I used to believe that a subject had to have a direct application to life in order for it to become meaningful to students. At the same time, the applications were often clunky and artificial when forced upon us. For example, Lord of the Flies had little to do with bullying and more to do with questions about freedom and safety, human nature and the relationship between chaos and order. I wanted to discuss those themes, but I had a teacher who quickly turned the discussion into a talk about “mean boys.”
Similarly, a well-intentioned math teacher once tried to develop a real-world scenario for algebra and for the life of me, I couldn’t figure out why I would ever want to know about the two different trains when the likelihood of being on a train in an era of air travel seemed minuscule. I remember she let some kids use blocks and draw pictures and for them it clicked. She wasn’t a bad teacher. Actually, she often made the subject come alive like our Fantasy Football unit. Still, the train lesson tanked.
So, I had kids who couldn’t figure out how to divide fractions. I first gave them a scenario of two different bags of chips and had them develop the question and answer for it. Some of them used backwards multiplications. Others drew pictures to get to the main point. They solved it and it felt meaningful, but still they missed the whole dividing fractions concept.
The next day, I gave the class a challenge. Each group had one item (a Lego, a ruler, a small clue) and had to work with other groups to figure out how many Legos it took to reach the ceiling in our classroom. I had students measuring the walls multiple times and finding the average (or floor is a bit slanted). I had students trying to multiply out the Legos.
Then, it happened. Three students who had completely bombed dividing fractions the day before started talking through it and in unison, they all say, “Divide it!” They went back to their notes and solved the problem.
In twenty minutes, we hit averages, percents, dividing fractions, writing an algebraic equation and converting from inches to centimeters. When the students took a common assessment the next day, every one of them aced it.
I am realizing that there is something besides “application” that makes math meaningful. I don’t completely get it. This challenge had no practical purpose whatsoever, but I had almost 100% student engagement.
One of the best things about teaching is that I get the chance to repair damage done to my own beliefs about subjects. Somewhere in my schooling, I picked up the message that I don’t “get” math because I am slow at working on the algorithms. I learned that math was great for engineers and accountants, but words were best for authors and poets and people who delight in a book. And I thought about a life on a spreadsheet and shuttered and I wrote out a few lines of free verse and I began to drift away slowly from the land of abstract numerals and it felt like a refreshing escape.
Now that I teach it, I’m drifting back and realizing that it’s a different way of thinking and that there is a beauty to math that I had once missed.