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

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.

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