LMS Newsletter: Talking Maths in Public

After attending my first Talking Maths in Public conference last August, I was asked by the London Mathematical Society to write a few words about the experience…

“Talking Maths in Public was hands-down the BEST conference I have ever attended. The incredible skill, passion and experience of the attendees was second only to the welcoming and friendly atmosphere across the 3 days. From planning a ‘Maths Cabaret’ show, to the ‘Treasure Punt’ along the River Cam, I enjoyed every minute and cannot wait for the next edition in 2021!

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James Grime from Numberphile/Singing Banana

For almost every session that I attended, I found something that I could take away to help to improve my ability to talk maths in public. However, the keynote given by magician Neil Kelso was particularly inspiring. The way in which he was able to control his audience through every little detail of his performance on stage was mesmerising to watch and hearing him break down these movements to explain exactly what role each one played within his show was fascinating. I will certainly be trying to use as many of his tips as possible in my next show!

If you’re thinking about whether maths communication might be for you, my advice is simple: just give it a go! As mathematicians, we are trained to focus on the details and to construct well-thought out and logical proofs, but unfortunately this approach can often be a barrier to trying something new and untested that perhaps feels outside of our comfort zone, like maths communication. My first YouTube video is awkward, its poorly shot and you can tell that I’m not very comfortable in front of a camera. But, fast forward 2 years and being on camera now feels natural, I know how to setup a shot correctly and editing is second nature. This wouldn’t have happened had I not jumped in head-first and just given it a go. No-one expects you to be perfect (or in fact even functional) on your first try, the most important thing to remember is that you learn from experience, so take that first step and hopefully in a few year’s time you can look back with fondness at that first video/performance/article and see just how far you’ve come.”

You can read the full newsletter here.

Teaching Mathematics

Following my talk in Madrid in November, I was asked to answer a few questions about the current status of maths teaching based on my experience as a university lecturer. Here are my answers…

How should mathematics be taught in schools?

Through stories. Teaching through story-telling is an incredibly powerful tool and one that is not used enough in mathematics. For example, when teaching trigonometry, rather than just stating the formulae, why not explain WHY they were needed in the first place – by ancient architects trying to construct monuments, by explorers trying to estimate the height of a distant mountain – these are the reasons that mathematics was developed, and I think that teaching it through these stories will help to engage more students with the subject.

Are teachers prepared to teach this subject correctly?

I don’t believe the teachers are at fault – they are told to follow a particular curriculum and due to their heavy workload have no time to develop lessons with engagement at the heart of their design. There are of course ways that we can help teachers, by providing examples of ways to make maths content more interesting and engaging. This can be through story-telling or applications to topics of interest to students such as sport and video games. This is what I try to do with ‘Tom Rocks Maths’, for example see my video teaching Archimedes Principle by answering the question ‘how many ping-pong balls would it take to raise the Titanic from the ocean floor?’.

In your view, how should a math teacher be?

The most important thing is to have passion for the subject. The level of excitement and interest that the teacher demonstrates when presenting a subject will pass on to the students. Just as enthusiasm is infectious, so too is a lack of it. Beyond passion, there is no typical profile of a maths teacher. Anyone can be a mathematician, and it is very important that people don’t feel that they have to conform to a particular stereotype to teach the subject. I have always just been myself, and hopefully as a public figure in mathematics will inspire others to do the same.

Sometimes, this subject becomes more complicated for some students, not so much because of its difficulty, but because of the way in which they have been taught. What should be done with these students?

The trick is to find a way to explain a topic that resonates with a particular group of students. Let me give you an example from my research: the Navier-Stokes Equations (NSEs). For students who have no real interest in mathematics, I would try to get them to engage by explain the $1-million prize that can be won by solving these equations. For students who have more interest in real-world applications such as in Engineering or Biology, I would tell them about how the aerodynamics of a vehicle or the delivery of a drug in the bloodstream rely on an understanding of Fluid Mechanics and the NSEs. If the students are fans of sport, I can explain how the equations are used to explain the movement of a tennis ball through the air, or for testing the perfect formation in road cycling. Finally, for students who are already keen mathematicians, I would explain how the equations work in almost every situation, except for a few extreme cases where they result in ‘singularities’, which as a mathematician are the ones you are most interested in understanding. Once you know the interests of your audience, you can present a topic in a way that will help them to engage with the material.

