How should mathematics be taught to non-mathematicians? (2012)

Much of advertising is emotional appeal.

Plenty of advertising, car sales, consumer financial products, lotteries, etc... rely on people not having an innate understanding of math, and especially probabilities.

Hell, if people understood those issues, they might even have something to say about Gerrymandering and the electoral college!

Probably not a direct consequence but...

The UK elected a Conservative government who decided to base all 16+ Maths for non-mathematicians on the revised GCSE Maths syllabus. Colleges are now coping with large numbers of students aged 16, 17 and 18 being required to take the GCSE exam again while studying vocationally based qualifications. I'm teaching maths to trainee hairdressers, trainee car mechanics and would-be fine artists.

Pass rates are not high (we are starting with a selected sample after all and schools are pretty good at getting non-mathsy youngsters through). The statutory requirement ends at age 19 and so the majority of late teens will experience three more years of failure in a subject that they experienced failure in at school. That should guarantee another generation of the general public whose loathing of Maths is pretty marked.

Taking a wider view, I think that we all tend to learn things in a situated way and I therefore have a lot of time for the 'Functional Skills' approach to Maths and English if done properly. This was the approach adopted in most vocational training courses prior to the Gove era.

I also think that there is a place for a qualification based around probability, statistics, and critical thinking. I'd love to call it "How to spot bullshit when you see it". I'd make discussions of issues like genetic defects and screening, obesity and health education and so on a core component. It will never happen of course...

The post is about suggesting more fermi estimates problems, see for example http://lesswrong.com/lw/h5e/fermi_estimates/

Fermi estimates require you to look for relations in the real world, construct a model of the situation and then iterate improving the model by adding more information. You don't use that process just to give an example of using a rule or solving an equation, instead you emphasize how the problem could be tackle mathematically. So there are more room for open questions, incentives for exploring and suggesting new approaches, in a more relaxed atmosphere creativity can flourish, perhaps maths is more than a single equation written in an old book.

Not sure if you're teaching in the above environment, but one of the schools I teach A-level at has a high number of maths-failing pupils, and as a result, many of those I teach are re-sitting maths in both their first and second years that I teach them. It's a typical case of Gove not thinking of the consequences of his (backwards, IMO) ideas - these people are definitely part of the generation you outline; it spreads so they not only think they are bad at maths (which admittedly is often true), but that they are incapable of any meaningful learning. Those who do take functional skills and pass at least feel they have made some progress - despite this being a level of maths which most people would feel was far below the age level of someone taking at aged 17.

I know that anti-Gove rants are all over the place, but most of the people I know outside education don't have a clue about how poisonous his ideas have been; they don't withstand any serious scrutiny, but on the face of it may seem sane, so people who haven't thought about it will defend them. His replacement isn't far off his level, and I seriously fear for the future of education in the UK.