**ERIC Identifier:** ED359065

**Publication Date:** 1993-07-00

**Author: **Davenport, Linda Ruiz

**Source: **ERIC Clearinghouse
for Science Mathematics and Environmental Education Columbus OH.

## The Effects of Homogeneous Groupings in Mathematics. ERIC/CSMEE
Digest.

The practice of homogeneous grouping, which is quite widespread in the United
States, uses a model that typically groups students together on ability or
achievement as the deciding variable. At the high school level, this practice is
most prevalent in mathematics, where students are placed in vocational, general,
or college-preparatory mathematics courses (McPartland, Coldiron, &
Braddock, 1987; Oakes, 1985, 1990a, 1990b; Slavin, 1990). It also occurs at the
middle or junior high school level in those schools that offer algebra at the
eighth grade (McPartland, Coldiron, & Braddock, 1987; Oakes, 1985, 1990a,
1990b; Slavin, 1990). According to the Second International Math Study (SIMS),
ability grouping is more extensive in the United States than any other country
studied (Oakes, 1990a). Students at the elementary school level may also be
tracked or grouped, although at this level students are more often grouped by
general measures of ability or achievement rather than ability or achievement in
mathematics (Oakes, 1985, 1990a, 1990b; Slavin 1987a, 1987b).

A second instance in which students are often homogeneously grouped is the
small groups in classrooms where clusters are based on ability or achievement
within that particular classroom. This has been an established practice for
reading instruction at the elementary school level for years. Teachers
frequently will organize their classrooms in a similar format for mathematics
instruction (Oakes, 1990a; Slavin, 1987a, 1987b). The practice of placing small
groups of students into high, medium, or low groups for mathematics instruction
is less common at the middle, junior, or high school level where students tend
to do less work in small groups and are sorted by the particular course (Slavin,
1990).

Such practices seem to stem from the widespread belief children's
intellectual differences are so great that students with different ability or
achievement levels need to be taught in separate classes or groups (Oakes,
1990a, 1990b). However, a number of concerns have been raised about the
long-term effects of these grouping practices.

### EFFECTS ON OPPORTUNITY TO LEARN MATHEMATICS

In a National
Science Foundation study of the way in which this nation's educational system
provides opportunities to learn mathematics and sciences, cross-sectional data
about mathematics and science programs, teachers, and classroom practices at the
elementary and secondary school level were analyzed (Oakes, 1990a). These data
were from the National Science Foundation's 1986 National Survey of Science and
Mathematics Education (NSSME). While an analysis of these data showed important
differences in opportunities to learn mathematics between schools, important
differences were also found within schools. This seemed to be related to the
practice of placing students into different tracks based on ability,
achievement, or career expectations. The report identified three areas in which
inequities in mathematics instruction were found: (1) access to strong
mathematics programs; (2) access to well-qualified mathematics teachers; and (3)
access to classroom opportunities.

In most of the high schools described in the study, fewer mathematics courses
were available or required for low-track students. Standard and advanced
college-preparatory courses were offered to students perceived as having high
ability, less often to students thought of as having average ability, and rarely
to students seen as having low ability, although some schools occasionally were
willing to bend traditional placement criteria to encourage lower-achieving
students to take more rigorous mathematics coursework. While it is true that
tracking at earlier grade levels may limit the numbers of students eligible to
take college-preparatory mathematics coursework, the end result is that many
students are denied access to important mathematics experiences which would
prepare them to pursue the study of mathematics and science beyond high school.
The study also found that schools often place their least qualified mathematics
teachers in low-ability classes and their most-qualified teachers in their
high-ability classes, particularly at the secondary level.

Finally, the study found that even when mathematics course titles are the
same, the curricular goals emphasized by the teachers and the instructional
strategies they employed to meet those goals differ in ways that lead to unequal
opportunity to learn mathematics. For instance, it was found that high-ability
groups at the elementary, middle, or junior and high school levels progress
further in the school curriculum over the course of the year than low-ability
groups. It was also found that lower-level courses expose students to fewer
mathematical topics and skills as well as less-demanding topics and skills.
High-ability tracks typically include more complex material and more difficult
thinking and problem-solving tasks. In addition, teachers of high-track students
reported spending more time preparing for class, and they appeared to be more
enthusiastic and more willing to push their students to stretch academically
than teachers of low-track students. Upper-track teachers also expected their
students to spend more time on homework than did teachers of low-track students.