Can you get to hate math?

It is certainly possible – though of course alien to mathematician such as myself! I think this feeling of ‘hate’ relates back to either the way that you have been taught the subject, or from a lack of understanding. If you did not enjoy your maths lessons at school and harbour ill feelings towards your teacher, then you will begin to develop negative feelings towards the subject. This is not because you dislike the subject, but more because of the way that it was taught to you. Likewise, if you do not understand mathematics then it is very easy to develop a ‘fear’ of the subject, which can quickly turn into hatred due to feelings of inadequacy or stupidity if not addressed. It all comes back to finding a way to approach the subject that fits with the knowledge and experiences that you already have. If you present a problem in an abstract manner of manipulating random numbers to find a given total, then most people will struggle – regardless of their mathematical ability. But the same problem presented in a relatable situation suddenly becomes understandable. Here’s an example:

(a). Using the following numbers make a total of 314: 1, 1, 2, 5, 10, 10, 20, 20, 50, 100, 100, 500.

(b). You go shopping and the total is €3.14. What coins would you use to pay for your items?

They are the same question, but in (a). the problem looks like a maths question, and in (b). it is an everyday situation that people all over the world are used to. Both require the same maths to solve, but even people who ‘hate’ maths could tell you the correct answer to (b). using their own real-life experience.

Women are at a great disadvantage compared to men when entering a STEM career, why do you think this is happening?

First of all, as a man I am certainly not qualified to answer this question, but I will at least try to provide you with my opinion based on personal experience. At high school level I believe that the difference is less severe (eg. see article here) and even at university there is a slightly higher number of females than males studying science-based subjects. BUT, the issue occurs after this. In graduate degree programmes and beyond there is a definite lack of female researchers, and this is amplified even further at more senior level positions. One explanation could be that academic ‘tenure-track’ positions exist for life, and so many of the men that now hold these positions have done so for the past 30-40 years and were employed when we were doing a much worse job of tackling the gender gap. Now that awareness of these issues has increased, and in general we are doing a much better job at addressing them that we were 30 years ago, hopefully we will begin to see more females in leading positions over the coming years, it will just take a little while for the effect to be seen. I also think that in general there are not enough female role models within many subjects (especially maths) that have reached the pinnacle of their field (through no fault of their own), and as such there is a lack of role models for young female researchers. The achievements of female mathematicians such as Maryam Mirzakhani (2014 Fields Medal) and Karen Uhlenbeck (2019 Abel Prize) should be even more celebrated precisely for this reason.

Do you think that enough importance is given to mathematics in the educational world?

In the past perhaps not, but attitudes are certainly changing. With the increased role that technology and algorithms play in our lives, people are beginning to realise that we need to better understand these processes to be able to make informed decisions – and maths is the key to doing this. Employers are certainly aware of the invaluable skillset possessed by a mathematician and as a result more and more students are choosing to study the subject at degree level and beyond to improve their competitiveness in the job market. Ultimately, attitudes are changing for the better, but there is still more that can be done.

In your opinion, what is the best way to teach this subject?

Exactly as I have described in questions 1 and 4. Storytelling is key to making the material as engaging as possible and knowing the interests of your audience allows you to present the subject in a way that will appeal to them most effectively.

What is the current situation of mathematics research in the university?

I think the main issue facing research mathematics is the relatively recent trend of short-term research outcomes. The majority of funding available to mathematicians requires either continuous publication of new results or outcomes that can readily be used in an applied setting.  The issue of continuous publication means that researchers feel the need to publish a new manuscript every few months, which leads to very small advances at each step, and a wealth of time spent writing and formatting an article instead of conducting actual research. In many cases, the work would be much clearer if published as one piece in its entirety after several years of careful work. The drive for short-term research outcomes means that it is now very difficult to study mathematics just for the sake of it – you have to be able to convince your funding body that your work has real-world applications that will be of benefit to society within the next 5-10 years. To show why this is a disaster for maths research, let’s take the example of Einstein and his work on relativity. Now seen as a one of the most fundamental theories of physics, his work had no practical applications until the invention of GPS 60 years later. In today’s short-term outcomes driven market, it is highly unlikely that Einstein’s work would have been funded.

