Retraining 15,000 teachers?

Philip Nye writes in a paper  Cameron needs to rethink maths and science plan (12 Dec 2014) that

Under No 10’s plan, 15,000 teachers of other subjects will also retrain as maths or physics teachers, as part of a “major push” to boost maths, science and technology skills.

However, Professor Alan Smithers, director of the Centre for Education and Employment Research at the University of Buckingham says: “It’s really easy to say ‘well, physics is science, so therefore there’ll be people teaching biology, or who have done medicine or engineering [degrees] that we can retrain as physics teachers’. But biology is really as different from physics as, say, history is.”

Perhaps the same skepticism can be applied to mathematics.

Hamid Naderi Yeganeh: Mathematical drawings made from segments

A cardioid

This figure is closely related to a cardioid.

This image shows 1,000 line segments. For each \(i=1,2,3,\cdots,1000\) the endpoints of the \(i\)-th line segment are:

\[\left(\cos\left(\frac{2\pi i}{1000}\right), \sin\left(\frac{2\pi i}{1000}\right)\right)\]

\[\left(\cos\left(\frac{4\pi i}{1000}\right), \sin\left(\frac{4\pi i}{1000}\right)\right).\]

Ofsted: Low-level classroom disruption hits learning

From BBC :

Low-level, persistent disruptive behaviour in England’s schools is affecting pupils’ learning and damaging their life chances, inspectors warn.

The report says too many school leaders, especially in secondary schools, underestimate the prevalence and negative impact of low-level disruptive behaviour and some fail to identify or tackle it at an early stage.


Source: Poll conducted by YouGov for Ofsted,

This is one of many low-level school issues that affect undergraduate mathematics teaching.  In a mathematics lecture, weaker students are more prone to “loosing the thread” than in most other courses. Also, students for whom English is not the first language,  in particular,  most from overseas are more sensitive to the signal-to-noise ratio than natives,  and, at a certain level of background noise,  their understanding of the lecture becomes seriously degraded. In my opinion,  this is one of many neglected issues of undergraduate mathematics education. I in my lectures always insist on complete silence in the audience (and usually start my first lecture with  a brief explanation of the concept of signal-to-noise ratio).

Matilde Lalin: Attending conferences with small children

[Republished from Terry Tao’s Blog — because of the importance of the issue.– AB]

[This guest post is authored by Matilde Lalin, an Associate Professor in the Département de mathématiques et de statistique at the Université de Montréal.  I have lightly edited the text, mostly by adding some HTML formatting. -T.]

Mathematicians (and likely other academics!) with small children face some unique challenges when traveling to conferences and workshops. The goal of this post is to reflect on these, and to start a constructive discussion what institutions and event organizers could do to improve the experiences of such participants.

The first necessary step is to recognize that different families have different needs. While it is hard to completely address everybody’s needs, there are some general measures that have a good chance to help most of the people traveling with young children. In this post, I will mostly focus on nursing mothers with infants (\leq 24 months old) because that is my personal experience. Many of the suggestions will apply to other cases such as non-nursing babies, children of single parents, children of couples of mathematicians who are interested in attending the same conference, etc..

The mother of a nursing infant that wishes to attend a conference has three options:

Continue reading

How to Play like a Mathematician

[Originally posted on Edmund Harriss’ blog Maxwell’s Demon, this is a transcript of a talk at the Twitter Math Camp 2014, a truly energising event, teacher organised peer professional development. Anyone interested in education, whether parent, academic, teacher or administrator should check it out.]


Start by clearing your mind.


Now imagine one dot pop into view.


A second dot joins it. Let the two dots flow around each other, rotating and getting closer and further apart.


Now a third dot, creating a line or a triangle…


Keep on adding, with each addition try to see all the dots, find a shape you like…














This is about having fun and playing with math, which often sounds a little:

TMC14_Talk_Images.002This is not the holy grail, it is not even a challenge to bring into the classroom. Teachers have too many challenges, sometimes the challenge is just to get through the day without messing up too badly. It is an encouragement to relax and have fun, yet remember that this fun is part of your teaching prep!

TMC14_Talk_Images.007Playing with maths can often start with going back, returning to something you know well, and trying something new, testing an idea. If it fails try something a little different, or go back to work out how it went wrong. If it works, can you try everything? Mathematicians can say everything and really mean it! Even then do not settle, go back with your new knowledge and try something new. You might notice once you have started you cannot escape! You can always just stop. This is play not work. Though it might not be relaxing, just as playing a sport is exciting, fun and cathartic but you put effort in.

