“When are we going to use this?” is masked frustration and lack of confidence. It’s easier to say “I won’t do this”, or “I don’t need to do this”, rather than say “I’m struggling to do this”.

One thing I would consider doing is preempting the question on the first day of school while you have the students’ attention and you have the momentum to have a sincere conversation about the purpose of math study and not solely be entertaining students’ frustrations. I believe most students know deep down, that at some level, math is useful. They know about the high paying careers, and they are all too familiar with the societal pressures to succeed in math.

That’s my belief. I think it mostly means “I am not engaged, because I just don’t get the point of this.”

I think the right answer is “you won’t,” because that’s the same answer in the other subject areas either. They’re also not going to diagram any sentences, do deep analysis of poetry, identify rhyming structures, name exact dates of historical events or a million other things.

Eventually they’ll get higher up in their studies and spend times on other things they’ll never do. Studying computer science required me to learn how to code linked lists and sorting algorithms. It’ll be a cold day in hell before I ever write another one – they have libraries packaged with every common current language for that.

But now I’m armed to recognize the core mistakes that writing a BAD sorting algo looks like. Just like people who diagram sentences are prepared to write good ones and folks who learn to analyze poetry will do better jobs of identifying what any written text says.

I think if I was in front of a classroom and felt like I HAD to answer this question I’d probably go with “you’ll use it when you spot people trying to cheat you.” If you rely on other folks to determine how much carpet or sod you need then you’re never going to be able to know when they’re offering you a bad deal.

I am in my 14 years of teaching, 10 years ago I realize there are application of math that were not presented in my algebra 2 book. Math has applications in most professions and in our everyday lives. When my wife was in labor, I gained a deeper understand of quadratics, because the graph of her labor pains could be fit to quadratics equations. This way also true when I saw the image of her eye, foci had a different meaning for me.

We must resist the urge to continue to teach the way we were taught.

I agree that it is not all just about applications. I suggest asking the kids why are we learning something.

For example, recently I asked my students to blog about complex numbers. Why are we learning them? What are they good for? They aren’t even real.

Kids came up with apps eg art – Mandelbrot set, extra dimensions, electromagnetic fields etc. But also many kids said the beauty was that before we were just writing “no solution” but now we can express the answer with more precision, and that is satisfying for many of them. Others talked about the development of the number systems over time: looking at how negative numbers and irrationals have seemed “unreal” too, when first discovered. It is the beauty of taking our number system to a new level. Many students appreciate that fact in its own right, without there needing to be an application.

I like the idea of asking the students because they are the ones that have to resolve the questions of why are we learning it, so they need to “own” the response. Also it invites them to think more deeply about the context of the mathematics, which I also value.

I am currently teaching a second year “math methods” course for preservice primary teachers. Many of them don’t really “get” math in any real or useful sense, but I get the sense they accept that the math they will teach to 5-12 year olds is actually useful, and so the question “When will [they] every use this??” isn’t an issue.

However, asked to justify the teaching of introductory algebra or intermediate geometry, for example, I believe my students would struggle to answer in any meaningful way. For them, math really is a functional pursuit that you need, like you need to floss your teeth and carry out the garbage.

Thanks for all the high-school teaching perspectives (special mention to @Bob, @Mr Vaudrey and @Sam, about explaining the benefits of learning to think mathematically, without necessarily being able to identify a specific adult life context for using everything you teach.

Great discussion!

Here you speak about the future: “That means that all I have to do is tie future content/skills back to these reasons.”

Did you ever ask your students if the math they already learned in the past was useful? What do you think they would reply to that question? I’m wondering if math becomes useless in grade x in their head?

Carl