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Quadrilateral Puzzle

I’ve been immersed in puzzle and lesson creation lately, and I thought I should take advantage and throw some of them out here on the blog. Please take, solve, use in your classrooms or at home, and let me know what you think. If people like the puzzles, I’ll make a point of putting them out here more often. A …

Twin Prime Hero

I just read this wonderful interview with Tom Zhang, who made recent, important progress on the Twin Prime conjecture. It’s a strange, quiet interview, and a lovely departure from the world of the fame-obsessed. Another thing I like: he emphasizes the love and the persistence. Here’s how the interview ends: What would you say to a young student who wants …

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A spoonful of transgression

I was just observing a third grade class learning/reviewing basic fraction to decimal conversion, and I overheard a great remark. A girl, reading a word problem, said to her table mate, “Jessica ate 6/10 of a cake?! She’s fat.” There’s a part of me that hates comments like that, and a part that loves them. I hate the comment because, …

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Teaching Perseverance

Reading an Alfie Kohn’s article on what kids learn from failure made me think of the most common question I hear from teachers about the Common Core Practices: How can I teach perseverance? It’s an excellent question, and the answer isn’t necessarily obvious. As Kohn points out, experiencing failure and having a teacher prod you to keep trying isn’t—or letting you …

How to Save Common Core

Those who believe the Common Core Standards are a good thing should take notice. The next year or two will probably make or break them, and the criticism is already starting to mount. This matters. Reforms only work when the people who have to implement them on the ground—teachers and, to a lesser extent, administrators—buy in. And thanks to a …

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Productively Stuck

When I try to describe great teaching, I notice a certain phrase pops out of my mouth again and again. Productively stuck. As in, the goal of the teacher is to get her students productively stuck as soon as possible. As in, we want to hook the students with a compelling question and then leave them productively stuck. As in, …

Can Modesty Cure a Hurry?

ANNOUNCEMENT: Sign up now for our Common Core Crash Course for 1st-5th grade teachers, this August 20-21 in Seattle. __________________ It’s happened to every teacher. It’s Thursday, but your students don’t seem to remember Wednesday or Tuesday, and you’ve got three times as much material to cover if there’s any chance of Friday’s lesson working. Finally, you gather them together. …

Proofiness

When Stephen Colbert introduced the word truthiness on his show, he told us to trust our guts. That’s where the truth comes from, ladies and gentlemen: in the gut. Do you know that you have more nerve endings in your stomach than in your head? Look it up. Now somebody’s going to say, I did look that up, and it’s …

Inversion Problem Update

I recently posted this interesting inversion problem: The question is this: in mod n, how many functions f(x)= ax +b are their own inverses? For example, the function f(x) = 5x + 2, applied twice in mod 12, is equal to the identity. It’s direct to check: f(f(x)) = f(5x+2) = 5(5x+2) + 2 = 25 x + 10 + …

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A curious inversion problem

I’ve been exploring a new problem with a couple of students recently that I find incredibly compelling, and I thought I’d mention it here. The main idea is looking at the behavior of functions of the form f(x) = ax + b in various mods. There’s actually a huge amount to explore here, from fixed points to invertibility to the …