At some point in the past, I decided that it was important that students know that the question “Where does this function have a maximum?” meant “At what x-value does this function have a maximum?” and “What is the value of the maximum?” meant “What is the y-value of the maximum?” I told them what those code-words meant repeatedly. It would show up on homework, on warmups, and on quizzes. And kids would still miss it on the test. They knew how to find the maximum, but they couldn’t remember how to phrase the answer, or they forgot whether I wanted the x or the y, or they gave me both. So I could tell that they knew the math, but they forgot the code word, so they didn’t get full credit.
I’m not sure where this came from. My textbook? But I’ve largely abandoned my textbook, especially in precal, so I don’t really care about how it phrases things. A glance at what the AP Calc test requires? But the AP test typically specifies when they want x-values (I think. Someone tell me if I’m wrong.) And why am I beating pre-cal kids who will never take AP Calc over the head with AP Calc code words that are keeping them from showing me how much math they know? Sure, in Calculus, we should talk about the College Board’s code words and how to phrase their answers. That’s an important thing for them to know. But why am I making everyone else learn it to?
I’ve decided that this is a stupid teaching choice. I don’t actually care about the code words. If I want to know that they can find the x-value where the maximum occurs, I should just ask that and make it clear that I mean the x-value. And then I can tell how many kids don’t know how to find the x-value, instead of how many kids forgot about a code word.
Will I continue to talk about it? Probably. It can foster a discussion of how we think about functions, about how the value of a function means the output, etc.
I wonder how many other things I require kids to know that I don’t actually think are important. What else am I imposing on them that’s getting in the way of the math? What are other areas where I’m on teacher auto-pilot and not thoughtfully evaluating the curriculum?
Oh, and if you have your students learn this and have a really good reason for it, please tell me. Maybe I just forgot why it matters.