Effective use of grouping In mathematics classes

Whole-class instruction, combined with flexible groups for remediation or enrichment, appears to be effective in raising the math achievement scores of diverse students. These are the findings of DeWayne A. Mason, University of California/Riverside, and Thomas L. Good, University of Missouri/Columbia. In their study, the researchers combined a model of active teaching and learning with different grouping arrangements to determine which contributed more to the mathematics achievement of 1,736 fourth-, fifth-, and sixth-grade students in 81 classrooms in nine Midwestern elementary schools.

Previous research

Although tracking students has been criticized for its negative effect on lower-achieving students, as well as its lack of significant effect on middle- and upper-level students, previous research results have indicated that certain forms of grouping within a classroom can lead to higher basic-skill achievement. Mason and Good also report that studies have shown that an active-teaching model which describes key teaching techniques can improve significantly certain types of mathematical achievement. However, they note that most of these earlier studies have methodological flaws. Also, studies of within-class grouping have not controlled the type of instruction used and lack observational data to confirm their results. The conflicting research resulting from such studies makes it difficult for educators to agree on the benefits of various models.

Current study

Mason and Good sought to determine the effects of different ability-grouping formats on achievement. At the same time, they attempted to compare effective and commonly used teaching formats and to explore how new models that combine key elements of successful models, such as active teaching and cooperative learning, affect students’ learning processes and achievement.

The Midwestern schools included in the study were made up largely of middle-class students. Student population was 85 percent white, 15 percent black and 3 percent Asian. Dividing students into higher and lower math classes on the basis of the previous year’s performance had been the school district’s policy, and traditionally teachers went a step further by dividing students in their classes into two math groups.

In three 90-minute training sessions, teachers taking part in experimental classrooms were instructed in the use of 16 techniques of active teaching that research has shown to be effective for improving student achievement. Teachers learned procedures for developing new concepts and for actively assessing student understanding. They also were trained in classroom management techniques for time on task, accountability, reinforcement, peer tutoring and enrichment. Recommendations from the National Council of Teachers of Mathematics Curriculum Standards also were incorporated into the training. These included encouraging the development of mental math skills and estimation, increasing problem solving and projects, and cooperative work.

For purposes of this study, similar classes (matched for aptitude and achievement on the basis of the previous year’s performance) were randomly assigned to one of three treatments:

1. Whole class/flexible groups with teachers trained in active teaching/learning strategies. Teachers used whole-class presentation of new content, assessing student understanding of the lesson, and then breaking the class into small groups for remediation and enrichment.

2. Two-group classes with active teaching/learning. Based on their performance in the previous year, students were divided into two permanent groups with the top group receiving higher-level content at a faster pace than lower-achieving students. Instruction of both groups included active teaching methods and cooperative learning.

3. Two-group control classes. Teachers did not receive training in active teaching, and continued the district’s policy of dividing math classes into two groups.

The significant difference between the two experimental groups was that the whole class/flexibly grouped classes emphasized the daily formation of groups tailored to address specific deficiencies after a thorough assessment of the students’ understanding of that day’s instruction.

Measuring effects of different models

Through observation, trained personnel assessed the extent to which teachers implemented the appropriate treatment model, as well as the degree to which the different teaching techniques contributed to student achievement. Videotapes and narrative descriptions of classroom activities were collected, teacher and student behaviors were categorized, and the materials and activities used were recorded. To measure student achievement, each grade level was given a math test based on its curriculum. Tests were made up of 10 items each in the areas of computation, concepts, problem solving and mental mathematics.


Results varied significantly between the three treatment models. Differences between the control and experimental classrooms were significant in almost all areas. The training in active teaching and learning methods seemed to contribute to increased achievement. However, teachers of whole-class/flexibly grouped students utilized the active teaching/learning strategies to a greater degree than the two-group experimental teachers.

Compared to two-group teachers, flexible-group teachers gave their students substantially more time to develop their understanding of mathematical concepts and they gave them more remediation and enrichment activities. Teachers using two fixed groups spent a greater percentage of class time on nonacademic activities. Whole-class/flexible-group teaching was rated highest in accomplishment, accountability and management routines. Two-group experimental classes were rated higher than the control classes in these areas. More cognitively complex activity and more cooperation among students were apparent in the experimental groups than in the control groups.

As expected, the whole-class/flexibly grouped students demonstrated higher achievement overall than students in either two-group model. However, students in the higher-achieving schools tended to outperform those from lower-achieving schools. In addition, certain teachers produced higher student achievement regardless of their treatment model or the achievement level of their school.


Students in the whole-class/flexibly grouped model scored higher in all four areas of math achievement than either two-group model. These differences were greatest in the areas of computation and mental mathematics, but sizeable also in concepts and problem solving. Mason and Good offer no simple explanation for these results. They state that a number of factors contribute to achievement results and that many were uncontrolled in this study. Nevertheless, they report that several factors appeared to contribute to these results. For one, whole-class teachers had more time to spend discussing mathematical concepts and processes. Observers reported that whole-class teachers used the extra time to make thoughtful and thorough presentations and to direct students in active learning.

Teachers using two groups were compelled to make two presentations in less time. Two-group teachers also had less time for inquiry-oriented activities, explanations, illustrations or questions, answers and discussions with each group. Whole-class teachers also had more time for individual attention – 7 minutes per lesson as compared to an average of only .7 and 1.1 minutes in the two-group models. Including the time spent in review and reteaching during whole-class presentations, student in the whole-class/flexibly grouped model received twice as much review as students in the two-group classes. They also were given twice as much time to discuss mathematics during the assessment portion of the whole-class lesson.

In addition, seatwork tended to be lower-level drill in the two-group classes, presumably because teachers needed to have uninterrupted presentation time for the other group. Dividing classes into separate groups for instruction appears to place multiple, competing demands on teachers. As a result, two homogeneous groups are not necessarily easier to teach than one diverse group.

Mason and Good believe that teachers and principals should think carefully about placing students in permanent, within-class groups for mathematics. Whole-class teaching, using flexible regrouping as needed following daily lessons, may provide students with more challenging material, better instruction and more active learning environments. Emphasis on thorough development and assesment of understanding, active learning with peers and individualization in small groups as necessary can accommmodate a fairly wide range of student diversity.

Mason and Good caution that more research is needed on how much diversity whole-class models can accommodate. It must be remembered that in this study, some initial sorting of students on the basis of math achievement was done by schools prior to placement in classes. They recommend further study in more diverse school districts. The differential effects of these models on high and low achievers need to be studied as well.

“Effects of Two-Group and Whole-Class Teaching on Regrouped Elementary Students’ mathematics Achievement”, American Educational Research Journal, Volume 30, Number 2, pp. 328-360.

Published in ERN, November/December 1993, Volume 6, Number 3

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