several times a week About once a week or less Percentage of students who use a mathematics worksheet At least several times a week About once a week Less than weekly Pwantage Percistage Percentage Students Teacheri Students Teachers Students Teachers 33 ( 1.9) 61 ( 2.8) 35 ( 4.8) 57 ( 8.9) 28 ( 2.5) 50 ( 4.4) 26 ( 1.1) 31 ( 2.6) 29 ( 2.8) 39 ( 7.6) 28 ( 1.4) 43 ( 4.1) 42 ( 1.8) 8 ( 1.2) 36 ( 4.8) 3 ( 2.2) 44 ( 2.9) 8 ( 2.0) 21 ( 1.4) 21 ( 2.8) 36 ( 3.5) 34 ( 8.2) 28 ( 1.8) 22 ( 3.7) 25 ( 1.2) 63 ( 3.1) 28 ( 1.8) 57 ( 6.4) 31 ( 1.2) 69 ( 3,9) 53 ( 1.7) 17 ( 2.3) 36 ( 3.3) 8 ( 3.0) 41 ( 2.2) 9 ( 2.6) Percentage Percentage Percentage Students Teachers Students Teachers Students Teachers 79 ( 4.4) 72 ( 2.5) 71 ( 3.5) 55 ( 6.0) 74 ( 1.9) 62 ( 3.4) 13 ( 0.7) 23 ( 2.3) 15 ( 1.5) 36 ( 5.1) 14 ( 0.8) 31 ( 3.1) 8 ( 1.1) 5 ( 1.3) 14 ( 3.1) 9 ( 4.9) 12 ( 1.8) 7 ( 1.8) 31 ( 1.9) 32 ( 3.2) 35 ( 4.0) 25 ( 5.2) 38 ( 2.4) 34 ( 3.8) 29 ( 1.2) 32 ( 2.5) 23 ( 2.6) 34 ( 4.8) 25 ( 12) 33 ( 3.4) 40 ( 1.5) 36 ( 2.8) 41 ( 4.1) 41 ( 5.8) 37 ( 2.5) 32 ( 3.6) 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. C3 TIIE 1990 NAEP TRIAL STATE ASSESSMENT Arizona SUMMARY Because classroom instructional time is typically limited, teachers reed to make the best possible use of what is known about effective instructional delivery practices and resources. It appears that mathematics textbooks and worksheets continue to play a major role in mathematics teaching. Although there is some evidence that other instructional resources and practices are emerging, they are not yet commonplace. According to the students' mathematics teachers: More than half of the students in Arizona (61 percent) worker'. mathematics problems in small groups at least once a week; relatively few never worked in small groups (8 percent). The largest percentage of the students (63 percent) used objects like rulers, counting blocks, or geometric shapes less than once a week, and some never used such objects (17 percent), In Arizona, 72 percent of the students were assigned problems from a mathematics textbook almost every day; 5 percent worked textbook problems about once a week or less. Less than half of the students (32 percent) did problems from worksheets at least several times a week; less than half did worksheet problems less than weekly (36 percent). And, according to the students: In Arizona, 42 percent of the students never worked mathematics problems in small groups; 33 percent of the students worked mathematics problems in small groups at least once a week. About half of the students in Arizona (53 percent) never used mathematical objects; 21 percent used these objects at least once a week. About three-quarters of the students in Arizona (79 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 Arizona (31 percent) used worksheets at least several times a week, compared to 38 percent in the nation. P 4 THE 1990 NAEP TRIAL STATE ASSESSMENT 59 Arizona 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 cpmputations and to pennit them to focus on more challenging tasks.' The increasing availability of affordable calculators should make it more likely and attractive for students and schools to acquire and use these devices. Given the prevalence and potential importance of calculators, part of the Trial State Assessment focused on attitudes toward and uses of calculators. Teachers were asked to report the extent to which they encouraged or permitted calculator use for various activities in mathematics class and students were asked about the availability and use of calculators. National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, NJ: Educauonal Testing Service, 1988). National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 1989). 5 60 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona Table 17 provides a profile of Arizona eighth-grade public schools' policies with regard to calculator use: In comparison to 33 percent across the nation, 22 percent of the students in Arizona had teachers who allowed calculators to be used for tests. About the same percentage of students in Arizona and in the nation had teachers who permitted unrestricted use of calculators (17 percent and 18 percent, respectively). TABLE 17 I Teachers' Reports of Arizona Policies on 1 Calculator Use PERCENTAGE OF STUDENTS 1980 NAEP TRIAL STATE ASSESSMENT Arizona West Nation Percentage of eighth.grade students in public schools whose teachers permit the unrestricted us 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 calculators owned by the school Percentage Percentage Percentage 17 ( 2.3) 20 ( 4.9) 18 ( 3.4) 22 ( 2.8) 48 ( 8.8) 33 ( 4.5) 60 ( 3.2) 72 ( 7.4) Se ( 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. THE 1990 NAEP TRIAL STATE ASSESSMENT 61 Ariwna THE AVAILABILITY OF CALCULATORS In Arizona, most students or their families (97 percent) owned calculators (Table 18); however, fewer students (44 percent) had teachers who explained the use of calculators to them. From Table A18 in the Data Appendix: In Arizona, 38 percent of White students, 49 percent of Black students, 52 percent of Hispanic students, and 61 percent of American Indian students had teachers who explained how to use them. Females were as likely as males to have the use of calculators explained to them (42 peramt and 46 percent, respectively). TABLE 18 Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How To Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Arizona West Nation I Do you or your family own a calculator? Yes No Does your mathematics teacher explain how to use a calculator for mathematics problems? Yes No Percentage and Proficiency 97 ( 0.4) 260 ( 1.1) 3 ( 0.4) 241 ( 3.0) Percentage Percentage and and Proftciamy Pronciency ( 0.6) 263 ( 2.6) 4 ( 0.6) 97 ( 0.4) 263 ( 1.3) 3 ( 0.4) 234 ( 3.8) Percentage Percentage Percentage and and and Pronciency Protkiency Prollciancy 44 ( 1.8) 255 ( 1.7) 56 ( 1.8) 264 ( 1.2) 59 '34) 260 2.7) 41 ( 3.4) 265 ( 3.0) 49 ( 2.3) 258 ( 1.7) 51 ( 2.3) 266 ( 1,5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r7 62 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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 Assessnl students were asked how frequently (never, sometimes, almost always) they us. calculators for working problems in class, doing prIblems at home, and taking quizzes or tests. As reported in Table 19: In Arizona, 27 percent of the students never used a calculator to work problems in class, while 46 percent almost always did. Some of the students (18 percent) never used a calculator to work problems at home, compared to 29 percent who almost always used one. Less than half of the students (37 percent) never used a calculator to take quizzes or tests, while 23 percent almost always did. TABLE 19 I Students' Reports on the Use of a Calculator I for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 MAP TRIAL STATE ASSESSMENT Arizona West Nation - Percentage and Proficiency Percentage and Proficiency Percentage and, Pfonciency How often do you use a calculator for the following tasks? Working problems in ciass Almost always 48 ( 1.0) 53 ( 2.1) 48 ( 1.5) 252 ( 1.3) 255 ( 2.6) 254 ( 1.5) Never 27 ( 1.2) 14 ( 2.4) 23 ( 1.9) 274 1.5) 265 ( 3.0) 272 ( 1.4) Doing problems at home Almost always 29 ( 1.2) 29 ( 30 ( 1.3) 280 ( 1.5) 263 ( 261 ( 1.8) Never 18 ( 0.9) 19 ( 1.6) 19 ( 0.9) 268 ( 2.0) 258 ( 3.7) 263 ( 1.8) Taking qulzzes or tests Almost always 23( 1.1) 25 ( 1.6) 27 ( 1.4) 250 ( 1.7) 259 ( 3.9) 253 ( 2.4) Never 37 ( 1.3) 22 ( 3.0) 30 ( 2.0) 273 ( 1.1) 270 ( 3.3) 274 ( 1.3) 1=11111111. 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 permntages may not total 100 percent because the "Sometimes" category is not included. THE 1990 NAEP TRIAL STATE ASSESSMENT 63 Arizona 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 weir given calculators to use. The test administrator provided the students with instructions and practice on how to use a calculator prior to the assessment. During the assessment, students were allowed to choose whether or not to use a calculator for each item in the calculator sections, and they were asked to indicate in their test booklets.whether they did or did not use a calculator for each item. Certain items in the calculator sections were defined as "calculator-active" items -- that is, items that required the student to use the calculator to determine the correct response. Certain other items were defined as "calculator-inactive" items -- items whose solution neither required nor suggested the use of a calculator. The remainder of the items were "calculator-neutral" items, for which the solution to the question did not require the use of a calculator. In total, there were eight calculator-active items, 13 calculator-neutral items, and 17 calculator-inactive items across the two sections. However, because of the sampling methodology used as part of the Trial State Assessment, not every student took both sections. Some took both sections, some took only one section, and some took neither. To examine the characteristics of students who generally knew when the use of the calculator was helpful and those who did not, the students who responded to one or both of the calculator sections ere categorized into two groups: High -- students who used the calculator appropriately (i.e., used it for the calculator-active items and did not use it for the calculator-inactive items) at least 85 percent of the time and indicated that they had used the calculator for at least half of the calculator-active items they were presented. Other -- students who did not use the calculator appropriately at least 85 percent of the time or indicated that they had used the calculator for less than half of the calculator-active items they were presented. 13 9 64 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona FpgIm...m. The data presented in Table 20 and Table A20 in the Data Appendix are highlighted below: A smaller percentage of students in Arizona were in the High group than were in the Other group. A smaller percentage of males than females were in the High group. In addition, 49 percent of White students, 32 percent of Black students, 38 percent of Hispanic students, and 34 percent of American Indian students were in the High group. TABLE 20 J Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Arizona West Nation "Calculator-use" group Percentage and Proficiency Percentage end Proficiency Percentage and Proficiency Nigh 44 ( 1.2) 38 ( 2.6) 42 ( 1.3) 286 ( 1A) 273 ( 2.7) 272 ( 1.8) Other 58 ( 1.2) 62 ( 2.6) 58 ( 1.3) 263 ( 1.4) 253 ( 2.8) 256 ( 1.5) The standard errors of the estimated statistics appear in parentheses. lt can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 1- 2 standard errors of the estimate for the sample. 70 THE 1990 NAEP TRIAL STATE ASSESSMENT 65 Arizona SUMMARY Given the prevalence of inexpensive calculators, it may no longer be necessary or useful to devote large portions of' instructional time to teaching students how to perfomi 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, 22 percent of the students in Arizona had teachers who allowed calculators to be used for tests. About the same percentage of students in Arizona and in the nation had teachers who permitted unrestricted use of calculators (17 percent and 18 percent, respectively). In Arizona, most students or their families (97 percent) owned calculators; however, fewer students (44 percent) had teachers who explained the use of calculators to them. In Arizona, 27 percent of the students never used a calculator to work problems in class, while 46 percent ahno,t always did. Some of the students (18 percent) never used a calculator to work problems at home, compared to 29 percent who almost always used one. Less than half of the students (37 percent) never used a calculator to take quizzes or tests, while 23 percent almost always did. 71 66 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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 Arizona, 45 percent of the students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (73 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of the students were taught by mathematics teachers who were certified at the highest level available in their states. Less than half of the students (41 percent) had mathematics teachers who had a mathematics (middle school or secondary) teaching certificate, This compares to 84 percent for the nation. 9 National Council of Teachers of Mathematics, Professional Standards for the Teaching of Mathematks (Reston, VA: National Council of Teachers of Mathematics, 1991), THE 1990 NAEP TRIAL STATE ASSESSMENT 67 Arizona TABLE 21 Profile of Eighth-Grade Public-School I Mathematics Teachers PERCENTAGE OF STUDENTS 1660 NAEP TRIAL STATE ASSESSMENT Arizona West Nation Percentage of students whose mathematics teachers reported having the Mowing degrees Percentage Porcentage Percenteri Bachelor's degree 55 ( 2.8) 68 ( 52) 56 ( 4.2) Master's or specialist's degree 44 ( 2.8) 32 ( 5.2) 42 ( 4 2) Doctorate or professional degree 1 ( 0.4) 0 ( 0.0) 2 ( 1.4) Percentage of students *lose mathematics tachers have the foNowing types of teaching certificates that are recognized by Arizona No regular certification 4 ( 1.0) 8 ( 2.4) 4 ( 12) Regular certification but less than the highest available 23 ( 2.8) 20 ( 3.3) 29 ( 4,3) Highest certification available (permanent or long-term) 73 ( 2.7) 74 ( 3.3) 66 ( 4.3) Percentage of students wItose mathematics teachers have the following types of teaching certiflcates Mat are recognized by Arizona Mathematics (middle school or secondary) 41 ( 2.6) 88 ( 3.0) 84 ( 22) Education (elementary or middle school) 52 ( 3.0) 9 ( 2.8) 12 ( 2.6) Other 8 ( 1.9) 2 ( 1.3) 4 ( 1.5) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. EDUCATIONAL BACKGROUND Although mathematics teachers are held responsible for providing high-quality instruction to their students, there is a concern that many teachers have had limited exposure to content and concepts in the subject area. Accordingly, the Trial State Assessment gathered details on the teachers' educational backgrounds -- more specifically, their undergraduate and graduate majors and their in-service training. 73 68 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona Teachers' responses to questions concerning their undergraduwie and gaduate fields of study (Table 22) show that: In Arizona, 15 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Relatively few of the eiRhth-gride public-school students in Arizona (6 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 1SSO NAEP TRIAL STATE ASSESSMENT Arizona West Nation _ What was your undergraduate major? Percentage Percentage Percentage Mathematics 15 ( 2.2) 31 ( 5.9) 43 ( 3.9) Education 83 ( 3.5) 34 ( 8.6) 35 ( 3.8) Other r. 22 ( 2.7) 35 ( 6.6) 22 ( 3.3) What was your graduate major? Percentage Percentage Percentage Mathematics 8 ( 1.1) 19 ( 4.7) 22 ( 3.4) Education 58 ( 3.1) 36 ( 4.5) 38 ( 3.5) Other or no graduate level study 35 ( 3.0) 45 ( 5.4) 40 ( 3.4) The standard errors of the estimated statistics appear in parentheses. 11 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 Arizona Teachers' responses to questions concerning their in-service training for the year up to the Trial State Assessment (Table 23) show that: In Arizona, 23 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. About one-quarter of the students in Arizona (27 percent) had mathematics teachers who spent no time on in-service education devoted to mathematics or the teaching of mathematics. Nationally, 11 percent of thc 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 - 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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? 