Photo: Residencia de Estudiantes

Numberphile: Pi Million Subscribers

It’s incredible to see a channel dedicated entirely to maths reach this quite frankly ridiculous number of subscribers – congratulations Numberphile!! If you haven’t seen it yet check out the many famous faces, including yours truly at 1:27…

El Pais: The Oxford teacher who stays in briefs to teach mathematics

Tom Crawford talks about how mathematics can help win a football league or the real ability of algorithms to manipulate people’s behaviour.

Tom Crawford (Warrington, United Kingdom, 1989) is presented as an atypical math teacher. He teaches mathematics to first and second year students at the University of Oxford (United Kingdom) and carries out an intense dissemination work in which he tries to approach a discipline that is not usually found among the favourites of young students.

In his attempt to popularise science, he does not hesitate to stay in his underpants , using the striptease as a metaphor for his work deepening the meaning of equations such as Navier-Stokes, unveiling them layer by layer, to make something affordable that can result in principle esoteric.

This week, Crawford visited the Student Residence, in Madrid, where, within the Mathematics in Residence cycle organised by the ICMAT, he offered the conference  Mathematics of sport . In it, he uses sport as an example of a daily activity that can be better understood and practiced using mathematical equations.

Question. You undress or use sports to make mathematics impose less. Why is it necessary to show that mathematics is fun? I don’t see lawyers or judges, who also deal with very complex issues, trying to present the law as something fun.

Answer. I think it’s because people, for whatever reason, happily admit that they don’t like math, it’s socially acceptable. If you tell someone that you are a lawyer, their default answer is not going to be “I don’t like the law,” and that does happen with math. And it shouldn’t be like that. Everyone should have a basic understanding of math, but many people don’t have it. For me, that is why I want to emphasize that mathematics is fun and accessible. It doesn’t have to be something very hard or something that was taught badly in school.

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Q. Do you think mathematics is taught especially badly in school, worse than other subjects?

A. Mathematics has a hard time competing with other subjects in the sense of teaching them through stories. When you learn something, if they can teach you through stories, it is something very powerful, which serves to catch people. And that is easier with literature or history.

A very simple example of how to add stories to mathematics would be trigonometry. The properties of the triangles you learn in high school. If you think about how these functions were discovered or invented, why we invented the sine, the cosine and the tangent, it was the ancient architects who tried to build buildings, churches, pyramids and created those intellectual tools. This is how trigonometry should be taught to me. Imagine they are in ancient Rome and you have to build a concrete building. How would you do it with the technologies available at that time? This prompts you to think about angles and distances and that is where trigonometry is useful and what it was invented for.

Q. A little more than a century ago, in a country like Spain, more than half of the population was illiterate. Do you think it would be possible and desirable to get a large majority of people to be able to handle basic mathematical tools?

A. It is completely possible and I would say that we are already doing it. It depends on what you consider a basic level of mathematics. Most people can, for example, looking at a clock know that the needles return to the same place every 12 hours, it is modular arithmetic, something you don’t study until you get to college. Even being able to calculate changes when they give you a ticket is to do mental arithmetic. Or calculate when you have to leave home if it takes 35 minutes to the station and the train leaves at 12.45. There are many things you do without thinking, but that involve mathematical calculations. So it depends on what you consider a desirable level of mathematics, but a large part of the population already has some capacity to use them.

“You can question whether trying to influence voters is good or bad”

Q. He also talks about the possibilities of mathematics to improve the performance of athletes. There is a movie like Money Ball , which talks about the experience of a baseball coach who uses mathematical analysis to lead a small team to compete against the big ones in the league with much less budget. Do you use math a lot in elite sport?

