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The cover of the book "Children's Minds". It contains a photo of a young girl intently studying two pieces of wooden track for a toy train, as she attempts to assemble them. This is a beautiful illustration of the relationship between children's minds and their physical environments.
Questioning Piaget

Questioning Piaget

Note: An earlier version of this post was part of the Talking Math with Your Kids newsletter. The provider I used for that newsletter ceased operating a while back, but I saved all of the content and will republish some of that writing here on the blog from time to...

A colorful board book titled "In Our World: A Book of Shapes"
Two competing theories

Two competing theories

Why do you never see a square on the rectangle page of a shapes book for children? This is the sort of book I'm talking about. I asked this question of a colleague this summer. It turns out that my colleague and I have different answers to this question. I'll share...

Selfie. From left to right: Me, the 16 year-old, and [locally famous Radio Gal] on a sunny summer evening.
Same Idea or Different?

Same Idea or Different?

I am currently writing the teacher guide for my next book, How Did You Count? (See a couple of teaser photos at the end of this post!) A section of a chapter of that teacher guide has the heading Seek to Understand and to Be Understood. Those who know my teaching...

wooden tiling turtles spill out of a canvas bag that itself has an image of four tiled turtles on it
A Very Mathy Gift List

A Very Mathy Gift List

I am obsessed with this shape toy I saw in the gift shop at the Science Museum of Minnesota last week. Seen from above in the first photo, the triangle looks like a triangle. Seen obliquely, we notice that the triangle is embossed on a half-sphere, and so the sides...

A sign on a light pole reads "Como Lake. 1.6 miles - 3200 steps around the lake"
A walk around the lake

A walk around the lake

A very snowy winter is turning to a long, slow spring here in Minnesota. It is the kind of spring that makes us joyful for sunny 45° days. So I went for a long walk Sunday afternoon. Together with a meaningful percentage of the population of the city of Saint Paul,...