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Education Statistics Quarterly
Vol 2, Issue 1, Topic: Elementary and Secondary Education
Estimation Skills, Mathematics-in-Context, and Advanced Skills in Mathematics
By: Julia H. Mitchell, Evelyn F. Hawkins, Frances B. Stancavage, and John A. Dossey
 
This article was excerpted from Chapter 1 of the report of the same name. The sample survey data are from the NAEP
 
 

For more than a quarter of a century, the National Assessment of Educational Progress (NAEP) has been the only nationally representative and continuing assessment of what students in the United States know and can do in various academic subjects. In addition to the main NAEP assessment, NAEP periodically conducts special studies focused on areas of interest to educators and others. Topics for some of these studies arise as a result of how students performed on NAEP; others are generated simply from research questions about teaching, learning, and assessment of student achievement. This report focuses on studies in mathematics; special studies have also been conducted in, for example, reading and writing.

Studies covered by this report

This report presents information from three special studies conducted as part of the NAEP 1996 Mathematics Assessment: the Estimation Study, the Study of Mathematics-in-Context (also referred to as the Theme Study), and the Study of Students Taking Advanced Courses in Mathematics (referred to as the Advanced Study). The Theme Study and the Advanced Study were administered for the first time in 1996. The Estimation Study, on the other hand, had been administered twice before, in 1990 and 1992.

Audience and purpose of this report

This report is intended primarily for mathematics educators and others concerned with mathematics education, such as curriculum specialists, teachers, and university faculty in schools of education. The three studies reported here were designed to provide greater detail on how students perform on particular types of mathematics questions.

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The first study was designed to explore students' skills in estimation. It was implemented at three grade levels and was the only one of the studies that provided trend information. Findings from the Estimation Study include the following:

  • Although there has been significant improvement in mathematics performance overall since 1990 at all grade levels, the trend for student performance in Estimation over the 6 years since the inception of the Estimation Study in 1990 is less clear (table A).

  • Student performance in Estimation at grades 4 and 12 was stronger in 1996 than in 1990.

  • Student performance in Estimation at grade 8 appears to be level across the 3 assessment years.
Table A. Average scale scores for National NAEP and Estimation Studies, grades 4, 8, and 12: 1990, 1992, and 1996

Table A.- Average scale scores for National NAEP and Estimation Studies, grades 4, 8, and 12: 1990, 1992, and 1996

*Significant difference from 1990.

Significant difference from 1992.

NOTE: Because the Estimation Study was scaled separately from the main mathematics assessment, it is not appropriate to make direct comparisons of the average scale values obtained in a given year across the two scales.

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Assessment of Educational Progress (NAEP) 1990, 1992, and 1996 Mathematics Assessments. (Originally published as table 2.4 on p. 18 of the complete report from which this article is excerpted.)

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The Theme Study was administered at three grade levels and was designed to assess problem-solving abilities within contexts that allow students to make connections across mathematics content areas. Each student was given a block of questions centered around a single theme. For example, one fourth-grade Theme block was about planning a Butterfly Booth for the school's science fair. Of the six questions posed, one was classified as measuring Procedural Knowledge; the remaining five were classified as measuring Problem-Solving abilities. Questions were designed to assess content in four content strands: Number Sense, Properties, and Operations; Measurement; Geometry and Spatial Sense; and Algebra and Functions. In addition to solving the problems, students were generally asked to provide explanations of their answers, using mathematical computations, drawings, or words.

Findings from the Theme Study include the following:

  • At the fourth-grade level, with the exception of the first question, most students attempted to answer the questions posed, even though large percentages produced responses that were scored as "incorrect." Although not definitive, this may be evidence that the thematic context of the block of questions encouraged students' attention to the task of solving problems, even ones that proved to be difficult for most students.

  • At grade 8, unlike grade 4, many students did not attempt to answer the more complex questions that required them to write explanations or apply concepts in problem settings.

  • The response rate to the Theme questions at grade 12 was somewhere between the rates observed for grades 4 and 8, with most questions being attempted by at least 90 percent of the students.

  • At all grade levels, students appeared to have difficulty with complex multistep problems, even those that required only simple computational skills at each step of the problem.

