Sigcse2018 Proof

Next up from SIGCSE2018 is Connect the Dots to Prove It presented by Mark McCartin-Lim. This paper was presented during the same papers session as MacCormick paper I wrote up previously and my reaction to this one was similar to my reaction to MacCormick's.

My reaction to MacCormick was - "This is awesome but while he's talking about redesigning existing theory courses, I think we can get a lot of mileage out of bringing these ideas into lower level CS courses."

I felt similarly about this paper.

The premise is simple - proof is hard and teaching proof is hard. Students don't know how to begin, what's allowed, what's not allowed, what's sufficient etc. McCartin-Lim and his team developed a software tool to present proof as a puzzle and to provide students with necessary support.

The tool allows students to interactively construct a graph of their proof. The graph helps students visualize the proof and the relationships between the assumptions and assertions.

Here's an example:

And a more complex one:

My immediate thought was that this should be reskinned as a high school product and rolled out in Geometry classes. I've written before about the fact that proof is rarely taught and rarely taught well even though it's supposed to be the star topic between Algebra and Trigonometry. A tool like this could probably help. This made me think further of the disconnect between K12 and higher education. McCartin-Lim talked about students having difficulty learning proof but lost in the conversation is that students should start building there proof related foundations in high school and supporting them in those early years can go a long way to alleviate problems that only surface at the college level.