Mathematical Habits of Mind

I haven’t been blogging for a long time. As you can imagine, the pandemic took a toll on teachers, and at least for me and my teacher friends, we were working insane amounts of time, and it was so hard. Emotionally, physically, intellectually. At the time, I just didn’t have it in me to blog about the experience.

But now we’re about to start a new school year. And I’m vaccinated. And my students are vaccinated. And we’re wearing masks. And my classes are going to be with all my kids together in a single room [1], which is such an awesome thing compared to last year.

One of the classes I’m teaching this year is Advanced Precalculus. Another teacher, my friend James, is also teaching the same course. And he’s new to my school this year, and so when talking about the course, he shared with me how he formally incorporated Mathematical Habits of Mind in his teaching in previous years. And interestingly, last year, I toyed with the idea of formally getting kids to be metacognitive about problem solving strategies — but decided to focus on something else instead. So when James shared this idea with me, I got excited.

Right now I have an inchoate idea of how this is going to unfold. Hopefully I’ll blog about it! But for now, I wanted to share with you posters I made using James’ Mathematical Habits of Mind. Most importantly, here is a link to James’ original blogpost with his habits of mind and rubric.

Photo of the posters hung up in one of my rooms:

I know, I know, the lighting is terrible. The key words are:

Experimenter, Guesser, Conjecturer, Visualizer, Describer, Pattern Hunter, Tinkerer, Inventor

If you want these posters, the PDF file is here.

And here are all of them shared as a single sheet, and not as a poster.

Of course, if you’re a math teacher, you know there are a lot of lists of mathematical habits of mind. We agreed to use the ones James had already been using. But there are many alternative or additional things we could have included.

At the very least, I know that as we get kids to think about what strategies they’re using to solve problems, we’ll also see where there are lacuna in our curricula in terms of using those strategies. Or maybe we’ll discover it doesn’t have as much problem solving as I imagined in it. All entirely possible, since we — the kids and James and I — will all be looking through what we’re doing through our metacognitive Mathematical Habits of Mind lens.

[1] The reason I note this is because at the end of last year, I was teaching students live simultaneously in three places: they were in two different classrooms and there were a few at home on zoom. Yes, seriously. When I mention that to teachers and non-teachers alike, they asked how that was even possible. It was… a lot.



    1. I actually don’t use a book! I write my own materials to use with my kiddos. Most all textbooks are the same — which are bloated, bad explanations, tons of practice problems but not a lot of building up to them, not written with kids in mind. But if you’re just looking for something to help your daughter with, I’d just use whatever textbook your school is using.

      I do think this textbook (CME Precalculus) does a great job and if I were forced to teach from a textbook, I’d consider it. It looks very simplistic and not filled with a hundred problems per section — but that’s because it’s thoughtfully constructed. It has students build up the ideas doing the problems, and realizes you don’t need to do 20 problems of one type to understand it.

      Hope this helps?

      1. Thank you for the recommendation! I’ll take a look at the book. You might like the Art of Problem Solving books. They build on ideas and try to get the student to think about the ideas. They are for more advanced students, but a nice supplement too.

  1. I was going to recommend the Art of Problem Solving books, but I see Michelle has already done so. They are aimed at kids who love math, and they aren’t just a supplement. They are not suitable, however, for kids who need a lot of drill, as they concentrate on doing a few challenging problems, rather than many routine ones.

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