Really I should be marking essays and exams but I sat through a day of student project presentations so I guess I deserve a rest. I had a good time at the conference in Poland. There were a few delays on the way but as I was travelling with my students, two gentlemen of middle eastern origin, I guess this is to be expected in the current times.
The modern conference centre is in the grounds of a picturesque palace which is pictured below.
Bedlewo Palace
The interior is quite nice too.
Interior of palace
Interior of palace
But what about the talks? Well, one was so bad that I wished that I had brought a video camera. In the coming years I will be teaching our students how to give presentations and this talk was a perfect example of how to alienate an audience. The speaker gave a 55 minute talk in which used more than one slide per minute – all slides densely packed with maths naturally – and read them in a monotone, his eyes fixed to the screen except for three occasions where he looked towards us. Three times in an hour! And those times were all in the first half hour. How can anyone, especially a non-novice, believe that they can give a good talk without engaging in the audience?
The conference finished on Friday and as our flight home was on Saturday evening, we went to the centre of the nearby city, Poznan. While we were there we saw a bubble festival. Not sure why they were having a bubble festival…
I’m currently in a small village in Poland about to take part in a conference: http://bcc.impan.pl/sga/
The general public may find it hard to believe but new mathematics is being produced all the time. Not only that the volume of new mathematics is huge. So huge that even the best mathematicians know only a very small proportion of it.
This week’s conference focuses on the geometric side of my area of interest, Singularity Theory (it’s a descendent of Newton’s calculus). I’ll be giving a short talk at the end of the week. Haven’t written it yet…
Conrad Wolfram, younger brother of Stephen, created a bit of internet buzz with his TED talk last year. His basic thesis is that we should not focus on drilling students in hand-calculations. This idea is of course nothing new, in an article in the BBC’s Listener magazine, February 1st 1962, the late Peter Hilton argued against teaching of mindless arithmetic as you can see from these quotes:
Calculating is a dreadful bore and rotten material for eager young minds
I would teach the child how to use a calculating machine and approximate methods–it is important to be able to estimate the size of an answer, but this is rarely taught.
In this age of machines we do not need inaccurate, unreliable, and unwilling human calculators… Yet we employ eager and fresh minds in arid and sterile calculation although we have no need of their conscripted computations.
As you would expect, I was good at maths at school. But often I was bored. Really, really, brain achingly bored. We spent a lot of time doing tedious calculation after tedious calculation. One teacher gave us 100 exercises to do for homework and as a concession reduced it to 99. I was nearly crying with the boredom, banging my head off the table. Now, if I, someone who was good at maths and actually enjoyed it when exposed to interesting stuff (thank you Mr Milne, wherever you are), found it boring, what torture it must be for those without an aptitude?
For me mathematics really got interesting when we were exposed to ideas. I only took mathematics as A-Level because I wanted to be a computer programmer and was told I needed it for that. I was sceptical but had my head turned by ideas such as calculus. I can remember thinking what a clever idea differentiation was, why hadn’t I spotted something that simple and powerful? I was so impressed the day we started differentiation (it’s so clear in mind I can remember it was a Friday) that I tried to explain it to my parents. Calculus was then followed up with complex numbers. The idea of the square root of -1 was such a weird idea and yet, like differentiation, was somehow natural. Why hadn’t I thought of it earlier?
A link to Wolfram’s TED talk is given at the bottom of this entry. However, If you have an interest in the reform of mathematics education, then first watch the TED talk by Dan Meyer that I mentioned back in January. This guy is on the front line of teaching and has some really simple ideas.
I have problems with Wolfram’s talk though. Perhaps unsurprisingly for someone who is not in the business of day-to-day teaching he doesn’t give us many ideas about how to achieve the goal he wants. As teachers know, there is no silver bullet that will solve problems in education. I agree with a lot of what he says. And yet I was disappointed. We are burdened with the practicalities. How do you assess the work that the students do when freed from rote calculation. Often teachers have a lack of familiarity with such assessment (or the computing tools) and yet he seems to expect them/us to effortlessly to deliver his vision.
Also, I think that the major problem with education is not about rote learning. The biggest hurdle I face as a lecturer — and I’ll tell this to anyone who will listen — is that if I set a problem for students, many will look for a worked example in the notes and if they can’t find one will quickly give up and say they can’t answer it.
I would love students to be able to happily tackle a problem they haven’t seen before so that if they get stuck they persevere. If we give students computers, then I fear that setting a problem will result in them saying “I put it into the computer but it didn’t give me an answer so I gave up”.
I’m reminded of the famous quote that to a man with a hammer everything begins to look like a nail. Wolfram enjoys programming. Problem in education? Use programming.
It is the dream of any student: work less but be more successful.
However, this dream can be a reality according to Cal Newport’s philosophy. Actually, he isn’t saying that you shouldn’t work hard – he points out that successful people often work hard – he says that you shouldn’t work so hard that your life is miserable. You should be able study hard and enjoy life.