A. As far as I know, it is an important part of the scout systems of large teams. Today, these scouts, in addition to the classic analysis of a player’s performance, strengths and weaknesses, include teams of mathematicians and data scientists. As in Moneyball , your job is to analyse large amounts of data and detect marginal gains to take advantage of. That works well in baseball, because you have many controllable factors: The pitching of the pitcher, the batter, the race to the base. It is very formulable and they are repetitive behaviours. In football it is more difficult to find those marginal gains because it is less controllable.

The best example I can think of in football is Leicester City, which won the Premiere League in 2016. A big surprise. They had climbed to the first few years before and suddenly they win. In that victory, N’Golo Kanté was very important. He was the star of the season and won the player of the year award. He had been signed by a French second division team because the scout network had identified him among all the defensive midfielders in Europe at any level. As a defensive camper centre, one of your jobs is to stop the attacks of opponents. You can measure this in tickets, but one of the best ways to do this is through interceptions, which has to do with the player’s ability to read a game. It is something very difficult to assess with a number, quite subjective. But interceptions suggest that you are very often in the right place. And from that point of view, their number of interceptions was much higher statistically than the rest of midfielders. If the average of all midfielders in Europe is two, but most of the players are between 1.9 and 2.1 and Kanté is at 3, we see that it is an atypical case. It was not just a statistical analysis, because the human element is valued, but it was a factor to hire him.

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The mathematician Tom Crawford at the Student Residence, in Madrid. ÁLVARO GARCÍA

Q. Can mathematics tell us what is the limit of human performance in sport? There have already been examples in the past, such as Roger Bannister’s, which went down four minutes on the mile when almost everyone said it was impossible, in which the predictions were completely wrong. Can these limits be accurately identified using mathematics?

R.If you look at the men’s marathon record during the last century, the marks descend, but not at a constant pace. You can estimate, for example, that every 10 years, 10 minutes are trimmed at the beginning, but then, in the 1940s and 1950s, the curve begins to flatten out and already in the 1990s it seems completely flat. So if we had sat here 30 years ago, when the record was around two hours and five minutes, we could have thought we would never run below two hours, because even if it keeps going down, the pace is getting slower. But in recent years, there has been much progress in long-distance races, such as new shoes that can provide 4% more energy. In addition, there is a professionalisation that allows you to train all day and not have a job besides running.

“I could predict with some confidence that the human limit for the marathon would be about an hour and 55 minutes”

So these are new factors that modify our calculations. In the future, in 30 years, new improvements may appear, but it is certain that we will not run a marathon in less than an hour. Given what has happened in the past, I think I could predict with some confidence that the human limit for the marathon would be about an hour and 55 minutes.

Q. Some people, when talking about the possibilities of mathematics to bring humans to the limit of perfection, may think that sports will become more boring, because there will be less and less space for the unexpected.

A. I think that also has to do with the human psychological trait that is nostalgia. But sport evolves and there is always a human factor. If the study allows you to perfect the place where it is better to throw a penalty, the goalkeepers can also work with that information. And then, there are some players who do not shoot at that supposedly perfect space, such as Eden Hazard, of Real Madrid, who when he threw the penalties for Chelsea waited until the last moment to decide where he threw it, a method that goes against what he says The mathematical model. In the end there are many variables in sports.

Q. Can mathematics help us better understand human groups? Does that technology have the potential to improve living together or to make it worse?

A. With all the data available, there are huge technology companies that can make profiles of people. Knowing that you are white, American, that you earn so much money and live in such a state, they can try to predict what you like or what you do and influence your vote in one direction. But this technology could also be used for good and you can also question whether trying to influence voters is good or bad. I think that ultimately we depend on the big companies that have control over these data so that they assume their moral responsibility and use the data well.

In any case, I think that most of the mathematicians working in this field would say that the idea of ​​using mathematical data, algorithms and models to try to predict people’s behaviour is incredibly new and we don’t know exactly what we are doing. Algorithms may be a part of the decision making process, but not the only criteria for making a decision.

You can read the original article on El Pais here.

Struggling to engage your students with maths? Think outside the box…

New guidance, released by Pearson, says: If we want to tackle maths anxiety in Britain, we have to change the negative perceptions and experiences that so many learners have when it comes to maths. In this blog, Dr Tom Crawford, maths tutor at the University of Oxford, shares his take on the out-of-the-box approaches to help engage young people with the subject, spark curiosity and inspire life-long interest in maths.

