In recent years I have become interested in the history of mathematics. What is interesting is that a lot of what I learned about the history of maths, usually through asides from my lecturers, is actually wrong. And often what I hear on the radio and TV makes me cringe as it is usually innaccurate. One area I am developing expertise in is ancient Greek mathematics. (The name is misleading – most of the important maths happened outside of what we think of Greece although it was certainly influenced by Hellenistic culture.) Following my interest my favourite mathematical theorem is Archimedes Quadrature of the Parabola. Also, there are many great stories – see for example the Antikythera Mechanism. Another interesting story to emerge in recent years is that of a copy of work by Archimedes discovered written in a medieval prayer book. In the 12th century books were rare, precious and difficult to make so people would disassemble old books, scrape off the ink and write something new on the cleaned paper. This fate befell a text book on the work of Archimedes which was turned into a prayer book. Fortunately, some of the mathematical writing was still visible and the scholar Heiberg found it in a religious establishment, publishing a translation of some of it in around 1906. The book then mysteriously disappeared, resurfacing in the 90s in an auction where it was sold for $2 million. The project to find more secrets in the book was detailed in Archimedes Codex by Reviel Netz and William Noel. (Be warned the book is told in the first person by two people so can be a bit confusing!). The following video of the first author tells the story and discusses the work of...

## Teaching Students to Write Mathematics III...

posted by Kevin Houston

First anniversary of the blog! Celebrations later – time for the last video on the DVD I think. The final talk of our teaching students to write mathematics day was given by Mike Robinson. He was mostly telling us about the course he has been teaching for a few years so is full of practical advice on how to run such a course. For example he gives two marks for pieces of work: one for the maths, one for the quality of exposition. In the following slide you can see clearly how the new curriculum compares with the old. In the old the focus is on the content, in the new – where they still get the content – the focus is on thinking like a mathematician. Here’s the...

## Teaching Students to Write Mathematics II...

posted by Kevin Houston

Back to posts after the fun and games of updating my website and blog. The second video on the Teaching Student to Write Mathematics DVD is by Franco Vivaldi from Queen Mary, University of London. He covers more than just techniques of encouraging mathematical writing. One point of interest, starting at about 9:00 in the video below, is the following slide: The point here is to emphasize the difference between what lecturers see as important – theorems and definitions – and what students see as important – examples. I showed this part of the video during my CETL-MSOR talk and mentioned a student talk earlier in the day where students had said that what they want from lecturers is examples, examples, examples. (I probably came across as a bit more critical of them in my talk than I had intended!) Although Franco’s point is far from new, I think the slide is well worth showing as it gives a wonderful visual and clearly makes the point. (On the video he says that theorems and definitions are just a beam of neutrinos for the students!) By the way, I think Franco should add an extra box of examples that comes before and points to the theorems and definitions box since I believe that examples come before theorems. After all it is better to give some examples of groups before defining a group. Further on Franco also makes a point I keep trying to make to my students: Mathematics is about concepts and not processes. I’ll blog about this at a later date but basically the idea is that pre-university exams in this country give students the idea that maths is about processes. Hence, differentiation is about the process of differentiation, i.e., I give you a...

## Problems with my blog...

posted by Kevin Houston

I’ve recently reinstalled my blog following a hack attack. I think everything is back to normal (apart from the email letter sign up). Let me know if you see anything strange. Thanks. UPDATE: The style of the theme seems to have changed a bit so you have to click the title if you want to read the whole post....

## Teaching Students to Write Mathematics I...

posted by Kevin Houston

I’ve been away at the CETL-MSOR annual conference where I launched the Teaching Students to Write Mathematics DVD. Every conference attendee (nearly 100 of them) got a copy and the short talk I gave seemed well-received. The DVD mainly consists of three videos shot at the Teaching Students to Write Mathematics meeting at the School of Mathematics, University of Leeds on May 12th this year. We had three speakers: me, Franco Vivaldi and Mike Robinson. In total we got nearly two hours of great material. The videos on the DVD are now available on YouTube thanks to Peter Rowlett. I’ll be putting up a web page in the coming week for the DVD so that people can download it and the extra DVD-ROM content. (I haven’t done so yet because I’m having trouble with my website and blog – more on that some other time.) The first video is my talk. This was intended to introduce the subject to the audience and to show what I have been doing to encourage students to write mathematics properly. Looking back at the video, I think I may have committed the mistake that so many make: I lump all students together as being uninterested in study or unable to achieve. So when you hear me make generalizations about students, I should really say “some students”! Comments and suggestions are of course...