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,`~.~.~.r ''in BACKGROUND PAPER FOR THE CONVOCATION What Is Bth Oracle Mathematics: A Look from NAEP John Dossey Mathematics Department, Illinois State University One of the few sources that math- ematics educators, or policy makers, have upon which to base judgments about Sth grade is the data from the National Assessment of Educational Progress in Mathematics (NAEP). This federal large-scale assessment has been collecting data about the mathematical experiences of the eight graders (or 13- year olds), as well as data on fourth graders (or 9-year-olds) and twelfth- graders (or 17-year olds), since 1973. These random samples of the nation's students at these grade/age levels are taken to provide a picture of the status of mathematics education at critical junctures in their schooling. The national NAEP assessment, has been given in 1973, 197S, 1983, 1986, 1990, 1992, and 1996. There is a NAEP Trend assessment that employs forms of the 1973 examination to provide a trend knowledge relative to basic skills and knowledge in school mathematics over time since 1973. This test was given in the same years as NAEP, as well as in 1994. ACHIEVEMENT RESULTS National NAEP Achievement Results What kind of picture do the results of these assessments paint? First, they show that our eighth grade students have ma(le consistent progress over time in mathematics. The achievement trend on national NAEP is split into two sections, as the nature of the NAEP assessment was change(1 in 1990 by the National Assessment Governing Board to renect more open-en(le(1 problem solving anti to narrow the number of (lifferent content areas in mathematics that were to be assessed. Since that time, the assessment has focused on student work in Number anti Opera- tions, Measurement, Geometry, Alge- bra, anti Data Analysis/Statistics/
Probability. The mean student scores on the NAEP assessment from 1978 through 1986 were developed on ran- dom samples of the nation's 9-, 13-, and 17-year olds. The results for 13-year- olds showed a consistent picture, with improvement for students in the last two assessments given under the framework (I)ossey, Mullis, I~in(lquist, & Cham- bers, 19881. The scores for these assessments are shown in Table 1. Table 2 shows the scores for the new NAEP scale for Sth graders initiated in 1990 with the first assessment to be given under the new NAEP framework. Note that the scores shown in Table should not be compared with those Table ~ . NAEP Trencl Scores for ~ 3-year-olcls for National NAEP: ~ 973-] 986 Assessment Year National Mean 1 973 1 978 1 983 1 986 266 26A 269*t 269*t *t indicates that the score is significantly greater than the score in 1978 at the 0.05 level. Table 2. NAEP Trencl Scores for ~ 3-year-olcls for National NAEP: ~ 990-] 996 Assessment Year National Mean 1990 1992 263 268* 1996 272*t * indicates that the score is significantly greater than the score in 1990. *t indicates that the score is significantly greater than the score in 1992. APPE N DIX 6 shown in Table 2 as they are from two different scales, representing different content and different formats of exami- nations. These results show a steady and consistent improvement from 1990 through 1996. An analysis of the scores in Table 2 indicate a strong and significant in- crease in scores over the six year period of time. Comparing the increases to the benchmark of 10 NAEP score scale points equals one gra(le-placement level of progress, the (lata suggest that the nation's eighth gra(lers' achievement has increase(1 essentially one gra(le placement since 1990! This is an indica- tion of goo(1 things happening in the school classroom (Reese, Miller, Mazzeo, & Dossey, 19971. NAEP TREND ASSESSMENT RESULTS One might look at the above results anti have a feeling that the improve- ment in achievement is really only since 1990, as there was a dip in 1978 in the (lata anti that we essentially ma(le up in 1983 and 1986. Besides this. critics of school reform anti change in mathematics education might also in(licate concern over the change nature of the test anti fee} that the "basics" have been left out of the new NAEP assessment starting in 1990
