Design principles of inquiry-oriented tasks in integral calculus

Abstract

Designing and implementing purposefully developed tasks have been linked to students’ understanding of mathematical topics. We report on design principles and intentions that guided the development of inquiry-oriented tasks. Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design intentions: Provide Review; Introduce New Content; Provide Guidance; Prompt Graphing and Visualisation; Prompt Generalisation; Foster Mathematical Creativity; and Prompt Reflection. In the discussion, we align these themes with existing literature and recognise an intersection between designing inquiry-oriented tasks, creativity-fostering tasks and reflective assignments. We additionally provide some recommendations for practitioners and report on students’ feedback on these tasks.

KEYWORDS:

• Calculus
• task design
• inquiry
• undergraduate mathematics education

MSC:

• 97D99

Disclosure statement

No potential conflict of interest was reported by the authors.