Abstract:
A Model-Eliciting Activity (MEA) invites students to apply their mathematical understanding in resolving a problem. Having no defined pathway to a solution means student responses are wide ranging indicating mathematical insights and short-comings. MEAs also require communicating mathematical ideas successfully. Applications and communication of mathematics are difficult to teach, hence these competencies are underdeveloped even in mathematically confident students. Post-MEA, teachers are left with two responsibilities; the first is not allowing their students’ ideas to languish and the second is developing their students’ competencies. This is not adequately addressed by simply doing more MEAs. A common response by teachers can be a class discussion conducted after completion. However, teachers face barriers to orchestrating whole class discussion including the high level of skill required, a lack of guidance on structuring class discussions, and the amount of preparation and class time needed to be effective. In this study I propose an alternative strategy called ‘Follow-Up Activities’ (FUAs) which students complete post-MEA. FUAs adhere to six design principles of focus, consolidation, challenge, flow, maintaining the authority of student thinking, and ensuring that the thinking is held accountable. I design a process for generating these activities, called the FUA mechanism. It takes students’ written responses to the MEA, and uses an adapted literacy tool to guide students towards making evaluations. Two cycles of a design experiment are conducted with the purpose of developing the FUA mechanism through testing, reviewing and refining. In both cycles FUAs are created by teachers which require students to read, engage with the mathematics and evaluate other students’ methods. Each of these FUAs were successfully aligned to the required design principles. The involvement of teachers in this process highlighted refinements which were necessary and that would not have been anticipated otherwise. Consequently the final FUA mechanism provides a practicable option for developing and extending students’ ideas.
