Exploring a structure for mathematics lessons that initiate learning by activating cognition on challenging tasks

• Problem solving and reasoning are facilitated by a particular lesson structure.
• This report offers insights into the use of prompts that differentiate tasks and posing variations on the initial task to consolidate the learning.
• Activating thinking through an initial challenge is a feasible way of initiating a sequence of learning.
• Teachers who taught lessons structured in this way reported that the lesson elements were feasible and effective.
• The ways that some teachers used students’ responses to the initial challenge to plan subsequent experiences seemed critical in enhancing transfer to other situations.

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks intended to prompt problem solving and reasoning to students, not only to activate their thinking but also to develop an orientation to persistence. Data were sought from teachers and students in middle primary classes (students aged 8–10 years) via online surveys. One lesson focusing on the concept of equivalence is described in detail although mention is made of other lessons. The research questions focused on the teachers’ reactions to the lesson structure and the specifics of the implementation in a particular school. The results indicate that student learning is facilitated by the particular lesson structure. This article reports on the implementation of this lesson structure and also on the finding that students’ responses to the lessons can be used to inform subsequent learning experiences.