The Third National Assessment: Minorities and ...

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WESTINA MATTHEWS, Chicago Community Trust. THOMAS P. CARPENTER, University of Wisconsin -Madison. MARY MONTGOMERY LINDQUIST, National ...
The Third National Assessment: Minorities and Mathematics Author(s): Westina Matthews, Thomas P. Carpenter, Mary Montgomery Lindquist and Edward A. Silver Reviewed work(s): Source: Journal for Research in Mathematics Education, Vol. 15, No. 2, Minorities and Mathematics (Mar., 1984), pp. 165-171 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/748892 . Accessed: 01/03/2013 15:35 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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Journal for Research in Mathematics Education 1984, Vol. 15, No. 2, 165-171

THE THIRD NATIONAL ASSESSMENT: MINORITIESAND MATHEMATICS WESTINA MATTHEWS, Chicago Community Trust THOMAS P. CARPENTER, University of Wisconsin -Madison MARY MONTGOMERY LINDQUIST, National College of Education EDWARD A. SILVER, San Diego State University The Third National Assessment of Educational Progress in Mathematics was conducted in 1982. Data are available on exercises given to national samples of white, black, and Hispanic 9-, 13-, and 17-year-olds. Although black and Hispanic students continued to score below the national level of performance, they made greater gains than their white counterparts since the second assessment in 1978, especially on exercises assessing knowledge and skill. Students in schools with heavy minority enrollments made greater-than-average gains. The more mathematics courses taken by 17-year-olds, black or white, the higher the level of achievement. The assessment results support increased efforts to improve the learning of mathematics by minority students.

Most studies of the achievement in mathematics of students from minority groups use samples drawn from restricted populations that are not cross sections of the national population. One of the best measures of national achievement in mathematics is provided by the mathematics assessment of the National Assessment of Educational Progress. The National Assessment results are based on the performance of a carefully selected, representative national sample of students at ages 9, 13, and 17. The size and composition of the National Assessment sample permit a description of the performance of various groups within the national population. These groups are identified on the basis of such characteristics as sex, race, size and type of community, and racial composition of school. Therefore, for anyone interested in the mathematics achievement of minorities, the results from the National Assessment are especially important. The following discussion concerns the results of the Third National Assessment in Mathematics for white, black, and Hispanic students. Other minority racial groups are not included because they were not sampled in sufficient numbers to provide reliable measures of achievement. (For additional information on the third assessment, see National Assessment of Educational Progress, 1983.) ASSESSMENT PROCEDURES

The National Assessment assessed mathematics achievement in 1973, 1978, and 1982. Over 45 000 students participated in the most recent assessment. From 79% to 81% of the sample at each age were white, 12% to 14% black, 5% Hispanic, and 2% other minorities. The racial classification was based on the student's appearance and surname. Between 250 and 450 exercises covering a wide range of objectives were administered to the sample at each age group, with approximately 2 000

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ThirdNationalAssessment

students responding to each exercise. The exercises were classified according to four cognitive levels: (a) knowledge, (b) skill, (c) understanding, and (d) application. Knowledge exercises involved the recall of facts and definitions. They included such tasks as ordering numbers; recalling basic facts of addition, subtraction, multiplication, and division; identifying geometric figures; and identifying basic units of measurement. Skill exercises involved various mathematical manipulations, including computation with whole numbers, fractions, decimals, and percents. Also at the skill level were exercises in making measurements, converting units of measurement, reading graphs and tables, and manipulating algebraic expressions. Understanding exercises tested students' knowledge of basic principles such as the concept of a unit covering in measurement. Understanding exercises were constructed so that they could not be answered by simply applying a routine algorithm. Application exercises required students to apply their knowledge or skill to solve a problem. Both routine textbook problems and nonroutine problems were included in this category. Although the focus of this article is on the mathematics achievement of black and Hispanic students, selected results based on the achievement class of the student and the racial composition of the school have been included because they provide an additional perspective on the results. Achievement class is reported by quartile and is determined by a student's performance on the entire assessment booklet. Racial composition is based on the percentage of whites enrolled in the school, as reported by the principal. Although these variables represent an imperfect measure of a student's background, patterns can still be identified that might assist in understanding racial differences in achievement. RESULTS Change in Mathematics Achievement A major objective of the National Assessment is to measure change in achievement over time. To provide a valid measure of change, some of the exercises are not released to the public when the results of an assessment are reported. The unreleased exercises are readministered in subsequent assessments using identifical procedures for administration and scoring. The analysis of change, therefore, can be based on a common core of exercises administered more than once. For the third assessment, the change results for 9-year-olds are based on 233 exercises, and for 13- and 17-year-olds on 383 exercises. Consistent with earlier assessments, black and Hispanic students performed below the national level on the third assessment, and their white counterparts performed above the national level. Table 1 gives the mean percentage of the exercises common to the 1978 and 1982 assessments that various racial groups answered correctly. In 1982, 9-year-old black students

