Improving the Mathematical Skills of Low Achievers
This Digest discusses the performance and representation of Black and Hispanic students
in high school mathematics courses, the effect of federal programs to improve minority student achievement, and the special problems for minorities learning mathematics. The Digest also suggests instructional techniques for teaching mathematics.MINORITY PERFORMANCE IN MATHEMATICS COURSES
The mean performance of Black and Hispanic students in mathematics continues to rank below the national mean, according to the third National Assessment of Education Progress (Education Commission of the States 1982). Furthermore, performance differences between minority and White students increase with age: Blacks
are 11 percentage points below the national average at age 9; 12 points below at age 13; and 18 points below at age 17. However, 13-year-old Black and Hispanic students made substantial gains since the second Assessment--gains that were larger than those of their White counterparts.
Although minority students are weak in higher mathematical skills, they are no different from students in general. Between the second and third Assessments, all students significantly improved their performance of routine exercises testing simple computation, measurement, and figure recognition. Performance of more sophisticated skills--such as problem solving requiring the application of mathematics principles--continued to be low for all students.MATHEMATICS PERFORMANCE AND INSTRUCTIONAL EXPOSURE
The performance difference between minority and White students increases with age largely because minority students are underrepresented in the more advanced mathematics courses. For instance, 74 percent of White 17-year-olds have taken at least a half year of algebra compared to only 57 percent of Black students. Enrollment differences increase for the more advanced mathematics courses:
--Geometry: 55 percent White, 34 percent Black
--Algebra II: 41 percent White, 28 percent Black
--Trigonometry: 15 percent White, 8 percent Black
Other data indicate that more Black females than Black males enroll in higher mathematics courses, but these data have not been related to performance (Mathews 1983). National Assessment statistics show that, while minority students lag behind their White peers at each stage, they perform significantly better with each additional course taken.
Partly because of the enrichment provided by special federal programs, all students attending schools with heavy minority enrollments increased their mathematics skills between the 1978 and 1982 Assessments. Moreover, students in the lowest achievement quartile made greater gains than students in the highest quartile--pointing to the benefits of enriched instruction for students with lower-level skills.
indicates that the larger the Black student population in a school, the more likely Black students will be enrolled in lower level mathematics courses. Schools with a greater White student population are more likely to offer advanced mathematics courses. However, Black students currently are unlikely to be enrolled in these advanced courses (Mathews 1983).MINORITY STUDENTS AND MATHEMATICS ACHIEVEMENT
Fluency in English, mathematics anxiety and motivation, and preconceptions about mathematics influence minority students' mathematics achievement.
Reading and understanding English is a prerequisite for higher mathematics achievement. Creswell (1983) found that reading achievement influences mathematics problem-solving, regardless of sex or ethnicity. A study of the mathemetics reasoning of bilingual students also indicates that first language competence is important for reasoning mathematically in English (Dawe 1983).
Research on all populations shows that psychological factors such as anxiety and motivation are related to mathematics achievement. However, a survey of 24 studies indicates that minorities like mathematics, find it interesting, have little mathematics anxiety, and want to take more mathematics courses (Mathews 1983). The 1978 National Assessment, which included motivational questions, found that Black students expressed a greater interest in taking mathematics courses, although they took fewer courses than their White peers (Anick and others 1981).
Other research indicates that minorities may see mathematics as a White domain, are less likely than Whites to understand its future value, and are negatively influenced by the school staff's attitudes toward them and their work (Mathews 1983). School factors enhancing minority mathematics achievement include good discipline
and attendance, small class size, placement in advanced tracks, and materials that affirm the important role of minorities in mathematics (Mathews 1983; Taylor 1983).EFFECTIVE MATHEMATICS INSTRUCTIONAL TECHNIQUES
The National Science Board Commission (1983) found that successful mathematics instruction includes motivating techniques, sufficient time-on-task, high standards for participation and achievement, a coherent course of study with early "hands-on" experience, adequate resources, innnovative use of available facilities, and extensive homework.
The National Diffusion Network offers a catalogue of EDUCATIONAL PROGRAMS THAT WORK (1983). Some simple and inexpensive mathematics programs that have proven successful with students of all ages include some of the following elements:
--individualized instruction --student responsiveness --calculator usage --diagnostic testing with prescriptive planning --laboratory work --remedial pull-out --criterion-referenced testing --small group instruction --manipulative instructional materials --team games --cross-age tutoring
Although no single method has proven most effective, a variety of instructional methods do work. Moreover, the opportunity to learn mathematics through sufficient coursework is fundamental. Schools need to be flexibly organized so that all students, including low-achievers, can take a variety of individually- tailored mathematics programs that provide access to advanced mathematical learning.FOR MORE INFORMATION
Anick, Constance M., Thomas P. Carpenter, and Carol Smith. "Minorities and Mathematics: Results from the National Assessment of Educational Progress." MATHEMATICS TEACHER
Creswell, John L. "Sex-Related Differences in the Problem-Solving Abilities of Rural Black, Anglo and Chicano Adolescents." TEXAS TECH JOURNAL OF EDUCATION 10 (Winter 1983):29-33.
Dawe, Lloyd. "Bilingualism and Mathematical Reasoning in English as a Second Language." EDUCATIONAL STUDIES IN MATHEMATICS 14 (November 1983):325-353.
Education Commission of the States. THE THIRD NATIONAL MATHEMATICS ASSESSMENT: RESULTS, TRENDS, AND ISSUES. Washington, D.C.: National Institute of Education, 1982. ED 228 049.
Mathews, Westina. INFLUENCES ON THE LEARNING AND PARTICIPATION OF MINORITIES IN MATHEMATICS. A Report from the Postdoctoral Program, Program Report 83-5. Madison, WI: Wisconsin Center for Educational Research, 1983. ED 228 058.
National Diffusion Network, U.S. Department of Education. EDUCATIONAL PROGRAMS THAT WORK: A CATALOG OF EXEMPLARY PROGRAMS APPROVED BY THE JOINT DISSEMINATION REVIEW PANEL. San Francisco, CA: Far West Laboratory for Educational Research and Development, 1983.
National Science Board Commission on Precollege Education in Mathematics, Science and Technology. EDUCATING AMERICANS FOR THE 21st CENTURY: A REPORT TO THE AMERICAN PEOPLE AND THE NATIONAL SCIENCE BOARD. Washington, D.C.: National Foundation, 1983. ED 223 913.
Taylor, B. Ross. "Equity in Mathematics: A Case Study." MATHEMATICS TEACHER 76 (January 1983):12-17.
This Digest was prepared for the ERIC Clearinghouse on Urban Education, 1984.