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

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

#81

Post by M_Grey »

wolfgke wrote: post #80
M_Grey wrote: post #71

Earlier quoted context omitted.

The cooks are in the kitchen with their votes already, how could it be worse to have them actually know what the hell they're doing there?

Perhaps I am a little bit biased by the situation in Germany. In the past years there was an increasing number of non-voters in elections (typically people who are dissatisfied with the political system). Now in the last years a rather right-wing populist party (AfD) appeared that convinced many of these non-voters to vote for them. Compare this a little bit to the fictional situation as if Donald Trump would bring m…

That's an interesting perspective, and a good point.

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

#82

Post by eli_gottlieb »

inimino wrote: post #49
rimantas wrote: post #16

Earlier quoted context omitted.

Why exclude faith? For PC sake?

Not many people change their foundational epistemic stance in response to mathematical arguments.

It would help if fewer people had foundational epistemic stances. Fallibilism is much more realistic than foundationalism, as I understand the terms.

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

#83

Post by eli_gottlieb »

wolfgke wrote: post #80
M_Grey wrote: post #71

Earlier quoted context omitted.

The cooks are in the kitchen with their votes already, how could it be worse to have them actually know what the hell they're doing there?

Perhaps I am a little bit biased by the situation in Germany. In the past years there was an increasing number of non-voters in elections (typically people who are dissatisfied with the political system). Now in the last years a rather right-wing populist party (AfD) appeared that convinced many of these non-voters to vote for them. Compare this a little bit to the fictional situation as if Donald Trump would bring m…

>In the past years there was an increasing number of non-voters in elections (typically people who are dissatisfied with the political system). Now in the last years a rather right-wing populist party (AfD) appeared that convinced many of these non-voters to vote for them.

Well, maybe the Left should try actually appealing to the interests of the working class instead of the SDP going quietly along with the austerity measures.

>Compare this a little bit to the fictional situation as if Donald Trump would bring many people who did not vote in the last presidential elections back to the ballot boxes to vote for him.

That's not fiction.

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

#84

Post by Spivak »

tikhonj wrote: post #69
imgabe wrote: post #46

Do other disciplines ask similar questions? How should physics be taught to non-physicists? How should writing be taught to non-writers? How should car maintenance be taught to non-mechanics? I guess my point is, why should we teach mathematics any differently to "non-mathematicians" than we do to "mathematicians"? I mean, at the point when you're first teaching someone, how do you even know if they're a "non-mathema…

Yes, all the time. I've heard it for physics, I've heard it for CS and I've heard it for programming, all with good reason: the way you teach somebody deeply invested in your field is different than the way you teach somebody deeply invested in a different field, learning yours as a supplement. Or maybe a better way of putting it is that the way you teach somebody interested in a field in and of itself is different t…

This situation actually started a pretty nasty divide at my university. Engineering and Math are in separate organizational units which gives each a degree of independence. The politics worked out that most of the operational budget of the Math department came from teaching students from other disciplines. Over the years Engineering was dissatisfied that after going through the prerequisite Math courses their students had plenty of theoretical knowledge but couldn't actually do the Math -- even those that took the applied variants. So after Engineering came into more money they hired engineers to teach "Calculus/LinAlg/DiffEq For Engineers" courses that focused on application and topics that more directly applied to their other curriculum.

It was a success overall for the Engineers but Math wasn't happy. The engineers working on advanced coursework needed higher level math courses that were only available in Math. Not only were they constantly failing which angered Engineering but the professors teaching them had to devote more time to the Engineering students which took away from the math students and angered Math.

The sort of uneasy truce that they eventually came to was Engineering students take the regular Math courses and their Physics/Engineering curriculum supplements what they're taught in Math. This annoys double major Math/Eng students because there's far too much repeated material in their curriculum but it's the best they could do.

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

#85

Post by Myrmornis »

keithpeter wrote: post #21
Myrmornis wrote: post #6

Great article. Did anything come of the Gove-era math education policy changes he's referring to?

In my opinion: Gove's main change in Maths was in the exam syllabus that is taken at age 16. The new syllabus will be examined for the first time this summer, most schools started teaching the material in 2015. It will take another 3 years or so to see the effect of that on the GCSE classes (basically age 14 to 16) and then another five years for earlier years to shift what they do. Change takes a bit of time when it…

Can you say a few words about the direction he took the new GCSE syllabus in?

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

#86

Post by sn9 »

Sanjoy Mahajan [0], who is the author of perhaps the two best books on Fermi estimation (freely available online, too!), has linked on his website a really fascinating account of an experiment to reform mathematical K-12 education from 70+ years ago [1].

[0] http://web.mit.edu/sanjoy/www/

[1] http://www.inference.phy.cam.ac.uk/sanjoy/benezet/

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

#87

Post by keithpeter »

Myrmornis wrote: post #85
keithpeter wrote: post #21

Earlier quoted context omitted.

In my opinion: Gove's main change in Maths was in the exam syllabus that is taken at age 16. The new syllabus will be examined for the first time this summer, most schools started teaching the material in 2015. It will take another 3 years or so to see the effect of that on the GCSE classes (basically age 14 to 16) and then another five years for earlier years to shift what they do. Change takes a bit of time when it…

Can you say a few words about the direction he took the new GCSE syllabus in?

Well, there is plenty of stuff on t'web about the current state of play [1] [2] [3].

My recollection is that Gove's original idea was to scrap the GCSE completely and replace it with a new 16+ qualification consisting of a single 3h exam for each subject. Maths represents a difficulty of course as the range of ability encountered at age 16 for all 700,000 children each year is huge. Maths and science subjects differentiate by topic, wheras Humanities subjects differentiate by response to a brief.

As a concrete example you can ask a group of 30 students to write two sides about the best learning experience they have ever had. Everyone can leave the room feeling they gave it their best shot. Some will be excellent and creative with a good range of vocabulary and demonstrating some self-knowledge and analytical ability. Others will produce a description description, possibly with limited vocabulary, possibly with deficient skills in punctuation, grammar and spelling.

Now ask the same group of 30 students to take a single Maths test. Some will finish in 5 minutes with full marks (it wasn't the right test for them) and some will take an hour and score close to zero (it wasn't accessible to them either).

'The Blob' (the education establishment in the UK, i.e. the people at the sharp end) managed to head this one off together with the QCA and the House of Commons' select committee on education lead by Graham Stuart - a conservative but with experience of work in education unlike Gove. The result was a re-vamped GCSE Maths in which the Foundation tier has some topics previously only found on the Higher tier such as trigonometry, surds, rules of indices with fractional indexes, simultaneous equations, quadratics: solving by formula, factorisation and substituting into to plot graph. Much of the more useful statistics has been removed (graphical presentation &c) and replaced with harder probability. Much more emphasis on technical algebra and difficult fractions/ratio questions.

This lot is working its way down the school system now. If they stick to it the result might be OK in 5 years but my guess is they will get stick for the atrocious pass rates for the next couple of years (or fiddle them somehow) and then fudge it.

[1] http://qualifications.pearson.com/en/qualifications/edexcel-...

[2] https://bettermaths.aqa.org.uk/2014/06/28/gcse-maths-topic-c...

[3] https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web...

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