New book, summer math fun, podcasts, and more

updates from the wide world of children's mathematics

Author

Christopher Danielson
May 05, 2025

I have a new book out! 

How Did You Count? is the third in the series from Stenhouse. This book follows up Which One Doesn’t Belong? and How Many? by turning the reader’s attention to number structure—squares, triangles, arrays, addition, multiplication, exponents, etc. 

How Did You Count? features a similar style of gorgeous photography as How Many? and was shot in a

The following is a short excerpt from Chapter 2 of the Teacher Guide.

I want to address the term “mathematician” at the outset of this chapter, as it appears several times here. I think of mathematics as a discipline—one that has practices, language, and customs that are useful for studying numbers, patterns, and space. (Please forgive the vague and incomplete nature of this characterization; it is intended to be good enough to sketch out a big picture, not to be a rigorous definition. Writing a more rigorous definition of mathematics is a very interesting thing to attempt, but not essential to the current project.)

Anyone engaging in these practices is acting—in that moment—as a mathematician. We may be accustomed to “mathematician” only applying to people who work at a university, perhaps with a chalkboard on their office wall, and who publish mathematical papers. I used to think this way. I used to think doing mathematics meant expanding the boundaries of human knowledge—developing new ideas that the world had never known before. Now I understand that doing mathematics means expanding the boundaries of your own knowledge using the tools of the discipline. Naomi [a four-year-old mentioned earlier in the chapter], in noticing a pattern in the numbers on the tire gauge and inventing language (tenty) to describe that pattern, was very much behaving as a mathematician. When I use the term “mathematician” in this chapter, I am referring to the larger community, and I will use “professional mathematician” to refer to the subset of that community that consists of people spending their professional lives discovering and inventing ideas that are new to the community.

You—the reader—and I are members of this community of mathematicians. Most of us adults have little memory of our own process of learning to count, the challenges and the triumphs. In this chapter, I’ll highlight some typical landmarks for young mathematicians in this process, beginning with ways of understanding quantities that we come by naturally, and moving forward through much of elementary school arithmetic and far far beyond.

Links to the various versions of the book, via various outlets, are at the end of this email.

Summer of Math!

A while back, I had a project called Summer of Math. It was a tremendous amount of fun, and also quite a lot of work! After a hiatus of several years, Summer of Math is back! It is more streamlined, less expensive, and therefore more sustainable.

Summer of Math is a subscription to three mailings—one box in mid-June, and two envelopes in July and August—packed with mathy toys, prompts, questions, and The World’s Mathiest Scavenger Hunt. 

Toys are from the Turtle Factory; graphic design from Chris Nho; ideas based in research and years of practice; joy shared with and among the community. 

There are two versions; one for the younger mathematicians (4 to 7 years old), and one for the older mathematicians (8 to 12 years old). Click on through to learn more.

Do you know someone with children in that age range? Consider forwarding this email together with a short testimonial about the work.

Ayliean on Mathematical Objects

Anything Ayliean does for our playful and creative mathy world is worth paying attention to. Give the podcast a listen.

Simon Gregg’s WODB collection

You may know that Mary Bourassa handed the keys to the Which One Doesn’t Belong? website over to me, and that content lives on at talkingmathwithkids.com/wodb. 

And also, Simon Gregg has a fabulous collection of Which One Doesn’t Belong? sets available on his site. You should go have a look.

I wrote for the Routledge (née Stenhouse) blog!

What counts as counting? in which I take a somewhat contrary, though expansive, view of what “counting” means.

Talking Math with Math Chat

In celebration of the new book, I was invited to Mona Iehl’s Math Chat podcast. We had a lovely conversation, and I shared my hot take on diamonds as mathematical objects! Tune in!

The books

Comprehensive book-ordering info below.

  • book purchases from any source support the ongoing work

  • if you buy from Amazon, consider leaving a review (five is a really nice number of stars! and a substantive statement about the work is always welcome)

  • bookshop orders support local bookstores

  • if you’d like a signed copy, order from the TMWYK link and leave a note at checkout

  • a free-to-you way to support the work is to check-out or request from your local library

How Did You Count? is available for preorders (recommended for grades 3 and up)
picture book: Amazon—Bookshop.org—Stenhouse/Routledge—TMWYK
picture book with teacher guide: Amazon—Bookshop.org—Stenhouse/Routledge—TMWYK

How Many? (recommended for grades K–3, but also appropriate for older children)
picture book: Amazon—Bookshop.org—Stenhouse/Routledge—TMWYK
picture book with teacher guide: Amazon—Stenhouse/Routledge—TMWYK

Which One Doesn't Belong? (recommended for all grades K and up)
picture book: Amazon—Bookshop.org—Stenhouse/Routledge—TMWYK
picture book with teacher guide: Amazon—Bookshop.org—Stenhouse/Routledge—TMWYK
posters Stenhouse/Routledge

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