Abstract
In this study, we examined 10 integral lessons to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during integral lessons. Our findings reveal issues with implemented tasks as well as the way these tasks were presented to students. We also examined mathematicians' reasons behind their instructional practices, which show two common reasons of under-prepared students and time constraints. However, two mathematicians' in this study showed quite different instructional practices, which shows individualized faculty development might be critical in changing teaching and learning of calculus.
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