Knossos Games isn’t my day job. But it’s the part of my all-around occupation that I’ve been doing the longest. Let me try to explain.
I spend most of my time, quite enjoyably, being an educational psychologist. Basically, I study how people learn, specifically, mathematics. I have an undergraduate degree in mathematics from the University of Chicago, plus a Masters degree in mathematics and a PhD in educational psychology from the University of Wisconsin-Madison. I currently spend a lot of my time working with undergraduates who want to become teachers, to help them understand how their future students will think about math. But before all of this, I doodled on graph paper a lot.
I grew up making puzzles. I remember my very first puzzle that I made in kindergarten – a giant maze on packing newsprint. The teacher hung it on the blackboard near the door, so that my classmates could try it when we lined up for recess. Discovering graph paper soon after was a revelation. I went through reams of it in elementary and middle school. I became a member of the Study of Exceptional Talent (under the larger umbrella of the Center for Talented Youth at Johns Hopkins University) in the eighth grade, and the summer before my junior year I sent in some puzzles with a here’s-what-I-did-on-my-summer-vacation letter. One of those puzzles became my first publication in the SET newsletter, which a year later transformed into Imagine magazine. They asked me if they could publish more of my puzzles. Twenty-two years goes by really fast: college, grad school, now professor.
My primary job as a mathematics educator is to better understand how people think about mathematical concepts. I can then use that understanding to build better classroom experiences for my own students (and in the case of future teachers, their own students). How can I help them navigate a tricky concept most successfully? What will be the most common pitfalls for them? How can I ask just the right question to get them to think about an idea in just the right way? How can I pose the best activity so that the underlying reasoning of the concept they’re studying is self-evident? While the field is still young, there has been a considerable amount of research in this area that people like me can utilize in classrooms and pass on to other educators. And because there are still many unanswered questions, I help contribute to that body of knowledge by doing my own research.
Some of my colleagues over the years haven’t known what to make of my puzzle hobby. To them, it doesn’t have a clear connection to my occupation. Sure, some of the puzzles are math-related and sort of learning-related, but to them it’s a weird remnant of my origin story that defies explanation.
Really, making puzzles and being a math educator are different sides of the same coin. During my professional formative years, I learned a lot about learning. Theories of cognition. How people solve problems. What makes a problem hard. When I’m in my classroom with my students (or really, when I’m in my office before class deciding what we’re going to do), I’m using all of that knowledge to help make things easier for them. But when I’m designing a puzzle, I’m using all of that knowledge to make things harder for everyone.
For example, when designing the gerrymandering puzzles, I expect newbie solvers to bump around a bit before discovering the two main principles for gerrymandering: packing and diluting votes. When diluting votes, you only have so many districts to distribute heavy yes-voting precincts in to so they don’t overpower the collective no votes. With this realization, the puzzle then morphs into a pentominos-tiling problem (or septominos for the 7×7 puzzles). Don’t kid yourself – there’s a lot of mental work that needs to happen to just get this far. But the game’s not over. In designing each puzzle, I charted out all the different ways to consolidate precincts into districts, and then intentionally picked what cognitive science tells me is the least obvious way as the solution.
The same expertise that makes me a good educator also makes me a dastardly puzzlemaker. All the knowledge that helps me clear away hurdles inside my classroom allows me to throw them right in your path in a puzzle. All of the hair-pulling and teeth-gnashing that’s avoided by my students, well, you get the idea.
The interest in making puzzles came about early. I don’t know why. The understanding of what makes for a good, challenging puzzle ended up being an offshoot of my occupational journey. While I am only a puzzlemaker sometimes, I’m thankful that I can spend most of my time thinking about thinking, both as an educational psychologist and as a puzzlemaker.