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This was an interesting read. I think the author of the original paper though has some valid points and that this response labeling the original paper "anti-int

This was an interesting read. I think the author of the original paper though has some valid points and that this response labeling the original paper "anti-intellectual" is dishonest in that regard. In my opinion, the problems we have with Mathematics education in this country stem more from how the curriculum is structured than from particularly bad teaching or lack of natural ability. Looking back, it seems bizarre that all of elementary school gets devoted to performing arithmetic and then Algebra is suddenly introduced sometime in middle or early high school. In my opinion, arithmetic can be taught much faster than it is (Trachtenberg system et alia) and basic Algebra should really be introduced concurrently. The problem with this approach is that you can no longer sell neatly compartmentalized textbooks labelled "Addition," "Subtraction," ... , "Algebra" etc... The other thing that bugs me is the bizarre choice of topics taught in Algebra classes. I remember, I was forced to memorize the binomial theorem. At the time, it really made no sense. I'm now of the opinion that you shouldn't be taught math you don't have the machinery to develop on your own. Knowing arithmetic, you can build Algebra (not very rigorously, but the idea seems pretty obvious.) It's a much bigger leap to develop the binomial theorem, which requires more advanced machinery, which is generally not taught. Of course, once I could derive the binomial theorem on my own, it made much more sense. I did very well in math throughout my academic career, but didn't ever really feel like I had very much mathematical skill. Only now that I've developed an interest in doing math in a recreational capacity that I really feel like I've developed any sort of substantial mathematical ability. I'm really now convinced that the problem solving approach is the way to go and that this is how early math should be taught.

mangodrunk 14y ago
Now that you mention it, it does seem that too much emphasis and time is spent on counting and calculations. A symptom may be how some people equate doing fast calculations with being good at math.
- jinfiesto 14y ago
  It's funny how that escapes detection. I only realized looking back how baroque that was. I think people do equate doing fast calculations with being good at math. While I think everyone should certainly know how to add, subtract, multiply and divide without error, there's really no reason to be able to do so obscenely quickly, given the wide availability of calculators. If you did want to be able to do very fast mental math, there are much better systems than what are typically taught in schools. Really though, my point was that the school system spends far too little time on solving substantial problems in Math classes. I think an integrated problem solving approach that touches on many of the important branches of Math (graph theory, number theory etc...) would serve most people much better than the current system, where we spend 8 years building up to Algebra and then engage in a smattering of Geometry and Trigonometry. In the current system, if you're smart, you do AP Calculus, which is obscenely dumbed down. If you want to proceed to study Math in college, you'll almost certainly have to re-teach yourself calc to be successful.

mangodrunk 14y ago

Now that you mention it, it does seem that too much emphasis and time is spent on counting and calculations. A symptom may be how some people equate doing fast calculations with being good at math.

jinfiesto 14y ago
It's funny how that escapes detection. I only realized looking back how baroque that was. I think people do equate doing fast calculations with being good at math. While I think everyone should certainly know how to add, subtract, multiply and divide without error, there's really no reason to be able to do so obscenely quickly, given the wide availability of calculators. If you did want to be able to do very fast mental math, there are much better systems than what are typically taught in schools. Really though, my point was that the school system spends far too little time on solving substantial problems in Math classes. I think an integrated problem solving approach that touches on many of the important branches of Math (graph theory, number theory etc...) would serve most people much better than the current system, where we spend 8 years building up to Algebra and then engage in a smattering of Geometry and Trigonometry. In the current system, if you're smart, you do AP Calculus, which is obscenely dumbed down. If you want to proceed to study Math in college, you'll almost certainly have to re-teach yourself calc to be successful.