I watched Tracy Johnston Zager’s talk from Shadowcon today and it gave me tons to think about. The talk is here:

Tracy Johnston Zager’s Shadowcon Talk

One very interesting part of the talk was a collection of negative ideas that elementary school teachers shared about math. Those words are on the screen around 5:35 into the talk and here’s some of the words on the list – honestly, it makes me sad just typing them:

fear, dread, memorization, hard, humiliating, nervous, worksheets, stress, hate, alone, mistakes, boring, pointless, . . . .

She also shared a list of words that mathematicians use to describe math. Those words are happier:

Words that mathematicians use to describe math

They include: magnificent, passion, creative, elegant, beauty, absorbing, imagination, curiosity, discovery, . . . .

I asked her on Twitter if she had a list of some of the positive words that the elementary school teachers used to describe math and she shared this list:

Interesting.

If I’ve correctly understood one of the goals that Tracy has set for herself, it is to help move the people whose thinking about math is reflected at least partially in the first list closer to thinking about math using the words in the second list. Seems to me that this is an extremely worthwhile goal. But a difficult goal, too, because I’d venture to guess that when the mathematicians produced their list of words above, they probably weren’t thinking about elementary school math.

Elementary school teachers face a tough balancing act when it comes to teaching math. That have to help kids build up a good base in basic math skills while, using the language from the second list above, finding ways to show the magnificence of math, the creativity in math, the elegance in math, the beauty in math, and so on.

I struggled with that balancing act with my own kids and initially used a lot of old math contest problems to show some of the fun side of math. But then I saw some of the work that teachers like Fawn Nguyen ( My Fawn Nguyen-inspired blog posts are here ), Patrick Honner ( A slew of blog posts inspired by Patrick Honner ) and Dan Anderson ( Some posts inspired by Dan are here ) were doing and I realized two things. First – there was a lot more non-standard that I could be showing the boys. Second, the kids would *really* enjoy seeing it. Dan’s My Favorite blog post really helped me understand this last point.

So, I guess if I want to try to frame my thoughts with the word bubbles that Tracy shared, I’d say that if you want to move people from first list of words to the second list of words, a great way to do that is show some of the fun things in math that inspired that second list of words. Looking around, you may be surprised how many of these seemingly high level / abstract math ideas are not only accessible to kids, but are things that just blow kids away.

Just from this past weekend, here’s a short clip of a 4th grader reacting to cutting a Möbius strip in this project – listen for the “wow, that was kinda cool”:

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Here’s my son’s reacting to the Chaos game in an older project – no need to listen carefully here, they are screaming!:

Computer Math and the Chaos Game

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and here’s my younger son reacting to seeing the continued fraction for the square root of 2 – “that’s cool”

Geometry, Continued Fractions, and the Square root of 2

Another great source of math ideas to share with kids are the public lectures from mathematicians on youtube. Some of these lectures can help kids see incredible interesting ideas in math, and bits and pieces of these videos can form the basis of some great projects. I wrote about some of the ideas I’ve found from Terry Tao, Jacob Lurie, Richard Green, Bryna Kra, and a host of other professors and teachers in this blog post inspired by a tweet from Kate Owens: Kate Owens on Concrete vs Abstract

My goal with these projects has never been to bring the boys to a level of proficiency in whatever advanced math lies in the projects, but rather just to explore and show them fun math. Seeing Tracy’s talk today showed me the side benefit of (hopefully) having positive words and ideas come to mind for them when they think about math. You never know what simple ideas they’ll take away from these projects:

Five Tetrahedrons in a Dodecahedron

So, thanks to Tracy Johnston Zager for a great talk and for giving me a pile of things to think about!