There is much to agree with in Conrad Wolfram’s lecture in TED.
In Uncle Petros and Goldbach’s Conjecture Doxiadis’ main character refers to anything in a mathemaical problem that could be done by a machine as ‘shopping maths’. Wolfram has the same view and asserts that we should focus on those elements in the problem solving process that are NOT shopping maths. So far, so good. The problem is that Wolfram is stuck in a world that sees practical problem solving as somehow mathematical. He even uses the tired example of keeping track of your mortgage. Clearly people actually do this by looking at their statement and seeing how much they are paying, they do not engage with the calculations required to analyse the payments. As he says, in the real world, solutions are messy. The trick is (a) to develop opportunties to solve such messy problems in a school setting while keeping them real and (b) to put learners into settings where they actually care about the outcomes to the problems. Serious past experience does not auger well for the possibilities.
It is also troubling that doing mathematics by hand is ridiculed quite so comprehensively. Those quirky souls in the Isaac Newton Institute for Mathematical Sciences at Cambridge had chalk boards fitted in the seminar rooms, specifically to ensure that they can do their mathematics by hand. The problem for Wolfram is that he sees mathematical activity as necessarily applied. He is right to critique a school curriculum which is essentially a curriculum in pure mathematics dressed up as somehow useful, with a cloth of applicationm draped over an algorithm exercise. However, that does not mean that we should only be solving problems coming from the ‘real-world’, implying the entirely mathematical, i.e. pure-maths world is not why we should be teaching maths.
It is a genuinely good thing to see these sentiments aired and tempts the next steps … (i) an inclusive view of mathematics as an end in itself and a language for application, and (ii) a critical, credible view of how such thinking can be formatted for an institutional, compulsory, age specific, school system such as we work with.