- In this lesson analysis, the topic of the lesson is a module on choosing an appropriate differentiation strategy. The course context is a lesson used at two public, 4-year, open-admissions institutions in the southeastern United States. It occurs midway through a Calculus 1 course with a wide variety of STEM majors. The instructional challenge we seek to address is that calculus students are often mainly exposed primarily to procedural ideas and seldom experience ideas that are more conceptual and less procedural. Combining differentiation strategies, including the product, quotient, and chain rule, is one such idea that requires a conceptual understanding of functions, especially composition of functions, as well as a procedural understanding of finding derivatives. Finally, we give a brief overview of the instructional approach: this module uses differentiation strategies implemented conceptually through a Team-Based Inquiry Learning (TBIL) approach, which includes assessing a given function and communicating the properties that lead to choosing the appropriate derivative techniques. At this point in the semester, students have been exposed to the derivative rules, but not many applications or ideas where they are required to build on the procedural knowledge or synthesize large amounts of information. Students work with their teams, engaging with carefully scaffolded inquiry activities that are facilitated by the instructor. Students think critically about what they are doing versus just following a sequence of steps.
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