I attended a session recently about pattern blocks and young children. The presenter told us that “young children are hands-on learners; they are not logical.” 

My eyes got very big. 

We were offered an example. The tan rhombus pattern block has half the area of the orange square. Because children are not logical, our presenter told us, they can’t just know it; they have to experience it. They need to fill in a frame like the black one at left below. 

There are two ways to fill it in; each involves a green triangle. Two tan rhombuses and one green triangle have the same combined area as one orange square and one green triangle. Therefore two tan rhombuses have the same area as an orange square.

But hear me out here. That is a logical argument. Let’s assume for a moment that four and five-year-olds will make sense of it (which was our presenter’s contention, but which maybe not everyone agrees with). If they do, it’s because they are able to draw a logical inference from their experience with the blocks.

I am not at all concerned with the presenter’s ideas. I believe they were trying to tell us that young children need to experience things in order to build arguments about them; that telling them stuff about the pattern blocks is less useful than asking them to investigate their properties and reflect on the experience.

I am concerned with the message, “Young children are not logical.” That message is objectively false.

Yet it is pervasive. It is part of the foundation for our low expectations of children’s mathematical development.

A more nuanced message might be, “Young children’s logic is typically grounded in their experiences.”

When my 17-year-old was four, she reasoned her way through all the logical permutations of “If I am a Muppet, then I look like a cartoon.” I documented a three-year-old arguing that the fish she wanted to touch while wading in a lake should not be afraid of her because she is not a monster. Children are logical, but their logic stays closer to their own experiences than to adult-made abstractions.

So I say “YES!” to pattern blocks and frames for filling in. I say “YES!” to asking questions about sameness, and to encouraging young children to reflect on their experience. But the reason is not that children lack logic. The reason is that children’s minds thrive on rich experiences with which to think and build new ideas from.

Young children’s logic is typically grounded in their experiences. So let’s give them great experiences!

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Comparisons of size research

Relatedly, I read a new research article about the development of children’s usage of size comparison words. It puts some formality to the idea that children develop understanding of words such as bigger and smaller over time, rather than all at once. Commonly, they will notice that these two words each point to an intensification of the property size. Correspondingly, they will treat them as the same, producing larger block structures in response to a request for a “bigger” one and also to a “smaller” one.

It’s not a misunderstanding of bigger and smaller; it’s a developmental milestone.

Shapes made of paper

I have long been a fan of Paula Krieg’s explorations of geometry and creativity. I ran across a project she collaborated on: MATHshapes, paper cutouts for quick and easy geometry art. Read the extended piece and see examples here. Buy your own set here. 

Card game

This game looks fun! An image includes a card about “Famous Vehicles” so of course I am obligated to share. (Unfamiliar with the vehicle reference? I invite you to join #vehiclechat.)

Strombus

I read about the strombus via John Golden. While I always love a new shape name, I was most entranced by the embedded claim that Proclus, an ancient Greek philosopher, referred to darts as “four-sided triangles” and considered them a kind of paradox. My own adventures in early childhood shapes suggest that many kindergartners agree with Proclus.

Bathtime Mathtime

While we’re talking about underestimating and underrepresenting young children’s intellect, let’s invite Danica McKellar to make a simple improvement to her shapes book, shall we?

Three example of rectangles on the rectangle page! YAY! None of them a square! BOO!

CPM podcast

I was on the More Math for More People podcast from the CPM curriculum project recently. Lovely people over there. We had a fun conversation that went a little long. They made it into a two-parter.

Part 1: Where Joel and Misty talk about cheese curds and begin a conversation with Christopher Danielson 

Part 2: Where Joel and Misty talk about cats and finish their conversation with Christopher Danielson

Sesame Street & James Earl Jones

James Earl Jones passed away recently. In tribute, Sesame Street posted,

Click on through and enjoy.

Reciting the Alphabet

Counting to Ten

New home for Which One Doesn’t Belong?

Which One Doesn’t Belong, the website has moved! Thank to the diligent work of Mary Bourassa, this content has been housed for many years at wodb.ca. The time has come to pass the torch, and Talking Math with Your Kids will carry it for the foreseeable future. New home is talkingmathwithkids.com/wodb

Adjust any links on your own sites or documents accordingly, please. We intend to implement a redirect for about six months so that nobody gets surprised when the old site dies off sometime in 2025.

New book

Preorders are live for How Did You Count?, my new book which is due in March 2025. I describe it as number talks meets How Many? This book lives at the intersection of numbers and algebra, and features gorgeous photography by Asha Belk. We took the pictures last May in a rec center here in Saint Paul, MN. 

You’ll encounter triangles of brown eggs, pots of purple paint, a tetrahedron of basketballs, halves of apples, pairs of shoes, and oh-so-many pips on oh-so-many dice. You’ll solve the mystery of the blue pudding.

Ordering info below:

How Did You Count? is available for preorders (recommended for grades 3 and up)

picture book: Amazon—Bookshop.org—Stenhouse/Routledge 

picture book with teacher guide: Amazon—Bookshop.org—Stenhouse/Routledge

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The Talking Math with Your Kids newsletter is lovingly compiled and written by Christopher Danielson. Comments, questions, suggestions, and requests always welcome.