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It is not hard to get kids playing football. You leave them somewhere with a ball. At the weekend you take them to see the game. Imagine if we could do the same with mathematics!

We can. I have built mathematical sculptures with people in their own time, happily volunteered. I have taken mathematics to festivals and seen parents drag their children away to give time to the other exhibits. It is possible to get kids to play spontaneously with mathematics and to give them ideas from the deep reaches of the subject. I use my research in geometry and tilings. Leave children with wooden Penrose tiles and they start to play. They ask questions, and find answers. Add games with mirrors, and toys like http://www.zometool.com/ zometool] and polydron and you can give ideas from group theory, four dimensional space and Gödel's incompleteness theorems. In fact from primary to graduate school and beyond there are plenty of topics that can be motivated this way. As an example of more familiar maths, trigonometry can be used to help design a catapult and then quadratic equations will help aim it.

You will probably be surprised by how many students get inspired by these ideas, others might be interested but not want to get too deep and others will be bored. That is fine, the same happens for everything. As an example few would say that sport cannot be interesting, yet it holds little appeal to me. What we need to move on from is the idea that concepts should be hidden as they are too challenging or complicated. This is like forbidding someone learning football from seeing professionals play, or trying not to confuse a young pianist by playing them Bach or Rachmaninov. When they have entered school children have already worked out how to use their limbs, how to make sound and then how to give it meaning. They are used to challenge. Compared to that most mathematics is trivial. Education should be a challenge, with the acceptance that we might fail. In fact there is something wrong if someone does not fail. All schools and parents will find people around who have some area of expertise that excites them.

When people find the challenge that grips them they are inspired. They become activated to learn for themselves. However for most of history what they could find to learn was limited. This improved dramatically with public libraries, but the internet changed the game again. Now anyone who can get online can, with effort, find just about the whole of human knowledge. Internet access is rapidly expanding, how long before the majority of people on earth have access to all that knowledge?

So as the community of thinkers, artists, makers, musicians, sportsmen, we can put the challenges in front of people; help them find the goals that will drive them; set those sparks to the tinder of the internet. What then? Maybe we could take this a step further, to find those from all backgrounds who are getting excited and give them greater challenges? The internet has the knowledge, but good teachers can take things so much further. Maybe the answer is still in the internet? Something as simple as finding the individuals who are looking at a particularly high number of pages. They are almost certainly the ones diving in deep to try to find things. Identified they could be sent a "Harry Potter" letter, connecting them to a teacher; a postdoc, a young musician, someone who can guide them into the greatest challenges of whatever has got them going, providing its wisdom not just its knowledge. How many Einsteins or Ramanujans are out there waiting to be discovered? (and that is just the scientists)

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I have put my views on criticism forward for everyone so I am an open target, what are the flaws? what have I missed? (and what do you find great? ;)

@lucasgonzalez here:

Hi Gelada, like up to and including "So we can help activate people by challenging them,...", but don't really get the last bit. (it feels a bit too brief). Who is the "we"? Up to and including "So we can help activate people by challenging them,...", feels fairly inclusive and universal, but beyond is it "academics only beyond this point please"? or am I misunderstanding? Philralph 09:26, 22 July 2010 (UTC)

Thanks for the comments Philralph, I have tried to expand the final section and make it clearer. I am an academic, so there is probably some subconscious bias in what I had. I certainly believe that the academic education is incredibly valuable for the right people. On the other hand I do not think that this is the only way of pushing people further, and for many other things would be better. I hope the new version expresses this! What do you think? Gelada 17:19, 22 August 2010 (UTC)

Hi Gelada, nice final section, like it Philralph 16:23, 2 September 2010 (UTC)

Right. My concern is that I felt like you were talking about something really important and vital - about our approach to educating children. It hints at all sorts of other questions (the value of teching with no intention of testing for instance, especially for the young). But the conclusion seems to back away from realising the true potential of the idea. I think that targeting the people you talk about, people who are already harnessing the internet for off the cuff learning, sounds to me like it isn't ambitious enough, like preaching to the choir. That's not to say your version doesn't have value, but what I really wanted to hear was a suggestion for bringing these types of teaching approaches into the mainstream. --BlueChris 12 Sept 2010

minor edit by catlupton 16.8.11: the word 'find' added to fill a gap in this sentence: All schools and parents will find people around who have some area of expertise that excites them.

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