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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.

Design principles of inquiry-oriented tasks in integral calculus