"When am I ever going to have to use this?”
I have been teaching math for over 20 years, and have been asked some form of that question at least once in every one of those years. I have undergone many changes and paradigm shifts as a teacher in that time, and my answer to that question has evolved with them. I would like to think that my current “answer” (such as it is) is my final one, but before sharing it, I’d like to survey the ones that preceded it, in chronological order.
The Naïve Mathematician: “Who cares? Math is fun all by itself! Right?”
Many early-career math teachers—and I have to admit that I was one of them—believe that merely regularly insisting that math is fun will eventually cause their students to believe it, or that math’s inherent awesomeness and beauty, aided by their own enthusiasm, will just naturally shine through and cause students to love it the way that they do. This is, to put it mildly, not the case. So this answer is wholly unsatisfying for the student, and is oblivious to their concern.
The Jaded Smart Alec: “On our next test.”
While possibly solving the short-term motivation problem, this response sends the message that math class is a fully self-contained annoyance/torture device, and it bears no relevance to my life beyond the immediate future.
The Eternal Optimist: “You never know what your future holds! You just might wind up in a career that requires that you know how to… factor polynomials!”
The chances of this happening are slim, to say the least. (Though it must be said that the utility of manipulating polynomial expressions has popped up in odd places, such as in programming self-driving cars.) But even seeing themselves in a career that uses a lot of mathematical ideas is no guarantee that they will become interested and engaged in the material.
The Smart Alec Returns: “Use what, your brain?”
This always elicited little more than an eye roll, as well it should. And I finally learned that snark is not an effective way to change minds.
The Philosopher: “Is something only worth learning if it is useful? And what do we even mean when we label a thing we learn as ‘useful’?”
While answering questions with more questions is a valuable, time-honored tradition in teaching, and this is certainly a discussion worth having, it is not what students are looking for when they ask this question. They are looking for…
The Honest Truth: “Y’know what? Honestly? Probably never. But the analytical, quantitative perspective that we develop when we learn math is one of many lenses through which we can try to perceive and make sense of the world around us.”
This answer may still be unsatisfying to some students, but it has the distinct advantage of being true. And teenagers tend to appreciate authenticity and honesty from the adults in their lives! My answer to “When are we ever going to have to use this?” may continue to evolve, but I will always honor the students’ experience and perspective that led to them asking the question in the first place, and prioritize truth over cleverness or manipulation in my answers.