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Revisiting Internal Motivation

There is a tension between intrinsic and extrinsic motivation in teaching mathematics. Our answer to the classic student questions Why do I need to learn this? is a good measure of where we look for motivation. You can appeal to the extrinsic, or instrumental, rewards: you need math to succeed in get a good grade, to succeed in middle school, …

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Who is the most famous?

One fun thing math lets us do is measure difficult-to-measure things. Like fame. We all have an instinct for what fame is, and the more we put it into words, the more we’ll find we can translate fully into math. So what let’s us know if someone is famous? Well, famous people are well known. We tend to know them, …

The Mathematically Inclined Shall Inherit the Earth

“… at this point, it’s in the hands of people who are mathematically inclined.” —Stephen Hsu The January 6th New Yorker contains an article on B.G.I., a Chinese company seeking to do major work in the field of genetics. According to them, the massive amounts of genetic data they (and others) are collecting and interpolating will help “explain the origins …

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 …

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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. …

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 …