Wonder is a feeling of surprise, mingled with admiration, caused by something beautiful, unexpected, unfamiliar or inexplicable (definition from Google Dictionary). We already know how important surprise can be in turning the brain on to learn. Surprise wakes us up and makes a go “Wait, what?” Then, if we don’t find ourselves in a stressed flight state, we begin thinking about this surprise, trying to make sense of it.

The biggest reason we should focus on making math wonder-filled is simply to get the brain actively participating in the subject of math. Another reason is to avoid the temptation to push math into its own empty box. A common practice, even among educators who take the time to make sure other subjects are presented in rich and beautiful ways. We need to embrace that math is not separate from life, or some mundane hard-to-understand subject that requires some kind of monotonous boring instruction in order to achieve successful results.

I think sometimes we confuse wonder and ease. Math is not supposed to be easy, at least not all the time. Of course, some children seem to meet it with more ease than others, but always when we push into math deep enough, we can find concepts that are currently difficult to wrap our brains around. When we dumb math down to make it easy, we skip out on some of the natural wonder.

Keeping tough questions in math means your student has a chance to be surprised. Whether that surprise comes out of finding out how the Fibonacci sequence is found repeatedly in the natural world, or if it comes from a new, unfamiliar concept. Perhaps at times, math stirs up wonder within them because they find bits of it inexplicable for a time. But with time and exploration, understanding always comes. I have seen few things able to produce such confidence and joy in my children, as the moment of suddenly understanding a math concept they had been wrestling to comprehend.

While not making math easy, or dumbing it down, I think it is also important to keep is leisurely. Often we equate leisure as being the opposite of work. What we do when not being forced to do something else. However, many of the things we choose to do in our free time are in fact work, in other words, they require effort. Playing can be hard work, we can be exhausted when we are done. But play is also leisure. So, when I say we should study math in a leisurely way, I don’t mean taking away needed work or effort. I mean it should be a relaxed effort, a playful work. Math may absorb us and exhaust us, but it should leave us with that satisfied type of exhaustion that one feels after playing. Not the feeling you get after having to do something you hate for hours. We are not looking for a post-toilet de-clogging exhaustion. We are looking for a post day-at-the-zoo kind of exhaustion.

How do we make math leisurely and wonder-filled in our daily lives? There are many things I incorporate into our study of math, to keep it wonderful. I look for interesting materials to incorporate in three key areas.

1. Stories of math, here I look for engaging books on the history of numbers, biographies of mathematicians, and stories that use numbers and math.

2. Visual Beauty, here I include resources that cover Fibonacci sequences, tessellations, and Mandelbrot.

3. Things to touch, manipulatives make it real, whether you have an expensive manipulative math kit, or just grab items from around the house to manipulate, math concepts come to life when you connect concepts with tangible, touchable proof. I do not relegate the use of manipulatives to just kindergarten. It is important in understanding concepts at many levels and there are useful, inexpensive, easy-to-use resources available for advanced math. I also consider almost all board and card games as containing math in some form or another. Even scrabble flexes your math muscles. I encourage game-play as one of the ways we can learn new math concepts and keep old skills strong.

Stories, beauty, and touching math go a long way in keeping math wonder-filled and leisurely. Something your student looks forward to exploring and playing with every day, instead of something they dread.

If you are looking for some games to help you on your journey to making math wonder-filled here is a great collection.

## 3 Responses

“It is important in understanding concepts at many levels and there are useful, inexpensive, easy-to-use resources available for advanced math.” Do you have a list somewhere of these resources for advanced math? It is so hard to find interesting materials past basic algebra. I would love to find a resource that shows the beauty and usefulness of upper math that can be read/watched in a short time to inspire a teenager to tackle upper math concepts. Any ideas?

I don’t have a comprehensive list, but if you are looking for things to watch, here are my favorite short video channels: Numberphile - https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A and Vihart - https://www.youtube.com/channel/UCOGeU-1Fig3rrDjhm9Zs_wg

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