When I was a 5th and 6th Grade homeroom teacher, I always taught maths in homeroom groups, though I'm aware that in many schools maths is a subject that is often streamed or set, with high-ability students being taught in separate classes. I was interested to read what Jo Boaler writes about teaching heterogeneous groups, as her research seems to back up the observations I made from my own experience. She describes a pedagogical approach called "complex instruction", devised by Liz Cohen and Rachel Lotan, to make group work equal. This has implications for other subjects as well - so it can be used with any grade level or subject.

Complex instruction is basically made of up 4 interrelated ideas: multidimensionality, roles, student responsibility and assigning competence. Let's think about each of these and how they contribute to higher student performance in heterogeneous groupings:

Jo first starts of describing what a one-dimensional math class looks like - one where there is only one way to be successful and where the focus is on procedures. These are classrooms where some students rise to the top and others sink to the bottom. And yet, Boaler points out, mathematics is a broad and multidimensional subject. This can be encouraged by assigning open-ended and challenging real-world tasks that are difficult to solve alone, to mixed groups of students - the idea behind this is that there are many different approaches that can be used and that these differences are shared with the class so that all students benefit from seeing how problems can be solved in different ways. Following a multidimensional approach shows students that there are many ways to be successful with maths.

Along with assigning rich tasks to groups, complex instruction involves giving the students in the groups various roles. This shows that each person has a part to play, and every few weeks the students change groups and are assigned a different role.

This was an interesting concept for me. It involves raising the status of students who think they may be of lower status in the groups by praising something they have said or done and bringing it to the group's or whole class's attention.

This involves intentionally teaching students how to work in groups (listening to each other, respecting different viewpoints etc) and letting the group know that one member of the group will be asked about the work of the whole group and will be asked about the mathematical concepts the group was working on. As the other students in the group would not be able to help the student being asked, it was the responsibility of everyone in the group to make sure that all group members understood the concept. Jo Boaler writes that with this approach students start to see mathematics as a collaborative, shared pursuit that is all about helping each other and working together.

How does this help the high-achievers? Boaler writes that many students identified as high achievers are simply procedurally fast, but often they have not learned to think deeply about their ideas, explain their work or to see mathematics from different perspectives. Boaler noticed that while these students initially complained about working in groups and having to explain their work, they soon started to appreciate this approach because it gave them to chance to explain their thinking, which helped to consolidate their own understanding. In fact their learning accelerated when compared to students who were tracked, because explaining their work took their understanding to new levels. She writes, "Many of them had come in as fast, procedural workers, and the push to work with more breadth and depth helped their achievement enormously." Even more importantly, she writes "Neither the high nor the low achievers would be as helped if they were grouped only with similar achieving students."

Complex instruction is basically made of up 4 interrelated ideas: multidimensionality, roles, student responsibility and assigning competence. Let's think about each of these and how they contribute to higher student performance in heterogeneous groupings:

__Multidimensionality__Jo first starts of describing what a one-dimensional math class looks like - one where there is only one way to be successful and where the focus is on procedures. These are classrooms where some students rise to the top and others sink to the bottom. And yet, Boaler points out, mathematics is a broad and multidimensional subject. This can be encouraged by assigning open-ended and challenging real-world tasks that are difficult to solve alone, to mixed groups of students - the idea behind this is that there are many different approaches that can be used and that these differences are shared with the class so that all students benefit from seeing how problems can be solved in different ways. Following a multidimensional approach shows students that there are many ways to be successful with maths.

__Roles__Along with assigning rich tasks to groups, complex instruction involves giving the students in the groups various roles. This shows that each person has a part to play, and every few weeks the students change groups and are assigned a different role.

**Assigning Competence**This was an interesting concept for me. It involves raising the status of students who think they may be of lower status in the groups by praising something they have said or done and bringing it to the group's or whole class's attention.

__Teaching students to be responsible for each other's learning__This involves intentionally teaching students how to work in groups (listening to each other, respecting different viewpoints etc) and letting the group know that one member of the group will be asked about the work of the whole group and will be asked about the mathematical concepts the group was working on. As the other students in the group would not be able to help the student being asked, it was the responsibility of everyone in the group to make sure that all group members understood the concept. Jo Boaler writes that with this approach students start to see mathematics as a collaborative, shared pursuit that is all about helping each other and working together.

How does this help the high-achievers? Boaler writes that many students identified as high achievers are simply procedurally fast, but often they have not learned to think deeply about their ideas, explain their work or to see mathematics from different perspectives. Boaler noticed that while these students initially complained about working in groups and having to explain their work, they soon started to appreciate this approach because it gave them to chance to explain their thinking, which helped to consolidate their own understanding. In fact their learning accelerated when compared to students who were tracked, because explaining their work took their understanding to new levels. She writes, "Many of them had come in as fast, procedural workers, and the push to work with more breadth and depth helped their achievement enormously." Even more importantly, she writes "Neither the high nor the low achievers would be as helped if they were grouped only with similar achieving students."