How would you make maths seem fun?

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If you spoke with someone who knows nothing of maths and when asked seemed scared of the subject and mostly finds it seems boring because it's appearance seems bland - graphs, formulae, etc.

How would you make maths seem fun?

It depends very much upon the individual concerned. You have to ask yourself why this particular individual has got where they are now; and you have to ask what sorts of things would motivate them to move from where they are now.

Let's posit a division: (a) the aesthetic and (b) the functional. The second is possibly the easier to think about first.

Treating mathematics as a functional skill (meaning a skill that allows someone to do something they otherwise would not be able to do) requires a diagnosis of what they want to be able to do. This can range all the way from wanting not to be diddled when they are given change whilst shopping to wanting to be able to analyse the data they have obtained as part of their scientific PhD project. Mathematical phobia exists at all ability ranges! I think the key to the functional approach is to show the person concerned that they can achieve what they wish to achieve; it is a matter of building self-confidence by a staged approach, walking with them on the way.

Treating mathematics as aesthetics is probably much harder simply because the aesthetics of mathematics are objectively hard. But again this resistance to mathematics as a fundamental component of the make-up of a well-rounded individual occurs at all levels! Here it is a case of matching the current aesthetics of the individual with something at a comparable level in mathematics. Someone who enjoys the sort of puzzle book that is sold in supermarkets would be amenable to some of the popular expositions of mathematics; especially if they help them solve puzzles better. Someone who appreciated renaissance art would surely be open to the historical approach that parallels the perfection of the art of perspective with the development of geometry.

Reply 21

Plagioclase

One issue is that there are two major groups of people who use Maths - Mathematicians and Scientists - and both have very different attitudes on the matter. I'm really interested in the applications of Maths to natural systems so a more applied perspective would definitely have made Maths more interesting for me, but pure Mathematicians would probably scoff at that. Nevertheless, I do get the feeling that there are more people who are interested in applied Maths than pure Maths so maybe a more applied route might switch more people on?

Reply 22

FireGarden

Original post by morgan8002

This is the fundamental theorem of calculus. I don't see anything wrong with stating it.

Well stating it like that is a problem. Integration is hideously more general than differentiation, there's no way they are true "opposites" unless you make some pretty strong restrictions on the functions.

One example is if f is a function which is continuous but not differentiable, then

\frac{d}{dx}\int_a^x f(t) dt = f(x)

but

\int \frac{df}{dt} dt

doesn't make sense because f is not differentiable. So the "truly opposite" cases are where f is at least differentiable, however that's really quite a strong condition. To be integrable (in general) a function could have countably infinite discontinuities!

Reply 23

Tarte Tatin

If there's a big group of people, you could put them into teams and get them to solve problems and compete with each other.

Reply 24

Absent Agent

Original post by FireGarden

\frac{d}{dx}\int_a^x f(t) dt = f(x)

but

\int \frac{df}{dt} dt

But how would you define integration in itself? As in differentiation is the process of finding the gradient of a function and so it's rate of change.

Reply 25

Joinedup

Original post by Protagoras

The point of this thread is for everyone to share things that they think makes maths fun - in the hope that other people will find new things to stimulate some thinking about ideas, concepts, histories, etc.

The first reply was exactly what is needed and I've browsed some of the books and videos mentioned.

Marcus du Sautoy speaks about mathematician's lives on BBC radio, which is good to lay back and listen to. - Poincare, Cantor, Galois, etc. www.bbc.co.uk/programmes/b00srz5b/episodes

Melvyn Bragg with a podcast about mathematics http://www.bbc.co.uk/programmes/p00545hk

Melv does quite a lot... there was a recent one on P vs NP which is computer science flavoured maths http://www.bbc.co.uk/programmes/b06mtms8

and one on e http://www.bbc.co.uk/programmes/b04hz49f

A recent example of BBC radio and probably not a good one http://www.bbc.co.uk/programmes/b06pt0bp
the annoying Will Self droning over someone else talking about Maxwell's equations - the chap who knows what he's talking about fades into the background while dreamy piano music plays... Self goes on a bit about how incomprehensible maths is. The subject isn't maxwell - it's a show about Will Self

Reply 26

username1560589

Original post by FireGarden

\frac{d}{dx}\int_a^x f(t) dt = f(x)

but

\int \frac{df}{dt} dt

I disagree that this level of detail should be taught at AS. At that age they haven't been given a formal definition of integration and probably not for differentiation. Considering all of the functions met at A-level are integrable and differentiable, the knowledge is useless and would just serve to confuse.

Reply 27

.Devon

[video="youtube;t8XMeocLflc"]https://www.youtube.com/watch?v=t8XMeocLflc[/video]

Reply 28

kkboyk

Original post by Protagoras

I used to be that kind of person who despised the subject so much, until half way through yr12 :laugh:

I would teach them some applicable stuff: like basic group theory, hardy-weinberg equations in genetics, uses of matrices e.g. search engines, role of toeplitz matrix in signal processing to really draw them in. Most people hate the subject because of terrible experience at school.