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Maths IS Creativity

“One of the biggest problems of mathematics is to explain to everyone what it is all about. The technical trappings of the subject, it’s symbolism and formality, it’s baffling terminology, it’s apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were summed up as ‘a lot of tadpoles drawn on a row of lines.’….. The symbolism of maths is merely its coded form, not its substance…. Mathematics is not about symbols and calculations, these are tools of the trade…. Mathematics is about ideas…. It is about how ideas relate to each other….understanding why an answer is possible…. good mathematics has an air of economy and an element of surprise. But above all, it had significance.” (Ian Stewart, From here to infinity)

These lines are taken from the phenomenal opening to Ian Stewart’s From here to infinity, and I think they contain some very powerful imagery and sentiments about maths that are often missed by a lot of people.

Recently I was at a university open day for a psychology course and are one point, for a small scale taster “study” we were asked to put ourselves into groups based on Kirton’s Adaption Innovation theory. The lady running the session then discussed adapters and innovators (more info here). She said that adapters were people who liked order, liked to stick to rules and innovators liked to look creatively at problems, deconstruct them and try other approaches. All of which was fine, but then she said “adapters tend to be accountants, or something else mathematical.” I bit my tongue, I could see it might hold for accountants, but not mathematicians! And to lump accountants and mathematicians together in such a way…..

Mathematics IS creativity, it’s about looking for answers. When teaching an intro to complex numbers I talk about Hero, Bombellini and Co and the work they each did, the fact they couldn’t answer certain questions within the confines of what was already known, so they “invented” the complex plane. Mathematicians have been creating for millennia. It’s what maths, especially pure maths, IS.

This idea is something I’ve been thinking a lot about recently. Not least because I’ve seen some fantastically creative mathematics from a few students recently. One Y11 girl who is a gifted mathematician but has missed a lot of lessons was tackling a proportion based problem on a mock. She had missed the lessons on proportion, but still had an attempt. She didn’t do it the way I’d taught, and actually went an incredibly long way around, but she got the right answer. She saw a question she’d not encountered before, and she solved it. That’s the sort of mathematician we need to train.

A Y12 boy recently attempted a c1 paper, on a quadratic question you ended up with a quadratic in k for the discriminant (you know the ones…). It said “show that f(x) has 2 real roots for all values of k”. Or, show the discriminant is always positive. The way I would have done it, and the way most of my students did, was complete the square and state that a square plus a constant is always positive. He didn’t remember talking about this type of question. His solution? He found the discriminant of the discriminant (I.e. The quadratic in k), that was negative and showed the discriminant function had no roots, so didn’t cross the axis. The quadratic in k had a positive k squared, showing the discriminant was always positive, thus proving f(x) had 2 real roots for all k. I was amazed to see the proof written on the paper, and though “this kid needs to go onto study maths at HE.”

These are brilliant examples of the creativity of maths, and we need to change the way maths is viewed, perhaps it’s down to the curriculum, perhaps it’s down to the pedagogical style many of us encountered at school, perhaps it’s down to the focus on the C grade threshold pass, or perhaps it’s a combination of them all.

  1. March 29, 2014 at 8:08 am

    With slightly younger pupils, and their parents, the difficulty is getting beyond the idea that maths is stuff with numbers.

    I have recently been doing Escher inspired tessellations with top set year seven, and one or two pupils have asked, “What is the point of this, it’s not maths?” and the depressing “Will it be in the exam?” I did refer to the work now going on with designer vaccines and research into blocking viruses by creating interlocking molecules; they were slightly mollified. However, others have said, “This is brilliant, I actually understand what I am doing and there is no right or wrong.”

    The most interesting part has been the write up of the development of their design ie a record of the creative process. This has helped them to correlate this work with their experiments in science and see it as a proper bit of work, not just having fun with shapes!

    • March 29, 2014 at 8:36 am

      “Will this be in the exam?” I hammer that out of them early! When I took over my year 13 class last summer one of them asked me that, they still joke it’s the angriest they’ve ever seen me!

  1. March 30, 2014 at 10:01 pm

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