1 None One to 15 hours 16 hours or more Percentage Percentage Percentage 27 ( 2.7) 11 ( 3.0) 11 ( 2.1) 50 ( 3.1) 45 ( 7.0) 51 ( 4.1) 23 ( 1.9) 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 Arizona 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 Arizona, 45 percent of the assessed students were being taught by mathematics teachers who reported having at least a master's or education specialist's degree. This compares to 44 percent for students across the nation. About three-quarters of the students (73 percent) had mathematics teachers who had the highest level of teaching certification available. This is similar to the figure for the nation, where 66 percent of students were taught by mathematics teachers who were certified at the highest level available in their states. In Arizona, 15 percent of the eighth-grade public-school students were being taught mathematics by teachers who had an undergraduate major in mathematics. In comparison, 43 percent of the students across the nation had mathematics teachers with the same major. Relatively few of the eighth-gxade public-school students in Arizona (6 percent) were taught mathematics by teachers who had a graduate major in mathematics. Across the nation, 22 percent of the students were taught by teachers who majored in mathematics in graduate school. " Archie E. Lapointe, Nancy A. Mead, and Gary W. Phillips, A World of Differences. An International Assessment of Mathematics and Science (Princeton, NJ: Center for the Assessment of Educational Progress, Educational Testing Service, 1988). " Ina V.S, Mullis, John A. Dossey, Eugene H. Owen, and Gary W. Phillips, The State of Mathematics Achievement NAEPS I990 Assessment of the Nation and the Trial Assessment of the States (Princeton, NJ: National Assessment of Educational Progress, Educational Testing Service, 1991). a b THE 1990 NAEP TRIAL STATE ASSESSMENT 71 Arizona In Arizona, 23 percent of thc eighth-grade public-school students had teachers who spent at least 16 hours on in-service education dedicated to mathematics or the teachinc 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. About one-quarter of the students in Arizona (27 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 studeats had mathematics teachers who spent no time on similar in-service training. 72 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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, eir parents or guardians, and home factors related to education. 7S THE 1990 NAEP TRIAL STATE ASSESSMENT 73 Arizona AMOUNT OF REAMING MATERIALS IN THE HOME The number and types of reading and reference materials in the home may be an indicator of the value placed by parents on learning and schooling. Students participating in the Trial State Assessment were asked about the availability of newspapers, magazines, books, and an encyclopedia at home. Average mathematics proficiency associated with having zero to two, three, or four of these types of materials in the home is shown in Table 24 and Table A24 in the Data Appendix. TABLE 24 I Students' Reports on Types of Reading i Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Arizona Wast Nation Does your family have, or receive on a regular basis, any of the following items: more than 25 baoks, an encyclopedia, newspapers, magazines? Ufa tO two types Three types Four types Percentage and Proficiency Percentage and Proficiency POrefilt/190 and Proficiency 27 ( 1.3) 24 1.6) 21 ( 1.0) 246 ( 1.5) 245 ( 4.1) 244 ( 2.0) 33 ( 1.0) 31 ( 1.4) 30 ( 1.0) 259 ( 1.4) 258 ( 2.4) 258 ( 1.7) 40 ( 1.4) 45 ( 1.9) 48 ( 1.3) 270 ( 1.5) 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 enure population is within : 2 standard errors of the estimate for thc sample. The data for Arizona reveal that: Students in Arizona who had all four of these types of materials in the home showed hidier 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 TH E 1990 NAEP TRIAL STATE ASSESSMENT Arizona A smaller percentage of Black, Hispanic, and American Indian 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 seen as detracting from time spent on educational pursuits. Students participating in the Trial State Assessment were asked to report on the amount of television they watched each day (Table 25). TABLE 25 I Students' Reports on the Amount of Time Spent Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY NAEP TRIAL STATE ASSESSMENT Arizona West I100 Nation How much television do you usually watch each day? Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency One hour or fess 15 ( 0.8) 14 ( 1.8) 12 ( 0,8) 265 ( 23) 269 ( 3.6) 269 ( 2.2) Two hours 23 ( 0.8) 20 ( 1.6) 21 ( 0.9) 264 ( 1.4) 265 ( 3,6) 268 ( 1.8) Three hours 24 ( 0.9) 20 ( 1.2) 22 ( 0.8) 263 ( 1.6) 262 ( 3.2) 265 ( 1.7) Four to Ave hours 25 ( 0.9) 29 ( 1.7) 28 ( 1.1) 256 ( 13) 263 ( 2.9) 280 ( 1.7) Six hours or more 12 ( 0.6) 16 ( 2.0) 16 ( 1.0) 245 ( 2.0) 246 ( 2.6) 245 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -i: 2 standard errors of the estimate for the sample. THE 1990 NAEP TRIAL STATE ASSESSMENT 75 A rizona From Table 25 and Table A25 in the Data Appendix: In Arizona, 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 Arizona (15 percent) watched one hour or less of television each day; 12 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, 9 percent of White students, 31 percent of Black students, 15 percent of Hispanic students, and 13 percent of American Indian students watched six hours or more of television each day. In comparison, 17 percent of White students, 5 percent of Black students, 12 percent of Hispanic students, and 17 percent of American Indian students tended to watch only an hour or less. STUDENT ABSENTEEISM Excessive absenteeism may also be an obstacle to students' success in school. To examine the relationship of student absenteeism to mathematics proficiency, the students participating in the Trial State Assessment were asked to report on the number of days of school they missed during the one-month period preceding the assessment. From Table 26 and Table A26 in the Data Appendix: In Arizona, average mathematics proficiency was lowest for students who missed three or more days of school. Less than half of the students in Arizona (40 percent) did not miss any school days in the month prior to the assessment, while 26 percent missed three days or more. In addition, 25 percent of White students, 22 percent of Black students, 28 percent of Hispanic students, and 37 percent of American Indian students missed three or more days of school. 76 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona Similarly, 24 percent of students attending schools in advantaged urban areas, 32 percent in schools in disadvantaged urban areas, 29 percent in schools in extreme rural areas, and 25 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 1960 NM:. ti',.. STATE ASSESSMENT Arizona West Nation Pareentage and Preficioncy Percentaae and Prondency Percentage and Proficiency How many days of school did you miss last month? NOM 40 ( 1.0) 43 ( 2.7) 45 ( 1.1) 264 ( 1.4) 266 ( 3.5) 265 ( 1.8) One or two days 34 ( 1.0) 30 ( 1.4) 32 ( 0.9) 282 ( 15) 265 ( 3.0) 266 ( 1.5) Three days or more 26 ( 1.0) 27 ( 1.8) 23 ( 1.1) 252 ( 1.7) 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. F, 2 THE 1990 NAEP TRIAL STATE ASSESSMENT 77 Arizona STUDENTS' PERCEPTIONS OF MATHEMATICS According to the National Council of Teachers of Mathematics, learning mathematics should require students not only to master essential skills and concepts but also to develop confidence ia their mathematical abilities and to value mathematics as a discipline." Students were asked if they agreed or disagreed with five statements designed to elicit their perceptions of mathematics. These included statements about: Personal experience with mathematics, including students' enjoyment of mathematics and level of confidence in their mathematics abilities: I like mathemazics; I am good in mathematics. Value of mathematics, including students' perceptions of its present utility and its expected relevarce to future work and life requirements: Almost all people use muthematics 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 responde4 "strongly agree" were given a value of 1 (indicating very positive attitudes about the subject), those who responded "agree" were given a value of 2, and those who responded "undecided," "disagree," or "strongly disagree" were given a value of 3. Each student's 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 1), tended to agree with the statements (an index of 2), or tended to be undecided, to disagree, or to strongly disagree with the stat,,ments (an index of 3). Table 27 provides the data for the students' attitudes toward mathematics as defined by their perception index, The following results were observed for Arizona: Average mathernetics proficiency was highest for students who were in the "strongly agree" category and lowest for students who were in the "undecided, disagree, strongly disagree" category. About one-quarter of the students (25 percent) were in the "strongly agree" category (perception index of 1). This compares to 27 percent across the nation. About one-quarter of the students in Arizona (26 percent), compared to 24 percent across the nation, were in the "undecided, disagree, or strongly disagree" category (perception inden of 3). 12 National Council of Teachers of Mathematics, Curriculum and Evaluation Standards jor School Mathematics (Reston, VA: National Council of Te. .:.ers of Mathematics, 19e3 78 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE 27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Arizona West Nation Percentage and Pre Ardency Percentage and Proficiency Percentage and Prefidency Student "perception index" groups Strongly agree 25 ( 1.0) 27 ( 1.9) 27 ( 1.3) ("perception index" of 1) 271 ( 1.5) 273 ( 3.9) 271 ( 1.9) Agree 49 ( 0.9) 48 ( t5) 49( 1.0) ("perception index" of 2) 2to ( 1.3) 282 ( 2.4) 262 ( 1.7) undecided, disavee, strongly disagree 28( 1.1) 25 ( 2.1) 24 ( 1.2) ("perception index" of 3) 250 ( 1.4) 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 ± 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 Arizona who had four types of reading materials (an encyclopedia, newspapers, magazines, and more than 25 books) at home showed higher mathematics proficiency than did students with zero to two types of materials. This is similar to the results for the nation, where students who had all four types of materials showed higher mathematics proficiency than did students who had zero to two types. THE 1990 NAEP TRIAL STATE ASSESSMENT 79 Arizona Some of the eighth-grade public-school students in Arizona (15 percent) watched one hour or less of television each day; 12 percent watched six hours or more. Average mathematics proficiency was lowed for students who spent six hours or more watching television each day. Less than half of the students in Arizona (40 percent) did not miss any school days in the month prior to the assessment, while 26 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 (25 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. t: 80 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona THE NATION'S REPORT CARD PROCEDURAL APPENDIX This appendix provides an overview of the technical details of the 1990 Trial State Assessment Program. It includes a discussion of the assessment design, the mathematics framework and objectives upon which the assessment was based, and the procedures used to analyze the results. The objectives for the assessment were developed through a consensus process managed by the Council of Chief Csate 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 desigp that enables broad coverage of mathematics content while minimizing the burden for any one student. In total, 137 cognitive mathematics items were developed for the assessment, including 35 open-ended items. The first step in implementing the BIB design required dividing the entire set of mathematics items into seven units called blocks. Each block was designed to be completed in 15 minutes. 6 THE 2990 NAEP TRIAL STATE ASSESSMENT Arizona 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 coasistingo. mathematics background questions -- and three blocks of cognitive mathematics items. Students were given five minutes to complete each of the background questionnaires and 45 minuteslo complete the three I5-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 ar objectives for the Trial State Assessment Program were developed using a broad-bctsed 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 l). The three mathematical ability areas assessed were Conceptual Understanding, Procedural Knowledge, and Problem Solving (see Figure A2), Data Analysis and Scales Once the assessments had been conducted and information from the assessment booklets had been compiled in a database, the assessment data were weighted to match known population proportions and adjusted for nonresponse. Analyses were then conducted to determine the percentages of students who gave various responses to each cognitive and background question. Item response theory (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, ad 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 their overall performance in the assessment. 1 National Assessment of Educational Progress, Mathematics Objectives 1990 Assessment (Princeton, N): Educational Testmg Service, 1988), S 82 THE 1990 NA EP TRIAL STATE ASSESSMENT Arizona This content area focuses on students' understanding of numbers (whole numbers, fractions, decimals, integers) and their application to real-world situations, as wen 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, Vme, money, temperature, mass/weight, area, volume, capacity,And angles are also included in this content area. Geometry This content area focuses on students' knowledge of geometric figures and relationships and on their skills in working with this knowledge. These skills are important at all levels of schooling as well as in practical applications. Students need to be able to mode! 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 estabhsh geometric relationships. Data Analysts, 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 gathermg 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 functionai 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 tom Functions are viewed not only in terms of algebraic formulas, but also in terms of verbal descnptions, tables of values, and graphs. rs 8 THE 1990 NAEP TRIAL STATE ASSESSMENT 83 Arizona FIGURE A2 I Mathematical Abilities The foHowing three categories of mathematical abilities are not to construed as hierarchical. For example, problem solving involves interactions between conceptual knowledge and procedural skills, but what is considered complex problem solving at one grade level may be considered conceptual understanding or procedural knowledge at another. Conceptual Understanding Students demonstrate conceptual understanding In mathematics when they provide evidence that they can recognize, label, and generate examples and counterexamples of concepts; can use and interrelate models, diagrams, and varied representations of concepts; can identify and apply principles: know and can apply facts and definitions: can compare, contrast, and Integrate related concepts and principles; can recognize, interpret, and apply !he signs, symbols, and terms used to represent concepts: and can interpret the assumptions and relations Involving concepts in mathematical settings. Such understandings are essential to performing procedures in a meaningful way and applying them In problem-solving situations. Procedural Knowledge Students demonstrate procedural knowledge in mathematics when they provide evidence of their ability to select and apply appropriate procedures correctly, verify and Justify the correctness of a procedure using concrete models or symbolic methods, and extend or modify procedures to deal with factors inherent in problem settings. Procedural knowledge includes the various numerical algorithms in mathematics that have been created as tools to meet specific needs in an efficient manner. It also encompasses the abilities to read and produce graphs and tables, execute geometric constructions, and perform noncomputationai skills such as rounding and ordering. Problem Solving In problem solving, stueents are required to use their reasoning and an- .,tic abilities when they encounter new situations. Problem solving includes the ability to recognize and formulate problems: determine the sufficiency and consistency of data: use strategies, data, models, and relevant mathematics: generate, extend, and modify procedures: use reasoning (i.e., spatial, inductive, deductive, statistical, and proportional): and judge the reasonableness and correctness of solutions. 