## Do you need a maths degree to teach maths?

A few weeks ago I wrote a post in shock at the fact that a number of schools in the locality had been teaching rounding wrongly. By this I don’t mean I took issue with their pedagogical approach, but rather that the method of rounding they were teaching was wrong and would result in the wrong answer in some instances. This post received the following comment from Old Andrew (@andrewolduk):

*“Is anybody going to raise the obvious issue here that a lot of maths teachers don’t have maths degrees? In recent years the rise of “conversion courses” means that many have a background that isn’t in the least mathematical.”*

This stirred up some quite strong feelings on both sides. Sophie Skinner (@miss_skinner) wrote this excellent piece stating her views, and Dave Gale (@reflectivemaths) wrote this piece reflecting his view. Twitter has been buzzing with conversation on the matter, and I wanted to set out my own view on here as, well, 140 characters just isn’t nearly enough to get across what I want to say!

First, I’d like to note that from now on I’m not going to distinguish between strictly maths degrees and ones with a high maths content (i.e. Joint honours, Operational Research, Physics, the whole host of engineering degrees and plenty more) as I feel that those with a high maths content give all the same advantages as a maths degree.

**So, do I think you need a strongly maths based degree to teach maths?**

There are many levels to this massive question and they all need addressing. Firstly is the background. I know a maths teacher who scraped a C in his own GCSE maths and via a whole host of BTecs, HNCs, HNDs foundation courses etc ended up with a degree equivalent in Accountancy. This was deemed maths-y enough to qualify him for a place on a maths PGSE and he qualified as a maths teacher. He was a pretty good one too, when it came to teaching lower and middle ability pupils at KS3 and 4. I don’t think he’d have been able to teach higher tier GCSE topics, and I certainly don’t think he’d have been able to teach A Level.

I trained with a lady who had a degree in languages, and who repeatedly told me she didn’t like maths, was no good at maths and only wanted to work with year 7 and 8 pupils who suffered with SEN. She didn’t pass the course. I asked her why she had chosen to teach maths rather than languages, and she said it was due to the size of the bursary. She wasn’t the only person on my course who told me explicitly that they weren’t keen on maths and had only chosen to teach it due to the size of the bursary. (I’ve written before on the topic here).

This shows us a real problem, but it is a problem born out of necessity, out of the fact that far too few maths-y graduates are willing to go into teaching. I suppose it is a circular situation. Maths is seen as an important subject, so we need lots of maths teachers to teach it, but the big money professions such as accountancy, investment, finance etc see maths as important and recruit heavily form the maths-y degree pot, leaving teaching as something seen (sadly) by many as a low paid alternative and hence not worth it. Before I digress into a tirade about how this says some terrible things about our society, and how we need to address these issues pronto, I will move back to the topic at hand.

*So, what should the requirements be?*

**1: You must like maths.**

I would suggest that **no-one **should be teaching Maths GCSE if they **DON’T LIKE** maths. This seems like complete common sense, and surely people reading this will be thinking “Well, duh. Who on earth would become a maths teacher if they don’t like maths?” But I know a few maths teachers who don’t. I don’t think they should be teaching maths. Our job as maths teachers should not be solely to equip people with the numeracy skills to survive (although I agree this is important), but it should also entail inspiring the next generation of mathematicians. Inspiring the next Leonhard Euler, the next Pierre de Fermat, the next GH Hardy, the next Andrew Wiles, the next Colin Beveridge. If people teaching GCSE maths don’t like it, then they won’t inspire the pupils to look at it post 16. For me, this is the **most** important thing.

**2: You must have a good knowledge of maths.**

I would suggest that everyone teaching GCSE maths should have a good working knowledge of maths up to A Level. That should be because they have studied maths up to A Level (in whatever form – be it an A Level, or a conversion course). I think those with Maths-y degrees are in a better position. They have spent much longer in the world of maths and have seen where it leads to. But someone with a non maths-y degree who loves maths, reads around the subject, has a good working knowledge of A Level maths can also be excellent. I think that to teach A Level maths, you should have a degree that has a high maths content, or should at least have studied some maths post A Level, whether it be in a degree or additional courses, or even your own private study. Doubly so for Further Maths!

