I just read a very interesting answer on Quora about whether we have too much math and science education in the U.S. school system. You can read the whole thing at the link, but it made a pretty good discussion about why I’m shifting my calculus class to do some much larger, integrative labs (with writing) as well as the standard “put the n in front of the x and replace it with an n-1” sort of problem solving in calculus.
Here are some excerpts from the Quora post, written by a student, Monika Kothari:
I’m a social science student, but I’ve take more math than I’ll ever need or use, through calculus III. I earned decent grades in those classes by working my butt off. But those skills have never proven useful to me, and I forgot most of them within a year. Most high school students graduate having passed Algebra II, at least in my school district where it’s a requirement to complete four years of math. But most adults don’t know how to apply that algebra to basic life problems. Why?
Take a look at how math is taught, how it’s presented in textbooks, how standardized tests analyze math skills. The emphasis is completely misplaced. When are most people ever going to encounter a problem in life that explicitly tells you to “solve for x”? When are most people ever going to have to construct a geometry proof?
Here’s the thing: they’re not. Problems pop up all the time in every day life, problems that may even require some simple algebra. But people don’t know how to apply the skills they already have to solve those problems. They don’t know what the numbers represent, which formulas to use, which variables are which. They can’t even set up the problem. This is because, instead of teaching students the logic behind math, its uses and flexibility, its applications to everyday problems, etc. math education in the United States tends to emphasize rote memorization and the theoretical at the cost of useful lessons that could applied across fields. (Maybe more word problems would help solve this issue, but that’s something textbook writers need to address as well.)
So here’s my takeaway from this. There are lots of places, especially in social science where some more sophisticated statistical analysis could unlock a lot of useful information, where calculus could be really useful.
But I can guarantee you that outside of the context of a multiple-choice test, any amount of technical skill in calculus is definitely not going to be useful if you don’t know how to find the calculus problem when confronted with a real-world situation. This is why my class spends so much time wrestling with the problem of getting a robot to throw a ball into a cup. It’s not because I think they are all going into robotics or physics (though some are!), it’s because this is a good example of a real-world problem where the really interesting part is defining the math problem. And that process uses all of the skills that we’d really like to see in our students: logical thinking, analysis, problem-solving, and communication.