Art and Math

Symmetry is for Artists, Mathematicians, Students & Five-year-olds

My Symmetry Tiles, designed by Paula Krieg
My Symmetry Tiles

Start with symmetry.

During this time that we’ve suddenly become a nation of homeschoolers, I hope everyone will continuing learning. Home learning can be tough. As some of you know, I’ve become a great fan of taking a deep dive into learning about symmetry. I’ve become a fan because it’s become clear to me how, harnessing a formal understanding of symmetry, can be an incredibly powerful tool which can facilitate an understanding of wide ranging concepts. .

In my next post will be talking about extending symmetry to support other learning.

My last ten posts have been about exploring frieze symmetries. If you are looking for a compelling, thorough, mathematically rigorous and artistically beautiful inquiry, please start at my January 24, 2020 post and keep going.

If you are looking for something totally worthwhile and doable with young children, this post of is for you. No special materials needed. OH, but you do need at least two of things, like spoons, macaronis, pencils, shapes cut from paper, envelopes, pennies,  paperclips. crayons.

These images I’m showing are done by 4 and 5 year olds. The lesson is about mirror reflections. I put out a curated “mess” of stuff, and the children organize them into these mirrored arrangements. It’s fun to do this with a partner. You can see the yellow yarn in the center of the design. This is the line that the objects have been reflected across. Children take turns laying down an object on their side of the line, then their partner places an identical object on their side of the line so that it reflects in the same way that a mirror would reflect the object.


Using scissors is an interesting challenge. Some students immediately see that there needs to be some thoughtfulness in the orientation of the scissors. How do you explain to a child when they get the orientation wrong? I heard one young boy instruct his partner to flip the scissors so they match.

I have found that it takes very little direct instruction to get even 4 and 5 years olds to create these symmetries, which leads me to believe that they have an intutive connection to symmetry. Formalizing an understanding of this way of thinking about arrangements is something that can help develop a way of seeing deeply into things, whether it be concepts or constructions.

Over the next few weeks I intend to post often, mostly to recommend projects that have both a fun visual appeal as well as rigorous math appeal. My thought is that the connecting thread through all of them will be symmetries of many types.

3 thoughts on “Symmetry is for Artists, Mathematicians, Students & Five-year-olds

    1. Thanks Steve. Fortunately, both of my children graduated from their schools last year. I feel so lucky that they didn’t have their educations interrupted as they both had really fine educational experiences. I feel so bad for all the people whose lives are being disrupted, but especially for the kids who’ve are in the last lap of the their educations.


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