Abstract / Synopsis
Who owns the mathematical ideas in the undergraduate classroom? A traditional mathematics classroom and curriculum imposes several barriers that prevent students from discovering and engaging with mathematical concepts. Definitions, notations, and theorems require mastery before students can work meaningfully with the underlying mathematical concepts. Raising Calculus to the Surface utilizes a different approach by providing students multiple entry points to engage meaningfully with mathematics ideas and allows students to promote meaningful ideas and conjectures into the classroom discourse to formalize their explorations. In this paper, we describe several characteristics built into the project materials, including a rubric designed to encourage student discussion in small groups and for the whole class. We illustrate with three vignettes how these features allow students to explore mathematical ideas using their own creations leading to conjectures which are promoted and shared with the whole class, thereby making students involved in creating the course’s mathematics content.
Aaron Wangberg, "Fostering Student Discovery and Conjecture in Multivariable Calculus," Journal of Humanistic Mathematics, Volume 10 Issue 2 (July 2020), pages 315-347. DOI: 10.5642/jhummath.202002.15. Available at: https://scholarship.claremont.edu/jhm/vol10/iss2/15
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