The Importance of Sketching in Mathematics

Giliola uses digital aplets to bring these kinds of visual representations into learning experiences. Aplets are also expanding the types of problems they're able to challenge students with. Giliola: "Whenever you have the opportunity to visualize an object, it is important to do that"

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Episode notes

Professor Gigliola Staffilani, who teaches in MIT’s Department of Mathematics, was closely involved in designing and teaching the introductory-level 18.01 Calculus I course series now found on the MIT Open Learning Library. She’s also been involved in teaching calculus to students on campus. To help students become proficient in a notoriously intimidating subject, she has tried to design learning experiences that bridge the gap between the pure abstractions that mathematicians love, exemplified by the use of conventional notation such as x, y, and f(x), and the concrete real-world situations in which calculus is typically applied in other fields such as chemistry or physics. In this episode, Prof. Staffilani discusses her efforts to make calculus less abstract and more intuitive for learners–efforts that draw on a diverse mix of teaching tools and props: digital applets, sketching tools, bagels, croissants, donuts, and even a balloon in a box. She also discusses her commitment to increasing equity and fighting implicit bias in her field.

Relevant Resources:

MIT OpenCourseWare

The OCW Educator Portal

Share your teaching insights

Professor Staffilani’s faculty page

Single variable calculus courses on MIT’s Open Learning Library

18.01 Calculus I: Single Variable Calculus on OCW

Music in this episode by Blue Dot Sessions

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