By Peter Sullivan
There is widespread agreement that student-driven inquiry approaches can help students build understanding, solve problems and reason mathematically. But to ensure that all students are included in learning opportunities, specific teacher actions are needed and lessons can productively be structured in particular ways. These actions include the following:
- Posing tasks which are mathematically rich, which most students do not already know how to solve, and which require students to make decisions on the solution type and approach.
- Allowing students time to engage with the task. Perhaps the major difference between students is not their so-called ability but the time they need to engage with the ideas.
- Not only encouraging students to persist in their learning and being willing to take risks but also posing tasks which require those attributes.
- Introducing tasks carefully to ensure that required language is covered and prerequisite concepts are reviewed.
- Refraining from telling students how to solve the tasks. This is perhaps that most difficult of these actions in that it is counter to the natural instincts of teachers and requires teachers to trust that students can engage productively with the mathematical ideas.
- Preparing prompts that can be given after some time, to students experiencing difficulty. Such prompts are intended to allow students access to the task. After completing such a prompt, the intention is that students proceed with the original task.
- Planning further challenges for any students who finish quickly to extend their thinking and perhaps prompt abstraction or generalisation.
- Making time to review student work on the tasks, and prioritising students presenting and explaining their solutions and solution strategies.
- Posing subsequent tasks which are in some ways similar and in some ways different from the original task, with the intention that students see the underlying concepts more clearly and reduce the chance of students over-generalising from solutions to the initial task.
Note that, in this structure, it is not critical that all students solve the first task but engage with the idea sufficiently to be able to listen to the explanations of other students. Of course, tasks need to be appropriately challenging, meaning that most students will experience a sense of challenge but at least some will progress enough to contribute to classroom discussions. The intention, though, is that all students engage productively with subsequent tasks, having learnt from the initial efforts and the class discussions of students’ strategies.
The following newly released publication contains close to 100 suggestions of such learning sequences:
Sullivan, P. (2018). Challenging Mathematics Tasks: Unlocking the potential of all students. Melbourne: Oxford University Press.