84 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona .41111 A scale ranging from 0 to 500 was created to report performance for each content area. Each content-area scale was based on the distribution of student performance across all three grades assessed in the 1990 national assessment (grades 4, 8, and 12) and had a mean of 250 and a standard deviation of 50. A composite scale was created as an overall measure of students' mathematics proficiency. The composite scale was a weighted average of the five content area scales, where the weight for each content area was proportional to the relative importance assigned to the content area in the specifications developed by the Mathematics Objectives Panel. Scale Anchoring Scale anchoring is a method for defining performance along a scale. Traditionally, performance on educational scales has been defined by norm-referencing -- that is, by comparing students at a particular scale level to other students. In contrast, the NAEP scale anchoring is accomplished by describing what students at selected levels know and can do. The scale anchoring process for the 1990 Trial State Assessment began with the selection of four levels -- 200, 250, 300, and 350 -- on the 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 defme levels at the extremes would therefore have been highly speculative. To defir, performance at each of the four levels on the scale, NAEP analyzed sets of mathemm, 7s items from the 1990 assessment that discriminated well between adjacent levels. The criteria for selecting these "benchmark" items were as follows: To define performance at level 200, items were chosen that were answered correctly by at least 65 percent of the students whose proficiency was at or near 200 on the scale. To 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. (3 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 85 Arizona 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 proficiericy 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: curricuhim, instructional practices, teacher qualifications, educational standards and reform, school conditions, and conditions outside of the school that facilitate learning and instruction. Similar to the development of the materials given to students, the policy guidelines and the teacher and school questionnaires were prepared througli 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 degmes 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. Since there were insufficient numbers of eighth-grade questions at levels 200 and 350, one of the questions exemplifying level 200 is from the fourth-grade national assessment and one exemplifying level 350 is from the twelfth-grade national assessment. 86 THE 1990 NAEP TRIAL STATE ASSESSMENT Atizona FIGURE A3 I Example Items for Mathematics Proficiency Levels Level 200: Simple Additive Reasoning and Problem Solving with Whole Numbers EXAMPLE 1 7ww14 0 0 Tamil Gip If 114,16er D oi Dais 7. f.ano la led ANS lame buss t Ia. 444be rise 440 theft &bass; Irma oi leas it down /Yam If the 1104 mei bar *di the kind of balls skews, whack bes wil1 hare the ironic has as NO gZ) Tholes intli the mom balls CD TIN Ios tnik Ow pit bans ml be: wItli Ad Mem Ws Too wt ma EXAMPLE 2 100 40 70 I. 60 40 30 IOUS OF Finn PtaCeD AT FAamwAy rams No Tun wet raso Der CCM Wet Owego Looms Oespetwo 9. How many ham of clamps wet* *kid ow Tloondarl CD SS a) SO CD 70 CD 50 CD 90 CD 1 doet know. In Grade 4 Overall Percentage Correct: 73% Percentage Correct for Anchor Levels: 244 gt2 244 1,54 6s 91 100 Grade 4 Overall Correct: 80% Percentage L..eot for Anchor Levels: 2§4 322 75 91 100 Grade 8 Overall Percentage Correct: 89% Percentage Correct for Anchor Levels: afg Ni2 76 87 96 100 Arizona FIGURE A3 I Example Items for Mathematics Proficiency Levels (continued) [ Level 250: Simple Multiplicative Reasoning and Two-Step Problem Solving EXAMPLE 1 7. What is the value of n + 5 when n 3 Answer. EXAMPLE 2 KAM COLDS RIMY MILTS Coke O K* pampas' NNW Soso IMO Touts 4_ 17 10 11 to) The tole ewe than doe ss1imydi cola. On tit circle beksw, sae circle pap w lwn. M dos la eke table. LAW nett piLn DI doe ciwas 040 wail de semi bat iwire . Dad you use the calcoissar so this proseloo! 0 Ws 0 No EXAMPLE 3 6. Kodak= Is psekug bsocballs inus bon& loch boz holds A baseballs 5ht has 24 bells Muds ougsbee setwenee will help hot brut out how way bozos abe need; cp 21 + 6 + 0 24 + 6 0 cp 24 e- 6 + 0 CD I don't know. Grade 8 Oman Parcentaga Palmtop Comet 21717 28 139 Grade 8 Overall Percentage Percentage CorrfaCt 222 ZE1 21 58 Grad* 8 Overall Percentage Peroentag. Correct 2011 2E2 37 71 3 Correct 76% for Moho( LINVOIS: 22Q AN 95 98 Correct: 73% for Mchor Levels: 224 aN 92 92 Correct 77% for Anchor Levels: aN 95 100 Afizona FIGURE M I Example Items for Mathematics Proficiency Levels (continued) Level 300: Reasoning and Problem Solving involving Fractions, Decimals, Percents, Elementary Geometric Properties, and Simple Algebraic Manipulations EXAMPLE 1 10. Mich al ibe fallawtag skawe the moat a/ flipptim tba shot,. mane. ova dis U. r EXAMPLE 2 b t5t mak/ wan tbat a CUM it buildiai. cat IS kw lawg *mwesamsd My auk ala!d tachei kw& LI tie wit mak * a..J a hems 35 by kills would ke rept:mud by mala madlal bora way imams Wei, ni you wie the calculator oft ;146 itusaiaa? CI Yea 0 Pio Grade 8 Overall Percentage Correct 60% Percentage Correct for Anchor Levels: =MUM 33 49 77 90 Grade 12 Overall Percentage Correct: 75% Percentage Correct for Anchor Levels: 22Q if& 2%2 15D 48 79 95 Grade 8 Overall Percentage Conect 59% Percentage Correct for Anchor Levels: 2Q0 17 46 as gs Atizona 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 EJCAMPLE 1 119' %Maur 16-17 miss to the kilowsos mums el dot-liqures. 0 1 1 9 1 16. It this platers of dot-liquees s cootos*a oi. kat. many dou will be in Ike 10011160M 41 100 CD 101 OD 199 200 015 20) EXAMPLE 2 I. Espiein bow you found 'OW ea le question 16. Aaower Grade $ Overall Percentage Correct 34% Percentage Correct for Anchor Levels: 222 22C1 a22 13 19 53 88 Grade 12 Overall Percentage Correct 49% Percentage Correct for Anchor Levels: 222 224 222 22 48 90 Grade 8 Overall Percentage Correct: 15% Percentage Correct for Anchor Levels: g42 224 354 1 4 28 74 Grade 12 Overall Percentag Correct 27% Percentage Correct for Anchor Levels: afel2 /§f2 3 22 74 90 ThE 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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 aboutthe individuals who compkted the questionnaires, these wear 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 instniction received by representative samples of eighth-grade students in public schools. Although this approach may provide a differfnt perspective from that which would be obtained by simply collecting information from a sample of eighth-grade mathematics teachers or from a sample of schools, it is consistent with NAEP's goal of providing information about the educational context and performance of students. Estimating Variability The statistics reported by NAEP (average proficiencies, percentages of students at or above particular scale-score levels, and percentages of students responding in certain ways to background questions) are estimates of the corresponding information for the population of eighth-grade students in public schools in a state. These estimates are based on the performance of a carefully selected, representative sample of eighth-grade public-school students from the state or tenitory. If a different representative sample of students were selected and the assessment repeated, it is rikely that the estimates might vary somewhat, and both of these sample estimates might differ somewhat from the value of the mean or percentage that would be obtained if every eighth-grade public-school student in the state or territory were assessed. Virtually all statistics that are based on samples (including those in NAFP) are subject to a certain degree of uncertainty. The uncertainty attributable to using samples of students is referred to as sampling error. Like ahnost all estimates based on assessment measures, NAElys total group and subgioup proficiency estimates are subject to a second wurce of uncertainty, in addition to sampling error. As previously noted, each student who participate4 in the Trial State Assessment was administered a subset of questions from ine total set of questions. If each student had been administered a different, but equally appropriate, set of the assessment questions -- or the entire set of questions -- somewhat different estimates of total group and subgroup proficiency might have been obtained. Thus, a second source of uncertainty arises because each student was administered a subset of the total pool of questions, 5? 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 91 Arizona 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 LS 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 populat,:.n 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 et-*Irs 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 thai the average proficiency fbr the entin: population of eighth-grade students in public schools in that state is between 253.6 and 258.4. Similar confidence intervals can be constructed for percentages, provided that the percentages are not extremely large (greater than 90 percent) or extremely small (less than 10 percent). For extreme percentages, confidence intervals constructed in the above manner may not be appropriate and procedures for obtaining accurate confidence intervals are quite complicated. C 1 .1 92 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona 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 students in the population had been assessed, rather than a sample of students, or if the assessment had been repeated with a different sample of students or a different, but equivalern, set of questions, the performances of various groups would have been different. Thus, to determine whether there is a real difference between the mean proficiency (or proportion of a certain attribute) for two groups in the population, one must obtain an estimate of the degree of uncertainty associated with the difference between the proficiency means or proportions of those groups for the sample. This estimate of the degree of uncertainty -- called the standard error of the difference between the groups -- is obtained by taking the square of each group's standard error, summing these squared standard errors, and then taking the square root of this sum. Similar to the manner in which the standard error for an individual gi-oup 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 gioups is statistically significant (different) at the .05 level. THE 1990 NAEP TRIAL STATE ASSESSMENT 93 Arizona 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-gra& males in a particular state's public schools. Suppose that the sample estimates of the mean proficiencies and standard errors for females and males were as follows: Group Average _ Proficiency Standard Error Female 259 2.0 . Male 255 2.1 The difference between the estimates of the mean proficiencies of females and males is four points (259 - 255). The standard error of this difference is 212 = 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 :.hat are presented. If a statement appears in the report indicating that a particular group had higher (or lower) average proficiency than a second group, the 95 percent confidence interval for the difference between groups did not contain zero. When a statement indicates that the average proficiency or proportion of some attribute was about the same for two groups, the confidence interval included zero, and thus no difference could be assumed between the groups. The reader is cautioned to avoid drawing conclusions solely on the basis of the magnitude of the differences. A difference between two groups in the sample that appears to be slight may represent a statistically significant difference in the population because of the magnitude of the standard errors. Conversely, a difference that appears to be large may not be statistically significant. 3 The procedure described above (especially the esumauon of the standard error of the difference) is, in a strict sense, only appropriate when the statistics being compared come from independent samples. For certain comparisons in the report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard error of the difference was used. r 9 94 THE 1990 NAEP FRIAL STATE ASSESSMENT Arizona The procedures described in this section, and the certainty ascribed to intetvals (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 3ets of confidence intervals, statistical theory indicates thai the certainty associated with the entire set of intervals is less than that attributable to each individual comparison from the set. If one wants to hold the certainty level for the set of comparisons at a particular level (e.g., .95), adjustments (called multiple comparison procedures) must be made to the methods described in the previous section. One such procedure -- the Bonferroni method -- was used in the analyses described in this repert to form confidence intervals for the differences between groups whenever sets of comparisons were considered. Thus, the confidence intervals in the text that are based on sets of comparisons are more conservative than those described on the previous pages. A more detailed description of the use of the Bonferroni procedure appears in the Trial State Assessment technical report. Statistics with Poorly Determined Standard Errors The standard errors for means and proportions reported by NAEP are statistics and therefore are subject to a certain degree of 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 uncertaimy 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 arc discussed in the Trial State Assessment technicalreport. Minimum Subgroup Sample Sizes Results for mathematics proficiency and background variables were tabulated and reported for groups defined by race/ethnicity and type of school community, as well as by gender and parents' education level. NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaskan Native) and four types of communities (Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other Communities). However, in many states or territories, and for some regions of the country, the number of students in some of these groups was not sufficiently high to permit accurate estimation of proficiency and/or background variable results. As a result, data are not provided for the subgroups with very small sample sizes. For results to be reported for any subgroup, a minimum sample size of 62 students was required. This number was determined by computing the sample size required to detect an effect size of .2 with a probability of .8 or greater. 