In an ideal world, I would love to see more maths teachers engaged with maths outside the classroom too. I am a fan of recreational mathematics. I regularly attempt puzzles set by wrong but useful, by puzzlebomb, by Dara O’Briain and Marcus Du Sautoy on school of hard sums and a host of other puzzle sites. I’m currently reading Ian Stewart’s, “From Here to Infinity”, and I regularly read maths books. I’m a regular viewer of Numberphile, listener of Wrong but Useful, Allsquared and a number of other maths podcasts, and I’m always keen to watch maths based TV shows and listen to maths based radio shows. These are the things that keep my maths skills sharp, and I feel they add to my ability to teach maths.

**In short:** Do you need a maths(-y) degree to teach maths? No, but it helps.

**Should we be looking at ways to encourage more maths graduates into the profession?** Yes, I think we should. But that’s another post, for another day.

## Matrices

I love matrices, I loved them at school from the very basic matrices that I learned at high school to the more hardcore matrices that were involved in my A Levels I always enjoyed them. Their associative, but non-communicative properties for multiplication fascinated me. As for the things that happen at university with tensors…..

So recently, I have been really enjoying teaching the chapter on 2×2 matrices to my FM AS class. From basic arithmetic with matrices to using the inverses to solve simultaneous equations. I think its fascinating to look at the transformations matrices geometrically, and as think it is certainly one of the topics that shows the links between the different strands of mathematics really well. My class have enjoyed the topic, and have been equally as fascinated as I have by the algebra and geometry involved.

I have uploaded the resources I used to TES here If you do use them , please let me know how they went.

The lessons on the notebook/exported PowerPoint presentation follow the chapter from the Edexcel textbook. I think the order is quite good, although I taught the bit on simultaneous equations prior to reversing transformations.

## Newton, Raphson and Numerical Methods

I have recently taught Numerical Methods to my FP1 class. The topic itself is not one of my favourites, but I think there are definitely places that fun can be had when teaching it.

I have uploaded the notebook presentation and exported PowerPoint here.

Interval bisection is fairly dry, and there are always many questions on “Why do we have to do this, can’t a computer do it?” my usual answer here is that computers can do it, but someone needs to tell them how, so if they re going to be able to program computers to do this they need to understand it.

Linear interpolation is more fun, and it is fairly easy with a bright class and effective prompting to get them to work out how to do it themselves, which they always find satisfying.

The part of the topic I like the best is Newton-Raphson method. It is the bit which requires the most maths, rather than just an ability to substitute. I also find that it is the bit that generates most discussion. I pose questions such as “Why is it sometimes divergent?”, which encourages deeper thinking.

I also like to discuss Newton and Raphson, my students are well aware of Newton by the time the topic comes round. They have always, of course, heard the apple anecdote (be it true or not) and know about gravity. If I have taught them any calculus topics previously then they know about his great work in that field, his battle with Leibnitz and his fractious relationship with Hooke. But they don’t know a thing about Joseph Raphson.

Why would they? When I first taught the topic I spend ages trawling the internet to see if I could find a picture to include, but there was nothing. About all that is known of the poor fellow is the date he was admitted to the royal society, his signature, that he attended Jesus College and coined the word pantheism. What makes it worse is that the so-called “Newton-Raphson” method isn’t a method they came up with at all, but rather it’s entirely Raphson’s work! The reason for the name is that 50 years or so after Raphson published his method, Newton published his own more complex hence inferior version of the method. So his most notable achievement is a victim of Stigler’s Law.

## Euler, Konigsberg and WW2

Recently I taught a D1 lesson introducing the terminology involved in graph theory. Looking at trees, networks and all the other associated things. Graph theory is something I love. I never studied the decision modules at A level, so when I arrived at Manchester University in the autumn of 2001 and saw the module title: “Trees and Networks – with Professor Nigel Ray” I was intrigued by the name, but entirely unsure as to what it would contain. I loved every minute of that course, and have loved graph theory ever since. I’m certain that Nige’s inspirational lecture style deserves some of the credit, but I’m also fairly sure that graph theory itself deserves some credit too.

As you may or may not know, graph theory (sometimes called topology) is an area of maths which was built by Leonhard Euler (Oi! Read that name again, its pronounced “Oi-ler” not “you-ler”… don’t ever let me catch you making that mistake again….). Euler was prompted to discover this area of maths by the “Seven bridges of Konigsberg” Problem. In brief: The city of Konigsberg in Prussia (Now called Kaliningrad and in Russia) was dissected by the Pregel so that there are 4 distinct parts of the city. There were seven bridges, as shown below, and the problem was posed: was it possible to take a walk round the city traversing all the bridges once and only one?

