Lately, I've been feeling that the question "How is this used in the real world?" is a bit misguided. Sometimes there is a really good answer that fits into a 2-minute sound bite without completely disrupting the flow of your class. Quadratics are the classic example of this: How will you ever know where your rocket/football/rubber chicken will land if you don't understand projectile motion??? However, once you step into the realm of calculus it's difficult to encapsulate the usefulness of something like the derivative in 5 sentences or less. (Or not ... please let me know if I'm totally off-base here!) Most often, I find myself wanting to give one of these two responses to that dreaded question (although I never would):
- Asking how [insert complicated math concept here] is used in the real world is like asking how multiplication is used in the real world. It's everywhere, but could you sum up how it's useful in 2 sentences to a fourth grader who was just learning his times tables?
- The real-world connection is that you're going to have to be able to [insert tedious technical skill here] in order to pass your intro-level calculus/physics/engineering classes in college so that you can move on to bigger and better things.
- Does it matter??? Can't we just do it because it's interesting in its own right? A little abstract thinking never hurt anyone! (Shockingly, this argument doesn't actually seem to make concepts more interesting.)
My point is that its connection to the real world is only one (small) reason why I love math. What I really love is the feeling of success when I finally figure out something that I never thought I'd understand. I love discovering beautiful patterns. And yes, I sometimes even love the rules and the stability that they offer in the midst complete chaos. I'm also convinced that (most) high school students don't really want to learn about real-world math, except for maybe the occasional pretty picture of a fractal or 2-second snapshot of some grotesque computation that is used to solve a "real" problem. Instead, they (like all of us) just need a hook. Usually that hook is sinking their teeth into a problem that captures their attention, not doing a "realistic" mathematical analysis.
Don't get me wrong -- I do want my students to understand why mankind has spent hundreds of years studying the derivative. I want them to understand the equations of motion, and optimization, and differential equations -- but it's going to take an entire year of calculus to really answer that question, and I'd rather answer it well in a year than answer it superficially in 5 minutes. In the mean time, I can try my best to make the concepts engaging in their own right so that my students want to learn them, even if they don't instantly see the "real-world connection."