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Computer-Based Math Education

Posted 11 years ago
Hi everyone,

I live in the UK, where our maths education is pretty broken. I was an A-grade student, learning maths in the same way everyone else learned--rote and with hand calculating. By age 16, my understanding fell apart. Why was I learning this stuff?

Perhaps a little ironically, nowadays I manage projects and organise outreach for computerbasedmath.org. I can't help but think, why wasn't I taught this in school? The emphasis on teaching understanding through maths, rather than just calculating, is fantastic. I really like Conrad's TED talk, which some of you may enjoy:

Conrad Wolfram: Teaching kids real math with computers

People, even entire countries, are really starting to get this concept. The project is going from strength to strength and with the UNICEF-hosted Education Summit running this month, there will be a lot of exciting new partnerships developing soon.I'd love to hear from you if you can relate and are interested in what we're doing with computerbasedmath.org.

Any thoughts, ideas and experiences you have to share would be great to read. I'd also encourage you to pop over to the website.

Mike
POSTED BY: Michael Belcher
5 Replies
Posted 11 years ago
Hi Mike,

I have been using Mathematica since Version 2, a bit over twenty years, and I am a real proponent of math education.  I am not an educator, but I think Mathematica would be a great tool for helping students develop intuition in math. A good example is looking at the solution to a 2nd order differetial equation as the initial conditions, resonant frequency, and damping factor are adjusted. However, my first real exposure to that demonstration was in TV programs aired by the Open University, in the UK, before Mathematica became availabe.

Having said that, I think there are risks to computer-based math education. It could lead to the attitude that it's just the results that count. If I know how to put the problem into a computer and get the answer, that's all I need. Learning math is a lot more than that. It's about how to find the path between facts and their implications. How to formulate a question that can be asked of the knowns, and a process for getting to the unknowns. And even the ability to know when the knowns aren't enough to provide an answer. Maybe you can determine the loan payment for that car on your computer, and also balance your checkbook (does anybody still do that?) and decide if you have enough for a downpayment, but can the computer tell you if you can afford it? Even for people who will never work in a field employing math, math is important. (Especially the dreaded story problems.)

For those who will work in mathematics, doing it yourself is a critical part of understanding. Mathematica can solve that high order differential equation for you, but the process of learning to reduce that equation to a set of coupled first order equations, diagonalize the coupling, and transform the basis to a linearly independent set,  provides an insight that will transfer to many other mathematically similar situations.

In short, I think computer-based instruction can be very useful. But mathematics is not a spectator sport.

Kind regards,

David
POSTED BY: David Keith
Hi Mike. Good to hear of your efforts! I think you're definitely preaching to the converted over here... emoticon However, I'm not sure that the UK education system is quite so enthusiastic in adopting computer-based mathematics teaching. I don't know about many schools, but I get the impression, from the limited experience I have, that maths for 14 to 18 year olds is based on well-photocopied exam-style exercises and a brisk run through the syllabus before the business of going through old exam papers cuts in a few months before the exam, in order to achieve some reasonable final grades that the school can boast about on their web page. There are no computers in the maths classrooms (they're all being used by the ICT departments). Teachers have to administer this syllabus and get their students through it, and may not be able or willing to risk the introduction of new techniques and ideas without the approval and encouragement of their leaders or government.

But what makes change happen - when the current political regime feels that 'the system' (no doubt broken by a previous administration) must be modernized, rather than returned to 'good old-fashioned maths teaching'? Or when hundreds of overworked maths teachers rise up and march on parliament demanding free Mathematica licences?

The most effective strategy will probably involve competitions, scholarships, roadshows, and free prizes including iPads and Raspberry Pi's, along with plenty of high quality free educational material to appeal to our cash-starved schools!
POSTED BY: C ormullion
C ormullion - Some great ideas there. We ran a competition back in 2012 for students which we may will run again in 2014. Did you hear about it at the time?

Wolfram Programming Challenge 2012

David - I think you're spot on with your assessment of Maths regarding finding paths between facts and implications. I would also say that's exactly what we're trying to do with computer-based math. I think it's important to disginguish between computer-based (using computers as a tool to fully understanding context and implications), and computer-assisted (using computers to get an 'answer' - whatever that means...)

You might be intereted to know we're working on fully mapping out the 'process' of maths - something that i'm pretty convinced that not many people fully grasp.
POSTED BY: Michael Belcher
Don't forget - competitions shouldn't be open only to Mathematica users - you want to persuade people to be interested in Mathematica that aren't currently using it... emoticon
POSTED BY: C ormullion
Posted 11 years ago
Hi Michael,

I do think computers can be VERY valuable in obtaining intuition in maths, which is too often missing in instruction. I suspect most "discoveries" in math are led by intuition, but then they are put on a needed formal footing by developing linear transitive proofs. Unfortunately, math instruction then abandons the intuition, and teaches only the formal proof, where the result comes as a big surprise at the end. I think this is one reason physics departments so often teach the needed math along with the physics. When the math department does it, the professor spends half the class working with functions that are 1 on the rational numbers and 0 on the reals -- something quite pointless in classical mechanics.

I'm very much looking forward to your mapping of the process of maths. It usually seems to me that I write down a definition of the problem and then stare at the paper until the answer arrives in my head. Any work on process would be a real contribution!

Best,
David
POSTED BY: David Keith
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