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Math/Art Project: Reproduction and Extension of Tom Verhoeff's Dear Cor Always Busy

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Math/Art Project: Reproduction and Extension of Tom Verhoeff's Dear Cor Always Busy This is a collaborative post written by Izhar, Mahnaz, and Malik. The artwork we chose We chose Tom Verhoeff's Dear Cor Always Busy from the Bridges 2026 Math Art Gallery. The piece arranges the four words Dear, Cor, Always, Busy in all  4!=24 4!=24 possible orders, each word given its own colour. It looks like a poem, but every row is determined by a systematic rule. Our reproduction We reproduced the artwork by building it from scratch in LaTeX. We used the same four words, the same four colours (Dear = green, Cor = yellow, Always = blue, Busy = pink), and the same alphabetical ordering of the 24 rows. Reproducing the piece by hand taught us how easy it is to repeat a row or skip one, which is exactly why a systematic method is needed. Our extension We extended the artwork in two directions, asking two questions the original does not ask: Parity. If we count the number of inversions in each ar...
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Battleground Schools: three stops

  Battleground Schools: three stops First stop: the dichotomy table. The table of conservative vs. progressive stances stopped me because it clarified something I'd felt but couldn't name. I've heard people argue about math education for years without realizing they were operating from completely different assumptions about what mathematics  is,  authoritative and infallible versus exploratory and evolving. What struck me most is that this isn't just a debate about teaching methods. It's a debate about the nature of mathematical knowledge itself. If you believe mathematics is a set of perfect Platonic forms handed down through history, your classroom will look one way. If you believe it's patterns emerging from lived experience, it will look entirely different. I also noticed that the table labels one column "conservative" and the other "progressive," but I'm not sure those political labels always fit. The article itself points out that N...
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  What is meant by 'curriculum'? a response to Eisner My first thought about "curriculum" was simple: it's the list of things we're supposed to teach, the prescribed content and skills in a subject area, laid out in official documents. Eisner complicated that in a way I found genuinely useful. Three stops: First, the idea that schools teach three curricula at once, explicit, implicit, and null. I had never thought about what schools  don't  teach as a curriculum, but Eisner's point that "ignorance is not simply a neutral void" stopped me. What students never encounter shapes the questions they can ask and the lives they can imagine. That's curriculum too, even though it appears in no document. Second, the timetable as a teacher. Eisner's observation that the schedule itself teaches, that 50-minute blocks teach students not to get too involved, that arts placed on Friday afternoons teach students that art is play and not serious work, ...
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  The Locker Problem I started by shrinking the problem to 10 lockers instead of 1,000. After tracking each locker’s state through all the students, I noticed that lockers 1, 4, and 9 ended up closed, perfect squares. That pattern made me shift perspective: instead of tracking what each student does, I asked how many times a single locker gets touched. A locker is toggled once for every divisor of its number. Most numbers have divisors that come in pairs (like 1×12, 2×6, 3×4), so they get an even number of toggles and end up back where they started, open. But perfect squares have one divisor that pairs with itself (the square root), giving an odd number of toggles, so they end up closed. The twist here is that lockers start open and Student #1 closes them, so the perfect squares end closed instead of open. Final answer: Closed:  the perfect squares — 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, ...
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  Favourite math teacher: My favourite math teacher was in Grade 10. She never just handed us formulas. When we learned about area, she had us cut up rectangles and rearrange them to see why the formula worked. She asked “why” constantly, not to trap us, but because she genuinely wanted to know how we were thinking. She treated wrong answers as useful information, not failures. I remember feeling like I was building a map of mathematics instead of memorizing a list of routes. She made math feel connected and human. From her I learned that being slow is not the same as being bad at math, and that understanding " why "  makes the " what "  easier to remember. Least favourite math teacher: My least favourite math teacher was in Grade 11. He taught rules. “Just do this.” When I asked why, he said “because that’s how it is” or “you’ll understand later.” He was intimidating, and eventually I stopped asking questions. I still got good marks by memorizing procedures, bu...
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Skemp on two approaches to teaching and learning mathematics: My response Three things made me stop while reading this article. First, Skemp's idea of "faux amis",  false friends. A teacher and a student can both say "understanding" and mean completely different things, without knowing it. That made me think: how many times have I believed my students and I were on the same page when we really weren't? Second, the story about the 7-year-old boy with an IQ of 140 who cried over his math homework. He wasn't bad at math, he was trying to truly understand it in a classroom that only offered him rules. That's heartbreaking, and it shows the damage this problem can do. Third, the map example. Learning routes is like memorizing steps. Learning a map means you can find your way anywhere, and if you make a wrong turn, you can fix it. I also noticed something else: Skemp admits his own examples are "heavily biased" toward relational math, so I kept a...
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 Hello everyone !
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