This is why this can build into your teaching, once you have fun you have a chance to help your students have fun. If they have fun they will put far more effort in than if you have to push them. Also I do not feel that mathematics has a huge number of facts, but isolated they are not that useful, going back and playing with ideas helps build the dense web of connections that really drives understanding.

General strategies are great, but it can be hard to know where to start, I will describe two tools:

  • Analogy and the concept of same/different (mathematics is the world’s greatest metaphor!)
  • Breaking rules! (yes mathematics is often about creating them, but also about changing them and seeing what happens).

To get further, we need an example, and not one that will lose half the audience just with its title so…


TMC14_Talk_Images.009Three dots, are they the same or different? They are in different positions, but are the same shape. We have to be clear what we mean.

TMC14_Talk_Images.010Now we take pairs of dots, we can spin them around and pull them apart. We could say they were the same if they can be moved on top of each other. Yet to define that precisely we have to use most of plane geometry. We have not even counted past two and we already need that!

TMC14_Talk_Images.011Getting to three the line and the triangle, different in ways that the pair of dots can never be.

Lets change tack, we have been looking at how the same number of dots can be different, what about how different numbers of dots can be the same?TMC14_Talk_Images.012

These patterns for four, six and eight have some similar features. How might we describe those precisely so we can identify other ones? Saying that the numbers are all even is an obvious way to do it, but maybe they also share something with this:TMC14_Talk_Images.013

Like the earlier examples nine dots drawn like this form a rectangle (specifically a square). Following this definition we can define prime numbers (technically composite numbers!).

TMC14_Talk_Images.014Here are another collection of dot patterns that share features, one dimension, two dimension and three dimension, and at this point reality gives up on us. Yet we really went past our page after two, we can use the notions of analogy to push further. We know the next pattern will have sixteen dots. For example we can make this image, with lines to show the structure. Can you find the eight cubes?

TMC14_Talk_Images.016With a little work from here we can work out that an nn-dimensional cube has 2n (n-1)-dimensional faces. So we know very little about 172 dimensional space, but we do know that a hypercube in that space has 344 faces! Playing with some of these tricks we can get this:

TMC14_Talk_Images.017There is a lot more to discover in this image. If you are interested in getting a version send me an email, I am looking into options.

Lets move to the other trick, breaking the rules. Mathematics is made of rules, yet there is not one rule that is not broken somewhere else in mathematics. For example this might make you uncomfortable:

7 + 7 = 2

2 + 1 = 2

If I say instead that seven months after July (the seventh month) is February then the first makes perfect sense. In this case 7+7 is still 14 but 14 is the same as 2, we have modular arithmetic.

That trick will not work for 2 + 1 = 2. Yet in Chemistry two hydrogen molecules combine with an oxygen molecule to create two water molecules. There is an even greater rule, though one that has been enshrined in legend. Yet this image shows what happens when we divide by zero (at the centre)!

TMC14_Talk_Images.021(the mathematical trick is to use what is called the Riemann sphere).

In conclusion playing with math can happen with the simplest structures and lead to a variety of thoughts and adventures. No one should be shy of having a go!

Here is a neat animation from my play:


I have a list of some other materials to inspire your mathematical play, and there is a whole world of examples in Sue van Hattan’s book Playing with mathematics. That should be available for pre-order soon!

Many other have explored the idea of simple pictorial versions of numbers, often using prime factorisation. With dots and circles, with monsters, or even to make a game. Although my personal favorite are these dots, with their illusion of simplicity.


A. E. Kyprianou: The UK financial mathematics M.Sc.

A. E. Kyprianou: The UK financial mathematics M.Sc. arXiv:1405.6739v2 [math.HO]


Postgraduate taught degrees in financial mathematics have been booming in popularity in the UK for the last 20 years. The fees for these courses are considerably higher than other comparable masters-level courses. Why? Vendors stipulate that they offer high-demand, high-level vocational training for future employees of the financial services industry, delivered by academics with an internationally recognised research reputation at world-class universities.

We argue here that, as the UK higher education system moves towards a more commercial environment, the widespread availability of the M.Sc. in financial mathematics exemplifies a practice of following market demand for the sake of income, without due consideration for the broader consequences. Indeed, we claim that, as excellent as such courses can be in intellectual content and delivery, they are mismatching needs and expectations for such education and confusing the true value of what is taught.

The story of the Mathematical Finance MSc serves as a serious case study, highlighting some of the incongruities and future dangers of free-market education.