Similar qualitative differences in the mathematics instruction available to
students in high- or low-track classes is borne out in other research as well.
For example, an examination of the middle school mathematics instruction in six
different school districts found that in most districts a clear tracking
hierarchy existed. Low-track students received a more limited curriculum and
engaged in less favorable interactions with the teacher than did their
high-track counterparts (Ekstrom & Villegas, 1991). It is worth noting that
even within the same classroom, differing patterns of interactions between
teachers and high- and low-ability students have been found. With regard to
mathematics instruction, a case study of one particular classroom showed that
low-ability students received less teacher time and were asked a fewer number of
process-oriented questions (Leder, 1987).

### EFFECTS ON MATHEMATICS ACHIEVEMENT

The NSF study described
earlier (Oakes, 1990a) did not specifically examine the relationship between
tracking and achievement in science or mathematics. However, a substantial body
of research suggests that tracking, especially at secondary schools, generally
fails to increase learning and has the unfortunate consequence of widening the
achievement gaps between students judged to be more able or less able (Cole & Griffin, 1987; Eckstrom & Villegas, 1991; Gamoran & Berends, 1987;
Slavin, 1987a, 1987b, 1990). Studies examining the effects of homogeneous
grouping on achievement tend to take two approaches: (1) comparisons of the
achievement of students in heterogeneous classes with comparable students in
ability-grouped classes or (2) comparisons of the achievement of students in
different ability groups.

This distinction in the design of the research reported is an important one.
Given the varying opportunities to learn mathematics in the different tracks one
would clearly expect to find differences in mathematics achievement as a
consequence. Therefore, it is not a surprise that achievement differences in
mathematics due to tracking have been found even controlling for ability level,
socioeconomic status, and a variety of other variables (Gamoran & Berends,
1987).

In reviews of research comparing the achievement of students in heterogeneous
classes with comparable students in ability-grouped classes, few differences in
achievement have been found. In particular, a meta-analysis of studies examining
the effects of ability grouping on achievement of secondary students (middle,
junior high, and high school) reported that in comparisons of ability grouping
and heterogeneous grouping over periods of from one semester to five years,
overall achievement effects were found to be essentially zero at all grade
levels (Slavin, 1990). A similar meta-analysis for elementary students also
showed that overall effects of ability grouping on achievement were negligible
(Slavin, 1987b). Both meta-analyses refute the claim that ability group is good
for high-achievers and bad for low-achievers which has often been asserted.

Interestingly, the only exception to these findings was when students from
heterogeneously-grouped classrooms were regrouped homogeneously by reading and
mathematics achievement scores for reading or mathematics instruction (Slavin,
1987a, 1987b). Here, the research has been inconclusive, with several studies of
regrouping for mathematics instruction showing that homogeneous regrouping had
positive effects on mathematics achievement when materials appropriate for the
student's level of performance were used (Provus, 1960; Morris, 1969).

### EFFECTS OF RESEARCH ON TRACKING PRACTICES

In spite of the
findings that homogeneous grouping seems to have little effect on achievement,
some level of tracking persists in our public school system, particularly at the
middle and high school level:

"While
most people (including many educators) assume that students will learn better if
they are grouped together with those who have similar capabilities, research has
shown that putting children into separate classes to accommodate their
differences from earliest school years is neither necessary nor very effective.
Tracking does not work well for students in the low- and midde-ability groups,
who experience clear and consistent learning disadvantages. (T)rack does not
necessarily promote achievement for high-ability children either. Many studies
show that highly capable students do as well in mixed ability classes." (Oakes,
1990a, p. 6)

Oakes has suggested that the persistence of tracking in the public school
system is based on several assumptions: (1) that students learn better when they
are grouped with other students who are considered to be academically similar;
(2) that students develop more positive attitudes towards themselves and school
when they are not placed in groups with others who are more capable; (3) that
placement processes used to separate students into grouping both fairly and
accurately reflect past achievement and native abilities; and (4) that it is
perceived as easier for teachers to accommodate individual differences in
homogeneous groups (Oakes,1985).