1 0 0 THE 1990 NAEP TRIAL STATE ASSESSMENT 95 Arizona Tht 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 populaCon in the state or territory, divided by the standard deviation of the proficiency in the total population. If the true difference between subgroup and total group mean is .2 total-group standard deviation units, then a sample size of at least 62 is requirT4 to detect such a difference with a probability of .8. Further details about the procedure for determining minims= 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 "abnost all," depending on the size of the percentage in question. Any convention for choosing descriptive terms for the magnitude of percentages is to some degree arbitrary. The descriptive phrases used in the report and the rules used to select them are shown below, Percentage Description of Text in Report p = 0 None 0 < p LS 10 Relatively few 10 < p 20 Some 20 < p 30 About one-quarter 30 < p ..s. 44 Less than half 44 < p 55 About half 55 < p .S. 69 More than half 69 < p lc 79 About three-quarters 79 < p 89 Many 89 < p < 100 Almost all p = 100 All 96 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona ME NATION'S REPORT CARD DAT A APPENDIX For each of the tables in the main body of the report that presents mathematics proficiency results, this appendix contains corresponding data for each level of the four reporting subpopulations -- race/ethnicity, type of community, parents' education level, and gender. 1 n 2 THE )990 NAEP TRIAL STATE ASSESSMENT 97 Arizona TABLE A5 I Students' Reports on the Mathematics Class 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL Eighth-grade STATE ASSESSMENT Mathematics Pre-algebra Algebra TOTAL Percentage and Prafttancy Porcentage and Proficiency Percentage and Proficiency State 48 1.5) 29 ( 1.5) 18 1.3) 246 ( 1.3) 268 ( 1.6) 289 ( 2.4) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 296 ( 2.4) RACE/ETHNICITY White State 42 ( 1.8) 30 ( 1.9) 22 ( 1.7) 257 ( 1.4) 275 ( 1.3) 296 2.2) Nation 59 ( 2.5) 21 ( 2,4) 17 ( 1.5) 259 ( 1.6) 277 ( 2.2) 300 ( 2.3) Black State 59 ( 5.7) .11. ( M.) .4» ) Nation 72 ( 232 ( 4.7) 3.4) 16 ( 246 ( 3.0) 6.4) 9 ( 2.2) ) Hispanic State 57 ( 3.0) 27 ( 2.4) 12 ( 1.3) 234 ( 1.3) 252 ( 3.5) 271 ( 3.5) Nation 75 ( 240 ( 4.4) 2.4) 13 ( 3.9) 1144 ) 6 ( 1.5) American Indian State 56 ( 4.1) 27 ( 8.6) 12 ( 6.4) 228 ( 2.4)1 *** ( 4") *** ( "4) Nation 84 ( ( 5.7) *4.) 8 ( 4*. ( 7.2) "`) 5 ( 2,7)) TYPE OF COMMUNITY Advantaged urban State 34 ( 4.7) 41 ( 4.8) 19 ( 3.3) 256 ( 2,1)1 281 ( 2.2) Nation 55 ( 269 ( 9.4) 2.5)i 22 ( 7.9)) 21 ( *. 4 4).) Disadvantaged urban State 42 ( 3.3) 30 ( 5.1) 25 ( 5.1) 228 ( 2.1)f 254 ( 3.111 276 ( 3.7)1 Nation 65 ( 240 ( 6.0) 4.0)i 16 ( 4,1)) 14 ( 287 ( 3.3) 4.2)1 Extreme rural State 53 ( 237 ( 8.8) 8.3)1 36 ( *4* ( 9,9) "*) ) Nation 74 ( 249 ( 4.5) 3.1)1 14 ( 5,0)) ) Other State 51 ( 2.8) 27 ( 2,6) 17 ( 1.7) 248 ( 2.2) 265 ( 2.9) 268 ( 4.2) Nation 61 ( 2.2) 20 ( 2,1) 16 ( 1.4) 251 ( 2.0) 272 ( 2.8) 294 ( 2.7) 411,M1. .,Nomma, The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the enure population is within -± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics courses. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). r: 3 98 THE 1940 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A5 I Students' Reports on the Mathematics Clam (continued) 1 They Are Taking PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL EIghth-grade STATE ASSESSMENT I IliathsmatIcs Pre-algebra I Algebra - TOTAL PNVINItige and Prottdloc Percentage and Pmeclancy Percentage and Prat:tem State 48 248 ( 1.5) 1.3) 29 ( 26e ( 1.5) 1.6) 16 ( 299 ( 1,3) 2.4) Nation 62 ( 2.1) 19 ( 1.9) 15 ( 1.2) 251 ( 1.4) 272 ( 2.4) 295 ( 2.4) PARENTS' EDUCATION HS non-graduate State 60 ( 4.3) 2$ ( 3.7) 8 ( 1.8) 234 ( 2.3) ...+4. ( 0-...) Nation 77 ( 3.7) 13 ( 3.4) 3 ( 1.1) 241 ( 2.1) V.* ( *** ) *IV ( MR ) HS graduate State ii3 ( 2.5) .28 ( 2.6) 15 ( 2.0) 242 ( 1.6) 255 ( 2.0) 276 ( 4.2) Nation 70 ( 2.6) 18 ( 2.4) 8 ( 1.1) 249 ( 1.9) 266 ( 3.5) 277 ( 5.2) Some college State 44 ( 2.9) 32 ( 2.5) 18 ( 2.0) 253 ( 1.9) 272 ( 2.4) 288 ( 3.6) Nation 60 ( 3.1) 21 ( 2.9) 15 ( 1.9) 257 ( 2 1) 276 ( 2.8) 296 ( 3.2) College graduate State ,r0 r'.1) 30 ( 1.8) 25 ( 2.2) 1.6) 275 ( 2.0) 298 ( 2.0) Nation ',3 ( 2.7) 21 ( 2.3) 24 ( 1.7) d59 ( 1.5) 278 ( 2.8) 303 ( 2.3) GENDER Male State 49 ( 1.9) 27 ( 1.6) 19 ( 1.4) 250 ( 1.6) 269 ( 1.9) 294 ( 2.5) Nation 63 ( 2.1) 18 ( 1.8) 15 ( 1.2) 252 ( 1.6) 275 ( 2.9) 299 ( 2$) Female State 46 ( 1.9) 31 ( 2.0) 18 ( 1.6) 242 ( 1.4) 264 ( 1.8) 284 ( 3.1) Nation 61 ( 2.6) 20 ( 2.3) 15 ( 1.7) 251 ( 1.5) 269 ( 3.0) 293 ( 2.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because a small number of students reported taking other mathematics COUrst ;. Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 P4 THE 1990 NAEP TRIAL STATE ASSESSMENT 99 Arizona TABLE A6 Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AHD AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT None 15 Minutes 38 Litwin 45 Minutes An Hour or More TOTAL Perventage and Proficiency Pervertiage and Proildwcy 3a ( 25) Percentage and Proficbocy 48 ( 2.6) Percentage and Proficiency 10 ( 1.5) Percentage and Proficionoy 5 ( (.1.8) state ( 4") 253 ( 1.8) 281 ( 1.7) 271 ( 3.7) 276 ( 4.8) Nation 1 ( 0.3) 43 ( 4.2) 43 ( 4.3) 10 ( 1.9) 4 ( 0.9) "44 ( "4) 268 ( 2.3) 266 ( 2.6) 272 ( 5.7)1 27$ ( 5.1)1 RACE/ETHNIC1TY White State 2 ( 0.5) ) 38 ( 2.9) 264 ( 1.5) A6 ( 3.1) 273 ( 1.7) 9 ( 287 ( 1.5) 4.9) 6 ( 287 ( 12) 3.9)1 Nation 1 ( 0.3) ..*) 39 ( 4.5) 286 ( 22) 45 ( 5.1) /70 ( 2.7) 11 ( 277 ( 2.4) 7.8)1 4 ( 279 ( 0.9) 5.8)1 Black State 3 ( 2,0) 45 ( 5.7) 46 ( 52) 4 ( 2.3) 2 ( 1.8) Nation I ( 0.7) 55 ( 7.8) 40 ( 6.7) 3 ( 1.2) 2 ( 0.8) 232 ( 3.1) 248 ( 5.3) Hispanic State 3 ( 0.8) 34 ( 3.4) 46 ( 3.9) 11 ( 2.7) 5 ( oso ( 4r* ) 237 ( 2.4) 245 ( 2.1) 248 ( 3$)1 ( Nation I ( 0.8) 46 ( 7.8) 245 ( 3.0)1 34 ( 8.8) 251 ( 4.2)1 13 ( .44 2.9) 7 ( ** 2.1) "*) American Indian State 6 ( 3.8) 31 ( 8.6) ...) 53 ( 7.7) 234 ( 4,4) 10 ( "4 ( 5.6) 4" ) 1 ( ". ( 03)*) Nation 0 ( -.. 0.0) 74 (31.9) . 22 (282) **4 ) 0 ( 0.0) TYPE OF COMMUNITY Advantaged urban State 1 ( 0.3) 26 ( 4.2) 52 ( 4.4) 11 ( 3.8) 10 ( 4 1) 271 ( 2.8)1 '4" ( 4") Nation 1 ( 0.9) 81 (11.3) 32 ( 8.6) 5 ( 3.4) 0 ( 0.0) 273 ( 3.1 )! 4.44 ( 4*) ." ( 4*) ** ( ".) Disadvants9414 urban State 1 ( 0,8) 30 ( 6.8) 47 ( 7.5) 7 ( 2.9) 15 ( 3.6) ) 238 ( 5.3)1 244 ( 5.0)i 444 ( 444) 444 ( *44) Nation 0 ( *44 ( 0,0) **4) 41 (12.6) 236 ( 2.1)1 36 ( 9.4) 253 ( 9.0)1 12 ( "4 ( 5.9) 4") 10 ( ( 6.2) -4) Extreme rural State 4 ( 2.6) 37 (13.5) 53 (11.1) 7 ( 7.0) 0 ( 0.0) **4 ( 444) 444 ( *44) 244 ( 8,0)1 Nation 0 ( *** ( 0.0) ..4) 88 (14.9) 263 ( 6.4)1 14 (10.9) *** ( ***) 8 ( ( 5.6) ***) 10 ( 7.3) Other State 2 ( 0,8) 35 ( 3.7) 49 ( 4.7) 10 ( 2.4) 4 ( 1.2) ( "4) 253 ( 2.7) 262 ( 3.2) 259 ( 4.2)i ** ( 4") Nation 1 ( 0.4) 37 ( 4.3) 49 ( 5.1) 10 ( 2.4) 4 ( 1,1) ..... ( *-) 256 ( 3.1) 265 ( 2,5) 276 ( 8.6)1 282 (11.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample, ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 100 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE Ab (continued) Teachers' Reports on the Amount of Time Students Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY WOO NAEP TRIAL STATE ASSESSMENT Nons 16 Minutes 30 Minutes 45 Minutes An Noir or More NM% TOTAL Percentage and Profidancy ( 1 ( 0.3) *** ( 3 ( 1.4) 414 ) 1 0.8) ) 2 0.9) -- MR*) *04 ) 3 0.8) ) 1 0.9) --) 2 0.5) 0 0.3) 1 ( 0.3) 3 ( 0.6) ( 0.4) ( Percentage and Proficiency 36 ( 2.5) 253 ( 1.8) 43 ( 4.2) 256 ( 2.3) 38 ( 3.9) 237 ( 3.6) 49 ( 6.3) 240 ( 2.8) 40 ( 3.6) 247 ( 2.5) 43 ( 52) 249 ( 3.1) 36 ( 3.1) 260 ( 2.6) 44 ( 5.4) 265 ( 2.6) 35 ( 3.0) 263 ( 1.8) 40 ( 4.7) 265 ( 2.5) 36 ( 2.9) 257 ( 2.2) 44 ( 4.4) 257 ( 2.9) 37 ( 2.5) 250 ( 1.9) 41 ( 4.4) 255 ( 2.3) Percentage and Proficiency 4e ( 2.6) 261 ( 1.7) 43 ( 43) 266 ( 2.6) 43 ( 4.2) 242 ( 3.1) 40 ( 6.1) 246 ( 3.7) 44 ( 3.5) 250 ( 2.4) 44 ( 5.8) 258 ( 2.7) 45 ( 3.4) 267 ( 2.3) 43 ( 5.8) 270 ( 3.6) 47 ( 2.9) 274 ( 2.2) 44 ( 4.1) 277 ( 3.C) 48 ( 2.9) 264 ( 2.0) 43 4.3) 268 ( 2.9) 44 ( 2.7) 257 ( 1.9) 43 ( 4.7) 264 ( 2.8) Percentage and Proficiency 10 ( 1.5) 271 ( 3.7) 10 ( 1.9) 272 ( 5.7)1 13 ( 2.5) -- ) 6 ( 1.7)) 9 ( 2.5)) 9 ( 3.1) 10 ( 2.3) ( ***) ( ***) 10 ( 1.81 288 ( 4.4) 11 ( 2.3) 287 ( 6.1)1 10 ( 1.6) 277 ( 4.7) 9 ( 1.9) 273 ( 7.3)1 10 ( 1.7) 265 ( 3.8) 11 ( 2.0) 272 ( 5.7)1 Percentage and Proficiency 5 ( 0.8) 278 ( 4.8) 4 ( 0.9) 278 ( 5.1)) 4 ( 1.8) 4 ( 1.3) *** ( ***) 3 ( 1.0) 4 ) ( 1.1) ( ***) 4 ( 1.0) ** ( "4) 5 ( 1.3) ** 5 ( 1,3) 279 ( 7.7)1 6 ( 1.2) 271 ( 5.1) 4 State Nation PARENTS' EDUCATION HS non-graduate State Nation HS graduate State Nation Some college State Nation College graduate State Nation GENDER Male State Nation Female State Nation The standard errors of the estimated statist,...s appear in parrmtheses. It can be said with about 95 perLynt certamty that, for each population of interesL, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interprct with caution the nature of the sample does not allow accurate determination of the anability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than ('2 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 101 Arizona 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 1910 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes An How or More TOTAL Parcentage and Proficiency 9 ( 0.9) 257 ( 2.2) 9 ( 0.8) 251 ( 2.8) 9 ( 1.0) 268 ( 2.9) 10 ( 1.0) 258 ( 3.4) 6 ( 2.5) WO* ***) 7 ( 1.5) .*.) 9 ( 1.5) 240 ( 3.6) 12 ( 1.8) ) 10 ( 2.2) 4" ( 13 ( 5.3) OHH P ) ...) 8 ( 2.5) 8 *** ( ***) 12 ( 37) ( .") ( "*) 8 ( 2.3) ( 0+4) 10 ( 1.4) 256 ( 2.7) 9 ( 1.0) 250 ( 3.8) Poreentage end Pleadincy 24 ( 0.8) 260 ( 1.6) 31 ( 2.0) 204 I 1.9) 26 ( 1.1) 270 ( 1.2) 33 ( 2.4) 270 ( 1.9) OriNt 4,-** 26 ( 2.5) 241 ( 3.8) 24 ( 1.7) 242 ( 2.6) 27 ( 10) 246 ( 3.6) ...) 30 (10.0) ...) 24 ( 1.7) ...) 41 (123) 278 ( 3.0)1 24 ( 2,1) 247 ( 4.7)1 24 ( 3.3) 253 ( 4.9)1 23 ( 5.4) ...) 36 ( 4.6) 260 ( 3.5)1 26 ( 1.2) 261 ( 2,5) 30) 1.8) 263 ( 2.3) Porcentage and Proficiency 32 ( 0.9) 261 ( 1.5) 32 ( 1.2) 283 ( 1.9) 32 ( 1.2) 271 ( 1.8) 32 ( 1.3) 270 ( 2.1) ( 33 ( 2.7) 237 ( 33) 31 ( 1.8) 243 ( 1.8) 30 ( 2.6) 248 ( 3.4) .. .) 27 ( 6.7) .04 34 ( 3.7) 276 ( 2.3)1 31 ( 6.6) 280 ( 4.6)1 35 ( 2.5) 249 ( 4.5)1 31 ( 3.0) 247 ( 4.7)1 30 ( 1.2) .. ...) 31 ( 2.9) 255 ( 5.1)i 29 ( 1.2) 259 ( 2.4) 32 ( 1.3) 264 ( 2.3) Percentage and Proficiency 17 ( 0.9) 261 ( 1.6) 18 ( 1.0) 2061 1.9) 17 ( 1.1) 272 ( 2.2) 15 ( 0.9) 277 ( 2.2) 13 ( 3.3) 18 ( 2.3) 240 ( 3.8) 16 ( 1.3) 245 ( 3.0) 17 ( 2.1) 241 ( 4.3) 19 ( 3.7) ..) 24 (14.2) 00 ..) 18 ( 3.0) "4 ( #4`) 12 ( 3.3) 44. ( 12 ( 1.9) .. ...) 20 ( 1.9) 250 ( 4.8)! 20 ( 3.0) 44.4 ...) 18 ( 3.8) ...) 18 ( 1.3) 257 ( 2.5) 15 ( 1.1) 267 ( 2.1) Per tentage and ProficianeY 18 ( 1.0) 258 ( 1.9) 12 ( 1.1) 258 ( 3.1) 15 ( 12) 271 ( 2.1) 11 ( 1.3) 268 ( 3.3) 23 ( 5.8) *4* V** ) 16 ( 1,9) 232 ( 3.7) 20 ( 1.7) 245 ( 2.2) 14 ( 1.7) . ) 25 ( 4.9) . ) 6 ( 6.4) ...) 7 ( 3.4) ...) 14 ( 2.2) ...) 7 ( 2.7) 18 ( 1.5) 260 ( 3.3) 13 ( 1.1) 258 ( 3.6) State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNIlY Advantaged urban State Nation Disadvantaged urban State Nation Extreme ruraI State Nation Other State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -t 2 standard 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 7 102 THE 1990 NAEP TRIAL STA TE ASSESSMENT Arizona TABLE A7 I Students' Reports on the Amount of Time They (continued) Spent on Mathematics Homework Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT None 15 Minutes 30 Minutes 45 Minutes An Hour or More TOTAL PWcentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 9 ( 0.9) 24 ( 0.8) 32 ( 0.9) 17 ( 0.9) 18 ( 1.0) 257 ( 2.2) 260 ( 1.6) 261 ( 1.5) 261 ( 1.8) 258 ( 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 HS non-graduate State ( 2.0) ..) . ) 34 ( 238 ( 2.6) 2.4) ( ) Nation 17 ( 0) 26 ( 3.3) 34 ( 4.4) 246 ( 4.0) 246 ( 2.6) ) MS graduate State 24 ( 1.7) 31 ( 1.6) 16 ( 1.5) 18 ( 1.6) 11-11 ** ) 253 ( 2.8) 251 ( 2.5) 253 ( 3.1) 247 ( 2.7) Nation 1 0 ( 1.7) 33 ( 2.2) 31 ( 1.9) 16 ( 1.4) 11 ( 1.5) 246 ( 4.2) 259 ( 3.2) 254 ( 2.4) 256 ( 2.8) 244 ( 3.4) Some college State 7 ( 1.6) 26 ( 1.8) 29 ( 1.7) 18 ( 1.7) 20 ( 1.8) 266 ( 2.3) 268 ( 2.5) 285 ( 3,2) 282 ( 3.6) Nation 9 1.44 30 ( 266 ( 2.7) 3.0) 36 ( 266 ( 2.1) 2.6) 14 ( 274 ( 1.8) 3.5) 11 (. 1.5) College graduate State 7 ( 1.2) 24 ( 1.3) 35 ( 1.7) 16 ( 1.4) 17 ( 1.6) 266 ( 4.4) 272 ( 2.0) 273 ( 2.1) 275 ( 3.0) 272 ( 2.7) Nation ( 0,9) 31 ( 3.4) 31 ( 2.0) 18 ( 1.2) 14 ( 1,9) 265 ( 3.6) 275 ( 2.0) 275 ( 2.5) 278 ( 3,2) 271 ( 2.8) GENDER Male State 12 ( 1.3) 27 ( 1.1) 32 ( 1.4) 14 ( 1,0) 15 ( 1.2) 262 ( 3.0) 264 ( 2.2) 265 ( 2.1) 264 ( 2.4) 260 ( 2 7) Nation 11 ( 1.1) 34 ( 2.4) 29 ( 1.3) 15 ( 1.2) 11 ( 1.4) 255 ( 3.9) 264 ( 2.6) 266 ( 2.4) 265 ( 3.0) 258 ( 4.1) Female State 7 ( 0.8) 22 ( 1.2) 32 ( 1.5) 19 ( 1.3) 20 ( 1.2) 248 ( 3.2) 256 ( 2.1) 258 ( 1.6) 259 ( 2.0) 256 ( 2,1) Nation 7 ( 0.9) 28 ( 2.0) 35 ( 1.7) 17 ( 1.0) 13 ( 1.3) 246 ( 4.1) 263 ( 1.5) 260 ( 2.0) 267 ( 2.4) 258 ( 3.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample * Sample swe is insufficient to permit a reliable estimate (fewer than 62 students). 1 C S TKE 1990 NAEP TRIAL STATE ASSESSMENT 103 Arizona TABLE A8 I Teachers' Reports on the Emphasis Given To 1 Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1290 NAEP TRIAL STATE ASSESSMENT Numbers and Operations M*asurn O.om.y Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Llnie or No Emphasis TOTAL Percentage and Proficiency 52 ( 3.3) 259 ( 1.9) 49 ( 3.8) 260 ( 1.8) 50 ( 3.5) 272 ( 1.7) 48 ( 3.7) 267 ( 2.2) 50 ( 6.9) 54 ( 7.9) 243 ( 4.3) 57 ( 5.0) 243 ( 2.2) 47 ( 8.7) 24.6 ( 4.6) 53 (10.3) 233 ( 6.2)1 84 (18.5) 53 ( 7.8) 276 ( 2.5)1 28 (13.0) 43 (10.5) 242 ( 3.7)1 48 (12.1) 255 ( 6.3)1 56 (13.5) 243 ( 7.9)1 53 (12.4) 257 ( 7.1)1 56 ( 5.2) 261 ( 2.7) 52 ( 4.1) 260 ( 2.3) Percentage and Proficiency 12 ( 1 3) 286 ( 4.3) 15 ( 2.1) 287 ( 3.4) 14 ( 1.8) 225 ( 3.7) 18 ( 2.4) 289 ( 3.5) 10 ( 4.0) 11 ( 3.3) 44 ( *44 ) 1 0 ( 2.2) 270 ( 6.1)1 *411 ( *41 ) 6 ( 6.9) 0... ...) 11 ( 3.7) ..) 16 4.2) 18 ( 4,7) .. ..) 9 ( 4.0) .0. ...) 2 ( 1.5) 6 ( 3.6) 0 412 12 ( 2.5) 283 ( 5.5)1 16 ( 2.7) 286 ( 3.6) Percentage and Proficiency 10 ( 1.6) 250 ( 4$) 17 ( 3.0) 250 ( 5.6) 9 ( 1.1) 263 ( 4.1) 14 ( 3.4) 259 ( 6.9)1 12 ( 4.7) *44 ( *44 ) 25 ( 7.4) 228 ( 2.8)1 13 ( 3.9) 232 ( 5.0)1 23 ( 4,1) ...) 20 ( 5.5) .. ...) 9 ( 7.0) 21 ( 8.1) . ...) 39 (10.3) 238 ( 8.4)1 4 ( 3.1) .. ...) 6( 4.9) .. ..) 9 ( 2.1) 251 ( 7.0)1 16 ( 3.9) 253 ( 7.1)1 Percentage and Proficiency 43 ( 2.7) 206 ( 2.1) L3 4.0) 272 , 4.0) 47 ( 2.7) 276 ( 2.6) 36 ( 4.7) 277 ( 4.3) 48 ( 8.6) 0.1 23 ( 5.7) 238 ( 8.1)1 37 ( 4.0) 244 ( 3.2) 34 ( 5.8) 255 ( 4.4)1 29 (11.9) 13 (15.5) ...) 38 ( 5.6) 290 ( 8.5)1 ) 35 (10.0) 261 ( 3.6)1 21 ( 6.5) 35 (12,3) ) 32 (11.7) 265 ( 9.1)1 42 ( 5.1) 282 ( :3.0) 34 ( 5.3) 270 ( 4.6) Percentage and Proficiency 14 ( 1.3) 203 ( 3-7) 28 ( 31) 280 ( 3.2) 16 ( 2.0) 272 ( 2.8) 27 ( 4.4) 265 ( 3.3) 18 ( 9.3) ...) 33 ( 7.9) 242 ( 5.6)1 12 ( 2$) 237 ( 4.2)1 4114 ( 444 ) .-..) 16 (19.7) ...) 24 ( 7.7).) 38 ( 9.4) 267 ( 4.9)1 .. ) 33 (11.8) 248 ( 8.2)1 7 ( 4.0) 444 ( 44 ) 9 ( 6.1) .. .) 