  • At all grade levels, many students seemed to lack the mathematical knowledge needed to solve problems. Other students, however, appeared to understand the underlying mathematics but provided incorrect or incomplete responses as a result of carelessness, inexperience in writing out solutions to problems, or confusion over the wording of the question.

  • At all grade levels, no positive relationship was seen between student performance on the Theme blocks and the frequency with which students engaged in writing a few sentences about how to solve a mathematics problem, or engaged in writing reports or doing mathematics projects (tables B, C, and D).
Table B. Average percentage correct scores by Theme block, selected characteristics, and student responses, grade 4: 1996

Table B.- Average percentage correct scores by Theme block, selected characteristics, and student responses, grade 4: 1996
#Estimate too small to report.

NOTE: Because results from the Theme Study did not lend themselves to development of an achievement scale, results are reported simply in terms of percentages of questions that students answered correctly.

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Assessment of Educational Progress (NAEP) 1996 Mathematics Assessment. (Originally published as table 3.3 on p. 33 of the complete report from which this article is excerpted.)

Table C. Average percentage correct scores by Theme block, selected characteristics, and student responses, grade 8: 1996

Table C.- Average percentage correct scores by Theme block, selected characteristics, and student responses, grade 8: 1996
#Estimate too small to report.

NOTE: Because results from the Theme Study did not lend themselves to development of an achievement scale, results are reported simply in terms of percentages of questions that students answered correctly.

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Assessment of Educational Progress (NAEP) 1996 Mathematics Assessment. (Originally published as table 3.12 on p. 70 of the complete report from which this article is excerpted.)

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The Advanced Study was administered at grades 8 and 12 and was designed to provide students who were taking or had taken advanced courses in mathematics an opportunity to demonstrate their full mathematical proficiency. Findings from the Advanced Study include the following:

  • Students participating in the Advanced Study differed from those who did not qualify for the study in that they tended to come from homes providing a strong-er educational context, both in materials (newspapers, books, encyclopedias, magazines, etc.) and in level of parental education. In addition, based on their participation in Title I programs or qualification for the federal Free/ReducedPrice Lunch program, fewer Advanced Study students appeared to come from low-income homes.

  • As would be expected, students at both grade levels who met the criterion for inclusion in the Advanced Study performed substantially better than other students on the main NAEP mathematics assessment.

  • The results show that Advanced Study questions were quite difficult, even for students who were taking the more challenging mathematics courses that were prerequisite for participation in the study. Overall performance, measured by average percentage correct, was 36 percent at grade 8 and 30 percent at grade 12. At both grade levels, moreover, most of these students were unable to solve problems that required two or three successive steps to achieve the desired result.

  • At grade 12, students who were currently taking mathematics or who were, or had been, enrolled in an Advanced Placement (AP) mathematics course outperformed students in the study who were not currently taking a mathematics course or who had not taken an AP course in mathematics.
Table D. Average percentage correct scores by Theme block, selected characteristics, and student responses, grade 12: 1996

Table D.- Average percentage correct scores by Theme block, selected characteristics, and student responses, grade 12: 1996

#Estimate too small to report.

NOTE: Because results from the Theme Study did not lend themselves to development of an achievement scale, results are reported simply in terms of percentages of questions that students answered correctly.

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Assessment of Educational Progress (NAEP) 1996 Mathematics Assessment. (Originally published as table 3.26 on p. 112 of the complete report from which this article is excerpted.)

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Data source: The National Assessment of Educational Progress (NAEP) 1996 Mathematics Assessment.

For technical information, see the complete report:

Mitchell, J.H., Hawkins, E.F., Stancavage, F.B., and Dossey, J.A. (1999). Estimation Skills, Mathematics-in-Context, and Advanced Skills in Mathematics (NCES 2000-451).

For additional details on survey methodology, see

Allen, N.L., Carlson, J.E., and Zelenak, C.A. (1999). The NAEP 1996 Technical Report (NCES 1999-452).

Author affiliations: J.H. Mitchell, E.F. Hawkins, and F.B. Stancavage, American Institutes for Research; J.A. Dossey, Illinois State University.

For questions about content, contact Arnold A. Goldstein (arnold.goldstein@ed.gov).

To obtain the complete report (NCES 2000-451), call the toll-free ED Pubs number (877-433-7827), visit the NCES Web Site (http://nces.ed.gov), or contact GPO (202-512-1800).

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