What makes Mathematics so hard to learn?

In a recent essay, Artificial Intelligence guru Marvin Minsky explores problems in mathematics education. Minsky’s first distinction is between Arithmetic and Mathematics — grade schools emphasize the former, leaving grander concepts of Mathematics for later education. Minsky points out that if students are bored by Arithmetic, they may be turned off by math in general (that was certainly the case for me!).

Here’s a bit from Minsky’s essay:

Why do some children find Math hard to learn? I suspect that this is often caused by starting with the practice and drill of a bunch of skills called Arithmetic—and instead of promoting inventiveness, we focus on preventing mistakes. I suspect that this negative emphasis leads many children not only to dislike Arithmetic, but also later to become averse to everything else that smells of technology. It might even lead to a long-term distaste for the use of symbolic representations.

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Anecdote: I asked a younger child “how much is 15 and 15″ and she quickly answered, “I think it’s 30.” I asked how she figured that out so fast and she replied, “Well, everyone knows that 16 and 16 is 32, and then I subtracted the extra 1’s.”

Traditional teacher: “Your answer is right but your method was wrong: you should add the two 5’s to make a 10; then write down a 0 and carry a 1, and then add it to the other two 1’s.” The traditional emphasis on accuracy leads to weakness of ability to make order-of-magnitude estimates—whereas this particular child already knew and could use enough powers of 2 to make approximations that rivaled some adult’s abilities. Why should children learn only “fixed-point” arithmetic, when “floating point” thinking is usually better for problems of everyday life! More generally, we need to find out more about how each child regards each subject. How might it answer questions like “What am I doing here, and why? “What can I expect to happen next?” “Where and when am I likely to use this?

What do you think? How did your Mathematics education affect you — do you love or hate math? How would you have changed your Mathematics education? Share your experience in the comments! Also check out the whole essay, and AI fans will dig Wikipedia’s page on Minsky himself.

via MentalFloss