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When Am I Ever Going to Use This? — The Training Metaphor

by Aren Lew

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It is a perpetual conversation among math educators: how to respond to students asking, “When am I ever going to use this?”

One common response is to provide examples of specific math skills used by people in specific careers. I don’t love this as a default way of addressing students’ concerns because it can’t be done authentically with all the skills we are teaching and specific applications may not be relevant to the student inquiring. For example, hearing that people in health care professions make use of different systems of measurement may not be a satisfying answer to someone who is interested in a business career. That’s not to say that there are not authentic applications of a lot of the math that we teach, but we can end up sounding silly when we take it too far. While it’s true that a rocket scientist could factor a quadratic expression to figure out where a rocket will land, most of us will not encounter that application (and even rocket scientists use computers for their calculations!). So, while this application may be interesting to study, as an explanation of why it is important to learn to factor quadratic expressions it feels like a stretch.

There’s another response that I like much better, and I’ve heard it from lots of people. It’s that, in fact, you may not end up using a particular skill, but the act of studying it is training for your brain. We make our brains stronger and more flexible by struggling with challenging concepts. To use an athletic analogy, a basketball player will do a lot of exercises in their physical training that are never used in playing basketball, like lifting weights or jumping rope. However, these exercises benefit the athlete because they make the body stronger and more capable of reacting to the conditions on the court.

I like this metaphor for two reasons. One is that I have seen personally how studying math has made my own brain stronger and more flexible, and I have seen students grow as thinkers, question-askers, and investigators through studying math. The second is that it points to how we should and shouldn’t be teaching math. If we recognize that the goal of studying math is to build our problem-solving, thinking brains and not to get the answers to the questions in the textbook, then there is no point to teaching tricks that get us to the answers. To go back to the athlete, we recognize that the value in lifting weights is in the athlete using their muscles, not in getting the weights to go up and down. Suppose you invented a machine where you could push a button and it would lift the weights up and down for you. Do you imagine anyone at the gym would want to use it? People go to the gym to use their bodies, not to operate machines. The gym equipment provides a context for exercising our bodies. Math class provides a context for exercising our brains. If we as teachers and learners enter math class with the expectation that we will think hard, that our purpose is to exercise our brains, and that we’ve done well if we are tired from thinking at the end of class, then we won’t wonder, “When am I ever going to use this?” anymore. We’ll already be using our learning.

Arriving at answers is like lifting weights. If we find ways to get the answers without working for them, the endeavor will have as much value for us as if we had pushed a button to watch the weights go up and down. The value of the exercise, physical or mental, is in the challenge and the struggle. When we try to make math “easy” with tricks and shortcuts, we are removing the struggle, and thereby removing the value of studying math in the first place. Our students’ time is precious. Let’s make sure we treat it with the respect it deserves by providing them with challenging work and supporting them as they work toward understanding.

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