Session V (1:10–1:55 p.m.)
Pretty much every calculus book states the definitions of divergence and curl with no motivation, providing a hand-wavy notion of their geometric meaning or postponing these concepts entirely until after covering the theorems of Green, Gauss and Stokes (all of which are stated out of the blue with no inkling as to why they might be true). In this talk we will derive the formulas for divergence and curl using geometric notions of flux and circulation in a way that leads naturally to those “Big Three” theorems — and provide additional suggestions for revamping the way we teach vector calculus.
Are you looking for ways to get students more engaged in math? Brain teasers promote the development of critical-thinking skills and are a powerful way to inspire mathematical discourse. The idea is to develop pedagogical content knowledge by transferring previously learned skills when trying various techniques, asking questions, making conjectures and taking risks. By incorporating brain teasers into a classroom setting, students have an opportunity to collaborate and discuss mathematical strategies. The purpose of this session is to model three hands-on brain teasers that ignite learning through productive challenges and include: (1) looking for patterns, (2) collaborating as mathematical thinkers, and (3) exploring new approaches for solving problems that correlate with MP1 & MP7. At the end of the session, you will leave with ideas and examples of how to implement brain teasers into their educational setting.
This session will pose the following questions to participants: What is the purpose of math placement? How can we ensure math placement is fair? How can we ensure math placement is fair, while recognizing that some students have more resources than others? What are we worried students will “get away with” in gaming math placement?
A roundtable to discuss the process of converting to ctcLink and the resulting challenges, focusing on elements of particular importance to math departments. Participants are invited to share makeshift solutions their colleges have devised.
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