Stop teaching calculating; Start teaching math

So basically what he is saying is that drilling kids into memorizing math procedures like LONG DIVISION is not a good way to get people interested in math and analytical thinking in general. Ok. Sure. He is right that modelling is probably what "people who don't get math" struggle the most with.

But saying that math is just "computational stuff, turn the crank, let the computer do it" kind of thing is ludicrous. You can use mathematics as a blackbox model to do cool demos and stuff, but at some point you //have// to open the box and see how it is done.

It just happens that the standard math curriculum (numbers, functions, sin, cos, etc.) is a very good mix of conceptual complexity and computational complexity that can all be understood with pen and paper. You won't need to trust anyone, the proof is right there on the sheet. Anyone trying to take that understand in order to replace with with a SolveEquation[.] is not on the right side of intellectualism. Demos yes, but view source (is there view source for Mathematica functions?) and explain source are //sine qua non// for deep knowledge.

  > If we stop spending as much time on calculations we can
  > move kids more quickly into advanced concepts

Sound like "if we stop spending so much time on foundation we can have a roof sooner".

Though it isn't worth much, I'd like to put my two cents in as a student currently going through high school.

In the district in which I'm partaking in public education, there's a dead even split between contemporary and traditional math courses. Our school offers both the Core-Plus Mathematics Project (http://wmich.edu/cpmp/) and some variation of what I'd consider traditional (Geometry 1, 2, Algebra 1, 2, etc.).

The students more often than not will prefer the Core-Plus Mathematics Project over the traditional courses early on in their education - but once the math switches over to a primarily calculating class (take, for instance, Calculus), the opinions shift and favor the other one.

What we honestly have in my district is a case of a system that's trying to split itself down the middle politically - as we're attempting to switch to a modern, context driven approach to mathematics, whilst maintaining the link to processes like Advanced Placement, which only judge on the traditional aspects (http://www.collegeboard.com/student/testing/ap/sub_calab.htm...).

While it might be a better route for the future, the present is demanding math to be calculation based for the near future. It'll only start switching into a better realm when colleges and pre-college programs like those offered by CollegeBoard make the switch to context-based systems, rather than calculation based ones.

(I'm very well aware of how rambling that is, sorry!)

I remember to this day the lesson in primary school, when we first started solving word problems. It was sth like 3rd class. Teacher would ask simple question, like "how many apples we had to add to each chest, if there is 4 chests with 7 apples in each, and we need to have total of 32 apples". And kids had to "brainstorm" and translate that into mathemathic process and solve (not algebra, just "first we need to know how many apples we lack, so we substract, then we need to know how many apples per chest we lack, so we divide", we didn't knew algebra yet). If the question wasn't specific, the kid that pointed it out got praise for being observant, and teacher specified what he meant. Most kids liked that lesson, and there was fierce competition to be the first to guess. That was the moment I felt in love with math, before that I thought I'm more of a humanist (which meant it's OK I can't understand decimal fractions ;) ).

I think teaching kids to translate problem into math is very important, not only for math, but also if they want to be economists, computer programmers, etc. I cringe when I read that kids "know math, but don't know which equation to use to solve the problem". My wife taught math in secondary school for a while (in Poland, not USA, but we've recently had reform modeling our schools on those in "the West"). Many kids she taught had no idea how to translate word problem into math problem. They just pattern-matched keywords to equations. It's very sad, and I understand why they hate math - it must be completely frustrating to play this "guess the equation" game.

So - I think there should be more focus on teaching kids to understand the basic word problems, before they even know algebra. To be sure, that they understand when we need to substract x, and when we need to substract from x.

Try "Calculus Made Easy" (http://www.gutenberg.org/files/33283/33283-pdf.pdf) -- it was Richard Feynman's first calculus book, and it explains things in a way unlike any other book.

Here is a famous quote where he references a passage from the book's prologue:

"Right. I don't believe in the idea that there are a few peculiar people capable of understanding math, and the rest of the world is normal. Math is a human discovery, and it's no more complicated than humans can understand. I had a calculus book once that said, 'What one fool can do, another can.' What we've been able to work out about nature may look abstract and threatening to someone who hasn't studied it, but it was fools who did it, and in the next generation, all the fools will understand it. There's a tendency to pomposity in all this, to make it deep and profound." -- Feynman, Omni 1979 (http://c2.com/cgi/wiki?FeynmanAlgorithm)