The Joy of Discovering Mathematics… for Yourself! | exSTEMsions

The Joy of Discovering Mathematics… for Yourself!

Learning something the “hard way” in real life...

My husband tells a story about his childhood that involves a kerosene heater. As the story goes, his aunt told him over and over again not to touch that heater. She repeatedly explained what would happen to his finger if he touched the heater. So what did he do?  Of course, he touched the heater, burned his finger (not badly), and learned about consequences by actually experiencing them, the “hard way”. This story is told in our house, to our children, any time it seems that they are intent on doing something dangerous that we have repeatedly explained to them why they shouldn’t do.  

… isn’t the same as learning math “the hard way”!

When I hear this story from my husband, it makes me think about how we learn math (because, well, that’s what I think about!).  In math, the situation is somewhat different. To learn something and really, truly, have it stick in our minds, it often isn’t enough to listen to a teacher tell you about math, you just have to experience it for yourself.  For students, doing math, rather than just listening to someone talk about math, really is “the hard way”!  But for me, learning things “the hard way”, by doing it yourself, and probably struggling at least a little, is better named “the right way”.  When we learn through our own personal struggles with mathematical ideas and problems, we learn more deeply, which leads to better retention of what we’ve learned.

Active learning is better than passive listening in math... and everywhere else

Here’s a good example of a time when I had to learn through struggle. A teacher once gave me a puzzle, and I couldn’t get it. It made me crazy. At a certain point, I was actually SO frustrated, I tore it up into tiny pieces… and then went and printed another one. To this day, I remember the glory of finally solving that lovely, infuriating puzzle.  Ten years later, and I am still proud that I figured it out!  The experience, and my discovery, have stuck with me in a way they would not have if someone had simply said “Oh, it works like this….” The teacher had the chance to do just that - and didn’t. At the time it frustrated me greatly, but looking back I see that she had faith that I had the skills and knowledge to figure it out myself, and allowed me the chance to do just that.   

Think back to your own mathematics education, on a time where you remember learning something deeply, or walking away with a new idea crystal clear in your mind. Now think about how you actually learned that thing. Was it just from sitting and listening to someone talk about it? Was it reading a solution to a problem that was already done for you? Maybe, but I’d be willing to bet that it wasn’t. I’ll wager that, instead, it was something you actually did, an idea you experienced by playing with it in your own mind, or something you discovered as you were actively exploring and learning. Why would I be willing to make this bet? It’s pretty straightforward, actually. Learning by discovery, by experience, by action, is more powerful than learning passively.

Think of it like this.  If you read a book about football, will you instantly be able to play like a pro?  If you take a driver’s ed course, will you be an expert driver the first time you get behind the wheel?  If you watch a cooking show on TV, will the first time you bake a cake be the most amazing piece of delicious art ever?  If you’re anything like us here at exSTEMsions, the answers are no, no, and no! Reading about something, or watching someone else do something, doesn’t make you good at it. What will make you good at something is experiencing and practicing it yourself.  A lot.  You can gain information about mathematics by listening to others, that’s for sure, but to learn math deeply, and remember what you’ve learned, you need to explore it on your own!

The practical aspects of active learning in math... and everywhere else

And yet, sometimes we still find ourselves uncovering the answers for our kids; often we do this because we have to - there just isn’t enough time in the day to do otherwise. Believe me, I can relate. Other times, we short-circuit the power of discovery when we step in and provide a little too much help when our children are struggling through something, because it’s really hard to watch them struggle from the sidelines.  In truth, it’s not practical for all learning to be via discovery. But it is important to make room for discovery and active learning - even though it’s messy, and time consuming, and maybe even frustrating for us parents. From my own experiences, and from hearing those of many others, I know that these messy, frustrating learning experiences can lead to great triumphs!

Discovering things for yourself is powerful: it can make for a better learning experience.  These are the opportunities we want to provide for our kids. Give them room to learn, even when it’s messy. They’ll get more out of it!

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