I’ve written before about refining my “why math” elevator speech and being more deliberate in how I frame why math is worth learning. Both of those happen at specific times — my framing attempts to start each course with a clear vision of why math is worth learning, and my elevator speech is deliberately responsive to student protests about “when am I ever going to use this”. I’m working to send that message on a more regular basis in my classes, and one big opportunity is how I introduce a new topic or unit.
We started optimization today in my Calc A class. I framed it the way I see it. I said something like:
Optimization problems pretend that they’re problems you might need to solve in the real world, though they’re usually hilariously contrived questions that ask you to be unnecessarily specific about something that doesn’t matter very much. But they involve drawing fun pictures, finding creative ways to model things with algebra, and paying carefully attention to detail, so they’re worth solving.
I don’t know if that’s particularly inspiring. It probably sells optimization short. I hope someday I’ll have a repertoire of great, engaging three-act tasks and modeling scenarios that make optimization the most thrilling part of the differential calculus curriculum. But right now I don’t, and I want to be as forthright as I can — to avoid digging myself into a whole in the future, to build some element of trust that I see the world in a similar way to my students, and to be honest about the value of optimization. And if I’m being honest with myself about the value of optimization, I believe that it’s worth learning because it offers a great visual perspective into calculus, it requires students to build algebraic skills that aren’t necessary in many other areas of calculus, and often trips students up who lose the forest for the trees. I believe that’s worth learning.
This doesn’t mean saying, “I’m sorry this isn’t the most exciting topic.” I’m not apologizing for anything. I love teaching math, and I really believe it’s worth learning. But I don’t believe it’s worth learning because students will use it in the “real world”, and I enjoy poking some fun at that perspective when I get the chance. Instead, this is about framing the true value in math — reasoning, modeling, generalizing, questioning, arguing — and unapologetically teaching students through that perspective.