Tuesday, May 21, 2013

Real Math

Not long ago, we made our own paint by mixing liquid water color with water and corn starch. Around the internet, this is often referred to as something like "chalk paint" because it dries into a kind of powdery pastel color and washes off with the next rain, which in Seattle is any minute now. You can find "proper" proportions and "recipes," but the way we do it is to start each kid off with the color of her choice in a small mortar, to which the she adds however much water and corn starch she wants, then employs the pestle to mash it all together.

Some kids wind up with a paste, others with more of a soup. We then help them move their emulsion into a baby food jar, hand them a brush, and send them off to pretty much paint whatever they want in our outdoor classroom.

We've been doing it on our workbench because it's a classic tinkering project, one that brings kids back again and again and again, each time mixing new colors and textures of paint. Frankly, it seems we could do this activity every day without ever running out of customers.

It's such a simple thing, but it hits a sweet spot for kids, one that involves a step-by-step process, yet allows for endless experimentation, has no wrong answers, and is directly applicable to the children's lives.

As I took part yesterday in a Twitter party in my role as a Math Mentor for PBSKids.com (#PBSKIDSAddsUp), I found myself, as I often do when considering how we teach math to young children, thinking about applicability.

One of the most common gripes about math, especially about math homework, is "When am I ever going to need this stuff?" It's a question we asked when I was a boy. It's a question children asked long before my time, and it's a question kids still ask today. Of course, the answer I got back then was one that made me feel like it was a stupid question.

After all, from an adult perspective things like addition, subtraction, multiplication and division are manifestly useful, directly and practically applicable to our daily lives. And beyond that we know that math learning is more than mere calculation. In a broader sense, it's about using reason to discover immutable truths, forming the foundation of logical thinking. A professor once introduced his course to a group of us non-math majors by encouraging us to think of it as a "philosophy class," which was a stroke of genius when talking to young adults, just on their own in the world, and in the process of questioning everything. That was applicable.

You see, the stuff we so often call math -- the numbers on paper, the flash cards, the worksheets -- those are abstractions from the concrete world in which children operate. "Real math" is something we do with our hands, with our bodies, and it always applies to our real lives. The sequence of measuring out ingredients, then combining them with a mortar and pestle, then transferring them to a jar, and, finally, using a paint brush to apply our creation to the playhouse, a drum head, or the sandpit mailbox, is what I call "real math."

We have plenty of time to figure out how this all works on paper, but today we're really learning it, internalizing the concepts, making "mistakes" with them, and truly coming to an understanding of how they apply, so that when we do finally come across those algorithms, they aren't just ciphers to manipulate, but rather a new way to communicate something we already understand; not just as an abstraction, but as it applies to our lives.

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Anonymous said...

Thank you for this lovely post. I homeschool my two kids (aged 8 and 4) and 'What's Maths for?' is frequently asked by my son and sometimes I really have to rack my brain and it's still early days, we're not on calculus yet! However, we use a really 'think outside the box' set of books called 'Life of Fred' by Prof. Stanley Schmidt and we love learning maths this way www.fredgauss.com It's available in the US but we ship it all the way out to Dubai in the United Arab Emirates we love it so much! I hope my son continues to enjoy this programme and, more importantly, enjoys Maths and can see how it can be/is fun to use!

Sharelle Taylor said...

It's so annoying when adults miss the opportunity to show maths applicability (as they did when we were kids): The endless "how long do we have to wait" "how far do we have to go" questions are all maths / proportions and can be played out from the earliest games using the same language. I like how you do it, i liked how my daughter's year 4 teacher did it (even though her year 5 teacher scoffed that he didn't teach them 'tables'), but she excelled because he taught her concepts.