I get this question a lot from students and from people who ask me whether I ever use any of the math that I have learned as an undergraduate. I think it is a really hard question because a lot of times we don't use calculus or solve for polynomials in our everyday life. When people ask me these questions, I often tell them that I use the problem solving skills I gained as an undergraduate student in mathematics in every aspect of my life. But I'm not sure if that's just me trying to justify why a degree in mathematics is important or if I truly believe that higher mathematics gives me practice in better problem solving skills.
So, how do I answer a student who asks me "Why am I learning this?" The math I use daily usually consists of adding, subtracting, multiply, dividing, and taking percentages...you know, the stuff you learned in elementary school. Ava Erickson mentioned an interesting book on her blog by Eric Gutstein which touches on this issue. So, as a future math teacher, how can I encourage kids to value math and show that it has some relevance?
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Hai, I've gotten this question a lot (though this year less than others). And I don't think the teachers of other subjects get it as much. I think part of the problem is what is in math curriculum. I think there's way too much stuff that's not useful or about applying math in the real world. I had to review all of high school math when I took the math subject test for teachers. Do you remember synthetic division? Probably not. Because you've never even got close to using it in real life. Sure it's got its applications, but I have to imagine those are few and far between compared to say, the applications of graphing or using proportions). And the "applications" in text books leave a lot to be desired. They often feel so removed from real-life context to be interesting. It takes a lot of work to design curriculum around real applications, but when it works, kids get into it and stop asking, "Why is this important?"
In a way, a lot of people really don't use advanced math in their lives. But they also don't directly use a lot of what they've studied as students - many subjects have an implicit value that helps you appreciate how the world evolves and what we are capable of doing in it. This goes along with the general idea that math gives us problem solving skillz. It also lets us know what it is possible for anyone to do with math - even if you don't like studying physics, and don't "need" it for life, you can understand things much better if you know about, say, the conservation of energy. Similarly, someone with a math background will know the difference between a news article that implies causation based on some shady statistical techniques versus a truly strong argument beyond mere correlation.
Math also opens new opportunities for students. A lot of students might not know (esp before college) what their career will be like - and a lot of students really do end up using advanced math. I would never have appreciated math if I didn't have teachers that pushed me and revealed to me the power and generality of more advanced ideas - the very ideas that seem most useless to the typical skeptical student.
Overall, it is a huge problem that students don't see the utility of math. I think a good teacher will first honestly appreciate the usefulness themselves, and then make a conscious effort to connect with students on their terms (and not just saying "so you'll pass my class").
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