12 ( 2.7) 280 ( 5.3)1 28 ( 4.8) 280 ( 3.9) Pecentage and Proficiency 33 ( 2.3) 256 ( 2.1) 21 ( 3.3) 264 ( 5.4) 29 ( 2.3) 288 ( 2.8) 22 ( 3.4) 273 ( 5.8) 24 ( 7.3) 233 ( 4.7)1 32 ( 3.7) 239 ( 2.7) 16 ( 5.5) 444 ( 44* ) 59 ( 7.3) 240 ( 4.2) 8 (10.4) 26 ( 4.9) ..) ...) 41 ( 7.8) 250 ( 4.7)1 18 ( 7.6) ) 30 (11.4) ...) 16 ( 7.9) ) 30 ( 3.9) 251 ( 3.0) 24 ( 4.3) 265 ( 5.7) State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation American Indian 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 certainty that, for each population of interest, the value of the estimate for the sample. The percentages may n category is not included. ! Interpret with caution - determination of the variability of this estimated mean reliable estimate (fewer than 62 students). in parentheses. It can be said with about 95 percent for the entire population is within 1. 2 standard errors 01 total 100 percent because the "Moderate emphasis" - the nature of the sample does not allow accurate proficiency. *** Sample size is insufficient to permit a r r 104 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE AS I Teachers' Reports on the Emphasis Given to (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 !MEP TRIAL STATE ASSESSMENT Numbers and Operattore Maasirement Geometry Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL Nweentage and Profkiency Pereintage and Proficiency Pareentep and Proficiency Pireentap and Proficiency Percsntage and Proficiency MOM** and Proficiency State 52 ( 3.3) 12 ( 1.8) 10 ( 1.8) 43 ( 2.7) 14 ( 1.8) 33 ( 2.3) 259 ( 1.9) 286 ( 4.3) 250 ( 4.5) 206 ( 2.1) 200 ( 3.7) 256 ( 2.1) Nation 49 ( 3.8) 15 ( 2.1) 17 ( 3.0; 33 ( 4.0) 28 ( 3.8) 21 ( 3.3) 263 ( 1.8) 287 ( 3.4) 250 ( 5.8) 272 ( 4.0) 260 ( 3.2) 264 ( 5.4) PARENTS' EDUCATION HS non-graduate State 56 ( 240 ( 6.3) 3.3) 11-46 ) 13 ( 4.3) *44 ) 38 ( 240 ( 4.5) 6.0) 13 ( 3.3) ...) Nation 80 ( 6.9) 7 ( 2.3) 251 ( 3.4) sr** ) HS graduate State 53 ( 4.2) 12 ( 2.5) 36 ( 3.4) 15 ( 2.3) 34 ( 3.3) 253 ( 2.6) ) 251 ( 3.6) 251 ( 3.9) 245 ( 2.6) Nation 55 ( 4.8) 11 ( 2.8) 17 ( 3.9) 27 ( 5.0) 27 ( 4.5) 24 ( 5.1) 259 ( 2.9) 251 ( 6.1)1 253 ( 4.7)1 255 ( 4.2) 248 ( 4.8)1 Some college State 54 ( 286 ( 4.2) 2.9) 11 ( 2.2) ..) 4.5 ( 269 ( 3.2) 4.1) 16 ( 284 ( 2.2) 5.3) 29 ( 262 ( 2.8) 3.3) Nation 47 ( 4.4) 17 ( 3.3) 39 ( 5.5) 27 ( 5.0) 23 ( 4.1) 265 ( 2.6) 284 ( 4.1)' 279 ( 4.5) 262 ( 4.8)1 270 ( 4.7) College graduate State 49 ( 3.6) 15 ( 2.1) 8 ( 11) 48 ( 3.2) 14 ( 2.5) 33 ( 2.8) 289t 2.1) 300 ( 4.4) 282 ( 3.0) 272 ( 4.6) 268 ( 3.0) Nation 44 ( 4.1) 19 ( 2.4) 16 ( 3.3) 37 ( 3.8) 26 ( 3.4) 21 ( 2.9) 269 ( 2.6) 298 ( 3.4) 264 ( 7.2)1 283 ( 3.8) 270 ( 3.8) 280 ( 6.4) GENDER Male State 53 ( 3.6) 12 ( 1.7) 11 ( 2.1) 44 ( 2 9) 14 ( 2.0) 33 ( 2.8) 262 ( 2.1) 288 ( 5.1) 258 ( 4.8)1 271 ( 2.3) 264 ( 4.3) 259 ( 2.6) Nation 48 ( 4.1) 14 ( 2.1) 17 ( 3.3) 32 ( 3.9) 29 ( 4.1) 20 ( 3.3) 261 ( 2.5) 287 ( 4.4) 258 ( 6.7) 275 ( 4.8) 263 ( 3.8) 266 ( 6.8) Female State 51 ( 3.4) 12 ( 1.7) 10 ( 1.5) 43 ( 3.0) 15 ( 2.0) 32 ( 2.4) 256 ( 2,1 ) 284 ( 4.5) 241 ( 5.7) 260 ( 25) 257 ( 4.4) 252 ( 2.5) Nation 51 ( 3.9) 15 ( 2.4) 17 ( 3.2) 35 ( 4.3) 27 ( 3.9) 23 ( 3.5) 260 ( 2.0) 286 ( 3.3) 241 ( 5.4) 268 4.1) 25e 1 3.3) 203 ( 5.0) The standard errorr of the estimated statistics appear in parentheses. It can be said with about 95 percent certamty that, for each population of interest, the value for the entire population is within t 2 standard errors of the esumate 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). I 1 o THE 1990 NAEP TRIAL STATE ASSESSMENT 105 Arizona TABLE A8 I Teachers' Reports on the Emphasis Given To (ccentinued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1890 NAEP TRIAL STATE ASSESSMENT Data AnblYsis, Statistics, and ProbabNity and F Algebra urIctions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL poventage and Preaciency Percontaro and Proectiency Parcentsge and PralkiancY Parcontago and Praidancy State ( 1.3) 51 ( 2.8) 17 ( 1.9) 252 ( 19) 257 ( 1.8) 271 ( 2.0) 234 ( 2.5) 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) RACE/ETHNICITY White State 6 ( 0.8) 67 ( 3.1) 56 ( 3.3) 13 ( 1.7) 288 ( 4.3) 272 ( 1.9) 280 ( 2.3) 247 ( 3.0) Nation 14 ( 2.4) 53 ( 5.0) 48 ( 42) 18 ( 2,8) 278 ( 4,1) 271 ( 3.1) 281 ( 3.0) 251 ( 3.3) Black State 18 ( 9.7) 63 ( 8.9) 43 ( 8.5) 33 ( 5.8) 41111 ( HP* ) .141141. Nation 4.**) 53 225 ( 8.2) ( 4.3) 39 ( 253 ( 7.1) 8.3) 27 ( 226 ( 6.9) 22)1 Hispanic State 9 ( 2.4) 86 ( 5.9) 44 ( 4.0) 20 1 2.7) 232 ( 5.3)' 237 ( 2.6) 254 ( 2.9) 223 ( 2.7) Nation 15 ( 4.1) 56 ( 8.3) 46 ( 5.9) 18 ( 4.2) "4 ( ") 246 ( 4.4) 257 ( 4.0)1 ( American Indian State 7 ( 5.3) 71 ( 8.2) 36 ( 9.8) ( 444) 218 ( 4.0)1 Nation 3 4.2) 82 (29.1) 16 (21.5) 67 (51.6) "4 ( 4") 4" ( 44) TYPE OF COMMUNITY Advantaged urban State 9 ( 3.1) 74 ( 8.5) 61 ( 7.4) 15 ( 5.6) 278 ( 2.9)1 279 ( 4.3)1 Nation 11 ( «a. 6.6) 65 284 (19,4) ( 7.4)1 41 ( 296 ( 8.9) 7.9)1 18 ( 5.3) Disadvantaged urban State 15 ( 7.6) 63 ( 8.7) 46 ( 8.0) 29 ( 8.0) 4" ( ") 247 ( 7.6)1 268 ( 5.6)1 221 ( 5.2)1 Nation 19 ( 9.4) 34 (11.4) 53 (11.8) 236 ( 8.2)1 254 ( 8.3)1 Extreme rural State 11 ( 444 ( 7.0) 444) 49 224 (12.4) ( 7.1)1 its (10.0) 254 ( 8.4)1 17 ( 5.a) ...) Nation 65 254 (16.9) ( 67)1 33 ( 8.1) ..) 42 (16.0) 241 ( 5.9)1 Other State 7 ( 1,6) 65 ( 4.9) 52 ( 4.7) 15 ( 2.4) 257 ( 5.9)1 255 ( 3.3) 269 ( 3.2) 235 ( 3.9) Nation 15 ( 2,9) 53 ( 5.2) 47 ( 4.3) 17 ( 3.3) 267 ( 4.7) 260 ( 3.4) 276 ( 2.8) 245 ( 4.4)1 The standard errors of the esumated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 1 1 106 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A8 I Teachers' Reports on the Emphasis Given To (continued) I Specific Mathematics Content Areas PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT Data Analysis, Statistics, and Probability Aigebra and Functions Heavy Emphasis Little or No Emphasis Heavy Emphasis Little or No Emphasis TOTAL chrcontats and Proficiency Percentage and Planciancy Percentage and Proecloncy Percentage and Proficiency State 7 ( 1.3) 67 ( 3.1) 51 ( 2.8) 17 ( 1.9) 252 ( 3.9) 257 ( 1.8) 271 ( 2.0) 234 ( 2.5) 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 9 ( 2.5) 66 ( 5.5) 35 ( 4.1) 25 ( 4.3) ( *4.) 236 ( 3.7) 247 ( 5.4) Nation 9 ( 3.0) 53 ( 7.7) 0** ( *** ) 240 ( 62) NS graduate State 1 1 ( 2.3) 63 ( 3.9) 46 ( 3.5) 21 ( 23) 243 ( 2.7) 261 ( 3.1) 230 ( 3.5) Nation 17 ( 3.7) 54 ( 5.4) 44 ( 4.8) 23 ( 3.9) 261 ( 6.0)1 247 ( 2.9) 285 ( 3.5) 239 ( 3.4) Some college State 67 ( 3.7) 55 ( 3.6) 13 ( 2.2) ( *4*) 267 ( 2.8) 277 ( 2.9) Nation 13 ( 2.5) .**) 57 ( 270 ( 5.8) 3.7) 48 ( 278 ( 4.8) 3.0) 17 ( 3.1) College graduate State 6 69 ( 3.7) 60 ( 3.5) 12 ( 1.7) 41-8-* ( ) 274 ( 2.5) 281 ( 2.7) 246 ( 4.2) Nation 15 ( 2.4) 53 ( 4.4) 50 ( 3.9) 18 ( 2.4) 282 ( 4.5) 275 ( 3.8) 288 ( 3.0) 249 ( 4.0) GENDER Male State 7 ( 1.3) 68 ( 3.4) 48 ( 3.1) 18 ( 2.1) 258 ( 4.6) 261 ( 2.2) 273 ( 2.6) 236 ( 3.2) Nation 13 ( 2.2) 54 ( 4.7) 44 ( 4.1) 22 ( 3.6) 275 ( 5.8) 260 ( 3.5) 276 ( 3.2) 243 ( 3.0) Female State 7 ( 1.4) 67 ( 3.1) 54 ( 2.7) 16 ( 2.0) 247 ( 5.2) 254 ( 2.1) 270 ( 1.9) 231 ( 3.2) Nation 16 ( 2.4) 53 ( 4.5) 48 ( 3.6) 18 ( 2.9) 283 ( 4.4) 262 ( 2.8) 274 ( 2.7) 244 ( 3.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. The percentages may not total 100 percvnt because the "Moderate emphasis" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 107 Arizona TABLE A9 I Teachers' Reports on the Availability of Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT [ I Get All the Resources I Need I Oct Most of the Rooftrees I Need I Get Some or None of the Resources I Need TOTAL Percentage and Proficiency Percentage and ProRciency Poramtage and Proficiency State 17 ( 2.6) 53 ( 2.8) 31 ( 2.6) 261 ( 2.4) 261 ( 1.7) 257 ( 2.3) Nation 13 ( 2.4) 56 ( 4.0) 31 ( 42) 265 ( 4.2) 265 ( 2.0) 261 ( 2.9) RACE/ETHNICITY White State 16 ( 2.5) 53 ( 3.1) 31 ( 2.5) 271 ( 2.7) 273 ( 1.4) 269 ( 1.8) Nation 11 ( 2.5) 58 ( 4.6) 30 ( 4.6) 275 ( 3.5)1 270 ( 2.3) 267 ( 3.3) Black State 14 ( 5.1) ...) .. 38 ( 92) ...) Nation 15 ( 42) 52 ( 6,6) 33 ( 7 2) 241 ( 5.3)1 242 ( 2.4) 236 ( 4.9) Hispanic State 19 ( 5.0) 52 ( 4.6) 28 ( 4.5) 247 ( 2.9)1 243 ( 2.1) 238 ( 2.7) Nat:Dri 23 ( 7.6) 44 ( 4.9) 34 ( 7.7) 246 ( 7.7)1 250 ( 2.9) 244 ( 3.0)1 American Indian State 11 ( 3.4) ...) 55 ( 237 ( 9.8) S.7)1 .. ..) Nation 6 ( 7.4) ...) 72 (26Z) 22 (20.7) TYPE OF COMMUNITY Advantaged urban State 8 ( 1.6) ...) 57 ( 272 ( 6,5) 2.2)I 34 ( 280 ( 6,0) 4.2)1 Nation 38 ( 272 ( 9.2) 8.5p 59 ( 286 ( 8.9) 1.3)1 3 ( 3.1) Disadvantaged urban State 55 ( 8.6) 32 ( 9.4) 251 ( 5.8)1 241 ( 4.9)1 Nation 10 ( 6.8) 40 (13,1) 50 (14.5) 251 ( 5A)1 253 ( 5,5)1 Extreme rural State 8 ( 2.8)) 74 ( 251 ( 8.2) 6.1)1 18 ( 9.0) Nation 2 ( 2.6) 54 (10.4) 43 (10.3) 260 ( 8.8)1 257 ( 5.0)1 Other State 20 ( 5.1) 51 ( 4.8) 29 ( 4.0) 260 ( 4.5)1 261 ( 2.5) 253 ( 3.7) Nation 11 ( 2.9) 58 ( 5,4) 31 ( 5.6) 265 ( 3.9)1 264 ( 2.1) 263 ( 4.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. I Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. 4** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 log THE 1990 NAEP TRIAL STATE ASSESSMEN'l Arizona TABLE A9 I Teachers' Reports on the Availability of (car wed) Resources PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL I (let AU the Resources I I Oet Most of the I Del Some or None of STATE ASSESSMENT Need Resources I Need the Resources I Need TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proadency State 17 ( 2.6) 53 ( 2.8) ( 2.6) 261 ( 24) 261 ( 1.7) 257 ( 2.3) Nation 13 ( 265 ( 2.4) 4.2) 56 ( 2es ( 4.0) 2.0) 31 ( 201 ( 4.2) 2.9) PARENTS EDUCATION HS non-graduat State .44 ( 51 ( 241 ( 4.9) 3.7) 32 ( 236 ( 82) 3.3) Nation ( .4 ( 2.6) .4) 54 ( 244 ( 5.7) 2.7) 38 ( 243 ( 8.3) 3.5), HS graduate State 17 ( 3.5) 50 ( 4.0) 33 ( 3.9) 250 ( 3.4)1 252 ( 2.4) 248 ( 2.7) Nation 10 ( 2.5) 54 ( 4.9) 35 ( 4.9) 253 ( 4.8)1 256 ( 1.9) 256 ( 2.8) Soma colloga State 18 ( 3.4) 51 ( 3.9) 31 ( 3.5) 267 ( 3.5)1 267 ( 2.0) 285 ( 3.1) Nation 13 ( 44* ( 3.3) 444) 82 ( 289 ( 4.3) 2.5) 25 ( 267 ( 4.1) 3.8) College graduate State 16 ( 2.3) 56 ( 2.7) 29 ( 22) 274 ( 3.6) 274 ( 2.0) 269 ( 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 17 ( 2.7) 52 ( 3.3) 31 ( 3.0) 265 ( 2.6) 285 ( 2.0) 258 ( 2.7) Nation 13 ( 2.6) 57 ( 4.0) 30 ( 4.0) 264 ( 5.0)1 265 ( 2.6) 264 ( 3.3) Female State 16 ( 2.6) 54 ( 2.7) 30 ( 2.5) 257 ( 2,6) 258 ( 1.9) 255 ( 2.5) Nation 13 ( 2.4) 55 ( 4.4) 32 ( 4.7) 266 ( 3.9) 264 ( 2.0) 257 ( 3.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does nr,t allow accurate determination of the variability of this estimated mean proficiency, *** Sample size is insu'fietent to permit a reliable estimate (fewer than 62 students). 1 4 / THE 3990 NAEP TRIAL STATE ASSESSMENT 109 Arizona TABLE Al Oa I Teachers' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT AI Lust Once a Week Less Than Once a Week Never TOTAL Percentage and Praidenny Parcentag and Proficiency . Percentage and Proficiency State 61 ( 2.8) 31 ( 2.6) ( 1.2) 257 ( 1.6) 264 ( 1.9) 264 ( 3.3) Nation 50 ( 4.4) 43 ( 41) 8 ( 2.0) 260 ( 2.2) 264 ( 2.3) 277 ( 54)1 RACE/ETHNICITY White State 58 ( 2.8) 34 ( 2.6) 9 ( 12) 269 ( 1.5) 274 ( 1.9) 272 ( 3.7) Nation 49 ( 4.6) 43 ( 4.5) 8 ( 2.3) 265 ( 2.7) 271 ( 2.2) 265 ( 4.9)1 Black State 56 ( 9.3) ( ) Nation 47 ( 6.1) 240 ( 3.4) 45 ( 7.0) 238 ( 4.0) 9 ( 4.1) m Hispanic State 69 ( 3.4) 24 ( 3.3) 6 (1.6) 240 ( 1.9) 245 ( 2.5) Nation 64 ( 72) 246 ( 2.5) 32 ( 6.9) 247 ( 6.3)1 4 (1.4).) American Indian State 54 (143) 40 (12.3) 5 (3.7) 232 ( 2.4)1 234 ( 8.1)1 ) Nation 18 (24.3) 80 (27.2) TYPE OF COMMUNITY Advantaged urban State 52 ( 5.8) 276 ( 3.9)1 47 ( 5.6) 275 ( 3.2) 1 ( 0.3) *..) Nation 39 (22.9) 41 (17.9) 20 (12.2) 273 ( 6.0)1 Diudvantaged trban State 63 ( 8.3) 29 ( 7.8) 8 ( 3.2) 242 ( 3.1)1 Nation 70 (11.7) 21 ( 9.0) 248 ( 4.8)1 249 ( 8.7)1 Extreme rural State ea (15.3) 250 ( 7.2)1 28 (14.0) 4.4.) 4 ( 2.6) ( Nation 35 (14.6) 'd55 ( 5.5)1 56 (17.1) 258 ( 5.9)1 9 ( 9.6) 04-0) Other State 62 ( 4.0) 32 ( 3.4) 6 ( 1.6) 258 ( 2.8) 260 ( 2.5) 263 ( 6.1), Nation 50 ( 4.4) 44 ( 4.5) 6 ( 1.8) 260 ( 2.4) 204 ( 2.8) 277 ( 8.3)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ±. 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 5 110 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE AlOa. I Teachers' Reports on the Frequency of Small (cmtinued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY UM NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Percontage and Predicting/ Percentage and ProAciency Percentage and Proficiency State 61 ( 2.8) ( 2.6) 6 ( 12) 257 ( 1.6) 264 ( 1.9) 264 ( 3.3) Nation 50 ( 4.4) 43 ( 4.1) 8 ( 2.0) 200 ( 2.2) 264 ( 2.3) 277 ( 5.4)1 PARENTS EDUCATION HS non-graduate State 71 ( 4.0) 25 ( 3.6) 4 ( 1.9) 240 ( 2.5) ( ogre ) ( Nation 60 ( 6.4) 39 ( 8.5) 1 ( 1.4) 244 ( 3.2) 244 ( 3.2)1 HS graduate State 80 ( 3.8) 31 ( 3.4) 9 ( 2.0) 248 ( 2.1) 251 ( 2.5) 044 ***) Nation 49 ( 4.8) 45 ( 5.1) 8 ( 2.5) 252 ( 2.8) 257 ( 2.7) Some college State 03 ( 3.4) 30 ( 3.3) 8 ( 1.5) 268 ( 2.3) 286 ( 32) ( Nation 51 ( 266 ( 5.2) 3.1) 42 ( 288 ( 5.1) 3.2) *** ( ***) College graduate State 57 ( 2.8) 35 ( 2.6) 8 289 ( 2.1) 279 ( 2.3) Nation 46 ( 5.2) 43 ( 4.4) 11 ( 2.7) 271 ( 2.6) 276 ( 3.0) 285 ( 4.9)i GENDER Male State 61 ( 2.8) 32 ( 2.7) 7 ( 1,3) 261 ( 1.9) 268 ( 2.5) 262 ( 4.9) Nation 50 ( 4.5) 42 ( 4.0) 8 ( 2.1) 261 ( 3.0) 265 ( 3.1) 278 ( 5.3)1 Female State 60 ( 3.2) 31 ( 2.8) 9 ( 1.3) 253 ( 1.8) 259 ( 1.9) 265 ( 3.1) Nation 50 ( 4.7) 43 ( 4.7) 7 ( 2,1) 259 ( ?.2) 263 ( 2.1) 275 ( 6.6)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample, ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 111 Arizona TABLE AlOb I Teachers' Reports on the Use of Mathematical I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Wok Never TOTAL Percentage and Prodciancy Pen:enlarge and Pronciency Percentage and Proficiency State 21 ( 2.8) 63 ( 3.1) 17 ( 2.3) 256 ( 2.4) 259 ( 1.7) 266 ( 3.4) Nation 22 ( 3.7) 69 ( 3.9) 9 ( 2.6) 254 ( 3.2) 263 ( 1.0) 282 ( 5.9)1 RACE/ETHNICITY State 19 ( 2.5) 64 ( 2.9) 18 ( 2.6) 270 ( 1.8) 270 ( 1.5) 276 ( 3.4) Nation 17 ( 4.0) 72 ( 4.2) 10 ( 2.7) 261 ( 3.8)I 269 ( 2.1) 288 ( 6.2)1 Black State 23 ( 9.2) 54 ( 9.7) Nation 22 ( 5.9) 70 ( 6.3) 8 ( 3.9) 233 ( 5.9)1 241 ( 2.9) Hispanic State 28 ( 5.9) 58 ( 6.0) 14 ( 2.7) 241 ( 23)i 242 ( 2.2) 247 ( 5.8) Nation 39 ( 7.5) 55 ( 7.3) 247 ( 3.8) 245 ( 3.8)1 * American Indian State 77 ( 5.0) 14 ( 5.4) 231 ( 1.9)1 111. *11r4. Nation 78 (34.6) 22 (34.6) 0 ( 0.0) 41** *Hit TYPE Of COMMUNITY ltdvantaged urban State 64 (10.0) 26 (10.8) ) 272 ( 3.2)1 e* ( Nation 23 (14.4) 83 278 (11.5) ( 5.6)1 15 *** ( 9.3) ( ***) Disadvantaged urban State 32 ( 9.1) 56 ( 9.3) 12 ( 4.9) 237 ( 4.0)1 251 ( 5.3)1 ( '") Nation 39 (11.4) 59 (12.1) 247 ( 7.5)1 253 ( 7.0)1 *** ( Extreme rural State 17 ( 9.1) 73 ( 8.2) 10 ( 6.7) 242 ( 6.4)1 ( "*) Nation 27 (149) 65 (14.6) 111111 ( INN 262 ( 2.8)1 Other State 22 ( 4.9) 66 ( 5.4) 13 ( 3.5) 258 ( 3.8)1 258 ( 2.6) 261 ( 4.0)' Nation 19 ( 4.3) 72 ( 5.0) 9 ( 3.3) 253 ( 3.9)1 263 ( 2.2) 281 ( 7.1)1 The standard errors of the estimated statistics appear in parentheses. It tan 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 insuiTicient to permit a reliable estimate (fewer than 62 students). 112 17 THE 1990 NAEP TRIAL STAPi ASSESS1VENT Arizona TABLE MOb I Teachers' Reports on the Use of Mathematical (continued) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL and Proficiency 21 ( 2.8) Percent*. and Proficiency 63 ( 3.1) Percentage and Proficiency 17 ( 2.3) state 256 ( 2.4) 259 ( 1.7) 266 ( 3.4) Nation 22 ( 3.7) 69 ( 3.9) 9 ( 2.6) 254 ( 3.2) 263 ( 1.9) 282 ( 5.9)1 PARENTS EDUCATION liS non-graduate State ( ...) 62 ( 239 ( 52) 2.6) 13 ( ( 3.7) ..) Nation ( ...) 