Oct 26 2011: The major problem with education is in standardized testing. Specifically in multiple choice testing. Instead of open-ended questions, questions are now confined to four or five answers -- which promotes the memorize and regurgitate style of learning.
This becomes a huge problem in math. Instead of using tools (formulas, methods) to solve problems, the tools become the solution to problems.
Example: everyone learns about factoring in algebra II. In most schools in the US, it is taught by the FOIL method. So one of the "problems" that the teacher might give is expand (x+1)(x+2), or factor x^2+2x+1. And that would be the extent of learning factoring. So now, most kids should know and understand the concept of factoring, right? But what happens when you give most kids this problem: How many positive two-digit integers are factors of 2^24-1? Because this question wasn't given in the familiar form based on x's, many kids cannot solve this problem. But the method is the same, factor this expression into (2^12+1)(2^12-1) and so on. From there, you will need to find the prime factorization of the expression, and play around with the numbers a little bit to find out how many two digit integers are factors. The problem certainly isn't easy, but most kinds won't even know how to approach the problem because it wasn't given to them in a form that was explicitly taught to them. And this is where education fails kids -- what happens when society encounters a situation that hasn't been seen before, will the new generation be able to problem solve their way out of it, or will they be stuck with it because they weren't taught a solution?
http://www.maa.org/devlin/LockhartsLament.pdf
There's a good article, albeit long(25 pages), about the issues in math right now.
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This becomes a huge problem in math. Instead of using tools (formulas, methods) to solve problems, the tools become the solution to problems.
Example: everyone learns about factoring in algebra II. In most schools in the US, it is taught by the FOIL method. So one of the "problems" that the teacher might give is expand (x+1)(x+2), or factor x^2+2x+1. And that would be the extent of learning factoring. So now, most kids should know and understand the concept of factoring, right? But what happens when you give most kids this problem: How many positive two-digit integers are factors of 2^24-1? Because this question wasn't given in the familiar form based on x's, many kids cannot solve this problem. But the method is the same, factor this expression into (2^12+1)(2^12-1) and so on. From there, you will need to find the prime factorization of the expression, and play around with the numbers a little bit to find out how many two digit integers are factors. The problem certainly isn't easy, but most kinds won't even know how to approach the problem because it wasn't given to them in a form that was explicitly taught to them. And this is where education fails kids -- what happens when society encounters a situation that hasn't been seen before, will the new generation be able to problem solve their way out of it, or will they be stuck with it because they weren't taught a solution?
http://www.maa.org/devlin/LockhartsLament.pdf
There's a good article, albeit long(25 pages), about the issues in math right now.