> So you are arguing that we as a society need to lower our general education standards? Is this not the exact opposite of what we need to be doing? Math in particular is so important whether dealing with personal finances or simply thinking abstractly. What happens when the hypothetical taxi driver job goes away? If society didn't care enough to try and teach that person some general education when we had the chance, are we now going to do it in retraining?

I am arguing that as a society we need a different approach to assessing skills. That the incentive structure that the current model of teaching and assessment provides is not useful for providing the skills that our young and the labour market that they will hopefully become part of require in order to advance and profit. I am not necessarily saying that mathematics is not a valuable skill, but if it is valuable then it should show up in the course of teaching things that children are actually interested in - and if it is widely applicable then most of them should pick up a few mathematics badges here or there in the process of pursuing those interests. I do not believe that children will acquire and retain any great facility with a subject that they detest, or that bores them.

Is the taxi driver, with his five years experience of taxi driving and limited knowledge of mathematics, physics, law, medicine, et cetera; in other words the jobs that would be harder to automate entirely in the short and mid-term future (by which I mean the next 20 years or so); really going to compete with people who have been doing those jobs the last five years on the strength of half remembered mathematics, which he probably hated when he did them anyway? Especially since we don't have a system of retraining, at least not in any serious sense. There is no option to go to the local benefits centre, state that you are done with working in retail and want to retrain to be a programmer, and have funding and an education available to do so. I don't know of anyone, anywhere, that makes that sort of investment in people. If you want to retrain, you'd best have a bit of money.

The taxi-driver is probably better off not having taken a mathematics course (under the current curriculum) at school, if that subject did not appeal to him, and not thinking of learning the subject as an act of suffering, or operating under the impression that he cannot learn it based on failing a number of tests on the subject some time ago. I regularly work with people with a background in in low income industries, as part of my charity work, and a great many of them have the assumption that they are simply incapable of learning and trace the roots of this assumption back to their failures in the education system. They don't have a faith that they can learn, or an understanding that anything good for them will come from investing in subjects that they have previously hated. It won't have made him competitive with people who were actually interested in the subject in any case - and there's no clear route of retraining that would let him become so.

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As for the importance of mathematics to "thinking abstractly", I will observe that it is an old chestnut trotted out whenever one wants to justify a subject, and that as such I've ceased to take it seriously. That you claim it to be a particular virtue of mathematics, and others will claim it to be a virtue of English literature, philosophy, history, and so on and so forth. Indeed, it is hard to think of any subject that has not claimed it is a virtue of its own. At some point we simply have to stop taking the excuse seriously or accept that it is a general enough skill that you can pick it up in a wide range of subjects, and that as such it is not a great argument for retaining any specific subject.

If it is important to "think abstractly", and if we eventually come up with a way of understanding quite what people mean when they say that, then we may well profit by separating that skill out from the particular application of it and teaching the skill specifically. I understand that there are people trying to make a study of how one learns rationality, and that if one wish to teach the skill one might perhaps consult them and see what their methods were.