**ERIC Identifier:** ED237584

**Publication Date:** 1983-09-00

**Author: **Ascher, Carol

**Source: **ERIC Clearinghouse on Urban
Education New York NY.

## Improving the Mathematical Skills of Low Achievers. ERIC/CUE Fact Sheet Number 18.

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.

Other research 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 14 (1981):560-566.

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.