66 ( 243 ( 7.2) 2.2) 9 ( 444 ( 6.5) 4") HS graduate State 21 ( 3.8) BO ( 3,4) 19 ( 2.4) 250 ( 3.7) 249 ( 1.9) 254 ( 3.0) Nation 23 ( 4.8) 70 ( 5.3) 246 ( 4.0)1 255 ( 2.2) Some college State 23 ( 3.6) 61 ( 4.2) 17 ( 3.1) 265 ( 2.8) 264 ( 2.4) 277 ( 4.3) Nation 18 ( 4.0) 73 ( 4.3) 9 ( 2.4) 261 ( 44)1 269 ( 2.3) ( College graduate State 17 ( 2.7) 66 ( 3.1) 17 ( 2.5) 266 ( 2.9) 273 ( 1.9) 277 ( 4.7) Nation 20 ( 3.9) 69 ( 3.7) 11 ( 2.5) 266 ( 3.5)/ 274 ( 2.2) 297 ( 4.2)1 GENDER Male State 20 ( 2.9) 63 ( 3.4) 17 ( 2.6) 260 ( 2.9) 283 ( 1.9) 268 ( 4.3) Nation 22 ( 4.1) 69 ( 4.1) 8 ( 2.0) 255 ( 4.1) 265 ( 2.1) 287 ( 7.2)1 Female State 21 ( 3.1) 63 ( 3.0) 16 ( 2.2) 252 ( 2.8) 255 ( 1.8) 264 ( 3.3) Nation 21 ( 3.6) 69 ( 4.2) 10 ( 3.3) 254 ( 3.3) 262 ( 1.9) 278 ( 6.0)1 The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution -- the natu-e of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 S THE 1990 NAEP TRIAL STATE ASSESSMENT 113 Arizona TABLE Al la 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 Week About Once a Week or Less TOTAL and ProdiciencY 72 ( 25) 262 ( 1.5) 62 ( 3.4) 267 ( 1.8) 72 ( 2.8) 273 ( 1.4) 64 ( 3.7) 272 ( 1.9) 64 ( 8.4) 58 ( 7.7) 244 ( 4.0) 75 ( 3.4) 244 ( 1.8) 61 ( 6.8) 251 ( 3.1) BO (10.7) 237 ( 5.6)1 15 (24.9) R* 91 ( 4.9) 276 ( 1.9)1 63 (15.9) 283 ( 7.3)1 67 ( 9.2) 251 ( 5.4)1 66 (10.7) 252 ( 4.7)1 68 (11.0) 250 ( 43)1 50 (10.6) 268 ( 4.0)1 72 ( 3.8) 260 ( 2.4) 63 ( 3,9) 287 ( 2.3) Percentage and Proficiency 23 ( 2.3) 257 ( 2.4) 31 ( 3.1) 254 ( 2.9) 24 ( 2.8) 269 ( 2.0) 28 ( 3.2) 204 ( 3.4) 23 ( 5.4) 41 ( 7.9) 233 ( 3.9)1 21 ( 3.2) 240 ( 3.1) 32 ( 5.3) 240 ( 4.3)1 26 ( 6.7) ID** 83 (28.3) 4411. HP* . ) 23 ( 52) - ) *4 * flf ) 31 (11.1) 243 ( 8.0)1 29 (10.8) -- 40 (10.0) 247 ( 7.6)1 23 ( 3.9) 259 ( 3.5) 31 ( 3.5) 255 ( 3.1) Pereentlea and Proliciency 5 ( 13) 238 ( 4.6)1 7 ( 1.8) 200 ( 5.1)1 3 ( 1.1) ( 8 ( 2.3) 264 ( 5.4)1 14 ( 6.2) ( .01 2 ( 1.4) ( .41 5 ( 13) .fre) 8 ( 2.3) ( "") 14 ( 6.7) ( ***) 2 ( 3.0) ef" ( ***) 1 ( 0.7) es. -.) 14 (14.6) (, ) 4 ( 2.2) - ( 4 ( 2.6) 10 7.3) ( 4 ) 5 ( 1.6) 240 ( 8.4)1 6 ( 1.9) 257 ( 5.8)1 State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation American Indian 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 the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. m Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 114 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE Al la 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 Swami Threes a Week About Once a Week or Less TOTAL Percentage and Pro &linty Percentage and Proficiency Percentage and PrOneiVICY State 72 ( 2.5) 23 ( 2.3) 5 ( 1.3) 202 ( 1.5) 257 ( 2.4) 238 ( 4.6)! Nation ( 3.4) 31 ( 3.1) 7 ( 1.8) 287 ( 1.8) 254 ( 2.9) 260 ( 5.1)1 PARENTS' EDUCATION HS non-graduat State 68 ( 242 ( 4.3) 2.9) 27 ( ...... 4.5) ( Nation 67 ( 5.5) 27 ( 52) 6 ( 21) 245 ( 3.2) ( "4) HS graduat State 71 ( 3.6) 24 ( 3.4) 251 ( 2.0) 251 ( 32) ( "*) Nation 61 ( 4.4) 34 ( 3.7) 6 ( 1S) 257 ( 2.5) 250 ( 2.9) Some collage State 73 ( 2.9) 22 ( 2.8) 5 ( 1.6) 288 ( 22) 263 ( 3.7) ( "") Nation 68 ( 42) 26 ( 3.7) 6 ( 1.9) 272 ( 2.7) 25.9 ( 52) ( ) Co Ilega graduate State 75 ( 2.9) 22 ( 2.7) 4 ( 1.3) 275 ( 1.7) 269 ( 2.7) Nation 61 ( 4.0) 31 ( 3.9) 8 ( 3.1) 281 ( 2.2) 265 ( 3.1) ", ( "`) GENDER Male State 72 ( 2.8) 23 ( 2.6) 265 ( 1.7) 261 ( 3.2) Nation 60 ( 3.7) 33 ( 3.4) 7 ( 1.9) 269 ( 2.1) 256 ( 3.6) 261 ( 6,7)1 Female State 72 ( 2.4) 24 ( 2.4) 5 ( 1.2) 258 ( 1.5) 254 ( 2,5) ( Nation 6.5 ( 3.6) 28 ( 3.3) ( 2.2) 206 ( 1.8) 253 ( 2.5) The standard errors or the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within i 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 115 Arizona TABLE Al lb I Teachers' Reports on the Frequency of I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFnIENCY 1980 NAEP TRIAL Al Lout Several Times STATE ASSESSMENT a Week About Once a Week Less than Weekly _.. TOTAL Percentage and Proficiency Percentage and Proficiency Percentage end Proficiency State 32 ( 32) 32 ( 2.5) se ( 2$) 253 ( 1.9) 258 ( 2.3) 2ee ( 2.2) Nation 34 i 3.8) 33 ( 3.4) 32 ( 3.6) 258 ( 2.3) 200 ( 2.3) 274 ( 2.7) RACE/ETHNICITY State 30 ( 3.1) 31 ( 2.3) 39 ( 3.0) 285 ( 1.7) 269 ( 1.9) 278 ( 2.0) Nation 32 ( 4.1) 33 ( 3.5) 35 ( 3.8) 264 ( 2.7) 264 ( 2.7) 279 ( 2.9) Black State 33 ( 8.6) 29 ( 8.3) Nation 45 ( 7.5) 31 ( 7.6) 23 ( 8..?) 232 ( 3.1)1 243 ( 2.3)1 248 ( 7.0)1 Hispanic State 35 ( 5.8) 32 ( 4.0) 33 ( 3.6) 240 ( 2.8) 241 ( 2.6) 248 ( 2.7) Nation 41 ( 7.7) 26 ( 5.3) 33 ( 7 .5) 242 ( 3.2)i 244 5.1)1 257 ( 2.3)1 American Indian State 43 (14.4) 31 (13.4) 27 ( 9.6) 230 ( 2.7)1 ) ( ) Nation 10 (18.6) 76 (36.2) 13 (18.5) TYPE OF COMMUNITY Advantaged urban State 38 ( 7.0) 43 ( 8.2) .. 270 ( 2.1)1 287 ( 3.2)1 Nation 58 (13.9) 273 ( 3.4)1 20 ( 6.0) 21 ( 8.2) a. ( ...) Disadvantaged urban State 32 ( 9.4) 45 (10.7) 24 ( 8.7) 250 ( 3.0)1 237 ( 4.6)! Nation 50 (13.9) 22 (11.2) 28 (10.7) 237 ( 2.4)1 258 ( 8.3)1 263 ( 4.1)1 Extreme rural State 35 (12.8) 17 (12.9) 49 (13.2) .) 247 ( 7.7), Nation 27 (14.3) 49 (12.7) 24 (10.1) ) 258 ( 6.7)1 Other State 33 ( 5.5) 30 ( 3.9) 37 ( 4.3) 253 ( 3.4) 259 ( 3.0) 263 1 33) Nation 30 ( 4.4) 35 ( 4.3) 36 ( 4.2) 256 ( 3.3) 259 ( 2.8) 272 ( 2.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. ! Interpret with caution the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. C. Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 ri4 1 116 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A l lb Teachers' Reports on the Frequency of (continued) Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1500 NAEP TRIAL At Least Several Times STATE ASSESSMENT a Week About Oncs. a Week Less than Weekly _ TOTAL and Pralicioncy Percentage and ProAdency Percentage and Pronctencsy State 32 ( 3.2) 32 ( 2$) 36 ( 2.8) 263 ( 1.9) 258 ( 2.3) 266 ( 2.2) Nation 34 ( 3.8) 33 ( 3.4) 32 ( 3.6) 258 ( 2.3) ( 2.3) 274 ( 2.7) PARENTS' EDUCATION HS non-graduate State 38 ( 5.7) 35 ( 4.9) 29 ( 3.8) 236 ( 4.1) 239 ( 3.5) 246 ( 4.3) Nation 35 ( 6.0) 29 ( 6.3) 3FI ( 6.9) 239 ( 33) 250 ( 43)1 HS graduate State 35 ( 4.1) 31 ( 3.0) 34 ( 3.2) 248 ( 2.5) 249 ( 3.1) 252 ( 2.9) Nation 35 ( 53) 36 ( 4.5) 30 ( 4.8) 250 ( 3.8) 250 ( 2.7) 263 ( 3.41 Some college State 31 ( 3.8) 33 ( 2.9) 36 ( 3.1) 262 ( 2.6) 263 ( 3.1) 273 ( 3.9) Nation 33 ( 4.7) 32 ( 4.0) 35 ( 4.1) 260 ( 2.8) 266 ( 4.2) 278 ( 2.8) Cottage graduate State 29 ( 3.0) 31 ( 2.6) 40 ( 3.5) 264 ( 2.2) 269 ( 2.6) 281 ( 2.8) Nation 35 ( 3.8) 32 ( 3,4) 33 ( 3.5) 264 ( 2.6) 271 ( 2.4) 289 ( 2.9) GENDER Male State 32 ( 3.2) 30 ( 2.7) 38 ( 2.9) 257 ( 2.1) 261 ( 2.6) 289 ( 2,6) Nation 3,5 ( 4.1) 35 ( 3.6) 31 ( 3$) 257 ( 3.2) 261 ( 2.8) 275 ( 3.2) Ft/mate State 33 ( 3.6) 34 ( 2.8) 33 ( 3.0) 250 ( 2.2) 254 ( 2.4) 263 ( 2.2) 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 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 117 Arizona TABLE A 12 I Students' Reports on the Frequency of Small Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Lust Once a Week Less Tnan Once a Week Never TOTAL. and Proficiency Percentage 811d Proficiency Percentage and Proficiency State 33 ( 1.9) 26 ( 1.1) 42 ( 1.8) 258 ( 2.1) 264 ( 1.6) 261 ( 1.6) Nation 28 ( 2.5) 28 ( 1.4) 44 ( 2.9) 258 ( 2.7) 267 ( 2.0) 261 ( 1.6) RACE/ETHNICITY White State 29 ( 1.8) 30 ( 1.3) 41 ( 1.9) 269 ( 2.1) 273 ( 1.6) 271 ( 1.4) Nation 27 ( 2.9) 29 ( 1.7) 44 ( 3$) 268 ( 3.1) 272 ( 1.9) 270 ( 1.7) Black State 27 ( 6.1) 29 ( 4.1) VHF* ( 4t* ) - *Mb Nation 28 ( 3.0) 24 ( 3.6) ( 4.7) 234 ( 3.0) 245 ( 4.6) 234 ( 3.1) Hispanic State 40 ( 3.0) 20 ( 1.7) 40 ( 2.7) 241 ( 2.1) 244 ( 2.2) 244 ( 2.1) Nation 37 ( 5.2) 22 ( 3.6) 41 ( 5.0) 24,2 ( 3.9) 250 ( 3.4) 240 ( 2.8) American Indian State 41 ( 8.5) 19 ( 3.8) 41 (10.7) 231 ( 3.6)1 239 ( 3.8)1 Nation 31 ( 5.1) ** ( ) TYPE OF COMMUNITY Advantaged urban State 25 ( 3.8) 30 ( 36) 45 ( 4.8) 276 ( 5.3)1 278 ( 3.5) 272 ( 3.3)1 Nation 27 (13.9) 33 ( 4.5) 40 (13.4) 286 ( 5.4)1 279 ( 3.5)! Disadvantaged urban State 23 ( 5.6) 27 ( 3.5) 50 ( 6.4) 235 ( 3.3)1 251 ( 4.3)I 252 ( 4.8)1 Nation ( 5.7) 20 ( 2.8) 49 ( 6.3) 245 ( 4.0)1 207 ( 6.4)1 245 ( 3.7)1 Extrema rural State 25 ( 2.3) 27 ( 6.4) 47 ( 7.2) 242 ( 4.7)1 Nation 34 (10.8) 27 ( 3.8) 39 (11.8) 249 ( 5.2)1 264 ( 3.5)1 250 ( 6.2)1 Other State 38 ( 2.9) 24 .5) 37 ( 2.7) 256 ( 2.9) 264 ( 2.3) 259 ( 2.4) Nation 27 ( 2.6) 28 ( 1.7) 45 ( 3.3) 260 ( 3.3) 264 ( 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. "* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 3 118 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A 12 Students' Reports on the Frequency of Small (c'ntinued) Group Work PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRIAL STATE ASSESSMENT Al Least Once a Week Less Than Once a Week Never TOTAL norcenill. and Proliciancy Poteentage and Profidency Percentage and Proficiency State 33 ( 1.9) 26 ( 13) 42 ( 1.6) 256 ( 2.1) 264 ( 1.6) 261 ( tit) Nation 28 ( 2.5) ( 1.4) 44 ( 2.9) 268 ( 2.7) 267 ( 2.0) 261 ( tit) PARENTS EDUCATION HS non-graduate State 35 ( 3.3) 25 ( 2.6) 39 ( 3.4) 234 ( 2.9) f Mk* ***) 241 ( 2.9) Nation 29 ( 4.5) 29 ( 3.0) 42 ( 4.5) 242 ( 3.4) 244 ( 3.0) 242 ( 2.7) HS graduate state 34 ( 3.1) 24 ( 1.9) 42 ( 32) 248 ( 2.8) 254 ( 2.4) 252 ( 2.2) Nation 28 ( 3.0) 28 ( 1.8) 43 ( 3.4) 251 ( 3.7) 261 ( 2.6) 252 ( 1.7) Some college State 32 ( 2.9) 28 ( 2.6) 40 ( 2.6) 262 ( 2.9) 268 ( 2.8) 268 ( 2.3) Nation 27 ( 3.9) 27 ( 2.4) 48 ( 3.8) 285 ( 3.6) 268 ( 3.3) 266 ( 2.1) College graduate State 31 ( 1.8) 26 ( 1.7) 43 ( 2.3) 269 ( 9.6) 276 ( 2.4) 273 ( 2.0) Nation 28 ( 3.0) 28 ( 1.9) 44 ( 3.6) 270 ( 2.7) 278 ( 2.8) 275 ( 2.2) GENDER Male State 31 ( 1.8) 28 ( 1.3) 41 ( 1.8) 259 ( 2.4) 267 ( 2.1) 263 ( 1.8) Nation 31 ( 2.9) 28 ( 1.7) 41 ( 2.9) 259 ( 3.3) 26$ ( 2.6) 262 ( 1.8) Female State 34 ( 2.2) 24 ( 1.6) 42 ( 2.2) 252 ( 2.2) 260 ( 2.0) 258 ( 1.7) Nation 26 ( 2.4) 27 ( 1.8) 47 ( 3.2) 257 ( 2.8) 266 ( 1.7) 260 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within t 2 standard errors of the estimate for the sample. s" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 119 Arizona TABLE A13 I Students' Reports on the Use of Mathematics I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRLAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week Never TOTAL Pareantaips and Pndiciancy Pnrcentaips and Prolicisncy Percentage and Prodidency State 21 ( 1 4) 25 ( 1.2) 53 ( 1.7) 254 ( 1.8) 204 ( 1.9) 280 ( 1.3) Nation 28 ( 1.8) 31 ( 1.2) 41 ( 2.2) 258 ( 2.6) 289 ( 1.5) 259 ( 1.6) RACEIETHNICITY White State 19 ( 1.3) 27 ( 1.4) 54 ( 1.6) 287 ( 1.8) 274 ( 1.8) 271 ( 1.5) Nation 27 ( 1.9) 33 ( 1.6) 40 ( 2.5) 266 ( 2,6) 275 ( 1.6) 268 ( 1.8) Black State 23 ( 7.4) 21 ( 3.5) Nation 27 ( 3.3) 27 ( 32) 46 ( 4.5) 234 ( 3.7) 248 ( 4.5) 232 ( 2.6) Hispanic State 24 ( 2.0) 24 ( 1.9) 52 ( 3.0) 238 ( 22) 248 ( 2.4) 243 ( 1.7) Nation 38 ( 4.2) 23 ( 2.0) 40 ( 4.0) 241 ( 4.6) 253 ( 4.3) 240 ( 1.9) American Indian State 50 (10.1) ee* ( 237 ( 2.1)1 Nation 35 ( 3.4) .*) 37 ( 8.2) 28 ( 8.8) TYPE OF COMMUNITY Advantaged urban State 17 ( 4.0) 22 ( 4.2) 61 ( 8.1) ( *4* 274 ( 2.3)1 Nation 38 (90.3) 33 ( 4.8) 32 (11.1) 278 ( 8.1)1 284 ( 3.2)1 281 ( 5.9)1 Disadvantaged Lew State 27 ( 4.7) 53 ( 5.7) 240 ( 3.1)1 255 ( 4.9)1 Nation 35 ( 6.6) 19 ( 2.1) 46 ( 6.4) 249 ( 5.3)1 258 ( 5.7)1 246 ( 4.8)1 Extreme rtral State 48 ( 9.5) 4r44 243 ( 3.7)1 Nation 21 ( **. ( 3,1) 37 ( 282 ( 4.7) 4.7)1 43 ( 251 ( 5.0) 5.2)1 Other State 21 ( 1.4) 28 ( 2.0) 51 ( 2.6) 255 ( 3.0) 263 ( 2.8) 259 ( 1.7) Nation 27 ( 2.0) 31 ( 1.4) 41 ( 2.4) 256 ( 2.9) 270 ( 1.8) 260 ( 22) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire 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 variabihty of this estimated mean proficiency. *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 120 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A 13 Students' Reports on the Use of Mathematics (contin11"1) I Objects PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT At Least Once a Week Less Than Once a Week . Never _1 TOTAL Percentage and Prandancy Pareantaga and *Odom Parventaga and Proacioncy State 21 ( 14) 25 ( 1.2) 53 ( 1.7) 254 ( 1.8) 264 ( 1.9) 200 ( 1.3) Nation 28 ( 1.8) 31 ( 12) 41 ( 2.2) 258 ( 2.8) 269 ( 1.5) 259 ( LS) PARENTS' EDUCATION HS non-graduate State 23 ( 3.5) 23 ( 2.9) 54 ( 3.7) 111 ( le') ***) 241 ( 2.3) Nation 27 ( 42) 26 ( 2.7) 47 ( 5.0) 237 ( 3.0) 253 ( 3.5) 240 ( 2.3) HS graduate State 23 ( 2.9) 23 ( 1.7) 54 ( 3.1) 246 ( 3.1) 253 ( 2.8) 251 ( 21) Nation 27 ( 2.7) 31 ( 2.4) 43 ( 3.3) 250 ( 2.4) 259 ( 2.7) 253 ( 2.1) Some college State 21 ( 2.3) 26 ( 2.2) 53 ( 3.0) 262 ( 3.1) 266 ( 32) 267 ( 2,1) Nation 29 ( 2.8) 36 ( 2.3) 35 ( 2.6) 281 ( 3.5) 274 ( 2.2) 263 ( 2.1) Cofiege graduate State 20 ( 1.3) 27 ( 1.4) 54 ( 1.6) 265 ( 2.4) 277 ( 2.1) 272 ( 1.9) Nation 30 ( 2.5) 32 ( 2.0) 38 ( 2,6) 269 ( 3.0) 278 ( 2.0) 275 ( 2.0) GENDER Male State 24 ( 1.7) 25 ( 1.4) 50 ( 1.9) 255 ( 2.2) 268 ( 2.1) 264 ( 1.7) Nation 32 ( 2.0) 30 ( 15) 38 ( 2.2) 258 ( 2.9) 271 ( 2.1) 260 ( 1.8) Female State 18 ( 1.7) 25 ( 1.6) 56 ( 2.1) 252 ( 2.2) 259 ( 2.5) 257 ( 1.5) Nation 25 ( 2.0) 31 ( 1.9) 44 ( 2.6) 257 ( 3,0) 268 ( 1.5) 257 ( 1,9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within .± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 6 THE 1990 NAEP TRIAL STATE ASSESSMENT 121 Arizona TABLE A14 I Students' 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 Week About Once a Week or Less TOTAL Perantege and Proficiency 79 ( 1.4) 764 ( 1.1) 74 ( 1.9) 267 ( 1.2) 82 ( 1.5) 274 ( 1.2) 76 ( 2.5) 274 ( 1.3) 77 ( 62) 246 ( 3.0) 71 ( 28) 240 ( 2.9) 74 ( 2.1) 246 ( 1.3) 61 ( 3.7) 249 ( 2.3) 68 ( 5.1) 238 ( 2.7)1 61 ( 4.4) ( ...) 92 ( 1.7) 276 ( 1.9)1 73 (11.1) 288 ( 4.6)1 72 ( 5.0) 249 ( 3.6)1 69 ( 2.8) 253 ( 3.7)1 76 ( 5.0) 252 ( 4.8)1 68 (11.3) 264 ( 4.2)1 79 ( 2.1) 283 ( 1.9) 75 ( 2.2) 267 ( 1.6) Percentage and Proficiency 13 ( 0.7) 247 ( 1,9) 14 ( 0.8) 252 ( 1.7) 11 ( 1.0) 257 ( 1.8) 13 ( 0.8) 258 ( 21) 14 ( 4.6) 04. ( ....) 15 ( 1.7) 232 ( 3.1) 15 ( 1.3) 238 ( 3.0) 21 ( 2.9) 242 ( 5.1) 12 ( 1.8) "') 22 ( 3.6) ( ...) 7 ( 1.7) ( ...) ( ...) 17 ( 3.1) *.. 0-.) 15 ( 25) 243 ( 4.4)1 13 ( 2.7) ( ( 41.414) 12 ( 1.0) 24.8 ( 1.9) 14 ( 1.0) 252 ( 2 6) Percentage and Proliciency 8 ( 1.1) 241 ( 2.8) 12 ( 1.8) 242 ( 44) 6 ( 0.9) 257 ( 3.4) 11 ( 2.2) 252 ( 5.1)1 ( 14 ( 3.2) 223 ( 6.1)1 10 ( 1.5) 227 ( 3.7) 17 ( 2.7) 224 ( 3.4) 19 ( 4.6) 17 ( 4.0) ( ...) 1 ( 0.9) ( ..) 14 (10.4) ( ...) ( ...) 15 ( 2.2) 235 ( 6.5)1 11 ( 3.0) ( ...) ...) 9 ( 1.6) 241 ( 3.6)1 10 ( 1.9) 239 ( 4.3)1 State Nation RACE/ETHNICITY Mite State Nation Black State Nation Hispanic State Nation American Indian 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 percen, 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). 122 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A 14 Students' Reports on the Frequency of (continued) i Mathematics Textbook Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Almost Every Day Several Timis a Week _ About Once a Week or Less TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 79 ( 1.4) 13 ( 0.7) 8 ( 1.1) 264 ( 1.1) 247 ( 1.9) 241 ( 2.8) Nation 74 ( 1.9) 14 ( 0.8) 12 ( 1.8) 287 ( 1.2) 252 ( 1.7) 242 ( 4.5) PARENTS' EDUCATION NS non-graduate State 73 ( 246 ( 2.8) 1.9) 13 ( 2.0) 14 (- 2.4) Nation 64 ( 3.4) 18 ( 2.0) 13 ( 3,1) 245 ( 2.3) *YIP ( HS graduate State 76 ( 22) 16 ( 1.6) 8 ( 1.13) 252 ( 1.f.) 247 ( 3.0) Nation 71 ( 3.6) 16 ( 1.8) 13 ( 2.8) 258 ( 1.6) 249 ( 32) 239 ( 3.4)1 Some college State 82 ( 1.9) 7 ( 1.4) 268 ( 1.7) *4* 11-41 Nation 80 ( 2.0) 1 1 ( 12) 9 ( 1.7) 270 ( 1.9) ( .") ( College gra dust* State 85 ( 1.6) 9 ( 1.1) 6 ( 1.0) 275 ( 1.5) 256 ( 3.7) 254 ( 5.5) Nation 77 ( 2.7) 13 ( 0.9) 10 ( 2.3) 279 ( 1.6) 260 ( 2.8) 257 ( 6.4)I GENDER Male State 78 ( 1.7) 13 ( 0.8) 9 ( 1 ) 267 ( 1.5) 250 ( 2.4) 244 ( 3.5) Nation 72 ( 2.4) 16 ( 1.2) 12 ( 2.1) 268 ( 1.6) 252 ( 2$) 242 ( 6.1) Female State 80 ( 1.5) 12 ( 1.0) 8 ( 1.1) 260 ( 1.1) 244 ( 2.4) 238 ( 3.6) Nation 76 ( 1.8) 13 ( 1.0) 11 ( 1.6) 265 ( 1.3) 250 ( 2.5) 242 ( 3.