I follow a number of education writers and those who write about learning. One of these, Scott Young, is a high achieving recent graduate who seems to be making a living by giving learning advice. His latest claim to fame is his MIT Challenge where he studied a complete 4-year MIT course in one year as a way of learning new skills but also, presumably to prove the effectiveness of his methods. My opinion is that some of the methods are debatable as they don’t foster really deep understanding of a topic, a number are just ways of quickly mastering the necessary ideas to pass an exam. As an example, in one of the key documents he uses to advertise his Learning on Steroids programme he shows how someone used his methods to learn the mathematical concept of limits. There is a scan on page 7 of the notes. The student writes in a section headed “What is a limit, REALLY?” that “A limit is like a stalker, forever getting close to the target. Forever trying to close the distance between it and the target, but rarely ever succeeds.” This analogy is deeply flawed. Worse than that, leaving aside the word stalker, it is precisely what I have to stop students thinking a limit is. When I set an exam question on the definition of a limit, many students will give rather incoherent answers about “numbers getting close to other numbers but never quite reaching”. However, what I want students to realize is that the limit of 0,0,0,0,0,0,… is 0, i.e., every element of the sequence is equal to the limit — the sequence doesn’t get closer and closer to the limit. Another good example is interweaving this sequence with 1/n. I.e., 0, 1,...

## Lancelot Hogben

posted by Kevin Houston

No post last week – I seem to have spent the last two weeks on trains or motorways going from one part of the country to the next on various academic related missions so have not had the time to write a post. So back to business. Dara O’Briain’s Science Club is a new TV series that takes a Top Gearish approach to scientific topics (I often wondered why no one had attempted such an approach before). Last night one of the guests was Lucy Cooke who I’d never come across before but was very entertained by. As her unsung scientific hero she selected Lancelot Hogben as he pioneered the use of the African clawed frog in scientific investigation, including an early method of testing for pregnancy in humans. I had not known this side of him, I know him as the author of Mathematics for the Million. I bought a copy of this book from the thirties from a second-hand book shop in Ilford when I was an undergraduate. In its time it was a popular maths best-seller, though I doubt such an equation-packed book would do so well now. To give some idea of the content it starts with mathematics in ancient antiquity and gets up to calculus, modern algebra and probability. I have to confess that I have not read it cover to cover but have read chapters, dipped in here and there and used some material for my own courses. I would love to be able to teach the chapter on Mathematics for the Mariner as it covers a lot of interesting spherical geometry. Maybe some...

## XKCD on the maths of elections...

posted by Kevin Houston

Too much going on this week to post anything sensible so I’ll point in the direction of the latest xkcd: