Arts in Education · Math and Book Arts

Books, Symmetry, and Students

Pamphlets made by seventh graders
Sewn Pamphlets made by seventh graders

I’m in the busy part of my art-in-ed, itinerant artist season. The challenge is to keep what I do relevant to the students, to the curriculum, to the teachers, and to myself. Most of the work that I do in schools is done with teachers I’ve worked with in previous years. Usually I repeat a project each year with the teachers’ new classes, though there are always tweaks that are made. Then, sometimes, it’s time to retire a project that’s been working well for years.

I’ve just finished up quite a few projects in classrooms, many of which were new this year. I’m going to attempt to write a number of posts about these projects before the next set of classes that I teach start up.

This is a detail on one of my own drawings
This is a detail on one of my own drawings that starts with the graph of functions.

There’s been a shift in my approach to what I offer to the schools. Whereas I used to think of my work as a way to motivate and celebrate literacy, now I am more focused on using our bookmaking projects in a way that supporting the teachers’ math goals. I’ve been realizing that the math part of the curriculum is where many teachers most appreciate support. There is so much in the paper and book arts that can support the math that students need to learn that making this shift has been thoroughly enjoyable to me.

Symmetry is a theme that kept emerging in the projects that I presented these last few weeks. This is partly to do with the nature of making books, but I also deliberately focussed on it more than it other years. I’ve realized, just recently, that the symmetry of shapes is the visual equivalent of mathematical expressions. I probably won’t express this well, but here goes. Think about doing any sort of math problem that has an equal sign in it. 5+3 = 8. It’s balanced. If you add a 3 to one side you have to add a 3 to the other side to keep the expression true. Math calculations are all about symmetry and balance. It is, therefore, completely appropriate and desirable, to help kids develop their natural affinity to symmetry.

Starting with a pile of cards
Starting with a pile of cards

One of the projects that I did with kindergarten students had to do with these piles of square cards. Students worked in teams. The first student puts down a card, then the partner puts down a card that is a symmetrical reflection of color and shape. They take turns putting down a card and then reflecting it.

Making Symmetry
Making Symmetry

It took a bit of doing for these 6 year olds to get the hang of what we were doing, but, still, quickly, patterns emerged.

Reflection symmetry
Reflection symmetry

These cards, by the way, are an element within a larger math activity book that we made.

 Since these pieces are made from paper, I suggested to the teacher, as this becomes easy for the kids, to cut out one of the smaller squares from some of the cards so that mirroring the shape transformations becomes a bit more challenging.


Another symmetry project I tried out for the first time was with the Pre-K crowd. My friend Joan, who has worked with this age group, showed me this activity that she had developed with kids she had worked with. I’ve been excited to try it out.

Popsicle Stick symmetry
Popsicle Stick symmetry

What I did here was define a line of reflection. Then these five-year olds did the same kind of reflection symmetry that I described above, each taking turns putting down a stick, then the partner reflects it with one of their sticks.

Popsicle Stick symmetry
Popsicle Stick symmetry

Again, it was a struggle to get these students started, but it didn’t take long for them to catch on.

Four student symmetries
Four student symmetries

After a short while I combined groups so, instead of working in pairs, there were four people in a group, which led to different kinds of designs. The pattern above was made near the end of the activity. From start (first handing out the sticks) to finish, this activity took a mere twenty-two minutes, which was how long it took them to began to lose interest. At this point I suggested that they just used the sticks to make whatever arrangements that they wanted to make. Surprisingly, many started trying to use them to spell out their names. I heard their teacher remark something about the fact that they struggle to write their names but they seem to be able to construct them just fine. Which gave me an idea, which I will show in my next post. Now, though I want to jump back to the photo at the top of the post, which is the books made by seventh graders.

Folding and tearing  large paper
Folding and tearing large paper

I’ve been doing this project with the seventh grade for many years. I give them a large piece of paper (23″ x 35″), which they fold and tear to make a pamphlet.

Pamphlets in progress
Pamphlets in progress

I don’t explicitly talk about the symmetry of the folding we do, but I will talk about it in the future. The fact that the sequence of fold and tears results in a scaled down version of the original sheet is something I want them to be aware of.

Glueing out the spine piece of the pamphlet
Glueing out the spine piece of the pamphlet

In fact, every aspect of making this book is symmetrical, even the pattern of the thread that sews the pages together is totally symmetrical.
When building just about anything, even a book, symmetry rules.

Some finished books
Some finished books

These kids are so proud of their books.

Ok, enough for now. More tomorrow…..