Euler solved the problem. Of course he did, he was a total maths legend. Although by solved, I don’t mean he worked out a way to do it (or that he built an extra bridge), but rather he managed to prove that it could not be done. Something many had thought, but had been unable to prove beyond doubt. It was his method of analysis and proof that led to Graph Theory. All this, and my general love of all things Eulerian, meant that I digressed in my D1 lesson away from terminology and spend a lot of time discussing Eulerian graphs, semi-Eulerian graphs, Konigsberg and Euler himself. Not exactly what I was supposed to cover, but time well spent none the less.

The following day, I read this amazingly funny piece by Colin Beveridge (@icecolbeveridge) on Flying Colours Maths, and the two related articles that it linked to (this and this). I was excited, I could see the bridges on street view (although only two remain from Euler’s Time) so finally got to see (some of) the bridges that this area of maths was devised for! I was surprised to discover that since WW2 there are only 5 bridges, leaving the network traversable! (It is now semi-eulerian, you must start on one island and end on the other. So if you were to do it properly you would need to get to your start and from the finish point on a boat or other none bridge means). And I was happy to hear that google themselves use graph theory to find the best routes for their streetview cars! (Incidentally, I’m on streetview, sat in a bus shelter in LS1 –or at least I used to be…)

These two events (teaching D1 and Colin’s post) have reawakened my love for graph theory, and I’m looking to widen my knowledge of this wonderful area. If you’ve read anything good on it do let me know! First stop: Nige’s Lecture Notes!

## Logic and conjecture

A couple of months ago I was at my Gran’s house and I came across her copy of “Puzzler”. This instantly took me back to my childhood. Back then her and my Granddad lived on the Isle of Arran in Scotland and my mum, my brother and I would spend the majority of the summer holidays there. My dad would be there for some of it, but he wasn’t a teacher like mum, and as such couldn’t take the whole summer off. Granny was always a keen puzzler so there were always many of these compendiums around. She liked Crosswords and Wordsearches, but I much preferred these logic puzzles:

I also enjoyed the many number puzzles such as ken kens and sudukos. I think it was these puzzles at a very young age that might have been the first indicators of my love for maths.

When I came across this compendium a few weeks ago I immediately looked for and completed a logic puzzle. While I was doing so I realised that the reasoning being used was quite mathematical and that the able i was filling in was basically a two-way table. I decided that this would be a nice starter activity and so I made a purchase.

I’d not used these as starters yet, and then this week Emily Hughes (@ilovemathsgames) tweeted this link to her puzzle of the week (http://ilovemathsgames.wordpress.com/2012/03/06/puzzle-of-the-week/) Tis weeks included this puzzle: http://www.ilovemathsgames.com/Flashpuzzles/logic%20puzzle.swf

Which reminded me of my compendium! I have used Emily’s this week as a starter for a few classes and they loved it, so I am going to incorporate more of these in future lessons. I’ve used it with a variety of classes from KS3 – KS5 and all enjoyed it, the faculty members i gave it to also seem to enjoy it too!

## Revision Quizzes

Currently my further maths class are revising for tomorrows D1 exam. Due to the fact we changed the order of the modules we teach the year 12s are also revising for the same exam and I have my class last lesson on a friday at the same time my ATL has year 12, so over the ast few weeks we have been joining up for the last 20 minutes or so and facing of in a head to head “pub quiz” type revision event, these quizzes came from the ATL. They worked really well, helped consolidate some of the learning and gave the students chance to see where they needed to put more work in. In this vein I have made a C1 and a C2 quiz ( http://www.tes.co.uk/teaching-resource/Core-1-and-2-revision-Quizzes-6334839/ ). The C1 quiz went really well and I am going to run the C2 quiz for the first time tomorrow.

Given the success of these quizzes I am planning on doing some similar ones for GCSE classes next week!

Edit – 09/12/13 – I have added some new rounds to the C1 quiz and have also uploaded exported ppts for those of you unable to access notebook.

## New Toy!!!!

Last week this arrived!

A new toy that my super duper Area Team Leader got in. She got one for each of the teachers teaching A level and the arrival date was uncanny. She dropped mine in my classroom the evening before I was teaching sketching polar curves! I thought, “what a handy tool for tomorrow”! And it really was. My year 13’s loved playing with it and it was really handy to let them use it to check their sketches if polar curves.

I’ve not had chance to play with it much further, but I intend to investigate it’s full capabilities! I’m fairly sure I had this same model (or at least one very similar) when I completed my A levels, so it will be exciting to rediscover what I knew, and to discover many new things about it!

If you know of cool uses for it, please do let me know!