The persistence of homogeneous grouping is particularly troubling given the
long-term effects on female and minority students, both groups of whom are
dramatically underrepresented in the mathematics and science areas. The tendency
to place minority students in lower tracks has been described by Cole and
Griffin (1987) in their discussion of ability-grouping research:

"There
have been many accounts of differential treatment in ability groups reported by
researchers who have examined classroom interactions closely...These researchers
report that the distribution of students to high, middle, and low ability groups
seems to be related to characteristics associated with SES: Children from
low-income or one-parent households, or from families with an unemployed worker,
are more likely to be assigned to low ability groups. The work by Cicourel and
Kituse (1963) suggests that children from low income families with low grades
and low test scores could be tracked higher, particularly because of parental
intervention. The more telling finding...is that children from low income
families with adequate test scores and low grades were placed in a lower group,
while corresponding children from middle income families were placed in a middle
level group. (p. 21)

Females, because they are sometimes seen as less able mathematically or
because they express less interest in mathematics and science, may also be
inappropriately placed in lower tracks, particularly at the secondary school
level (Oakes, 1990b).

Recent assessments in mathematics achievement suggest students in the United
States are not generally strong in mathematics, with too few students,
especially minority and female, studying higher level mathematics. The reform
literature in mathematics education argues strongly for the need of a quality
mathematics education for all students. In the descriptions of exemplary
classroom practice there is a strong focus on diversity of approaches (NCTM,
1989, 1991; RAC, 1989). Is it too much to hope that as school districts adopt
approaches which are congruent with recent recommendations for mathematics
education reform the practice of homogeneous grouping will no longer be felt to
be necessary?

### REFERENCES

Cole, M., & Griffin, P. (1987). Contextual
factors in education: Improving science and mathematics education for minorities
and women. Madison, WI: Wisconsin Center for Education Research.

Ekstrom, R. B., & Villegas, A. M. (1991). Ability grouping in middle
grade mathematics: Processes and consequences. Research in Middle Level
Education, 15(1), 1-20.

Fullilove, III, R. E. (1987). Images of science: Factors affecting the choice
of science as a career. Educating scientists and engineers: Grade school to grad
school. ED 297 961

Gamoran, A., & Berends, M. (1987). The effects of stratification in
secondary schools: Synthesis of survey and ethnographic research. Review of
Educational Research, 57, 415-435.

Hassell, J., & Armistead, J. (1991). Meeting national goals for 2000 and
beyond in mathematics education. Columbus, OH: ERIC Clearinghouse for Science,
Mathematics, and Environmental Education. ED 335 210

Leder, G. C. (1987). Teacher student interaction: A case study. Educational
Studies in Mathematics, 18, 255-271.

National Council of Teachers of Mathematics. (1989). Curriculum and
evaluation standards for school mathematics. Reston, VA: Author.

Oakes, J. (1985). Keeping track: How schools structure inequality. New Haven,
CT: Yale University Press.

Oakes, J. (1988). Tracking in mathematics and science education: A structural
contribution to unequal schooling. In L. Weiss (Ed.), Class, race, and gender in
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Oakes, J. (1990a). Multiplying inequalities: The effects of race, social
class, and tracking on opportunities to learn mathematics and sciences. Santa
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Oakes, J. (1990b). Opportunities, achievement, and choice: Women and minority
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153-222.

O'Neil, J. (1991). Raising our sights: Improving U.S. achievement in
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Pisapia, J., & Gross, E. (1991). 1990 national assessment of educational
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mathematics achievement. Richmond, VA: Metropolitan Educational Research
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Reuman, D. (1989). Effects of between-classroom ability grouping in
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Slavin, R. E. (1987a). Ability grouping and its alternatives: Must we track?
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