(There is a video below that may not display if you are viewing this through Google Reader or something similar)
Sorry for the long delay between posts…and also the interruption of the series “Math in Process.” Graduating, relocating, and job hunting apparently take up your time. Who knew? Probably most people. I would say that we’ll return to your regularly schedule blog program after these messages but we both know there is about 50/50 chance of that actually happening until life slows down (it does slow down right?). So I’m not making promises, just sharing hopes.
Anyway, in the meantime I came across this video (by that I mean a friend sent me a link) and thought I would share it. I can’t remember if I have mentioned this here before I not, but I believe all mathematical problems throughout history can be broken down into three stages: 1) problem formulation, 2) theoretical abstraction, 3) multiple applications.
This is a poor example, but to give you an idea what I mean here we go:
1) Pythagoras needs to build a triangular ramp. He has a horizontal board that is 4ft long and a vertical board that is 3ft long. How long should he cut the diagonal board?
2) Turning the boards from the ramp into lines on paper, Pythagoras is able to determine the third side should be 5ft. He is also able to determine that a2 + b2 = c2 , a fact that is true but is not dependent on this specific ramp building project.
3) This new theory can now be applied to multiple situations, causing other problems to arise and the process to be repeated.
In my opinion, the number one reason students struggle with math because they are introduced into the subject in the middle of step 2. In word problems we attempt bring them into step 3 (without causing new problems). But students are rarely, rarely, introduced to step 1: developing the problem.
Here is a video that suggests ways we can get students back to step 1.