New Block Proof Tool To Power Discrete Math Instruction

Avatar photo Dr. Sandy Irani

Discrete mathematics is a foundational subject for computer science students, but it can also be a challenging one to teach. 

Challenge with teaching proofs 

Proofs are a case in point. Proofs are a difficult concept to help students master, because instructors should work one-to-one with learners to edit their work and point out mistakes. It’s a lot like teaching writing – labor intensive. But in typical large discrete math classes, this approach becomes untenable. Instructors don’t have the bandwidth to review and grade hundreds of proofs written by students and provide individual feedback.

As a computer science professor at University of California, Irvine, and the author of the Discrete Mathematics zyBook, I’ve been working with the zyBooks content team to overcome this challenge.  We’re releasing a new block proof tool this fall that will be included in both the Discrete Math and Linear Algebra zyBooks. The tool is a major update that gives instructors the capability to directly assess and teach proof writing skills and do it at scale to accommodate large classes.

“The tool is a major update that gives instructors the capability to directly assess and teach proof writing skills and do it at scale to accommodate large classes.”

Dr. Sandy Irani

How the block proof tool works

The block proof tool is a software tool that automates how students engage with proofs. While it doesn’t replace writing proofs, the tool gives students a scaffolded proof-writing experience, allowing them to drag and drop prewritten proof lines into the correct order instead of starting from scratch. It also provides students immediate feedback on and reinforcement for their work. The goal of these exercises is to teach students how to reason and how to articulate that reasoning. We’ve created block proof exercises for logic-based and text-based proofs, and these are integrated throughout the book. 

The block proof tool in action 

In this video, Dr. Irani explains how students learn with the new block proof tool. 

Related research

Efficiency of Learning from Proof Blocks vs. Writing Proofs

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Author Bio

Dr. Sandy Irani

Sandy Irani graduated with a degree in in EECS from Princeton University in 1986. She completed her PhD in Computer Science at University of California, Berkeley in 1991 and the following year was a recipient of the University of California President's Postdoctoral Fellowship. In the Fall of 1992, she joined the faculty of University of California at Irvine where she is currently a full professor. She served as chair of the Computer Science Department from 2005 to 2008 and from 2010 to 2012. In the first part of her career, her research focused on on-line algorithms and their applications to scheduling and resource allocation. More recently, she has been working in Quantum Computation with a focus on Quantum Complexity Theory. She is also the author of a web-based, interactive textbook replacement on Discrete Mathematics in collaboration with zyBooks, Inc. She is the 2021-2022 recipient of the UC Irvine Distinguished Faculty Award for Teaching and a Fellow of the ACM.