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{{TheFWD header}}{{DISPLAYTITLE:67. Challenging Education and the "Harry Potter Letter" - Edmund Harriss}}
<< Go back to [[The future we deserve]].
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!


Author: [http://maxwelldemon.com Edmund Harriss], aka [[User:Gelada|Gelada]]<br>
We can. I have [http://maxwelldemon.com/2009/04/25/building-mathematics-sculpture-system-5/ built mathematical sculptures] with people in their own time, happily volunteered. I have taken [http://maxwelldemon.com/2010/03/16/building-mathematics-the-maker-faire-in-pictures/ 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 [http://www.polydron.co.uk/ polydron] and you can give ideas from [http://en.wikipedia.org/wiki/Group_theory group theory], [http://en.wikipedia.org/wiki/Fourth_dimension four dimensional space] and [http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems 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.
Body of article: about 540 words.<br>
Discussion page for this essay: [[Talk:TheFWD_Gelada_-_Future_Education]]


The simplest form of education is training, you turn up, acquire a skill and leave. This is easy to structure, and more importantly to test. Yet training gets quickly out of date and cannot cope with rare events. We therefore require our education to do more. Not just teaching skills, but how to learn them, how to deal with the unknown, how to find new solutions. In short it should activate people to learn for themselves. There are now two essential skills: creativity and discipline. You need to have the idea, and then you need to work to make it happen. The problem is if your system worships creativity it can be hard to give discipline, if you worship discipline you can squash creativity.
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 [http://en.wikipedia.org/wiki/Bach Bach] or [http://en.wikipedia.org/wiki/Rachmaninov 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.


None of this is radical, I would think that most educationalists of the past 50 years would agree. Despite this however our education systems do not succeed in finding the balance. Exams and skills rule and the system pushes only discipline, often despite the best efforts of the teachers involved. Despite a long period of understanding, therefore, the solution still alludes us. We cannot predict how even the best ideas from the top might take effect in an actual school. In some cases they can even cause harm. At this point someone often says to just let teachers get on with it. I am not convinced by this. It gives freedom to bad teachers, and we have to admit there are plenty of them. Good teachers would get a break, but in most cases they are already "just getting on with it", sometimes fighting the system if they have to. So what can be done?
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?


Think about education. What matters? When it comes down to it, it is the teacher in the classroom, the parent in the home. It is the child sitting at the internet, vast swathes of the knowledge of humanity just in front of them. This is where we can make things better. Here we do not have to persuade the whole system, here we do not have to worry about how the system will mangle the message. Of course how to help here is also an issue, it needs to take account of the style and skills of the people involved.
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 [http://en.wikipedia.org/wiki/Einstein Einsteins] or [http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Ramanujans] are out there waiting to be discovered? (and that is just the scientists)


So the future is simple, talk to each other more. We have the tools to make it possible. If you are a teacher try new things and write about them. What worked? What didn't work?. Its already happening, there are some great blogs out there (some of the good maths ones are below). If writing things up is not your style, just take a look at what is out there. Try the suggestions and report back. Work out how you might improve. Build your own network and sources to give inspiration. Pick the battles where you can fight or subvert the system, Parents can do the same. Take advice from teachers, and find your own sources, make sure your children get exposed to lots of different ideas and activities. Finally children...no advice needed here. They have been doing this for years now, finding new ideas, learning to use computers, learning how to build things. Just imagine how much more could happen if we helped them?
'''Resources'''


[http://numberwarrior.wordpress.com/ Number Warrior]
* [http://www.maa.org/devlin/LockhartsLament.pdf A Mathematician's Lament]
** Paul Lockhart, Unpublished (widely circulated amoungst mathematicians)
** The case for revealing the beauty and not just the techniques of mathematics
*[http://www.theplayethic.com/ Play Ethic]
**Pat Kane, Pan, New Edition 2005
**The deeply thought through (yet readable!) account of how play can merge the inspiration and discipline required for creativity.
*[http://www.youtube.com/watch?v=Ud8WRAdihPg Alan Kay] on learning and context
*[http://www.nesta.org.uk/library/documents/idiscover_learning_framework.pdf Learning framework] from [http://www.nesta.org.uk/ NESTA]
*Blogs giving examples of how to challenge and engage children with mathematics
**[http://numberwarrior.wordpress.com/ Number Warrior]
**[http://101studiostreet.com/wordpress/ Think Thank Thunk]
**[http://blog.mrmeyer.com/ dy/dan]
*The benefits of toys (specifically LEGO) for developing mathematical ability.
**[http://www.informaworld.com/smpp/412443519-68016584/content~db=all~content=a714856615 Advanced constructional play with LEGOs among preschoolers as a predictor of later school achievement in mathematics]
***Charles Wolfgang; Laura Stannard; Ithel Jones, Early Child Development and Care, Volume 173, Issue 5 October 2003 , pages 467 - 475
**[http://store.tcpress.com/0807748471.shtml Blocks to Robots]
***Marina Umaschi Bers, Teachers College Press 2007


[http://101studiostreet.com/wordpress/ Think Thank Thunk]
{{TheFWD references}}


[http://blog.mrmeyer.com/ dy/dan]
[[Category:TheFWD]]

Revision as of 17:44, 11 March 2013

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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)

Resources

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