[ishkabible]

ya, my example shouldn't have been so fundamental. my point is that schools are trying to make kids computers when that is SOOOOO wrong.

take derivatives for instance. my teacher gave my class the definition of a derivative and asked us to use it to do the homework for that lesson. the next day he showed us a contrived rule for finding the answers quickly for the next lesson. latter on down the road we had a complete set of recursive rules that allowed us to evaluate any derivative composed of addition/subtraction, multiplication, division, and exponents. none of the inner workings of these rules were explained to us; it's like we were computers and our teacher was our programer.

*If* we had spent time defining the concept of a derivative(we did a bit) with out any math, then spent time to try and find the most abstract mathematical definition of this concept, then used that to create a recursive function that could evaluate any derivative we would have had a very deep understanding of those rules and why they worked. now we have a deep understanding of an algorithm for finding derivatives...that's where a computer should take over. there is no reason for a human to follow this algorithm when a computer can do it better and we already have a deep understanding of it.

In a nut shell: I think homework should be about finding a function that computes the desired result rather than being given the function and asked to compute it...in fact, it's the way programing classes work. I try to do my homework this way. problems tend to be so cookie cutter that my functions will work for multiple problems.

This post has been edited by ishkabible: 09 April 2012 - 10:46 AM

[jon.kiparsky]

Yeah, I'm with you there. If he'd shown the rule as a neat trick and then explained how it worked, as another way of getting at the idea, I'd be all for it. I'm a big fan of explaining a thing a bunch of different ways - even if you got it the first time, it sometimes opens up a new part of the idea for you. But just "here's the rule"? No way.

[CarDriver]

People don't like math because teachers don't teach it properly. I'm in algebra II, and based on the questions kids in my class ask the teacher, I'm pretty sure that most of them don't understand what basic functions are and how they relate to graphs. They just memorize magical rules. I think people would like math more and have the ability to use it more practically if schools taught why and let us figure out how.

This post has been edited by AVReidy: 09 April 2012 - 08:57 PM

[hiddenghost]

ishkabible, on 09 April 2012 - 11:29 AM, said:

jon: The idea is that you still learn arithmetic but rather than mindlessly following an algorithm to preform arithmetic you learn to make the algorithm. Arithmetic is kinda a bad example because it is so fundamental; it's what kids would build off of to create more complex algorithms but the idea is the same. The idea of applying this to addition is a bit radical, it was just an example.

That's not radical. I think pretty much all math is addition.
Except for irrational numbers.
Other than that it's all addition.

Hell, even subtraction is addition.