An Active-Learning Exercise for Understanding and Communicating Mathematical Proofs

Salil Vadhan, PhD
Vicky Joseph Professor of Computer Science and Applied Mathematics
Harvard John A. Paulson School of Engineering and Applied Sciences
LInc Faculty Fellow 2020-2021

Talk Overview: 

In the design of the new theoretical computer science course, “Introduction to Algorithms and their Limitations,” we developed a new active-learning exercise aimed at improving students’ skills at understanding and communicating mathematical proofs.  In these “Sender-Receiver Exercises,” half of the students (the “Senders”) explain a proof that they have studied in advance to one of the other students (a “Receiver”), through an interactive dialogue. The thesis is that, by preparing for and engaging in such a dialogue, students develop the skill to understand proofs at multiple levels of abstraction, and connect the high-level intuition to the formal details. Moreover, this exercise capitalizes on the asymmetry of students’ prior mathematical expertise as pairs work toward a shared goal of clarity and understanding.

In this talk, we will describe the Sender-Receiver Exercises and discuss our experience implementing them in the first two offerings of the course (with approximately 90 and 240 students, respectively). We will share summaries of the surveys that students filled out after each exercise, reflecting on what they learned from the exercise and how to improve.

Joint work with LInc research associate and SEAS lecturer Robert Haussman and postdoctoral fellow Deniz Marti, along with the course staff from both offerings of the class.

Biography: 

Salil Vadhan is the Vicky Joseph Professor of Computer Science and Applied Mathematics at the Harvard John A. Paulson School of Engineering & Applied Sciences, and Lead PI on the Harvard Privacy Tools Project. Vadhan’s teaching and research is in theoretical computer science, including algorithms, computational complexity, data privacy, combinatorics, and cryptography. His honors include a Harvard College Professorship, a Phi Beta Kappa Award for Excellence in Teaching, a Simons Investigator Award, and a Guggenheim Fellowship. As a LInc Faculty Fellow in Spring 2021, he worked on the design of a new introductory course in theoretical computer science, "Introduction to Algorithms and their Limitations."