A partial answer to the questions I brought up in the last post about what authentic mathematics consists of, and how we get students to learn it genuinely, might be found in this TED talk by Conrad Wolfram called “Teaching kids real math with computers”. It’s 17 minutes long, but take some time to watch the whole thing:
Profound stuff. Are we looking at the future of mathematics education in utero here?
Casting Out Nines 
Time to install Small Basic and Scratch on your computers. Follow up with Matlab and Mathematica. Add a dose of STEM. Voila!
I’ve been circulating the Wolfram talk for a while now. As to whether it’s ‘the’ future, just look at the present: there is a minority of teachers and others with influence in mathematics education who not only get Wolfram’s point about mathematics vs. calculation but have gotten it for decades and written and spoken about it (see, for one glaring example, Tony Ralston). And then there is everyone else, from the average person who assumes that Wolfram’s viewpoint is wrong because the ‘experts’ say so and because his vision is nothing like THEIR experiences in mathematics classes, to those who should know better but clearly don’t (see mathematicallycorrect.com and many similar sites filled with mathematicians, engineers, and others who should have a clue but apparently don’t – or more likely whose political agendas prevent them from admitting what they know is true about the real nature of mathematics). Of course, it’s possible that the latter are more naive and ignorant than one might expect, but I’d say such “naive experts” are more the exception than the rule.
My point is that while Wolfram’s view may be basically correct (and I think it is), the old guard manages to hang on far past all reason because it reproduces itself in succeeding generations. That old guard still has control of school mathematics and thus colors the viewpoints of the vast majority of past, current and near-future generations. Whether Wolfram and others like him will is probably not in question: eventually, sense must prevail over nonsense. I fear, however, that I won’t be around to see it do so. I’m 60, and the average mathematics classroom today looks not all that different (save for the use of calculators) than those of my youth. A half-century or more hasn’t really shaken up school mathematics very much. If the Mathematically Correct crowd has its way, this will be a war of attrition. Time is on the side of the sensible, but some of us wish time would hurry up. ;^)
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