Equity in Math Cooperative Groups

Just as there are buzzwords associated with the standards-based reform movement in literacy, there are also words that have come to be associated with the math reform movement such as "math for all" and "equitable classroom". As a former public school teacher in a large urban city and as a math staff developer who travels around the country, I often work with teachers and school leaders grappling with the issue of "cooperative groups" as a way to equitably distribute mathematics instruction and peer interaction among all students in the class. In fact, many teachers struggle daily with issues around an equitable grouping of students for math instruction while simultaneously fulfilling a need for whole group, direct instruction and individualized instruction.

Many teachers in the standards-based math reform movement have re-thought classroom instruction that is based on "every student on the same page at the same time". However, many of us are continually trying to answer the question: what does it really mean to have a math class where each student has access to the materials and thinking required in order to develop higher order thinking skills and mathematical understanding? Cooperative groups are commonly used to address the issue. However, the larger question still remains: what constitutes an equitable grouping of students and what do these groupings offer in terms of the depth of mathematical content in the curriculum, as well as goals for individual students?

In many classrooms, cooperative groups for math simply mean a gender, racial and/or ability balance of students in a small group context working on an activity or problem. There is a good reason for this type of organization. Without specific actions to support students working with each other, some students will choose to work with their peers that are most like them (racially, based on language preferences, gender or even socio-economic characteristics). Teachers want all students to have the same chance in math class and to work with a diverse group of their peers. Nevertheless, grouping students in this way may seem to promote educational parity but it often does not.

This notion of equity as "same treatment for everyone" is problematic for all students. It often is not based on the mathematical task at hand and creates a chasm between students irrespective of their math interests, language experience and mathematical understanding. Grouping students based on notions of equity can, at times, "inhibit" the math thinking of some group members while perpetuating the low math self-esteem of others.

For example, students in my third grade class were working on a multiplication problem:

Two friends Melissa and Margaret were starting a daycare business so they thought they would put flyers on cars in a huge parking lot at a toy store. It was getting late but they knew that lampposts were positioned at every tenth row. They also knew that there were 19 cars in each row because the rows were completely filled. By the time they stopped, Melissa and Margaret had put flyers on every car up to the sixth lamppost. How many flyers did they use? (one flyer per car)

When I arranged cooperative groups in which students were grouped solely based on language ability or mathematical understanding the students did not benefit as much as students that were grouped based on more similar strategies or investment in the problem. For example, when fluent English speakers were forced to work with students beginning to learn English or groups in which students who needed to use unifix cubes or draw pictures were immediately paired with students who mentally were able to solve this problem and develop extensions, all students were not able to work up to their potential. In the spirit of community, students were more than willing to "slow down" their thinking or clarify their statements while other students were working hard to understand strategies and language unfamiliar to them. However, in the limited math time, all students would have been better served in groups based on mathematical content and strategies first and then asked to work together in more heterogeous groups to share their thinking.

I am not suggesting that cooperative groups should be consistently homogeneous based on experience, confidence and skills. However, as with book groups in a classroom literacy context, I am suggesting that math cooperative groups need to be grounded in the mathematical content that surrounds each math activity and lesson. Groups need to be formed and re-formed so that all students are able to work together to explore and understand the mathematical ideas necessary in order to work in increasingly more complex ways rather than simply being assigned to a group based on their gender, linguistic abilities, or ethnicity.

This notion of looking at the mathematical content of each lesson presupposes that teachers deeply understand the spectrum of mathematics in each strand and are keenly aware of a multitude of strategies from the least to most efficient. Cooperative groups based on mathematical content also presuppose that teachers are adept at questioning; pushing students to search for connections, patterns and meaning in mathematics. Math work times must be flexible in order to allow students to pursue their hypotheses and share their work with the entire class while meeting the individual and group goals that the teacher has developed.

During a recent mathematics lesson in a sixth grade class at a public school in an urban setting, I asked students to solve a problem:

The captain of a stranded ship is told that there are 4,000 biscuits left. The crew consists of 64 members. Each person gets three biscuits a day. This means 192 biscuits a day for the whole crew. How long will this supply last?

Students began working as I walked around the room asking questions to help students clarify their thinking or to "jump start" them. In this classroom of six girls (less than a fourth of the class), many did not know how to begin. Two boys very quickly calculated their answers using their own invented strategies and the majority of the class rounded numbers, skip counted, used their knowledge of multiplying by 200 and were stuck trying to figure out what to do with the remainder.

I decided to gather the two students together who were separately working on how closely they could calculate the exact time that the crew would run out of biscuits. These students were extremely motivated to answer this (their own question) and worked very diligently talking with each other and making connections that were extremely complex. Other students were not interested in this question or did not even recognize it as a possible extension for the problem. For most students, this extension seemed disconnected to the math problem at hand. There would have been no point in forcing students to work in a group with this wide degree of interest and mathematical thinking.

I continued to support the other students in the class, particularly the group of girls that did not know how to start. I asked them to work together in order to come up with ideas about how to proceed. Indeed there were boys in the class that were also talking about how to begin working on the problem. However, the fact that this group consisted of all girls did not seem as important at this particular moment compared to the goal of helping them to understand the context of this lesson and to develop strategies for proceeding.

As all students in this class became increasingly more satisfied with their work, they were asked to share their strategies with their peers who had solved the problem in different ways. During this time, I was careful to encourage students to work in heterogeneous groups. This type of group work and sharing of ideas is different than a preconceived organizational system based on outside parameters of gender, ethnicity, etc. rather than mathematical content.

In thinking about conceptions of equity particularly within cooperative groups, it became clear to me that to have chosen students to work on the very specific questions that were a driving force for some students simply to employ the notion of same treatment for everyone would have been a disservice for all of the students involved. This is not to say that students with varying interests, ability levels or mathematical confidence should not share their strategies, frustrations and solutions together. However, just as students need numerous opportunities to work within these diverse groups, they also need time to work within groups where the mathematical content is the driving force. For teachers, it's our job to make sure that we have classrooms that focus on the mathematical content and that when doing so, our cooperative groups are diverse and therefore, mathematically equitable.

Many researchers have differing opinions about the effectiveness of cooperative groups and the variety of ways in which to organize them. In looking at your own classroom, what are some of the issues that resonate when thinking about cooperative groups? How do you organize such groups? Upon what is the grouping based and how does it benefit or interfere with the mathematical thinking and understanding of students? How does the mathematical content of the lesson or activity influence the way in which students work together? Feel free to post specific examples.