As he talked I thought about the Year 8 (Grade 7) lesson that I observed in a local secondary school this morning. The lesson was about finding the midpoint of a line drawn on a four quadrant grid. The teacher did a reasonable job in explaining the idea that to work out the midpoint of any line you need to take the x1 value and the x2 value and then divide it by half.. you do the same for the y1 value and the y2 value. The resultant x1+x2/2 and y1+y2/2 will give you the co-ordinates of the midpoint of the line.
Now depending on your experience and skills in mathematics you may have read the above statement as if a piece of simple prose in some novel and understood it fully or you will be lost in a load of letters and numbers and unable to understand what the hell I am talking about!
Therein lies the problem of the teaching of mathematics. Wolfram is right we spend an inordinate amount of time in classes working out purely mechanical calculations. Why would I need to know the mid-point of a line drawn on a grid? Well,if I were in the military and I was trying to fix a point half way between some point in a certain terrain and another point then I may well need to know where that point is. Would I work it out on a piece of paper using a grid? I don’t think so. I would probably have a simulation on a computer and get the computer to work it out for me.
I loved the model he showed about variables related to working out life insurance and what would make it the best deal. I could see a lot of relevance in this for real life skills.
He did not say that we never need to use mental calculation but that the skill to learn (as he does on a daily basis) is estimation… about how many miles will I get to on 10 litres of fuel? (In the real world we may use more fuel stopping in jams or have a clear more energy efficient run).
The real world has a number of what he calls “hairy problems”. They are not solved by using a simple (or not so simple algorithm or algorithmic processes). He is right to say that we can learn so much from computer programming and also from computer simulations.
I was thinking, as he spoke, about the bored faces of many of the Year 8 children who had just come into school first thing on a Monday morning and were faced with the problem of how to calculate the midpoint of a line. Frankly most of them did not see why they needed to (and this wasn’t explained to them) and wouldn’t be bothered to do so if they were given the option of choosing.
He is so right to say that we need to make mathematics live. We ned to connect it to the real world and we need to take the boring calculation out of the heart of what is taught. We should problem solve and explore we should bounce ideas off of each other and we should show how we can apply our mathematical analysis in electronic portfolios which future employers may find somewhat more revealing of our potential to add significant value to their workforce than a certificate or a diploma.
Although Wolfram was not one of the best and most dynamic speakers I have ever seen deliver a TED Talk he actually delivered a very well thought out and significant one… if you get the chance try and watch it.