Why a degree in Mathematics is no use for teachers of Mathematics

And what to do about it

I frequently see comments in the papers that there ought to be more degree courses to prepare teachers of mathematics. I suppose these people think that the content of a degree course coincides with the requirements for the most able pupils in the secondary schools. This, at least in my days at Oxford in the 1950s, was completely untrue. It seemed clear to me that what was taught in a mathematics degree course had nothing to do with the requirements for teaching boys and girls in their final year in the Mathematical Sixth Form. Hence I totally disagree with what these people are saying.


On the other hand I had seen evidence that sixty or seventy years before, some of the questions in the degree final papers were being used in school textbooks at sixth form level. This can only mean one thing: that the degree requirements had moved during that sixty years to a point far beyond the sixth form requirements.


Summarising my own mathematical education, I had been well taught at my prep-school, from age 8 to age 13. I then went on to Eton, where I was placed in the top mathematical entry class, E Select. I remained in the top mathematical class for the next three years, passing through D Select and C Select.


In these two latter years we had to do a weekly "Problem Paper". As it happens I still have copies of all these "Problem Papers". We were encouraged to discuss these problems with one another, and my chief collaborator was J.L. (Johnny) Wood. In class we generally went through all the issues involved, and in addition read chapters in books like "Statics" and "Dynamics" by Ramsay.


There was a voluntary book of choice that we had to read on our own during the middle part of each term. You could choose a book that would help you with your studies in French, German, Spanish, History, Mathematics, or any other course. It was of course additional to the official syllabus. I always chose Mathematics, because I could see that all I had to do was to work  my way through all the exercises in the book, and as the examiner (Mr H.K. Marsden) had to set the exam using the exercises in the book, I was bound to get full marks. These marks were added into the end of term exam results, with the result that I almost invariably got "Distinction in Trials", resulting in a collection of book-prizes. I think Johnny Wood did the same.


I must admit, though that when it came to O-Levels, I got Distinction in almost all subjects, Latin, Greek, French, English Language, English Literature, Physics, Chemistry, Elementary Mathematics, but not Advanced Mathematics. This was because I had been swimming in the river Thames the day before, and had picked up something nasty which made me vomit. I did as much as I could before leaving the Examination Hall in order to be sick, and I wasn't allowed back in. I did get an "A" though.


I had initially no intention of going up to Oxford, but by a curious turn of events I found myself there a week or two after the beginning of the Michaelmas Term. I found out that there was a scholarship exam at the end of the term, in November or early December, intended of course for boys who would be coming up to Oxford in a year's time, October 1953. I remembered that, apart from the book of "Problem Papers", we had worked our way at school through Hardy's "Pure Mathematics", Ramsey's "Statics" and "Dynamics", in two volumes each I think, and several books by C.V. Durell (Clement Vavasor Durell), of which I still have copies of a few, such as "Projective Geometry". So I just sat down and, interspersing with rowing in various Balliol eights, worked my way through these books.


As I well remember the Scholarship exam was of four papers. A morning and an afternoon paper, three hours each, for two days. All the candidates for scholarships to the different colleges sat the same paper, in the same room. During the morning of the second day, when I was about two-thirds of the way through that third paper, the examiner entered the room and whispered in my ear, "You needn't bother with the fourth paper, because you are so far ahead of everybody else that you've got the Balliol Scholarship." this was welcome news but I was rather enjoying myself so I did in fact complete the third and fourth papers.


But I found the work for the degree (mods and finals) so different and so hard that I really could not get interested in it. I did achieve considerable success as an oarsman, but none at all as a mathematician. After a serious discussion among the examiners I was awarded an Honours Degree, based on my distinguished work as the 1952 Domus Scholar in Mathematics, but only a Fourth.


I did several years teaching at Eton, and later at Radley. I actually taught Physics and Chemistry to O-Level, as well as Mathematics to A-level and S-level. The latter grade was for pupils preparing for a Scholarship Exam to a University. I never found that I needed any more skill and knowledge than what I had acquired in working for my own Domus Scholarship.


So what am I really saying - what is the bottom line, as some people say nowadays?


What I am saying is that I do not want to see people intending to teach mathematics at secondary level trying to get to a University in order to read mathematics there. Unless things have changed, reading Mathematics at a university would be a complete waste of time for intending maths teachers.


What we need is some sort of institution providing monastic seclusion, where people can work through the text and examples in books like those by Hardy, Ramsey, and Durell. Perhaps there are later heroes of the school world. Books by the above are all still in copyright. Durell for instance died in December 1968 which means his books come out of EU copyright in 2038 - a very long time ahead.


Personally I think this idea of mine is rather a good one.