Leveraging asymmetry in student's prior knowledge through peer learning exercises

Salil VadhanSalil Vadhan, Vicky Joseph Professor of Computer Science and Applied Mathematics & Lead PI on Harvard’s Privacy Tools Project, teaches COMPSCI 120: Introduction to Algorithms and their Limitations, a new introductory course in theoretical computer science “aimed at giving students the power of using mathematical abstraction and rigorous proof to understand computation with confidence.” Many computer science students are “builders” who enjoy the creative aspect of the field, yet their mathematical backgrounds are often quite diverse; to some, mathematical theory is unfamiliar. In redesigning the undergraduate computer science curriculum, it was a priority to make this “new language, reasoning, and way of thinking” accessible to students early in the program.


Vadhan supplemented traditional assignments, lecture material, and teaching fellow support with novel “Sender-Receiver” exercises, which were used repeatedly throughout the semester. In designing these, he worked with research associate Robert Haussman and postdoctoral fellow Deniz Marti from Harvard’s Learning Incubator (LInc).


In these exercises – where half the students are assigned to be “Senders” while the other half are “Receivers” – “Senders” review a mathematical proof and come to class prepared to teach a “Receiver” classmate both the high-level gist of the proof and some of the formal details. Students are randomly assigned into pairs for the interactive dialogue. Throughout the conversations, they practice engaging in and communicating across varying levels of conceptual complexity and, by the end, come away with a deeper understanding of the proof. Vadhan noted that “right from the first execution of it, we were really happy with what we saw happening in the class.”

The benefits

The “Sender-Receiver” exercise proved to be an effective tool for engaging students across a wide range of mathematical backgrounds and developed students’ skills for communicating complex ideas at multiple levels to their peers. Over time, students discovered which strategies worked best for them when tasked with the “Sender” role and reflected on the value of learning through two-way dialogue. By the end of the semester, some students had even adopted the protocol for their study groups to prepare for exams.

"One of the things that draws us to teaching is that through the process of explaining, we come away with a much deeper understanding than we had before.”

The challenges

One of the core challenges of peer learning exercises in courses with a wide range of background knowledge is ensuring that “everyone comes away feeling like it was a valuable experience for them.” Oftentimes it leaves behind students who get lost in the material, and students who are most comfortable feel like they haven’t learned anything new. In implementing these exercises, it’s crucial to be intentional about the concepts you select and be attentive to how the conversations are progressing.

Takeaways and best practices

  • Calibrate the complexity.
    This exercise relies heavily on the “Sender” students coming to class prepared. It’s essential that instructors calibrate the complexity of the concepts these students need to grasp to ensure that the time can be used most effectively. If the concept is too difficult, students will be lost, but if it is too simple, the exercise won't generate as much conversation. Instructors should also be mindful of the balance between student-led instruction and providing an instructor-led digest of the concepts.
  • Encourage collaborative spirit and reflection.
    Active learning exercises provide a way for emphasizing a collaborative, rather than competitive or adversarial, spirit in classes. To formally support this dimension, students in COMPSCI 120 were expected to complete a short reflection survey after each activity and maintain a participation portfolio documenting the best examples of where they helped advance their classmates’ learning or improved the class.

Bottom line

Active learning exercises like the “Sender-Receiver” peer learning activity used in COMPSCI 120 can be an effective tool for developing a sense of community of learners, increasing student engagement, and helping students build skills for communicating complex information to other students with different knowledge backgrounds.