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 28 THE 1990 NAEP TRIAL STATE ASSESSMENT 123 Arizona TABLE A15 I Students' Reports on the Frequency of I Mathematics Worksheet Use PERCENTPGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 10410 NAEP TRIAL STATE ASSESSMENT At Lust Several Times a Week About Once a Week Less Than Weekly TOTAL Percentage and Proficiency Peroardaga and Prolkioncy Parcerdaye and Proliciency State ( 41.9) 22 ( 12) 40 ( 1.5) 250 ( 1.8) 259 ( 14) 287 ( 1.8) Nation 38 ( 2.4) 25 ( 1.2) 37 ( t5) 253 ( 2.2) 281 ( 1A) 272 ( 1.9) RACE/ETHNICITY White State 25 ( 2.1) 30 ( 1.5) ( 2.0) 283 ( 1.8) 210 ( 1,7) 276 ( 1.5) Nation 35 ( 2.9) 24 ( 1.3) 41 ( 3.0) 262 ( 2.5) 289 ( 1.5) 277 2.0) Black State 26 ( 5.4) 041 38 ( 5.0) 38 ( 5.1) Nation 48 ( 3.8) 32 ( 2.7) 20 ( 3.1) 232 ( 4.3) 241 ( 2.9) 241 ( 4.4) Hispanic State 36 ( 2.6) 29 ( 1.8) 35 ( 2.8) 236 ( 2.0) 244 ( 2.1) 248 ( 22) Nation 44 ( 4.1) 25 ( 3.4) 32 ( 4.3) 238 ( 3.9) 247 ( 3.3) 248 ( 3.3) American Indian State 58 ( 3.9) 22 ( 4.1) 20 ( 3.4) 232 ( 2.1)I ( ) Nation .41 ( 4.2) 30 *** (113) ( ***) 28 (12.5) *4-4, TYPE OF COMMUNITY Advantaged urban State 17 ( 2.4) 37 ( 3.9) 48 ( 4.2) 278 ( 2.0)1 280 ( 3.7)1 Nation 50 ( 271 ( 9.0) 3.3)1 19 ( 4.9) .441 31 ( 299 ( 9.3) 5.3)1 Disadvantaged urban State 34 ( 6.0) 25 ( 2.9) 41 ( 5.3) 241 ( 4.9)I 244 ( 3.6)1 256 ( 5.2)1 Nation 37 ( 5.8) 23 ( 3.6) 41 ( 8.7) 240 ( 4.8)1 253 ( 41)1 255 ( 4.2)1 Extreme rural State 37 ( ( 7.0) 4.) 33 I,. ( 4.6) 30 ( ( 8.6) 0+1 Nation 42 (10.1) 30 ( 4.4) 28 ( 74) 249 ( 4.0)1 258 ( 3.4)1 267 ( 7,30 Other State 32 ( 3.5) 29 ( 1.8) 39 ( 2.9) 252 ( 3.0) 257 ( 2.2) 255 ( 2.5) Nation 38 ( 2.9) 26 ( 1.2) 38 ( 2.9) 252 ( 3.0) 261 ( 2,1) 272 ( 1.8) 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, 41" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1. iv 9 124 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A15 Students' Reports on the Frequency of (continued) I Mathematics Worksheet Use PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT , At Lust Sward Times a Week About Once a Wuk ., Lass Than Wieldy .... TOTAL Pawning@ and Proficiency Percentage and Proliciency Pawning' and Pa:stickmen/ State 31 ( 1.9) 29 ( 1.2) 40 ( 1.5) 250 ( 1.8) 259 ( 1.5) 267 ( 1.6) Nation ( 2.4) 25 ( 1.2) 37 ( 2.5) 253 ( 2.2) 261 ( 1A) 272 ( 1.9) PARENTS' EDUCATION 11,1 non-graduate State 38 ( 3.9) 30 ( 3.2) 32 ( 3.4) 232 ( 3.1) 244 ( 3.0) 246 ( 3.1) Nation 41 ( 4$) 30 ( 2.7) 29 ( 4.0) 235 ( 3.1) 243 ( 2.7) 253 ( 2.8) NS graduate State 35 ( 2.8) 26 ( 2.3) 39 ( 2$) 245 ( 2.6) 251 ( 2.3) 255 ( 2.3) Nation 40 ( 3.2) 29 ( 2.2) 32 ( 3.6) 247 ( 2.7) 256 ( 2.5) 262 ( 2.2) Sam collge State 26 ( 2.3) 30 ( 2.3) 43 ( 2.6) 257 ( 2.5) 263 ( 2.4) 272 ( 2.7) Nation 34 ( 3.4) 26 ( 2.2) 40 ( 3.6) 259 ( 2.3) 269 ( 2.8) 271 ( 2.8) Co hp. graduate State 27 ( 2.4) 30 ( 1.4) 43 ( 2.0) 262 ( 2.3) 271 ( 2.2) 280 ( 1.9) Nation 38 ( 2.8) 22 ( 1.8) 41 ( 2.6) 264 ( 2.6) 273 ( 2.5) 285 ( 2.3) GENDER Male State 30 ( 2.0) 31 ( 1.7) 39 ( 1.8) 253 ( 2.2) 262 ( 2.0) 271 ( 2.0) Nation 39 ( 2.7) 25 ( 1.6) 35 ( 2.7) 253 ( 2.7) 263 ( 2.3) 274 ( 2.4) Female State 31 ( 2.3) 28 ( 1.4) 41 ( 1.6) 246 ( 2.0) 256 ( 1.5) 264 ( 1.6) Nation 37 ( 2.5) 25 ( 1$) 38 ( 2.6) 253 ( 2.1) 259 ( 1.8) 269 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. 130 THE 1990 NAEP TRIAL STATE ASSESSMENT 125 1.1 Arizona TABLE AIS Students' Reports on Whether They Own a Calculator and Whether Their Teacher Explains How to Use One PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT Own a Calculator Teacher Explains Calculator U. Yes No Yes No TOTA1. Percentage and Proficiency Percentage and Proficiency Peroentage and Proficiency Percentage and Praficiency State 97 ( 0.4) 3 ( 0.4) 44 ( 1.8) 56 ( 1.8) 200 ( 1.1) 241 ( 3.0) 255 ( 1.7) 284 ( 1.2) Nation 97 ( 04) 3 ( 0.4) 49 ( 2.3) 51 ( 2.3) 263 ( 1.3) 234 ( 3.8) 2581 1.7) 286 ( IS) RACE/ETHNICITY White State 98 ( 0.4) 2 ( 0.4) 38 ( 2.0) 62 ( 2.0) 271 ( 1.1) 267 ( 1.7) 273 ( 1.2) Nation 98 ( 270 ( 0.3) 1.5) 2 ( .44 0.3) 48 ( 286 ( 2.8) 1.8) 54 ( 273 ( 2.6) 1.8) Slack State 94 ( 2.9) 6 ( 2.9) 51 ( 5.9) 247 ( 3.0) ( .") Nation 93 ( 1.5) 7 ( 1.5) 53 ( 4.9) 47 ( 4.9) 237 ( 2.8) ( 235 ( 3.6) 239 ( 2.7) Hispanic State ( 0.9) 6 ( 0.9) 52 ( 3.0) 48 ( 3.0) 243 ( 1.3) ( 242 ( 1.9) 244 ( 1.8) Nation 92 ( 245 ( 1.2) 2.7) 8 ( *** ( 1.2) **) 83 ( 243 ( 4.3) 3.4) 37 ( 245 ( 4.3) 2.9) American Indian State 94 ( 2.2) 6 ( 2.2) 61 ( 4.3) 39 ( 4.3) 236 ( 1.7)1 ( ***) 236 ( 4.3)1 233 ( 5.1)1 Nation .441 71 (16.7) 29 (16.7) --) TYPE OF COMMUNITY Mvantaged urban State 99 ( 275 ( 0.5) 2.0)1 1 ( *** ( 0.5) ***) 27 ( 275 ( 4.8) 3.6) 73 ( 275 ( 4.8) 2.6)1 Nation 99 ( 1.0) 45 (12.2) 55 (12-2) 281 ( 3.8)1 4-** 276 ( 2$)1 285 ( 6.4)1 Disadvantaged urban State 94 ( 246 ( 2.0) 3.4)1 6 ( ** ( 2.0) 58 ( 245 ( 4.6) 3.0)1 42 ( 252 ( 4.6) 5$)1 Nation ( 1.2) ( 1.2) 53 ( 7.5) 47 ( 7.5) 250 ( 3$)1 247 ( 4.1)1 251 ( 3.6)1 Extreme rural State 92 ( 2.9) 8 ( 2.9) 58 ( 5,6) 42 ( 5.6) 248 ( 5.0)1 251 ( 4.9); 241 ( 6.6)1 Nation 96 ( 1.3) 4 ( 1.3) 42 ( 8.7) 56 ( 8.7) 267 ( 3.9)1 *" 251 ( 4.8)1 261 ( 4.4)I Other State 96 ( 0.6) 4 ( 0.6) 42 ( 3.1) 58 ( 3.1) 260 ( 1.9) 255 ( 2.9) 262 ( 1.8) Nation 97 ( 0.5) 3 ( 0$) 50 ( 2.7) 50 ( 2.7) 263 ( 1.7) 233 ( 5.4) 258 ( 2.1) 266 ( 2.0) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 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, *** Safi* 9,2e is inst fficient to permit a reliable estimate (fewer than 62 students). t) 126 ME 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A 18 (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 1960 NAEP TRIAL STATE ASSESSMENT Own a Calculator . i Teacher Explains Calculator Use Yes No Yes No TOTAL and Proficiency 07 ( OA) 260( 1.11 97 ( OA) 263 ( 1.3) Percentage end Proficiency 3 ( OA) 241 ( 3.0) 3 ( 0.4) 234 ( 3.8) Percenhige and Proficiency 44 1.8) 255 ( 1.7) 49 ( 2.3) 25$ ( 1.7) Percentage and Proficency 58 ( 1.6) 264 ( 1.2) 51 ( 2.3) 266 f 1.5) State Nation PARENTS' EDUCATION HS non-graduate State 93 ( 1.7) 7 ( 1.7) 50 ( 3.6) 50 ( 3.8) ( 1.9) ( .") 238 ( 2.8) 242 ( 2.5) Nation 92 ( 243 ( 1.6) 2.0) $4.4, ( 1.6) ..**) 53 ( 242 ( 4.6) 2.9) 47 ( 243 ( 4.8) 2.5) HS graduate State 96 ( 0.6) 4 ( 0.8) 48 ( 2.3) 54 ( 2.3) 250 ( 1.5) ( ***) 249 ( 2.1) 252 ( 1.9) Nation 97 ( 0.8) 3 ( 0.6) 54 ( 3.0) 48 ( 3.0) 255 ( 1.5) ( "*) 252 ( 1.9) 258 ( 2.0) Some co/legs State 97 ( 0.8) 48 ( 2.8) 54 ( 2.8) 266 ( 1.7) ( "") 262 ( 2.7) 269 ( 1.7) Nation 96 ( 268 ( 0.9) 1.8) 4 ( 0.9) ( **al ( 265 ( 3.2) 2.4) 52 ( 268 ( 32) 22) College graduate State 98 ( 0.5) 2 ( 03) 39 ( 2.3) 61 ( 2.3) 273 ( 1.4) 266 ( 2.1) 277 ( 1.6) Nation 99 ( 0.2) 1 ( 0.2) 46 ( 2.6) 54 ( 2.6) 275 ( 1.6) "") 268 ( 22) 280 ( 1.9) GENDER M. State 96 ( 0.6) 4 ( 0.6) 46 ( 2.0) 54 ( 2.0) 264 ( 1.4) ( 258 ( 2.1) 288 ( 1.6) Nation 97 ( 0.5) 3 ( OS) 51 ( 2.6) 49 ( 2.8) 264 ( 1.7) 258 ( 21) 269 ( 2.1) Female State 97 ( 0.6) 3 ( 0.6) 42 ( 21) 58 ( 2.1) 257 ( 1.1) ( ***) 252 ( 1.8) 260 ( 1.3) Nation 97 ( 0.5) 3 ( 0.5) 47 ( 2.5) 53 ( 2.5) 262 ( 1.3) ( .") 258 ( 1.7) 263 ( 1.6) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample, *" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 132 THE 1990 NAEP TRIAL STATE ASSESSMENT 127 Arizona TABLE A19 I Students' Reports on the Use of a Calculator for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT orking Problems in Class Doing Problems at Home Taking Quizzes or Teets Almost Always Never Almost Always Ne VW' Almost Always Never TOTAL Percentage and Proficiency 46 ( 1.0) 252 ( 1.3) 48 ( 1.5) 254 ( 1.5) 42 ( 1.5) 263 ( 1.3) 48 ( 1.7) 262 ( 1.7) 52 ( 4.9) 57 ( 3.2) 232 ( 2.4) 50 ( 1.5) 236 ( 1.5) 51 ( 2.9) 239 ( 2.8) 55 ( 3.4) 232 ( 3.0)1 ) 39 ( 3.7) 270 ( 2.5)1 51 ( 5.4) 270 ( 4,7)1 50 ( 2.9) 241 ( 3.2)1 52 ( 3,1) 241 ( 3.8)1 ( 2,4) 241 ( 4,5)1 46 ( 7,4) 246 ( 4.3)1 46 ( 1.9) 252 ( 2.0) 48 ( 1,9) 254 ( 2,1) Percentage and Proficiency 27 ( 1.2) 274 ( 1.5) 23 ( 1.9) 272 ( 1.4) 32 ( 1.7) 280 ( 1.4) 24 ( 2.2) 278 ( 1.3) 14 ( 3.2) ) 20 ( 3.9) 249 ( 4.0) 20 ( 1.8) 257 ( 3.0) 16 ( 3.5) 252 ( 3.3)1 14 ( 3.8) ..) 23 ( 4.9) ** ( ...) 37 ( 4.6) 278 ( 3,0)1 23 (10.7) ) 19 ( 2,5) ) 22 ( 4.5) 259 ( 5.4)1 20 ( 3.5) . . 29 ( 6.5) 268 ( 6.1)1 27 ( 2.0) 274 ( 1.8) 22 ( 2.0) 272 ( 1,8) Percentage and Proficiency 29 ( 1.2) 260 ( 1.5) 30 ( 1.3) 261 ( 1.8) 31 ( 1.4) 268 ( 1.4) 31 ( 1.5) 270 ( 1.7) 641. 31 ( 2.9) 233 ( 3.3) 25 ( 1.9) 242 ( 2.6) 26 ( 3.2) 238 ( 4.8) 24 ( 3.3) ) 15 ( 4.9) .. ) 37 ( 3.6) 274 ( 3.5) 32 ( 6.1) 274 ( 4.9)1 27 ( 2,6) 248 ( 5.3)1 30 ( 3.3) 246 ( 5.2)1 .. ...) 29 ( 2.1) 259 ( 2.1) 32 ( 1.7) 263 ( 2,3) Percentage and Proficiency 18 ( 0.9) 268 ( 2.0) 19 ( 0.9) 263 ( 1.8) 18 ( 1.2) 280 ( 1.9) 18 ( 1/) 269 2.3) 13 ( 3.5) 18 ( 1.9) 248 ( 5.5) 20 ( 1.8) 247 ( 2.9) 21 ( 2.1) 244 ( 3.1) 12 ( 3.5) ) 32 (10.1) ( 04* ) 15 ( 2.1) ) INN ( ) 13 ( 1.6) ) 24 ( 2,3) 254 ( 4.6)1 13 ( 2.7).) 23 1 3,9) 263 ( 4.4)1 19 ( 1,5) 266 ( 3,1) 18 ( 1.1) 263 ( 2.8) Percentage and Proficiency 23 ( 1.1) 250 ( 1.7) 27 ( 1.4) 253 ( 2.4) 22 ( 1.4) 262 ( 2.0) 25 ( 1.8) 263 ( 2.6) ) 38 ( 3.3) 230 ( 3.6) 25 ( 1.8) 233 ( 1.9) 26 ( 2.7) 237 ( 3.2) 26 ( 6.8) ) 20 ( 6.2) .. ) ...) 31 ( 3.8) 281 ( 7.6)1 23 ( 2.0) 242 ( 4.0)1 27 ( 2.9) 240 ( 4.9)1 24 ( 5.6) s* ( *IND ) 24 ( 6.6) .. ) 24 ( 1,8) 250 ( 2.6) 27 ( 1.8) 253 ( 2.7) Percentage and Profitieney 37 ( 1.3) 273 ( 1.1) 30 ( 2.0) 274 ( 1.3) 1.6) 280 ( ; .2) 32 ( 2.3) 279 ( 1.2) 26 ( 4.3) 11,114 4Nt 24 ( 3.1) 251 ( 4.1) 30 ( 1.8) 257 ( 1.8) 22 ( 3.1) 256 ( 4.2) 18 ( 4.5) .. 21 ( 7.8) ...) 47 ( 2.3) 280 ( 2.5)t 28 ( 9.8) 285 ( 4.2)1 25 ( 3.1) 264 ( 3.8)1 27 ( 4.8) 263 ( 5.0)1 28 ( 5.1)) 37 ( 8.3) 270 ( 4.0)1 38 ( 2.2) 272 ( 1.7) 29 ( 2.1) 275 ( 1.9) State Nation RACE/ETHNICITY White State Nation Black State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Advantaled when State Nation Disadvantaged 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 percvnt certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. The percentages may not total 100 percent because the "Sometimes" category is not included. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1I 128 THE )990 NAEP A ASSESSMENT &? Arizona TABLE A 19 I Students' Reports on the Use of a Calculator (mntinued) for Problem Solving or Tests PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1980 NAEP TRIAL STATE ASSESSMENT Working Problems in Class Doing Problems at Home Taking Quizzes or Tests Almost Always Never Almost Always , Never Almost Always Never TOTAL Percentage and Proficiency Percentage and Proliciency Percentage and Prolicieney Percentage and Proaciena Percentage and Proficiency Percentage and Proficiency State 48 ( 1.0) 27 ( 1.2) 29 ( 1.2) 18 ( 0.9) 23 ( 1.1) 37 ( 1.3) 252 ( 1.3) 274 ( 1.5 2 ( 1.5) 268 ( 2.0) 250 ( 1.7) 273 ( 1.1) Nation 48 ( 1.5) 23 ( 1.9) 30 ( 1.3) 19 ( 0.9) 27 ( 1.4) 90 ( 2.0) 254 ( 1.5) 272 ( 1.4) 261 ( 1.8) 263 ( 1.8) 253 ( 2.4) 274 ( 1.3) PARENTS EDUCATION HS non-graduate State 47 ( 233 ( 3.2) 2.5) 17 ( 2.4) 20 ( 2.9) *41 16 ( 2.3) 30 ( 235 ( 3.4) 3.3) 29 ( 257 ( 3.1) 3.4) Nation 54 ( 3.3) 2e ( 3.1) 22 ( 2.6) 32 ( 3.0) 24 ( 3.2) 240 ( 2.3) 244 ( 3.8) 244 ( 4.2) 237 ( 2.3) 251 ( 4.6) HS graduate State 50 ( 2.0) 22 ( 1.8) 25 ( 2.0) 18 ( 1.9) 27 ( 2.5) 29 ( 2.0) 245 ( 1.8) 264 ( 2.2) 249 ( 2.2) 261 ( 3.3) 242 ( 1.9) 264 ( 1.9) Nation 52 ( 2.5) 20 ( 2.4) 29 ( 1.9) 18 ( 1.5) 26 ( 1.8) 27 ( 2.2) 249 ( 1.4) 265 ( 2.7) 250 ( 2.4) 256 ( 2.4) 246 ( 2.8) 265 ( 2.0) Some collage State 42 ( 2.4) 31 ( 2,4) 29 ( 1.9) 19 ( 1.8) 23 ( 2.8) 43 (2.8) 257 ( 2.2) 275 ( 2.8) 264 ( 3.0) 274 ( 3.9) 255 ( 3.8) 278 ( 2.1) Nation 48 ( 2.8) 26 ( 2.8) 28 ( 2.0) 20 ( 1.9) 26 ( 2.4) 35 ( 2.5) 258 ( 2.1) 272 ( 2.5) 267 ( 3.0) 268 ( 3.2) 255 ( 3.8) 27$ ( 2.0) College graduate State 44 ( 1.8) 31 ( 2.0) 34 ( 1.9) 18 ( 1.4) 20 ( 1.5) 42 ( 1.9) 264 ( 2.0) 283 ( 2.2) 2ea ( 2.1) 281 ( 3.1) 263 ( 3.1) 282 ( 1.5) Nation 45( 1.9) 25 ( 2.4) 33 ( 2.0) 16 ( 1,4) 28 ( 1.8) 33 ( 2.7) 265 ( 1.7) 284 ( 1.8) 274 ( 2.2) 278 ( 2.8) 288 ( 2.8) 285 ( 2.0) GENDER Male State 48 ( 13) 25 ( 1.4) 28 ( 1.8) 20 ( 1.1) 22 ( 1.3) 35 1.8) 255 ( 1.6) 279 ( 2.3) 2e3 ( 1.8) 272 ( 2.2) 253 ( 1.9) 278 ( .7) Nation 50 ( 1.7) 20 ( 2.0) 29 ( 1.6) 19 ( 1.3) 27 ( 13) 26 ( 2.1) 255 ( 1.9) 275 ( 2.2) 264 ( 2.8) 263 ( 2.5) 256 ( 3.0) 277 ( 1.9) Female State 44 ( 1.3) 28 ( 1.7) 30 ( 1.5) 16 ( 1.1) 25 ( 1.4) 39 ( 1.7) 248 ( 1.4) 269 ( 1.5) 257 ( 1.8) 262 ( 2.3) 247 ( 1.9) 289 ( 1.1) Nation 46 ( 2.0) 26 ( 2.1) 32 ( 1.6) 18 ( 1.2) 27 ( 1.8) 33 ( 2.1) 254 ( 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 a 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), THE 1990 NAEP TRIAL STATE ASSESSMENT 129 Arizona TABLE A20 I Students' Knowledge of Using Calculators PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1 no MEP TRIAL STATE ASSESSMENT Nigh "Calculator-Use" Group Other "Calculatar-Use" Group TOTAL Pordentaapa and Proficiency Paccantaga and Proliclangzi State 44 ( 1.2) 58 ( 1.2) 206 ( 1.4) 253 ( 1.4) Nation 42 ( 1.3) 56 ( 1.3) 272 ( 1.6) 255 ( 1.5) RACE/ETHNICITY Witte State 49 ( IS) 51 ( 1.5) 275 ( 1.4) 206 ( 1$) Nation 44 ( 1.4) 58 ( 1.4) 277 ( 1.7) 263 ( 1.7) Black State 32 ( 7.0) 88 ( 7.0) Nation 37 ( 3.4) ( 3.4) 24$ ( 3.9) 231 ( 3.0) Hispanic State 38 ( 2.2) 82 ( 2.2) 249 ( 2.1) 237 ( 1.7) Nation 36 ( 4.2) 84 ( 4.2) 254 ( 4.8) 238 ( 3.0) American Indian State 34 ( 5.3) 86 ( 5.3) ".) 230 ( 2.7) Nation 29 (12.0) 71 (12.0) ( ( TYPE OF COMMUNITY Advantaged urban State 49 ( 2.7) 51 ( 2.7) 277 ( 4.3)1 268 ( 35)1 Nation 50 ( 3,$) 50 ( 3.8) 288 ( 4.9)1 275 ( 4.4)1 Disadvantaged urban State 39 ( 2.5) 81 ( 2$) 254 ( 42)1 243 ( 4.2)1 Nation 3$ ( 4.2) 62 ( 4.2) 262 ( 5.6)1 244 ( 3.9)1 Extreme rural State 57 ( 3.6) 239 ( 6.1)1 Nation 39 ( 5.8) 81 ( 5.6) 269 ( 4.4)1 248 ( 4.3)1 Other State 45 ( 2.2) 55 ( 2.2) 267 ( 1.7) 252 ( 24) Nation 42 ( 1.4) 58 ( 1.4) 271 ( 1.9) 255 ( 2.0) Molommpww, 11.11% The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency, '1" Sample size is insufficient to permit a reliable estimate (fewer than 62 students). .1 L. d 130 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A20 I Students' Knowledge of Using Calculators (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1960 NAEP TRIAL "Calculator-Us*" "Ca STATE ASSESSMENT High CiroUp Other lculator-Usa" Group TOTAL. Percentese and Proficiency Poraontaga and Prefidency State 44 ( 12) 56 ( 1.2) 206 ( 14) 253 ( 14) Nation 42( 1.3) 58 ( 1.3) 272 ( 1.6) 255 ( 1.5) PARENTS EDUCATION HS non-graduate State 04* ( 64 ( 236 ( 3.3) 2.3) Nation 34 ( 3.3) 66 ( 3.3) 246 ( 4.4) 242 ( 2.4) HS graduat State 41 ( 2.4) 59 ( 2.4) 254 ( 2.5) 246 ( 2.0) Nation 40 ( 263 ( 22) 2,0) 80 ( 249 ( 22) 1.8) Some college State 46 ( 2.6) 54 ( 2.6) 269 ( 2.4) 261 ( 2.5) Nation 48 ( 22) 52 ( 22) 277 ( 2.6) 258 ( 2.5) Cottage graduate State 51 ( 1.8) 49 ( 1.8) 278 ( 1.9) 266 ( 2.2) Nation 46 ( 2.0) 54 ( 2.0) 282 ( 2.1) 268 ( 1.9) GENDER Male State 42 ( 1.9) 58 ( 1.9) 271 ( 1.9) 255 ( 1.9) Nation 39 ( 2.0) 61 ( 2.0) 274 ( 2.0) 265 ( 2.3) Femal state 47 ( 1.9) 53 ( 1.9) 262 ( 1.6) 251 ( 1.5) Nation 46 ( 1.8) 55 ( 1.8) 269 ( 1.7) 254 ( 1.3) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. '* Sample size is insufficient to permit a reliable estimate (fewer than 62 students). THE 1990 NAEP TRIAL STATE ASSESSMENT 131 Arizomi TABLE A24 I Students' Repons Ar 44 Types of Reading Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Four Types _ TOTAL Pereentsge and Machina Percentage and Proliciancy Percentage and Prcactency State 27 ( 1.3) 33 ( 1.0) 40 ( 1.4) 248 ( 1.5) 252 ( 1.4) 270 ( 1.5) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) RACE/ETHNICITY White State 18 ( 1.4) 34 ( 1.4) 49 ( 1.8) 260 ( 1.8) 288 ( 1.5) 277 ( 1.4) Nation 16 ( 1.1) 29 ( 1.3) 56 ( 1.5) 251 ( 22) 288 ( 1.5) 276 ( 1.7) Stack State 33 ( 3.8) 42 ( 4.8) 24 ( 4.8) ( Nation 31 ( 1.9) 36 ( 22) 33 ( 2.4) 232 ( 3.2) 233 ( 3.9) 245 ( 3.3) Hispanic State 44 ( 2.8) 31 ( 2.0) 25 ( 2.3) 238 ( 1.8) 244 ( 2.21 253 ( 2.2) Nation 44 ( 3.0) 30 ( 2.4) 26 ( 2.3) 237 ( 3.4) 244 ( 4.3) 253 ( 2.4) Amorican Indian State 36 ( 3.7) 32 ( 3.6) et. ft* ) 232 ( 35)1 fff 991 Nation 29 (11.1) 40 ( 4.9) *1* ) TYPE OF COMMUNITY Advantaged urban State 1 i ( t6) 35 ( 2,8) 55 ( 3.2) 271 ( 2.4)1 280 ( 3.2)1 Nation 13 ( 3.6) I**) 26 ( ( 2.1) *Me ) 61 ( 287 ( 4.9) 3.6)1 Disadvantaged urban State 41 ( 2.9) 32 ( 1.5) 27 ( 2.5) 239 ( 3.2)1 245 ( 2.9)1 263 ( 5.7)1 Nation 32 ( 3.9) 31 ( 2.3) 37 ( 3.6) 243 ( 2.9)1 247 ( 3.7)1 257 ( 4.9)1 Extrema niraI State 32 ( 3.9) ( ) Nation 17 ( 4.9) 33 ( 3.2) 50 ( 5.1) 253 ( 4.3)1 283 ( 5.6)1 Other State 27 ( 1.9) 35 ( 1.4) 39 ( 2.4) 247 ( 2.6) 25* ( 2.5) 288 ( 2.3) Nation 22 ( 1.5) 30 ( 1.3) 48 ( 1.5) 244 ( 2.6) 259 ( 2.2) 272 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the 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). 