tag:blogger.com,1999:blog-7821055994181766793.post6169908126702480482..comments2023-10-21T14:36:26.307-05:00Comments on The Chalkboard: How to (what?) Our Math Education?!!?Richard Brownhttp://www.blogger.com/profile/02890750341504212951noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7821055994181766793.post-81357490343401835152011-09-16T12:21:06.424-05:002011-09-16T12:21:06.424-05:00Well said, Jake. Certainly, our educational syste...Well said, Jake. Certainly, our educational system in mathematics needs a thorough review and reformation, in my mind. Not that that will happen. But really, if designed from the ground up, the process of self-discovery of mathematical concepts, the importance of talking about mathematics as a way of learning mathematics, the rigorous development of the formal relationships among mathematical ideas through inquiry and initially through intuitive reasoning would not be things only brought in when one reaches the senior level in university. <br /><br />Math is not really about solving problems. It is about understanding structure. Once the underlying structure of any complicated thing is well-enough understood, knowing how to say something conclusive about it becomes the consequence. It matters not at all if the thing one is studying involves numbers or not.Richard Brownhttps://www.blogger.com/profile/02890750341504212951noreply@blogger.comtag:blogger.com,1999:blog-7821055994181766793.post-35153370562735857162011-09-15T18:20:09.798-05:002011-09-15T18:20:09.798-05:00And poems aren't just sets of words that rhyme...And poems aren't just sets of words that rhyme. Sure, rhyming is part of it, but we don't read Shakespeare for the rhymes. If all that high school students are taught is cookie-cutter equations and the shapes they can make (which is what this "applied math" curriculum seems to reduce to), then how will they fare baking a math cheesecake? To solve real-world problems - which are never cookie-cutter compliant - requires understanding. Otherwise, how will students solve the problems (not just in math) no one has ever seen before? Sure, if I had just learned physics, and not paid attention to the finer mathematical details, I would still know how to solve lots of physics problems. But throw in some of those details, and that's the difference between "I wonder why the potential of an infinite line charge is logarithmic" and "Hey! It's the fundamental solution to Laplace's equation with n=2."Jakehttps://www.blogger.com/profile/10423976041503588043noreply@blogger.com