Table 3. NAEP Trencl Assessment Scores for] 3-year-olcls for Trencl NAEP: ~ 973-] 996 Assessment Year 1973 1978 1983 1986 1990 1992 199A 1996 National Mean 266 26A 269 269 270*t 273*t 27~*t 27~*t *I indicates that the score is significantly greater than the score in 1973 at the 0.05 level. since it has been somewhat loosely based on the NCTM Standards. It was just this concern that the Department of Education and NAGB had in deciding at the inception of NAEP to continually give the 1973 examination to random samples of 13- year-olds over time as a measure of change from a baseline examination. This examination was, and is, heavily grounded in paper-and-pencil skills and knowledge that was considered basic in 1973, a period marked by "back-to-the- basics" following the New Mathematics of the 1960s. Table 3 shows student performance on this examination over time. Again note, one should not compare the scale numbers for this assessment with the previous two, as it is a third different assessment. However, the data here, together with the two previous sets of assessment data, suggest that the mathematics achievement, be it on new content, or on traditional content, is improving over time (Campbell, VoelkI, & Donahue, 19971. None of the assessment results suggests that the "baby has been thrown out with the bathwater" in the move to reform school mathematics. BACKGROUND PAPER ON NAEP OTHER NAEP RESULTS In addition to the achievement infor- mation, the National NAEP program collects information from the students relative to their beliefs anti (1emographic backgrounds, from their teachers relative to their instruction and their education, and from their schools about the organization and curriculum of the school program. These (lata permit the description of the context in which these students encounter mathematics and the resources that they have as they approach the study of mathematics. Course Taking Data from the 1996 NAEP assessment indicated that 81 percent of the nation's eighth graders attended a school that offered the stu(ly of Algebra ~ as an option in the eighth gra(le curriculum. Further, the data indicated that 25 percent of the nation's eighth graders actually enrolled in Algebra ~ as their eighth grade math- ematics course. The remaining students either participated in a classroom where mathematics was taught from an eighth grade text from a basal K-S curriculum series (43°/O), participated in a preaIgebra
class (26%), or were in some other form of mathematics instruction (6%) (Hawkins, Stancavage, & Dossey, 19981. Calculator Usage Data from the 1996 assessment indicated that 80 percent of the nation's eighth graders have access to school- owned calculators. This percentage was the same whether students were in Algebra i, preaIgebra, or eighth-gra(le mathematics. No significant difference was noted between the performance of the students having and not having access to school-owned calculators (Hawkins, Stancavage, & Dossey, 19981. Teacher Backgrounds The teaching of eighth-grade math- ematics falls between elementary and secondary preparation in many states, as few states have a special middle school/ junior high school certification level. Data from the teachers of the students in the 1996 NAEP sample indicated that 62% of these teachers either had degrees in mathematics (49°/0) or mathematics education (13%~. The remaining teach- ers either had degrees in education but not mathematics or mathematics e(luca- tion (32%), or had degrees in some other discipline (7°/01. Analysis of the student achievement of the students of these four groups of teachers by collegiate major in(licate(1 that the students whose teach- ers hall (1egrees in mathematics outper APPE N DIX 6 formed the students of teachers whose degrees were either in education abut not mathematics education or in another discipline. The students whose teachers had degrees in mathematics education had achievement scores that were not significantly (lifferent from the achieve- ment of students whose teachers had degrees in either mathematics or educa- tion/other (liscipline (Hawkins, Stancavage, & Dossey, 19981. Professional Development arc! KnowIecIge of the NCTM StancIarcIs Eighth-grade teachers reported that on average 26% of them ha(1 ha(1 less than 6 hours of professional (levelop- ment in mathematics during the past year, 29% had from 6 to 15 hours of professional development in mathemat- ics during the past year, and 45% had over 15 hours of professional develop- ment in mathematics during the past year. When one considers that 15 hours of professional development is less than two working days' time, one recognizes that over half of the nation's eighth- grade students are being taught by teachers who are receiving precious little opportunity for growth in their major teaching field. Teachers were also asked about the level of knowledge they felt they had of the NCTM Curriculum and Evaluation Standards for School Mathematics
