Thoughts from a reflective educator.
This is another in a series of posts about how one could find mathematics in the world around us.
I've been learning how to program for a long time, a task that has much in common with mathematics. Both programming and mathematics involve being able to solve problems. Some of the problems in programming and mathematics have well established solutions and other problems do not. On a micro-level, programming involves manipulating code, a task much like the symbolic manipulation often used in mathematics. On a macro-level, programmers and mathematicians both need to be able to trouble-shoot, organize, and communicate their solutions.
This presentation is based in part on the TED talk Conrad Wolfram gave a couple of years ago, and on some insights gained at the Computer Based Math summit I attended in November. The below presentation is slightly abreviated to make it easier to share on the web.
Here is an idea I am exploring.
I'd like some feedback on this idea. If anyone can point me at research already done in this area, that would be appreciated. My objective is to use this to justify the use of technology in mathematics as a way of reducing algorithmic complexity so that deeper concepts can be more readily understood.
Personally, I think an exit exam for school (an exam a student needs to graduate from secondary school) is not necessarily the best way to determine if a student has been prepared by their school. That aside, some of sort of assessment of what a student has learned from their school, whatever form that would take, should satisfy an important criterion; that the student is somewhat prepared for the challenges that life will throw at them.
Algebra is just mumbo jumbo to most people. Seriously.
If you asked 100 high school graduates to explain how algebra works, and why it works, I'd guess that 99% of them couldn't, not in sufficient detail to show that they really deeply understand it. Remember that I am talking about high school graduates, so these people have almost certainly had many years of algebra and algebraic concepts taught to them. Most of these people will only be able to give you some of the rules of algebra at best, and some of them don't even remember that much.
Every elementary school classroom should have about $20 in change. Not fake money printed on a piece of paper, but real money. Yes, some of it will go missing over time, and you might need to lock it up depending on your community, but honestly it's worth the risk. It's only $20.
Stephen Shankland posted an interesting article on CNET today. Here is an exerpt from his article, which you should read in full. He says:
Today I decided to record the process of solving a mathematical puzzle I found at the Project Euler website, in an effort to try and begin to analyze the problem solving techniques I use. My interest here is mostly in how the process unfolds, and the skills I use to solve these problems, rather than the actual problems themselves, although those are interesting. Below is the video I recorded when solving this problem.