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.

Koch Snowflake

A short sneak preview of the full-length ‘Mandelbulbs’ video currently in production. A Koch Snowflake is an example of a 2D fractal with infinite perimeter but finite area. Full details of the calculation in the final video… COMING SOON!

BIG STEM Communicators Network

As a new member of the BIG STEM Communicators Network I was very pleased to be featured in the member spotlight for spring 2019. (The original article is ‘members only’ so I’ve copied the text below.)

“As a new member of the BIG community I would like to introduce myself as the ‘Naked Mathematician’ (yes you did read that correctly). I am a Maths Tutor at the University of Oxford with a goal to reduce fear and anxiety towards maths. One of the ways in which I do this is to take my clothes off – what better way to emphasise that the subject is not as serious and intimidating as many people think than by teaching in my underwear! The concept began as a series of videos on my YouTube channel entitled ‘Equations Stripped’ where I strip back some of the most famous equations in maths (and myself) layer-by-layer so that everyone can understand, and has since evolved into a live performance now touring universities across the UK. My efforts to bring maths to a new audience have been recognised by the University of Oxford, where I was awarded first prize in the Outreach and Widening Participation category at the OxTALENT awards, and I have also been shortlisted for the Institute of Physics Early Career Communicator award.

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The ‘Naked Mathematician’ is of course not appropriate for every audience and as such is only a small part of the work that I do to share my love of maths. My ‘Funbers’ series was broadcast throughout 2018 on BBC Radio, where in each episode I look at numbers more closely than anyone really should to bring you the fun facts that you didn’t realise you’ve secretly always wanted to know… I also try to involve my audience in the creative process as much as possible by issuing a call for questions on social media and then hosting a vote to decide the topic of my next video in the ‘I Love Mathematics’ video series. Finally, I combine my love of sport with maths in my popular ‘Maths v Sport’ talk which features a live penalty shootout on stage and an attempt to break a running world record (appropriately scaled of course!).

All of the material that I produce is available for free on my website tomrocksmaths.com and associated social media profiles @tomrocksmaths on Facebook, Twitter, Instagram and YouTube. I am very excited to have joined BIG and look forward to working with the community to help to share STEM subjects with the world!”

Maths and the Media

Arriving at St John’s in 2008 to begin my study of mathematics, I was certain that within 4 years I would be working in the city as an actuary or an investment banker. Whilst I loved my subject, I saw it as means to obtain a good degree that would set me up for a career in finance. I’m not sure I could have been more wrong…

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My current journey began towards the end of my second year, where I found myself enjoying the course so much that I wanted to continue to do so for as long as possible. This led me to research PhD programmes in the UK and the US, and I was fortunate enough to be offered a place to study Applied Maths at the University of Cambridge in 2012. During my time at Oxford, I found myself straying further and further into the territory of applied maths, culminating in a fourth-year course in fluid mechanics – the study of how fluids such as water, air and ice move around. This ultimately led to my PhD topic at Cambridge: where does river water go when it enters the ocean? (If you’re interested to find out more I’ve written a series of articles here explaining my thesis in simple terms.)

As part of my PhD I conducted experiments, worked on equations and even took part in a research cruise to the Southern Ocean. It was on my return from 6 weeks at sea that I had my first taste of the media industry via a 2-month internship with the Naked Scientists. I would spend each day searching out the most interesting breaking science research, before arranging an interview with the author for BBC radio. It was great fun and I learnt so much in so many different fields that I was instantly hooked. Upon completion of my PhD I went to work with the Naked Scientists full time creating a series of maths videos looking at everything from beehives and surfing, to artwork and criminals. You can watch a short trailer for the Naked Maths series below.

My work with the BBC and the media in general ultimately led me to my current position as a Mathematics Tutor at three Oxford colleges: St John’s, St Hugh’s and St Edmund Hall. This may not sound like the media industry, but the flexibility of the position has allowed me to work on several projects, including launching my website and my YouTube channel @tomrocksmaths where I am currently running two ongoing series. In the first, Equations Stripped, I strip back the most important equations in maths layer-by-layer; and for the second series in partnership with the website I Love Mathematics, I answer the questions sent in and voted for by students and maths-enthusiasts across the world.

Alongside my online videos, I am also writing a book discussing the maths of Pokémon – Pokémaths – and have a weekly show with BBC radio called ‘Funbers’ where I tell you the fun facts about numbers that you didn’t realise you’ve secretly always wanted to know. I have also recently presented at conferences in the US and India and hold regular talks at schools and universities, including for the Oxford Invariants and the Maths in Action series at Warwick University where I faced my biggest audience yet of 1200.

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Looking back at my time at St John’s, I never would have imagined a career in the media industry lay before me, but the skills, experience and relationships that I formed there have undoubtedly helped to guide me along this path. I think it just goes to show that Maths is possibly the most universal of all subjects and really can lead to a career in any industry.

You can follow Tom on Twitter, Facebook and Instagram @tomrocksmaths for the latest updates.

SJC Inspire: how to design a successful video game

Very excited to announce the launch of the SJC Inspire digital magazine this week – a project I’ve been working on for the past few months in my role as Access and Outreach Associate for STEM at St John’s College, Oxford.

The first issues is ‘how to design a successful video game’ and features articles by researchers at St John’s, video interviews with students at the college, and practice puzzles set (and solved) by real Oxford tutors (myself included). I’ve highlighted some of my favourites below, but be sure to check out the full contents of the issue on the website here.

Maths in video games

My former tutorial partner, James Hyde, now works for Creative Assembly developing hit titles such as Halo Wars and Halo Wars 2. Here he explains how maths has helped him to land his dream job…

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Fun and games at the circus

Try out this maths puzzle set by St John’s maths tutor Dr David Seifert. If you send your answers in to inspire@sjc.ox.ac.uk you might even win a goodie bag!

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How to earn billions by giving something away for free

St John’s Economics tutor Dr Kate Doornik explains the pricing strategy behind the incredibly successful ‘Fortnite: Battle Royale’. Originally given away for free, it is expected to make over $3 billion in sales in 2018…

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