157 132 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A24 I Students' Reports on Types of Reading (continued) I Materials in the Home PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 19410 NAEP TRIAL STATE ASSESSMENT Zero to Two Types Three Types Four Types TOTAL Percergage and Proficiency Percentage and Proficiency Percentage and Prondmicy State 27 ( 1.3) 33 1.0) 40 ( 1.4) 246 ( 1.5) 259 ( 1.4) 270 ( 1.5) Nation 21 ( 1.0) 30 ( 1.0) 48 ( 1.3) 244 ( 2.0) 258 ( 1.7) 272 ( 1.5) PARENTS EDUCATION NS non-graduate State 57 ( 4.U) 26 ( 3.2) 236 ( 2.3) 239 ( 4.4) ( *44 ) Nation 47 ( 4.0) 28 ( 3.0) 25 ( 2.8) 240 ( 3.4) 243 ( 3.3) 246 ( 3.3) HS graduate State 30 ( 2.2) 40 ( 2.2) 30 ( 2.0) 244 ( 2.5) 252 ( 2.0) 254 ( 2.4) Nation 26 ( 22) 33 ( 1.9) 40 ( 1.7) 246 ( 2.2) 253 ( 2.7) 260 ( 2.1) Some college State 24 ( 1.9) 36 ( 1.8) 41 ( 2.4) 259 ( 2.5) 283 ( 2.5) 272 ( 2.2) Nation 17 ( 1.5) 32 ( 1.7) 51 ( 2.0) 251 ( 4.0) 262 ( 2.6) 274 ( 1.9) College graduate State 13 ( 1.5) 32 ( 1.4) 55 ( 1.6) 258 ( 3.1) 268 ( 2.1) 278 ( 1.8) Nation 10 ( 0.8) 28 ( 1.8) 62 ( 2.0) 254 ( 2.8) 269 ( 2.5) 280 ( 1.8) GENDER Male State 27 ( 1.4) 4 ( 1.3) 39 ( 1.7) 249 ( 2.1) 262 ( 1.9) 274 ( 1.7) Nation 21 ( 1.5) 31 ( 1.5) 48 ( 1.4) 244 ( 2.3) 259 ( 2.1) 273 ( 2.0) Female State 27 ( 1.5) 33 ( 1,1) 41 1.6) 243 ( 1.7) 256 ( 1.5) 266 ( 1.7) Nation 22 ( 1.2) 29 ( 1.4) 49 ( 1.9) 244 ( 2.2) 258 ( 1.9) 270 ( 1.7) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students), 128 THE 1990 NAEP TRIAL STATE ASSESSMENT 133 Arizona TABLE A25 I Students' Reports on the Amount of Time Spent I Watching Television Each Day PERCENTAGE OF STUDENTS AHD AVERAGE MATHEMATICS PROFICIENCY 1990 NAEP TRIAL STATE ASSESSMENT One Hour or Lass Two Hours Three Hours . Four to Five Hours .. Six Hours or More TOTAL State Nation RACE/ETHNICITY Percentage and Pro& tem 15 ( 0.8) 265 ( 24) 12 ( 0.8) 26a ( 2.2) 17 ( 1.1) 277 ( 2$) 13 ( 1.0) 276 ( 2.5) 5 ( 2.3) - 6 ( 0.8) INF* Mk* ) 12 ( 1.4) 240 ( 3.2) 14 ( 2.4) 0*. i) 17 ( 2.5) *** 13 ( 5.0) ***) 16 ( 2.0)) 18 1.4) *4 10 ( 2.4)) 9 (1.2)- 16 (1.5)) 14 3.3) *- -** 16 ( 1.4) 266 ( 3.8) 12 ( 1.0) 268 ( 2.6) Percentage and Pro Wan 23 ( 0.8) 264 ( 1A) 21 ( 0.9) 2ea ( 1.8) 25 ( 1.1) 275 ( 1.6) 23 ( 12) 275 ( 2.2) ( 13 ( 1.7) 239 ( 7.0) 21 ( 1.6) 246 ( 2.3) 20 ( 2$) 245 ( 3.2) 24 ( 4.1) - ,) 17 ( 8.4) *** ( 25 ( 2.0) 278 ( 4.9)1 25 ( 4.3) it ( ) 17 ( 1.5) - --) 17 ( 3.1) 250 ( 4.0)1 22 ( 0.8),) 19 ( 2.6) . ( Hr.) 23 ( 1.3) 263 ( 2.6) 21 ( 1.0) 269 ( 2.3) Percentage and Pre &dem 24 ( 0.9) 263 ( 1.6) 22 ( 0.8) 265 ( 1.7) 25 ( 1.1) 272 ( 1.4) 24 ( 1.1) 272 ( 1.9) 17 ( 2.1) 239 ( 5.0) 25 ( 1.8) 248 ( 2.2) 19 ( 2.1) 242 ( 5.8) ft** ( ) 21 (103) «Hi) 30 ( 2.9) 280 ( 2.2) 21 ( 1.8) - -.) 28 ( 2.3) 253 ( 3.7)1 19 ( 2.1) 285 ( 5.0)1 25 ( 23) **I.) - frfrfr 24 ( 1.2) 261 ( 2.7) 23 ( 1.2) 265 ( 2.1) Percantege end Preeciency 25 ( 0.9) 256 ( 1$) 28 ( 1.1) 260( 1.7) 24 ( 1.2) 266 ( 1.6) 27 ( 1.4) 267 ( 1.7) ( 5.6) .44 ....) 32 ( 1.8) 239 ( 4.0) 27 ( 1.7) 243 ( 2.0) 31 ( 3.1) 247 ( 3$) 25 ( 2.4) , -- ) ...) 22 ( 2.6) ( 30 ( 4.3) 4-4,4) 27 ( 3.1) 248 ( 3.9)1 34 ( 2.4) 251 ( 4.7)1 28 ( 2.6) -.) 26 ( 2.7) 256 ( 3.6)1 25 ( 1.4) 255 ( 2.0) 27 ( 1.2) 259 ( 2.2) Percentapp and Pro Odom 12 ( 0.6) 245 ( 2.0) 16 ( 1.0) 245 ( 1.7) 9 ( 04) 257 ( 2.5) 12 ( 1.2) 253 ( 2.6) 31 ( 6.5) 11441 .44) 32 ( 22) 233 ( 25) 15 ( 1.4) 234 ( 24) 17 ( 1.7) ria ( 3.8) 13 ( 2.2) - ) 22 ( 8.4) 444) 7 ( 2.4) -- it* ) 6 ( 2.0) 17 ( 1.9) ( 4," 20 ( 3.2) 238 ( 4.5)1 11 1.8) - 4-4.) 19 ( 3.8) **ID Hi* ) 12 ( 0.9) 247 ( 2.8) 17 ( 1.4) 248 ( 2.5) White State Nation Slack State Nation Hispanic State Nation American Indian State Nation TYPE OF COMMUNITY Advantaged urbsn State Nation Disadvantaged urban State Nation Extreme rural State Nation Othaf State Nation The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. ** Sample size is Msufficient to permit a reliable estimate (fewer than 62 students). 1 () t.% 11, 134 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A25 Students' Reports on the Amount of Time Spent (continued) I Watching Television Each Day PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT One Hour or Less Two Hours - Three Hours Four to Five Hours Six Hours or More TOTAL Percentage and Pronciency Percentage and Proadeetcy Percentage and Psvadency . Percentage and ProNciency Percentage and Proeciency State 15 ( 0.6) 23 ( 0.8) 24 ( 0.9) 25 ( 0.9) 12 ( 0.6) 265 ( 2.5) 264 ( 1.4) 263 ( 1.6) 258 ( 15) 245 ( 2.0) Nation 12 ( 0.6) 21 ( 0.9) 22 ( 0.8) 2$ ( 1.1) 16 ( 1.0) 269 ( 2.2) 268 ( 1.8) 265 ( 1.7) 260 ( 1.7) 245 ( 1.7) PARENTS' EDUCATION HS non-graduate State 13 ( *** 2.2) 22 ( *** 2.7) ***) 20 ( .*** 2.3) 27 ( 236 ( 2.0) 3.7) 19 ( H ( 2.6) *4.) Nation 12 ( **** ( 2.2) *41 20 ( *** 3.1) ***) 21 ( 2.8) 4.1 28 ( 244 ( 2.9) 3.2) 20 ( 2.4) ***) HS graduate State 13 ( 1.4) 21 ( 1.8) 24 ( 2.2) 28 ( 2.1) 14 ( 1.9) 2.51 ( 3.4) 252 ( 2.7) 253 ( 2.8) 251 ( 2.4) 242 ( 2.9) 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 ( 23) 248 ( 3.0) Same college State 12 ( 271 ( 1.8) 4.5) 27 ( 287 ( 2.2) 3.0) 26 ( 272 ( 2.0) 3.0) 25 ( 258 ( 1.8) 2.6) 10 ( ( 1.1) .01 Nation 10 ( *** 1.4) ***) 25 ( 275 ( 2.4) 2.7) 23 ( 289 ( 2.8) 3.5) 28 ( 287 ( 2.2) 2.5) 14 ( 242 ( 15) 3.4) College graduate State 19 ( 1.5) 25 ( 1.3) 25 ( 1.4) 23 ( 1.3) 8 ( 0.9) 279 ( 2.8) 278 ( 2.1) 273 ( 2.1) 268 ( 2.3) 251 ( 3.3) Nation 17 ( 1.3) 22 ( 1.6) 23 ( 1.1) 25 ( 1.5) 12 ( 1.1) 282 ( 2.8) 280 ( 2.5) 277 ( 2.2) 270 ( 2.4) 255 ( 3.2) GENDER Male State 13 ( 1.0) 24 ( 1.1) 23 ( 1.2) 25 ( 1.2) 14 ( 0.9) 269 ( 3.3) 267 ( 1.9) 266 ( 2.1) 260 ( 1.9) 250 ( 2.5) Nation 11 ( 0.9) 22 ( 1.2) 22 ( 1.0) 28 ( 1.3) 17 ( 1.5) 289 ( 3.3) 287 ( 2.6) 207 ( 2.2) 262 ( 2.1) 248 ( 2.5) Female State 18 ( 1.3) 23 ( 13) 25 ( 1.3) 25 ( 1.1) 10 ( 0.8) 262 ( 2.7) 262 ( 1.9) 260 ( 1.9) 252 ( 2.0) 238 ( 2.9) Nation 14 ( 1.1) 20 ( 1.3) 23 ( 1.4) 28 ( 1.6) 15 ( 1.2) 269 ( 2.8) 289 ( 2.2) 264 ( 1.8) 258 ( 1.9) 241 ( 2.2) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 140 THE 1990 NAEP TRIAL STATE ASSESSMENT 135 Arizona TABLE A26 I Students' Reports on the Number of Days of I School Missed PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1900 NAEP TRIAL STATE ASSESSMENT None One or Two Days Three Days or Mors _ TOTAL Portontege and Proficiency Percentege and Proficiency Perceniago end Padden, State 40 ( 1.0) 34 ( tO) 26 ( 1.0) 264 ( 1A) 282 ( 1.5) 252 ( 13) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 265 ( 1.8) 266 ( 1.5) 250 ( 1.9) RACE/ETHNICITY white State 41 ( 1.3) 34 ( 1.3) 25 ( 1.1) 273 ( 1.7) 273 ( 1.3) 265 ( 1.4) Nation 43 ( 1.2) 34 ( 1.2) 23 ( 1.2) 273 ( 1.6) 272 ( 1.7) 258 ( 2.1) Black State 48 ( 114rft 5.5) ***) 33 ( *44 4.9) **) 22 ( 4.0) *1111 Nation 56 ( 21 ( 1.8) 23 ( 2.5) 240 ( 3.2) 240 ( 4.1) 224 ( 3.5) Hispanic State 33 ( 2.1) 34 ( 1.7) 28 ( 1.9) 247 ( 1.6) 244 ( 2.1) 236 ( 2.3) Nation 41 ( 3.3) 32 ( 2.2) 27 ( 2.6) 245 ( 4.6) 250 ( 3.3) 235 ( 3.1) Anurican Indian State 32 ( 5.3) ** ( *") ***) Nation 23 ( 6.6) 38 ( 5.2) ) ( "*) TYPE OF COMMUNITY Advantaged urban State 41 ( 2.3) 35 ( 2.8) 24 ( 3.4) 278 ( 2.7)1 274 ( 23)1 270 ( 3.5)1 Nation 47 ( 2.3) 38 ( 2.6) 15 ( 3.7) 284 ( 4.4)1 279 ( 4.5)1 Disadvantaged urban State 36 ( 2.2) 33 ( 2.4) 32 ( 3.2) 250 ( 3.8)1 251 ( 5.2)1 243 ( 5.5)! Nation 42 ( 3.3) 26 ( 1.8) 32 ( 2.7) 254 ( 3.7)1 256 ( 4.2)1 238 ( 6.3)! Fathom* rural State 35 ( 4.0) ( Nation 43 ( 4.4) 32 ( 4.2) 257 ( 41)1 264 ( 5.8)1 fa* ( f ) Other State 41 ( 1.6) 34 ( 1.3) 25 ( 1.2) 283 ( 1.9) 260 ( 2.3) 251 ( 2.9) Nation 45 ( 1.3) 32 ( 1.1) 23 ( 1.1) 265 ( 2.2) 266 ( 1.9) 251 ( 2.4) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within -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). 136 1 1 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A26 I Students' Reports on the Number of Days of (continued) I School Missed PERCENT/4E OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1090 NAEP TRIAL STATE ASSESSMENT None One or Two Days Tbree Days or More TOTAL Percentage and Proficiency Percentage and Proficiency Percentage and Proficiency State 40 ( 1.0) 34 ( 1.0) 20 ( 1.0) 264 ( 1.4) 262 ( 1.5) 252 ( 1.7) Nation 45 ( 1.1) 32 ( 0.9) 23 ( 1.1) 285 ( 1.8) 266 ( 1.5) 250 ( 1.9) PARENTS' EDUCATION HS non-graduate State 30 ( 3.0) 32 ( 3.5) 38 ( 3.4) 247 ( 3.6) 245 ( 3.8) 232 ( 2.5) Nation 36 ( 3.2) 26 ( 3.1) 38 ( 3.5) 245 ( 3.0) 249 ( 3.3) 237 ( 3.1) HS graduate State 39 ( 2.1) 35 ( 2.0) 26 ( 2.0) 253 ( 2.1) 252 ( 22) 244 ( 2.6) Nation 43 ( 2.1) 31 ( 1.9) 27 ( 1.9) 255 ( 2.0) 257 ( 2.6) 249 ( 2.4) Some college State 39 ( 2.0) 32 ( 2.1) 30 ( 2.2) 269 ( 2.5) 267 ( 2.2) 260 ( 2.3) Nation 40 ( 1.8) 37 ( 1.6) 23 ( 1.6) 270 ( 3.0) 271 ( 2.5) 253 ( 3.1) College graduate State 43 ( 1.5) 36 ( 1$) 22 ( 1.4) 275 ( 2.0) 273 ( 2.0) 265 ( 2.4) Nation 51 ( 1.6) 33 ( 1.2) 16 ( 1.3) 275 ( 2.1) 277 ( 1.7) 265 ( 3.1) GENDER Male State 41 ( 1.4) 35 ( 1.2) 24 ( 1.3) 267 ( 1.8) 263 ( 1.8) 256 ( 2.3) Nation 47 ( 1.6) 31 ( 1.4) 22 ( 1.4) 266 ( 2.0) 267 ( 2.1) 250 ( 2.6) Femal State 39 1.3) 33 ( 1.4) 2$ ( 1.4) 260 ( 1.5) 260 ( 2.0) 249 ( 1.9) Nation 43 ( 1.4) a2 ( 1.1) 25 ( 1.3) 264 ( 2.3) 260 ( 1.7) 250 ( 1.8) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within 2 standard errors of the estimate for the sample. 1 4 2 THE 1990 INAEP TRIAL STATE ASSESSMENT 137 Arizona TABLE A27 I Students' Perceptions of Mathematics PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY MO titAEP TRIAL STATE ASSESSMENT StronglY Agroo Ag loo Undecided, Disagree, Strongly Maine TOTAL and Pro *dewy Percentage and ProAdency Percentage and Preeiclency State 25 ( 1.0) 49 ( 0,9) 26 ( 1.1) 271 ( 1.5) 200 ( 1.3) 250 ( 1.4) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 12) 271 ( 1.9) 262 ( 1.7) 251 ( 1,8) RACE/ETHNICITY White State 27 ( 1.2) 50 ( 1.4) 23 ( 1.4) 280 ( 1.8) 271 ( 1.3) 261 ( 1.4) Nation 26 ( 1.6) 48 ( 1.3) 26 ( 1,5) 279 ( 2.0) 272 ( 10) 257 ( 2.0) Mack State 32 ( 4.5) 47 ( 5.4) 20 ( 4.4) Nation 32 ( 2.5) 52 ( 2.3) 18 ( 1.9) 247 ( 4.1) 233 ( 3.3) 227 ( 4.2) Hispanic State 21 ( 1.5) 49 ( 1.3) 31 ( 1.7) 255 ( 2.1) 242 ( 1.7) 237 ( 2.0) Nation 24 ( 2.5) 48 ( 2.6) 28 ( 2.1) 257 ( 5.5) 244 ( 2.2) 238 ( 3.8) American Indian State 22 ( 3.1) 46 ( 3.3) 32 ( 4.1) ( ***) 238 ( 2.5)1 Nation 23 ( 7.4) 48 (14.9) *** ( "b) ( .") TYPE OF COMMUNITY Advantaged urban State 29 ( 2.8) 48 ( 3.7) 23 ( 2.6) 286 ( 2.7)1 275 ( 2.5)1 Nation 17 ( 3.2) 55 ( 2.4) 28 ( 42) 280 ( 4.1)1 Disadvantaged urban State 22 ( 2.1) 50 ( 2.5) 28 ( 3.4) 249 ( 4.0)1 241 ( 4.8)1 Nation 26 ( 2.9) 4$ ( 2.9) 26 ( 32) 280 ( 56)1 249 ( 4.6)1 240 ( 4.5)1 Extrema rural State 50 ( 5.6) 249 ( 3.9)1 Nation 34 ( 2.8) 49 ( 2.2) 17 ( 1.4) 270 ( 3.9)? 252 ( 4.1)1 Other State 26 ( 1.6) 4$ ( 1.4) 26 ( 1.7) 271 ( 2.3) 258 ( 1.9) 249 ( 2.5) Nation 27 ( 1.4) 48 ( 1.2) 25 ( 1.4) 271 ( 2.4) 263 ( 2.2) 250 ( 1.9) The standard errors of the estimated statistics appear in parentheses. It can be said with about 95 percent certainty that, for each population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. ! Interpret with caution -- the nature of the sample does not allow accurate determination of the variability of this estimated mean proficiency. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 3 138 THE 1990 NAEP TRIAL STATE ASSESSMENT Arizona TABLE A27 I Students' Perceptions of Mathematics (continued) I PERCENTAGE OF STUDENTS AND AVERAGE MATHEMATICS PROFICIENCY 1990 ::AEP TRIAL STATE ASSESSMENT - _ Si0fl94Y Ar Ares Undecided, Disagree, Strongly Diugree TOTAL Percentage and Proficiency Parentage d Prei !dewy Parentage and Prelicieecy State 25 ( 1.0) 49 ( 0.9) 28( 1.1) 271 ( 1.5) 290 ( 1.3) 250 ( 1A) Nation 27 ( 1.3) 49 ( 1.0) 24 ( 1.2) 271 ( 1.9) 262 ( 1.7) 251 ( 1.8) PARENTS EDUCATION HS non-graduate State 20 ( 2.7) 53 ( 3.6) 27 ( 3.4) ( 4911 239 ( 3.1) 237 ( 3.7) Nation 20 ( 2.6) ***) 50 ( 243 ( 3.3) 2.6) 30 ( 238 ( 3.6) 4.3) HS graduate State 24 ( 1.8) 50 ( 2.3) 26 ( 2.1) 280 ( 3.0) 250 ( 1.8) 243 ( 2.4) Nation 27 ( 2.1) 47 ( 2.3) 26 ( 2.0) 282 ( 2.7) 255 ( 2.3) 245 ( 2.4) Some collage State 29 ( 22) 48 ( 2.2) 26 ( 2.1) 274 ( 2.8) 267 ( 2.0) 255 ( 2.7) Nation 23 ( 2.5) 47 ( 2.4) 25 ( 1.8) 274 ( 3.1) 267 ( 1.9) 258 ( 32) College graduate State 28 ( 1.6) 52 ( 1.7) 20 ( 1.8) 282 ( 2.2) 271 ( 1.7) 263 ( 2.6) Nation 30 ( 2.3) 51 ( 1.8) 19 ( 1.8) 280 ( 2.4) 274 ( 2.2) 268 ( 24) GENDER Male State 27 ( 1.3) 48 ( 1.4) 25 ( 1.5) 274 ( 2.1) 264 ( 1.6) 253 ( 1.8) Nation 28 ( 1.5) 48 ( 1.2) 24 ( 1.4) 273 ( 2.3) 263 ( 2.0) 251 ( 2.4) Female State 24 ( 1.3) 50 ( 1.6) 2$ ( 1.5) 269 ( 1.9) 258 ( 1.5) 247 ( 1.7) Nation 26 ( 1.7) 50 ( 1.7) 25 ( 1.9) 289 ( 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 ± 2 standard errors of the estimate for the sample. *** Sample size is insufficient to permit a reliable estimate (fewer than 62 students). 1 ,4 4 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 US. Department of Education. Emerson Elliott, NCES Acting Conunissioner, 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 destrve 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 Eugene Johnson and Donald Rock. John Barone managed the data analysis activities; Jules Goodison, the operational aspects; Walter MacDonald and Chancey Jones, test development; David Hobson, the fiscal aspects; and Stephen Koffler, state services. Sampling and data collection activities were carried out by Westat under the supervision of Renee Slobasky, Keith Rust, Nancy Caldwell, and the late Morris Hansen. The printing, distribution, and processing of the materials were the responsibility of NCS, under the direction of John O'Neill and Lynn Zaback. The large number of states and territories participating in the first Trial State Assessment introduced many unique challenges, including the need to develop 40 different reports, customized for each jurisdiction based on its characteristics and the results of its assessed students. To meet this challenge, a computerized report generation system was built, combining the speed and accuracy of computer-generated data with high resolution text and graphics normally found only in typesving environments. Jennifer Nelson created the system and led the computer-based development of the rftrt. John Mauro oversaw the analyses for this report. John Ferris, David Freund, Bruce Kaplan, Edward Ku lick, and Phillip Leung collaborated to generate the data and perform analyses. They were assisted by Drew Bowker, Laura McCamley, and Craig Pizzuti. Debra Kline coordinated the efforts of the data analysis staff. Stephen Koffier wrote the text for the report. Kent Ashworth was responsible for coordinating the cover design and final printing of this report. Special thanks are also due to many individuals for their invaluable assistance in reviewing the reports, especially the editors who improved the text and the analysts who checked the data. ,) U. S. GOVERNMENT PRINTING OFFICE : 1991 0 - 293-275 (BX.2) QL 3