Designing extension questions: Mathematical communication and creativity to assist with secondary-tertiary transition

Abstract

The secondary-tertiary transition (STT) period in a learner's mathematical journey is a period that continues to be of interest in the mathematics education literature. This period presents many challenges to learners, both in the cognitive and affective domains. Students’ relationship and understanding of mathematics can change significantly during this period, and a successful transition requires educators to support students through these changes.

This is a practitioners article describing our approach to designing bonus/extension tasks for secondary school students undertaking two first-year mathematics courses (Linear Algebra and Calculus). We describe how the literature has informed the task design process. We introduce four criteria for task design that involve: situating and extending learner’s mathematical knowledge; developing independence and self-efficacy; developing mathematical writing and communication; and developing creativity and exploration. We provide some examples of tasks to demonstrate what implementing these criteria look like and how they are assessed in our courses.