Grouping in math: Pro and con

Researchers observed the mathematics classes of 33 teachers in order to describe grouping and instructional practices. Thomas L. Good and Douglas A. Grouws, University of Missouri-Columbia, DeWayne A. Mason, University of California-Riverside, Ricky L. Slavings, Radford University, and Kathleen Cramer, University of Wisconsin-River Falls, observed 4th, 5th and 6th grade classes primarily in three midwestern states.

Good and his colleagues report that while results of research on effective whole-class teaching methods are available, there are few observational or experimental studies which focus on small group teaching in math – particularly on the capacity of grouping to help promote higher order thinking or problem-solving skills.

Two previous studies are cited by Good et al. One, by Slavin (1987), indicates that cooperative learning groups can improve computation skills. A second, by Gerleman (1987), describes classes using ability grouping. Gerleman’s study revealed that instruction in ability groups consists chiefly of a brief introduction by the teacher followed by individual written drill work. In Gerleman’s study, there was little emphasis on development of conceptual understanding and 50% of the group time was used for review.

Consequently, Good et al. centered their study on three questions:

1. What forms of small-group teaching do teachers use?

2. How do teaching functions (review, development of concepts, controlled practice, seatwork, etc.) vary among the different types of small-group formats?

3. Do some forms of small-group teaching appear to be more effective than others for certain teaching goals?

Data on many variables collected

Math classes in 21 midwestern states were observed over a period of 2 to 3 months. To facilitate the collecting of data from so many classes, the researchers developed an observation recording instrument to collect information on the format, techniques, number of groups, number of students per group and the nature and content of assigned work. Observers recorded the amount of time teachers spent on each of 12 teaching tasks: giving directions, checking homework, review, practice with review material, supervising seatwork, checking seatwork, development of new concepts, controlled practice with new material, testing, transition, nonmathematical and other activities. A 5-point scale was designed to rate six teacher-directed and six independent-group variables.

The teacher-directed variables assessed were: meaningful presentation, accomplishment, accountability, managerial routines, emphasis on higher-order thinking and teacher use of manipulatives. The six independent group variables were: time on task, group interaction, student cooperation, higher-cognitive student behavior, student use of manipulatives and group self-management. The observers were carefully trained to observe and rate these variables. Videotapes were used and training sessions continued until agreement between observers on actual in-class lesson recording and rating exceeded 80% in all categories.

In general, Good et al. found that teachers were using a variety of small-group teaching formats and the amount of time they devoted to the various teaching tasks differed greatly both within and across formats and teachers. Still, a few general formats were identified:

Whole class ad hoc: instruction mainly to the whole class but small ad hoc groups were formed for remediation or enrichment.

Two or three ability groups: class was divided into groups by achievement with separate lessons taught to each.

Heterogeneous work groups: cooperative learning – heterogeneous groups of 3 to 5 students worked collectively on tasks.

Other groupings: mixed, flexible groups of various sizes based on specific objectives or other considerations with individualized instruction.

Whole-class lessons more academically meaningful

Analyzing the variance between formats revealed significant differences in the use of time for directions and overview, seatwork, transition and non-mathematical activities. Teachers using small-group formats tended to spend more time on non-academic activities and less on concept development than did teachers using whole class formats. However, the diversity of formats within a single classroom, as well as the variety of activities within each format, make generalizations difficult. It should be noted that few teachers used small groups exclusively.

Nevertheless, observers consistently rated whole class lessons as significantly more meaningful academically, in part, because greater emphasis was placed on higher-order thinking and use of manipulatives. However, in small group formats, students were more likely to be on task and to demonstrate self-management than students in whole-class lessons. Heterogeneous and other flexible groupings were found to stimulate more student interaction and cooperation which, in turn, seemed to lead to an increase in the exchange of ideas among students.

Achievement greater in whole-class and ad hoc groups

Good et al. did not measure the effectiveness of these different formats in terms of student achievement. Recently, however, in another study, Mason and Good (1990) followed up by comparing a two-group model with a whole-class ad hoc model. The effect of each model on student achievement in the areas of computation, concepts, problem-solving and mental mathematics/estimation was examined. The mathematical performance of students in this study was consistently higher in whole class ad hoc classes than in those which used two fixed groups. In yet another study, Mason (1990), found that teachers using a whole-class model were able to provide more individual attention (through flexible grouping for remediation and enrichment) as well as more seatwork assistance, than did teachers who used a fixed ability group model.

Good et al. conclude that these recent studies – both descriptive and experimental – indicate that whole class instruction in math appears to be most effective when combined with small heterogeneous and flexible group work sessions.

Editor’s Note: These studies do not prove that certain instructional formats are inherently better than others – only that in the classrooms studied by Good et al., effective teaching practices appear more frequently in some types of grouping arrangements than others. Researchers need to explore why classes grouped by ability do not spend more time on concept development or make better use of effective teaching techniques.

“An Observational Study of Small-Group Mathematics Instruction in Elementary Schools” American Educational Research Journal, Spring 1991, Volume 27, No. 4, p. 755-782

Published in ERN May/June 1991 Volume 4 Number 3

Leave a Reply

  • (will not be published)