The Doing/Thinking/Loving Math Classroom

This summer, we had the opportunity to draw up and institute a wholesale program from scratch, using our own lesson plans and providing the PD and support. Following that program, we began some fascinating conversations about how to articulate our vision of excellent math classrooms in more detail. From 30,000 feet, the direction we want everyone to move feels clear: …

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Breaking and Remaking Lesson Plans

I just had an interesting lab session with a school district we’re working with this year. The teachers (K-2) want to extend the scope and dynamics of their lesson plans, and make sure they challenge their students. But the teachers also don’t have much free time, are, in many cases, new to the curriculum, and also feel that they need …

Thoughts on story problems

Story problems! They are the great bugaboo of math class, the problems everyone remembers hating, On the other hand, when educators think of “real-world” math, useful math, or motivated math, story problems are where they want to go. And this instinct makes sense. Story problems should be a fantastic resource in the classroom—a chance for reading comprehension, making sense of …

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What are the aims and goals of math education, K-2?

As part of the Math for Future Elementary School Teachers class we’re teaching at the UW, we regularly ask our students to reflect on what they’re learning in the class. This particular student reflection felt so dense and comprehensive that I thought it would be worth sharing here (with her permission, and her name removed). The prompt: What do you …

How to help your kids fall in love with math: a guide for grown-ups

So you want your kid to know math? Of course you do. Math is an important tool, used widely in many disciplines, and helps us make sense of our world. It’s also beautiful, fun, and interesting, especially for young children. Kids are just entering the world of patterns and numbers, and their love of math is ready to bloom. They …

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Thoughts on linear equations

I recently received this email from a teacher I work with: “Dan, I have a question for you. I just introduced my [pre-algebra students] to slope and then to slope-intercept form of linear equations and wanted to explore with them some word problems which could be written in that form. (Ex: . For babysitting, Anna charges a flat fee of …

Phi is the new root 2

My knowledge about the foundation history of irrational numbers was challenged today, and I’m pretty happy about it. I had recently tweeted a Vi Hart video that gave a fun, geometric proof of the classic first proof of irrationality: is irrational. If it weren’t, that would mean you could build a square that had integer sides and an integer diagonal, …

Saying Yes: Joi Ito’s 9 Principles

Recently, Dan gave a TEDx talk based on the blog post 5 Principles of Extraordinary Math Teaching. In the conversations we had with each other and with other educators in the run up to the talk, one principle came up repeatedly as the most nuanced of the five: Say Yes to Your Students’ Ideas. Perhaps the most challenging principle to …

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Goodbye hexagon, hello 6-gon!

A colleague of mine once remarked how strange it is that while the Greeks talked about 6-cornered shapes and 4-sided shapes, we talk about hexagons and quadrilaterals. Why is it, aside from the historical accident that it is, that we persist in making people learn Greek to talk about shapes they see everyday? And quadrilaterals and hexagons are the easy …

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The Four Questions

We’ve argued for a long time that the real experience of mathematics is inextricably tied to play. But if you’re a parent or teacher, you’ve seen kids play in mathematically irrelevant ways. How do we hit that sweet spot of mathematical play? One way is to recognize mathematical questions and ideas when they arise from the play itself. Another is …