Wednesday, November 15, 2006

Real World Applications

What math teacher hasn't heard "when will we use this in real life?" a thousand times already? Typically you hear this when the going gets tough, but sometimes it's asked as a genuine question - not just teacher-baiting. I've posted on this before, and there was quite a bit of response. It's still an open question, obviously, and based on some discussion we had at our staff meeting today, I wanted to approach the question from another angle.

Though students will always be using their numeracy skills, I don't try to convince them that they will be using algebra, geometry, or trig in their "daily lives", because it is simply not true. I do write word problems that use their names and put them in familiar situations, but just because it is fun for them and me - not because I think this will dramatically increase their buy-in and engagement, or their understanding of mathematical concepts. I talk about how math helps you build logical thinking and problem solving skills, but this doesn't help much for the unmotivated students.

The idea we generated today was not to focus on how students might use advanced math concepts in their own daily lives, but to teach them how they are used by professionals in different lines of work. My quadratic functions unit is coming up. Sure, basketballs fly through the air in lovely parabolas, but does that really create a meaningful connection for a kid, even if they love sports? Maybe, but I doubt it. Does a basketball player quickly use x=-b/2a before taking a shot? Instead, what about some applications of quadratic functions that show how they are really used by scientists, engineers, sociologists, astrophysicists, biologists, etc. Maybe a 5 minute, detailed presentation on how headlights and satellite dishes work? It may not connect to students on a personal level, but it could help them see the value math has to society, and why it's worth studying.

So that's my new task: gathering relevant, interesting applications of math concepts that our department can use for each unit in algebra, geometry, trig, and calculus. I have some ideas already, but I would love to hear other people's thoughts on this. Do you think this will be beneficial? Do you know of good resources regarding these questions? Do you have good examples of applications for specific concepts?


Anonymous said...

I had a student ask my on MySpace when she's going to use the quadratic formula in real life. I pointed her here:

druin said...

One of our teachers did an activity with logs with a murder mystery using Newton's Law of Cooling. The kids really got into the idea of being CSI like people

Darren said...

I split the url up over two lines so that you can see the whole thing. It may not be exactly what you're looking for, but it makes for a great story!

Dan Wekselgreene said...

Thanks for the comments so far.

Here is a good summary of how complex numbers are used.

Keep 'em coming!

Anonymous said...

In calculus, I do go over some applications (especially in Calculus Calc II, there isn't as much time for applications). However, I rarely get the "when are we gonna use this stuff?" question anymore. I believe that the reason for that is because this is my common answer:

Have you ever been to a museum and seen priceless works of art? Do you enjoy music? What about television or video games? [after getting at least one "yes"...] Okay, are any of these things going to be directly relevant to your future career? No? Then why not do away with them?

I'll tell you why: because they're a part of our heritage. And mathematics, too, is a part of our intellectual heritage.

Anonymous said...

Since you're doing solutions of systems of equations, you might point out that such systems are at the heart of physics and computer science. For example, each one of the matrices that your kids put together represents a transformation from one space to another. When their video games rotate the camera, they're doing matrix multiplication with 3x3 matrices.

-- xn

Anonymous said...

This post really caught my eye because I distinctly remember asking that exact question myself in high school. I was a terrible student who preferred to sleep and draw on my pants. Well, I eventually went on to study science at Harvard and worked for years as a video game programmer. My "real" life ended up including quite a lot of math applications. Ironically, though, I think the pushing of applications were a large part of my confusion. They give a false sense of what mathematics *is*, and there are inherent difficulties in using math to interpret experience that turn teaching into babbling.

The proper response to the question, I believe, is a quote I read recently that goes something like this: "When you decide to stop studying math, listen closely. That sound you hear are doors closing."

Anonymous said...

Does anyone know a good book to get specifically about curves and their application to man-made structures (i.e. bridges, rollercoaster, etc.)?