I teach a course on the History of Mathematics but today’s post concerns a TED talk on the Mathematics of History. This very short talk by Jean-Baptiste Michel serves as a follow up to the one given with Erez Lieberman Aiden on What we learned from 5 million books.
The idea is that we can use mathematics to understand history. Unfortunately, the talk is too short to develop a coherent argument and the examples given are not exactly new so I’m not yet convinced that they have something. It should be interesting to see whether this develops though.
Over the last few weeks I’ve been thinking about producing more videos. I’ve certainly fallen behind my planned schedule of producing them – too many other tasks get in the way! Anyhow, I have to produce some so that my school can complete a project for HE-STEM. As part of this I’ve had to consider what makes a good video and for me one of the most interesting debates about videos in education has been triggered by the huge success of Salman Khan’s video series. You can see him explain the history and the philosophy behind it in the following TED video:
Looks good doesn’t it? However, his videos have been strongly criticized. This is not surprising, educators were always going to object to an ex-hedge fund manager – backed by Bill Gates and with no educational training – coming in and saying “This is how you do it”. Nonetheless, many of their criticisms have foundation. I’m particularly against the “gamification” of education. Whilst games can be a useful tool in education when you wrap all learning in a game, then students lose sight of the importance of education; they see it just as collecting points for their scorecard.
Audrey Watters gives a good explanation of the arguments against Khan and various links in her post The Wrath Against Khan which arose as in response to an article in Wired on the Khan Academy.
(Aside: I think that video’s threat to teaching jobs is greatly exaggerated. When the printing press was invented people probably said “No more need for teachers, you can learn from a book”. Every new technology is predicted to revolutionize teaching and to cause the disappearance of the bulk of teaching jobs. People said it about radio, they said it about film, they said it about TV. They now say it about YouTube videos and laptops. (Aside to aside: Currently, the main threat to jobs is funding. Teachers are losing their jobs because governments are cutting budgets. But that’s a different story.))
Khan (along with most of the general public, in my opinion) has this naive notion that teaching is really just explaining. And that the way to be a better teacher is to improve your explanations. Not so! Teaching is really about creating experiences that allow students to construct meaning.
Actually, I doubt Khan believes that teaching is just explaining – although it’s true many of his videos are just explaining – I think the difficulty is that his courses do not do enough to construct the meaning mentioned in the second half of the quote.
I’m a fan of Dan Meyer. He recently blogged about an article on the Khan Academy featured on the TV programme 60 Minutes. Meyer’s post is here but maybe you should watch the report first. (It has a couple of annoying adverts near the beginning but it is worth persevering.)
There is also a follow up video in which the reporter makes a Khan Academy video with Khan. (See it here. One interesting thing to note is how well Sal Khan presents himself. He seems genuinely likeable and self-effacing (see the “My mum wishes I was you” comment). Since the videos I am preparing are about mostly about how to give a presentation it would be a good idea to use him as an example of how important likeability is. I’m guessing that if Kahn was a grumpy man who railed against the world his videos would not be so popular.)
One of the best videos I have seen explaining why Khan’s videos are problematical whilst praising their use in certain situations is by Derek Muller who has a good collection of YouTube videos.
The video relates to science education generally rather than mathematics but I think the point for mathematics is clear too. For example, one can apply the idea of showing common errors when introducing the rigorous definition of limit. This is a subject students think they know when they come to university so don’t pay attention to the correct definition. When asked to define a limit in an exam they write “it’s the thing that gets closer and closer to a number but never actually reaches it”. (Aside: A common complaint I hear from students is that before we taught them limits they understood the concept and afterwards they don’t! Ditto for integrals and Riemann integration.)
Now if you’ll excuse me I’ve got to go and create some online video materials. No, seriously, I have to…
It’s been a while since we had root around the collection of TED talks. Here’s one by Arthur Benjamin who seems to be more well known in the United States than he is here in the UK. If you want to emulate his tricks, then read his book with Michael Shermer, Think Like A Maths Genius. (Which, incidentally, had me in two minds about calling my own book How To Think Like a Mathematician but plans for my book were too far advanced for me to change.)
I haven’t linked to a TED video in a while so here is a very interesting one that is not very mathematical but I’m sure is of interest to mathematicians – even if it tells us that mathematics does not lead to fame.
Of particular interest is one of the speakers, Erez Lieberman Aiden, who will be familiar to reader of Cal Newport’s Study Hacks Blog as he has written about him here and here. If you don’t have time to read those (and if you are a student I strongly suggest that you do), then the short story is that Lieberman Aiden has published only six papers but has had an enormous impact because they have been good papers. And I mean good. All have been in Science or Nature and two have been cover articles. The talk in the video is about one of those, the hunt for cultural shifts using the data from Google’s controversial book digitization programme. You can read about it here in the New York Times.
Unusually for TED the talk is a two-hander with Lieberman Aiden sharing the stage with Jean-Baptiste Michel. You’ve got to feel a bit sorry for Michel. He’s obviously a smart guy – he holds a post-doc position at Harvard and is a Visiting Fellow at Google – and yet is overshadowed in the media’s reception of the work.
When Scott Kim cropped up in the Martin Gardner video it occurred to me I should post a link to his TED talk. Like the Martin Gardner programme it is not strictly maths but is a close enough relation for mathematicians to enjoy!
