Doing Math Through Problem-Solving

What exactly does that mean? Doing math? Well to consider this question, we first need to ask ourselves, what is math? Most of our initial thoughts or responses would more than likely have something to do with numbers and computation. Right? And while it is true that numbers play a significant role, math is actually much more encompassing. More recently, definitions of math look something like this: the science of patterns and order. By thinking of math in this way, everyday real-life applications of math come to life right before our very eyes.
So back to our original question. What does it mean to “do” math. Many of us grew up doing arithmetic, not math. If the definition for mathematics above holds true, I’m sad to say that as a child, I did very little math consciously. I believe that we all “do” math every day (both children and adults), but once one is made aware of the world of pattern and order, the level of consciousness of this type of thinking heightens. Therefore, part of my job is helping children discover this order through patterns and helping them make sense of it all through the process of discovery.
I believe that we all are creators of our own knowledge. We encounter information, formulate ideas, and then connect these things to one another in our brains. The more connections we make, the better and more thoroughly we understand a concept. Some people think of understanding as a light switch – at some point, the person “understands” and the light comes on with the flick of a switch in an all-or-nothing fashion. Others think understanding is more of a process happening over time by accumulating multiple and various experiences and connecting them to one another. I prefer Arthur Hyde’s metaphor for understanding:

“I like to think of it as building a snowman. First, you find some good snow for making a snowman – not too wet and slushy, not too dry and powdery. You make a snowball with your hands and roll it in some good snow. The ball gains size as more snow sticks to it. You do this to make a big sturdy ball of snow for the foundation. You repeat this process for other parts of the snowman. But you must continue to roll it in the right kind of snow; the wrong snow, or worse, rolling it on grass, will not accumulate more snow.?”
from Comprehending Math by Arthur Hyde.

So I know it’s summer, and you probably don’t want to even think about snow, but this is such a powerful comparison. This is my goal for your child this summer – to roll them around in the right kind of snow to help build that indispensable foundation of deep, conceptual understanding.