I always considered mathematics education to be much like calesthenics in athletics. The goal isn’t so much the technique of the exercise as it is in preparing for a proper outcome. In athletics, it is to improve the odds of winning with less injury. In education, mathematics is about honing the mind for more productive thinking. Trevor Thomas takes on How Math Should Work prompted by modern ideas in teaching and education valuation such as “integrated mathematics.

Amateur Radio provides an example. The talk now is about a “ham cram” followed by the license test. The goal is simply being able to remember enough of the answers from the test question pool to pass. It isn’t about knowing anything — if knowing means solving problems and putting into practice what one can spout as an ‘answer’ in real world applications.

“Why would Common Core provide curriculum direction for an approach to mathematics that is almost never used in the U.S.? I believe that it is because of the international appeal of the integrated approach and the desire by many on the left to make us more like other nations.

Don’t get me wrong: I’m not saying that every mathematics course in Georgia (or other states) high schools should be replete with rigorous proofs, but I think it benefits all concerned when the curriculum is laid out in a manner such that, for the most part, one topic logically flows (and proof could be incorporated) from the previous topic. This should be the case at least for college prep courses.”

The integrated mathematics idea is to put the focus on learning techniques in algebra, geometry, statistics and related topics and not on how these subjects actually work and what makes them what they are. There is no ‘story’ of the journey but simply a rote learning of the destination. That simplifies things and makes teaching and evaluation of learning appear to be similar. It is much like programming a computer where one can evaluate the quality of the program by the fact that it produces correct output. What this ‘integrated mathematics’ is not is the kind of learning that fosters capabilities to actually write the program as a solution to a problem, especially a new problem.

This also highlights differences between US and foreign education. While the US academic establishment seems bent on copying foreign educational ideas in public schools, education in the US still maintains a unique edge that puts it at a competitive advantage when it comes to creating new things and new ideas and new concepts. … so far, anyway.

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