Kevin Houston

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.

One for researchers. Last year I, with my colleagues Roger Bielawski and Martin Speight, edited a book, Variational Problems in Differential Geometry. There is currently a US promotional offer for this book:

In a previous post on the Khan Academy I said in an 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.

I was asked for evidence for the “They said it about film” part. Given that when I was school we watched educational films projected on the wall at least someone was eager to use the medium in education so someone must have said it.

However, the quote comes from an interesting source: Thomas Edison.

I believe that the motion picture is destined to revolutionize our educational system and that in a few years it will supplant largely, if not entirely, the use of textbooks.
I should say that on average we get about two percent efficiency out of schoolbooks as they are written today. The education of the future, as I see it, will be conducted through the medium of the motion picture … where it should be possible to obtain one hundred percent efficiency.

Thomas Edison (1922) quoted in Larry Cuban, Teachers and Machines: The Classroom Use of Technology Since 1920.

Whilst researching this quote I came across Quote Investigator which discusses the history of the quote. This led to an interesting article using the quote to comment on the current Let’s-give-all-the-kids-laptops/iPads movement. Of course, I could have easily found a dozen such articles.

And when was television the answer to all educational ills? Well, recently I found a University of Leeds prospectus from 1968 which highlighted the university’s use of television as a teaching method. The hope was that the lecturer would be unnecessary as students could just watch pre-recorded programmes, or at the very least one lecturer could broadcast to many students. In fact, until the major refurbishments following the introduction of student fees, in many teaching rooms here you could see the old sockets used for the coaxial TV cables.

I think the point is that in most situations the best type of teaching comes from real people. Yes, books are good, videos are good, etc, but there is no better to way to learn than to have a teacher there interacting with you. People know this and will pay good money for it whether employing a personal trainer for exercise or attending a educational institution with good access to staff.

Probably, like me, your most inspirational learning experiences came from teachers and not books. Am I right?

Fake quote?
Whilst researching this post I came across a quote spookily similar to the Edison quote above but it seems to be made up. The alleged quote is attriduted to BF Skinner, the famous behaviourist who studied pigeons and rats. He invented a “teaching machine” (which he patented!) that was going to solve the education problem. (Aside: I can remember a children’s educational book about the “World of the Future” that featured the machine. What I remember is that it had a little roll of paper and a small window. A question could be asked, the student would be able to write the answer on the paper, the paper would advance behind the window so the student’s answer could not be changed while the true answer was given. I like the way Skinner had taken into account that students might try to cheat but had not taken into account that we’d communicate with machines via a TV screen.)

Anyhow, according to the source, Skinner viewed the machine as a solution to our education problems (compare with the Edison quote):

I believe that teaching machines are destined to revolutionize our education system and that in a few years they will supplant largely, if not entirely, the use of teachers.

This was referenced with Skinner, 1968, p1. See here.

Well, I’ve checked the works by Skinner in 1968 and can’t find it. (The obvious publication in that year is his major book The Technology of Teaching.) Also, it seems unlikely that Skinner would plagiarize a comment so badly!

What’s funny is that the quote has been repeated many times in other places. Why have those authors not checked their sources. Or am I missing something here?

I’ve been busy this week. On Monday I gave my new Auto-Tune talk to the School of Maths (I spent the previous Saturday reading the patent for Auto-Tune. Very interesting.) And yesterday I was in London to give a talk on Teaching Analysis. The meeting was also interesting but poorly attended as just about every project is running conferences and workshops. During my talk I showed my Pi is 4 video as an example of something I am using in my lectures. You can see it here.

Anyhow, Vi Hart has a video on the subject which is worth watching:

Cover of College Mathematics Journal

The issue is, as one might expect, a mixed bag. Of interest is a reprint of Gardener’s original article on Hexaflexagons (these were a childhood favourite for me); in the provocatively titled Martin Gardner’s Mistake Tanya Khovanova discusses the errors in solutions to Tuesday’s child problem (a problem which surfaced at Gathering for Gardner before ricocheting around the internet); Arthur Benjamin has a very simple (I mean that in a good way) article on Squaring, Cubing, and Cube Rooting. There’s also an article by Ian Stewart, who (I suppose it goes without saying) has a new book out.