Maths is boring, serious and irrelevant to everyday life – at least according to the results of my survey amongst friends, students and colleagues working in education. This isn’t necessarily something new, but it does highlight one of the current issues facing maths education: how do we improve its image amongst society in general?

With ‘Tom Rocks Maths’ my approach is simple: improve the image of maths by combatting each of the three issues identified above, and do it as creatively as possible…

Tackling “Maths is boring”

The misconception that maths is a boring subject often develops from maths lessons at school.  Due to the extensive curriculum, teachers do not have the time to explore topics in detail, and in many cases, resort to providing a list of equations or formulae that need to be memorised for an exam.

My attempted solution is to do the hard work for them by creating curiosity-driven videos that explain mathematical concepts in exciting and original ways. Take the example of Archimedes Principle – a concept that explains why some objects are able to float whilst others sink – a key part of the secondary school curriculum. It’s perhaps not the most engaging topic for teenagers with no interest in weight regulations for maritime vehicles. But, if instead the topic were presented as part of a video answering the question ‘how many ping-pong balls would it take to raise the Titanic from the ocean floor?’ then maybe we can grab their attention.

Generating curiosity-driven questions such as these is not always easy, but the core concept is to present the topic as part of the answer to an interesting question that your audience simply has to know the answer to.

When teaching my second-year undergraduate students about Stokes’ Law for the terminal velocity of an object falling through a fluid, we discuss the question ‘how long would it take for Usain Bolt to sink to the bottom of the ocean?’ – something I think almost everyone wants to know the answer to! (Don’t worry you can watch the video to find out).

Tackling “Maths is irrelevant to everyday life”

Of all of the issues facing maths in society at the moment, this is perhaps the one that annoys me the most. The majority of people that I speak to who don’t like maths will tell me that it’s the ‘language of the universe’ and can be used to describe pretty much anything, but yet they almost always go on to say how they stopped trying to engage with it because it simply doesn’t apply to them. This is what we mathematicians call a contradiction.

To try to tackle this issue, I go out of my way to present as large a range of topics as possible from a mathematical viewpoint. This has seen me discuss the maths of dinosaurs, the maths of Pokémon and the maths of sport to name but a few. Throughout 2018, my weekly ‘Funbers’ series with BBC radio examined the ‘fun facts about numbers that you didn’t realise you’ve secretly always wanted to know’, where each week a new number would be discussed alongside an assortment of relevant facts from history, religion and popular culture. When working with the BBC, I was very insistent that the programmes were introduced as a ‘maths series’ to help listeners to make the connection between maths and everyday life.

Tackling “Maths is too serious”

At first this surprised me. I’d never personally thought of my subject as ‘serious’ and speaking to my friends and colleagues, they seemed equally perplexed. But then it hit me. Looking at maths and mathematicians from the outside, where you cannot understand the intricate details and beautiful patterns, calling the subject ‘serious’ is a very valid response. There are endless rules and regulations that must be followed for the work to make sense, and most people working in the field can come across as antisocial or introverted to an outsider, which is where I come in.

To try to show that maths isn’t as serious as many people believe, and just to have some plain old fun, I created my persona as the ‘Naked Mathematician’. This began with the ‘Equations Stripped’ video series on YouTube, where I strip-back some of the most important equations in maths layer by layer, whilst also removing an item of my clothing at each step until I remain in just my underwear. As well as providing an element of humour to the videos (as no mention is made of the increasing lack of clothing), the idea is that by doing maths in my underwear it shows that it does not have to be taken as seriously as many people believe.

I have also seen an added benefit of this approach in attracting a new audience that otherwise may not have had any interest in learning maths – from my perspective I really don’t care why people are engaging with the subject, so long as they have a good experience which they will now associate with mathematics.

Whilst I am aware that my approach to tackling the issues faced by mathematics in society may not be to everyone’s tastes, our current methods of trying to engage people with maths are not working, so isn’t it about time we tried thinking outside of the box?

The original article published by Pearson is available here.

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