Have you ever noticed how students always want a real-world example--often phrased "when are we ever gonna have to use this?"--but they hate (real-world) word problems? Joanne (see blogroll) points to a study that says that real-world problems confuse students, and that we'd often be better off just sticking to the math.
So much for relevance.
6 comments:
I think it would be better to say what higher math needs you to understand the concepts. At least that way nothing has to be simplified or stretched to be a real world example and it at least provides some incentive for the student to master the concepts. Had I known I would be doing so much work in polar coordinates these days I probably would have paid more attention to such an abstract concept in high school. I think students just feel a need to have a reason to learn things, with lower math applications are abundant and easily identified, but when it comes to mid-level stuff I think they need to know it will be important later.
Ron, if you'd provide some details about what you're doing and how polar coordinates play such an important role, I'd love to share that with my current dumplings.
Calculus 21D, Vector Analysis, so far we have been dealing with multiple integrals and it has been somewhat stressed that being able to convert integrals from rectangular to polar might be the only way to solve them. Engineering 6, Engineering Problem Solving, polar representations of complex numbers, including their usefulness when looking at rotations of complex numbers. Both classes expected polar coordinates to be well known beforehand, including knowledge of cardioids which I never paid attention to. It's also somewhat useful when your having to think of different coordinate systems like cylindrical and spherical if you have a strong background in polar.
But my main point is that everything that I saw as abstract and meaningless has eventually been made important in later classes. I think if you stress the fact that they will need to know pretty much everything they are taught in high school for college level calculus they might be more willing to learn the material. A possible idea would be to go get a college level calculus book and anytime someone says "When will I use this" pull it out and show them how they at least will need to know it for another class later.
Consider who you're dealing with. The concept of abstract concepts is still pretty novel in the teenage years.
Then there's the need to accept the delayed gratification that the teaching of concepts implies.
Look who's requiring the acceptance of delayed gratification - the folks who force you to be in that school. The trust that's key to the acceptance of delayed gratification isn't exactly building on a strong foundation when attendance is mandatory. How much faith can someone have in the future value of what's being purveyed if attendance is mandated?
And we've had "real-world problems" as long as people have been teaching math. They're called story problems.
I hate that question, along with "is this for a grade?" Having just come from the first day of TAKS testing I can tell you that some kids take things seriously and other do not. One particular behavior problem, who managed to tick me off before he even sat down by complaining about having to put his backpack at the front of the room, finished the sophomore level math test in 45 minutes so he could sleep. Another diligent student finished right before 11:45. Who do you think will do better? And no matter how many "real world examples" I could give the first kid, he still wouldn't see the practical uses of math.
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