(NCTM, 19891. The teachers of 16% of the students said that they felt they were very knowledgeable, 32% were knowl- edgeable,33% somewhat knowledgeable, and 19% reported having little or no knowledge of the Standards. Analysis of the mean achievement scores of students related to these four groups of teachers indicated that students of teachers who reported being knowledgeable or very knowledgeable of the Standards per- formed significantly higher than those of teachers reporting little or no knowledge of the Standards. However, one is unable to determine the cause for this difference. It may be in hiring practices of districts, or that some districts have more resources, give more professional development, or pay higher salaries (Hawkins, Stancavage, & Dossey, 19981. Performance in Content Sub- Areas When students' achievement work is examined by content sub-areas, their performance in each area showed a significant increase from 1992 to 1996. The sub-areas and 1996 achievement scores for each are as follows: Number Sense, Properties, and Operations (274), Measurement (270), Geometry and Spatial Sense (269), Data Analysis/ Statistics/Probability (272), and Algebra and Functions (2731. Like the results from TIMSS, the lowest performance areas were Geometry and Measurement BACKGROUND PAPER ON NAEP (Mitchell, Hawkins, Jakwerth, Stancavage, & Dossey, 19991. Item Types arc! Special StucIies The items in the 1996 NAEP were approximately distributed as follows: 55% multiple choice, 38% short student constructed answer, and 7% extended student constructed answer format. Overall it was expected that students would have spent about 40% of their response time working on items that called for student constructed re- sponses of one type or another. Results of the testing showed improvement on students' abilities to construct answers to questions in 1996 over prior years. This was an in(lication that communica- tion and reasoning are playing greater roles in classroom assessment pro- grams across the nation. However, when one looks at the results of student performance on extended student constructed response items, graded by a 5 point rubric, one sees that there is still considerable room for improve- ment, as few students achieved the highest levels of score on these items. As part of the 1996 assessment, eighth-grade students were also given a block of items where the context for the block was common, although the actual items were locally independent that is, no item's answer depended on the answer to another item. Student perfor- mance on these items, including the
extended constructed response items tended to be slightly higher than that on similar format items in the regular NAEP. This may indicate that the changing of contexts within regular NAEP from item to item may slightly suppress student performance levels, or alternatively, maintaining a context helps students develop a positive focus (Hawkins, Mitchell, Stancavage, & Dossey, in press). Summary While this is but a brief overview of teh eighth-grade results Tom 1996 NAEP, these data and results provide a gestalt for the context and nature of eighth-grade students' achievement patterns at present. A thorough reading of the NAEP reports wait provide an even more complete picture of eighth- grade mathematics in the United States today. APPE N DIX 6 References Campbell, I.R, Voelkl, K.E., & Donahue, P.L (1997~. NAEP 1996 Trends in Academic Progress. Washington, DC: National Center for Education Statistics. Dossey, J.A., Mullis, I.V.S., Lindquist, M.M., & Chambers, D.L. (1988~. The Mathematics Report Card: Are We Measuring Up? Princeton, NI: Educational Testing Service. Hawkins, E.F., Mitchell, J.H., Stancavage, F.B., & Dossey, J.A. (in press). Focused Studies in the NAEP 1996 Mathematics Assessment: Findings from the National Assessment of Educational Progress. Washington, DC: National Center for Education Statistics. Hawkins, E.F., Stancavage, F.B., & Dossey, J.A. (1998~. School Policies and Practices Affecting Instruction in Mathematics: Findings from the National Assessment of Ed ?Y cational Progress. Washington, DC: National Center for Educa- tion Statistics. Mitchell, J.H., Hawkins, E.F., Jakwerth, P.M., Stancavage, F.B., & Dossey, J.A. (1999~. Staidest Work and Teacher Practices in Math- ematics. Washington, DC: National Center for Education Statistics. Nationa Council of Teachers of Mathematics. (1989~. Cavrric?`l?`m and Evaluation Standards for School Mathematics. Reston, VA Author. Reese, C.M., Miller, KE., Mazzeo, J., & Dossey, I.A. (1997~. NAEP 1996 Mathematics Report Card for the Nation and the States. Washing- ton, DC: National Center for Education Statistics.