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Matthews, Carpenter, Lindquist, and Silver Table 1 Mean Percentage of Exercises Correct in the Second and Third Assessments Sample National White Black Hispanic

Age 9 1978 1982 Change 1.0 56.4 55.4 58.8 0.7 58.1 2.1 45.2 43.1 1.1 46.6 47.7

Age 13 1978 1982 Change 60.5 56.6 3.9* 3.2* 59.9 63.1 48.2 6.5* 41.7 45.4 51.9 6.5*

Age 17 1978 1982 Change -0.2 60.4 60.2 -0.2 63.1 63.2 1.3 43.7 45.0 0.9 48.5 49.4

Note. Percentages based on 233 exercises at age 9, 383 at ages 13 and 17. * < .05. p

were about 11 percentage points below the national average; for 13-year-olds the difference was 12 percentage points; for 17-year-olds, it was 15 percentage points. Hispanic students showed a similar pattern, with less pronounced differences; Hispanic 9- and 13-year-olds were about 9 percentage points below the national average, and Hispanic 17-year-olds were 11 points below. Although the position of white, black, and Hispanic students did not change relative to national levels of achievement, the rate of change for each group did. At each age, black and Hispanic students made gains in achievement that were greater (even if not statistically significant) than those of their white counterparts. At ages 9 and 17, black students made slightly higher gains than Hispanic students. All groups made the greatest gains at age 13. As Table 2 shows, the pattern is similar when the data on change are Table 2 Mean Percentage of Exercises Correct in the Second and Third Assessments by Cognitive Level Age 17 Age 13 Age 9 1978 1982 Change 1978 1982 Change 1978 1982 Change Sample National White Black Hispanic

66.9 69.6 54.3 58.7

68.3 70.8 57.8 58.7

1.4 1.2 3.5* 0.0

National White Black Hispanic

49.8 52.5 37.1 41.3

50.6 53.1 38.7 43.8

0.8 0.6 1.6 2.5

National White Black Hispanic

41.6 44.2 30.5 32.6

41.2 43.4 31.4 32.4

-0.4 -0.8 0.9 -0.2

National White Black Hispanic

39.1 41.8 27.6 29.9

39.6 42.4 27.0 30.5

0.5 0.6 -0.6 0.6

Knowledge 73.8 69.3 72.2 76.1 63.8 55.8 65.3 59.0 Skills 57.6 53.6 60.4 57.0 44.0 37.3 42.0 49.2 Understanding 60.5 56.6 63.6 60.0 46.4 40.5 43.8 49.7 Application 43.4 45.6 46.3 47.9 30.4 34.8 32.8 38.8

4.5* 3.9* 8.0* 6.3*

74.7 77.3 59.6 64.1

74.9 77.3 62.6 66.1

0.2 0.0 3.0 2.0

4.0* 3.4* 6.7* 7.2*

59.7 62.7 42.4 47.9

60.0 63.0 44.2 48.4

0.3 0.3 1.8 0.5

3.9* 3.6* 5.9* 5.9*

61.8 64.8 45.0 48.9

61.5 64.7 44.8 49.7

-0.3 -0.1 -0.2 0.8

2.2* 1.6* 4.4* 6.0*

43.5 46.5 26.2 31.0

42.4 45.5 26.0 31.4

-1.1 -1.0 -0.2 0.4

*p