summer art/math

Encouraging Visual Math Thinking with 4-year olds

I was invited to work with 4-year olds this summer as one of five Arts-in-Ed people. My part, as I defined it, was to create an experience with math thinking that merged with visual arts. Or was it the other way around? My biggest discovery was that this math/art is a completely natural activity for four-year-olds. I could only understand this, however, after having already having unlearned then relearned some things about math. The surprise was uncovering how much math thinking has in common with the ways I think about art.

children thinking

The important detail in the photo above, is that these two young fellows don’t look like they are having fun. They are not having fun, but they are not unhappy either. They are thinking. They are engaged. They are doing some independent explorations and are figuring out how to respond to a challenge I’ve posed.

The reason that I am showing this first is that it reflects how my thinking about arts-in-education has evolved through listening to math educators. There’s a teacher from Brooklyn, Michael Pershan, who is vocal about things not having to be fun to be valuable. Then there’s Mike Lawler, whose postings have introduced me to the way mathematicians ask questions, make predication about the answers, then go at it to see what happens. Christopher Danielson has validated the value of forming math opinions (like, “these things are the same because….”) and then forming a divergent opinion (“these things are different because….”). Malke Rosenfeld has enriched my understanding of thinking about the powerful lessons within examining the shifting relationships in the physical world. John Golden and Simon Gregg have caught my attention by the way they approach an idea, looking at it and playing with it every which way they can think of. These are things mathematicians do, and these are things that artists do. Turns out that these values resonate with 4-year-olds, too.

Star made from triangles and rhombuses
Star made from triangles and rhombuses

People who think about math as a vehicle for doing calculations might have a hard time following my thinking here. If that’s where you’re at, suspend that belief for the rest of this post (or the rest of your life!) and think of math and art both as a way to discover, examine and develop insights about the world around us. With this in mind, each week that I worked on with the students, 1/3 of my plan was to introduce an activity that aspired to develop mathematical thinking while working with artful materials.


One of our projects was based on research I had read about–WJ4LCbVq8EZ which I wrote about at the end of a post a few weeks ago. The idea is to have two different piles of items (we used mancala beads) then estimate which pile has more. No counting allowed, which is great because even the students who can count do not count accurately! I extended the ideas that the researched suggested by then telling each child that I thought that they were wrong, that their other pile had more. I then asked them to prove their estimation. That’s when this got really delightful!

Comparing Lines of beads
Comparing Lines of beads

The first configuration that emerged for proving which pile of beads was bigger was to line up the beads. The longer line had the most beads. But not everyone connected to that system. One of the students lined up the beads with the short edge of the folded paper, then when he ran out of room he continued his line by forming a sideways “L,” finally comparing the shape of the L’s made by each pile.

The Bigger Circle has more
The Bigger Circle Has More

One young lady made circles with her beads, explaining that the larger circle had more beads.

Bead Array
Bead Array, with a counselor looking on, maybe helping?

Here’s someone who worked on making arrays out of beads in order to compare them!

Then there was the student who just didn’t participate. I was able to figure out pretty quickly that she didn’t know what the word “more” meant. What was hard for me was figuring out how to explain to her what more meant. Go on, try to explain that word. Finally, after many failed attempts to convey the meaning I made two lines of beads, each of which were made up of six beads. She knew word “same.” Yes, she agreed, the lines were the same. Then I took one bead away from one of the lines

.Are they still the same?



Not the same. This line has more.

She got it! Very exciting.

This is about all I can write for today. I will write about the other activities that we did in a later post.

5 thoughts on “Encouraging Visual Math Thinking with 4-year olds

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