Christopher Danielson’s Blog

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On vehicles and the meanings of words

The following is an extended excerpt of a cover letter for Is It a Vehicle?, a book I have play-tested many hundreds of times in a wide range of situations over the last five-plus years and not yet found a publishing home for. I hope you enjoy the writing, and I...

On the left, an equilateral triangle (green) oriented with a horizontal base. On the right, a triangle (orange) with one short, vertical side, and two elongated diagonal sides pointing off to the right.
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Minnesota’s Largest Pattern Block Mosaic

To celebrate ten years of Math On-A-Stick, we built Minnesota's Largest Pattern Block Mosaic yesterday at the Minnesota State Fair. Careful study of this next image reveals 24 jaggedy "rows" of 7 large hexagons, totaling 168 regular hexagons (with a few more than...

Foreshortened view of the developing mosaic.
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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...

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.
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Two competing theories, resolved

I wrote about two competing theories recently. Each is an answer the question Why do you never see a square on the rectangle page of a shapes book for young children? That question stands in for lots of other specific questions, such as Why do counting books tend...

a two-by-two grid of yellow Post-its with hand-drawn shapes—three convex hexagons and a trapezoid