My reading for this week included two short letters explaining reasons to study geometry. Both point out that geometrical reasoning is another form of reasoning with mathematical concepts, and that, while it may not train students directly for the job market, it can train students how to think.
IN a similar vein, Last summer, a (younger) friend of mine got her first teaching job, and was a bit worried as she was teaching a block of Math 8, and wasn't too comfortable with math. Nonetheless, as a new teacher, she was super-keen to try to do a good job, and sent me an email asking for advice. In her email, she told me she had always hated math as it never seemed at all interesting, relevant or useful to her, and that she thought she should spend most of the Grade 8 year focusing on the stats and probability units as these were the only ones she saw any real life connections to. This was my response to her...
you can't really think of all the math we teach in schools as being useful for the regular person in the real world. some is, some isn't. studying math and learning the problem solving, patterning etc. generally makes people more intelligent - builds brain cells allowing them to be more adept at problem solving, following patterns, understanding logic in various aspects of life. furthermore, things like linear relations, integers, fractions etc. are important for future math. at a grade 8 level, you're still focusing on a general education - (most) 13 year old kids aren't mature enough to decide where they want to specialize, so some of the things we teach are just to give background for future math.
I think it is interesting to study geometry which helps us make sense of shapes and space around us. It is applicable to other disciplines that train architects and painters, and it provides good exercises for the right brain. As a tutor, very often, I notice that students who are interested and competent in geometry love to draw as a hobby. Whenever I give them work on algebra, some of them zone out easily and begin to draw pictures on paper that show geometric properties, such as symmetry and congruency. From time to time, I am too curiosity to pick up their drawings, fold them in half, and test for symmetry. Surprisingly, both sides of the drawings, for example the face of a cartoon character, are almost perfectly matched. I am totally amazed by my discovery. I believe that the precision of their artistry has a lot to do with their strong geometric skills. Hence, it is beneficial that students study geometry since it is highly practical.
ReplyDeleteWhile indeed geometry has wonderful grounding in practicality and the real world, so to speak, I highly identify with the case David makes above. Mathematics very much for learning how to think, I try to market myself as a professional problem solver when someone questions my degree's usefulness- `but I know how to think and figure things out!' (and not just math..) I tell my own (admittedly reluctant adult) students when they arrive in my classroom convinced their semester with me will be useless, that we are mostly just going to practice figuring things out. In my experience, framing it that way has lead to some reasonably positive responses. I don't know how extendable that is to other populations, but it's certainly a message that can be very valuable.
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