On 15 November 2013 the Physics Department at the University of Oxford welcomed Dr Julia Collins as the speaker for the Physics Colloquia (a series of weekly seminars of general interest to the whole department). Julia is the mathematics engagement officer at the School of Mathematics, University of Edinburgh (http://www.maths.ed.ac.uk/~jcollins/index.html), and her brilliant talk was about the birth of knot theory, with a special focus on the men who (somehow involuntarily!) pioneered this area of research (particularly Peter Tait – http://en.wikipedia.org/wiki/Peter_Guthrie_Tait). After the seminar I had the opportunity to interview Julia and talk with her about her job, studying and teaching mathematics and successfully communicating science.

Numbers in parentheses refer to notes found at the end of this article.

*Why and how did you decide to study mathematics after high school? *

When I was preparing my A-levels, or maybe even my GCSEs, I wanted to be an archaeologist or an astronomer – or maybe a combination of the two! There is a discipline called archeoastronomy, which is the study of ancient societies and the way one can date temples, for example, by looking at when these monuments would have been aligned with specific stars at the time of construction… I thought this was an amazing subject, so I contacted the one person in the UK who was a professor of archeoastronomy to ask “What should I study? Shall I choose astronomy or archaeology?” His advice was “Do maths.” So I went to Bath, and then the maths turned out to be just too exciting – I never stopped wanting to study it.

*What about your current position – mathematics engagement officer at the University of Edinburgh? *

To be honest, I made the job title up myself! During my PhD I undertook lots of science communication training – Edinburgh is very good for this – and then started going out to schools to give talks whenever the department received a request. When the funding for my PhD ran out the department offered me a six-month contract to pay me until the end of my degree, as well as to support my science communication activities. When I finished writing my thesis, they asked me if I would be interested in another one-year contract as they liked my work – I accepted, and now the one-year contract has been renewed as a three-year one.

*The School of Mathematics seems to have proved quite supportive, in the way they decided to let you continue what you had started as a science communicator while you were a PhD student. *

Yes, our Head of School is very enthusiastic about public engagement. I would also like to stress that what I do is very different from recruitment in that I do not promote the university, I focus on the subject – mathematics. Interestingly, this choice – delegating one person from each department to present that area of research outside of an academic environment – is becoming more and more common.

*Indeed. When I moved to the UK I noticed the presence of a fairly active debate about STEM subjects – how to enthuse young people about science and how to fill in the so-called “gender gap”, if one agrees that there is one. I would like to know your opinion on this – when it comes to STEM subjects, is there an issue to start with, and what is your view on the representation of women? *

I believe there still exists a stereotype of scientists being male, old and bearded, and in this sense it is necessary to challenge it and show that this picture is not true (1). At the same time, as an undergraduate in maths the male-to-female ratio was 50-50, hence I don’t think that the problem is necessarily how to attract young people, particularly women to science. I believe it is more a question of keeping them as they go through the system.

*There is also much talking about role models, especially for prospective (as well as current) undergraduate and postgraduate female students. *

Yes, but I personally never felt the need for a female role model, or any role model. It was mathematics itself which inspired me and not a particular person. It never occurred to me that, as a woman, I wouldn’t be able to, or wouldn’t be good at, studying maths. For this reason I think that we need parents, teachers and lecturers to keep inspiring that self-belief in their children, pupils and students. Generally speaking, I don’t like positive discrimination either – to be asked to do science outreach because I represent “the other side” would not sound right to me. And when I prepare for a science communication event, my focus is completely on the subject. If, while they listen to me, pupils notice that I am a woman doing maths this is fine by me, but I would say that it is incidental… From experience, what seems to inspire most people, of any age, is hearing about the applications of a topic – why is it useful?

*I see, so your point is that the audience cares more about the applicability of a given result you presented rather than noting your gender – this is an interesting observation, and it leads me naturally to my next question! Here is a definition of mathematical literacy taken from the *PISA 2012 Assessment and Analytical Framework *document* (2): ‘Mathematical literacy is an individual’s capacity to formulate, employ, and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to recognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective citizens.’ *Do you agree with such definition? It seems to me that it emphasises greatly the “applications to real life” of mathematics, both as an intrinsic value and as a reminder of how science is an important part of our every-day lives. *

I think that this definition of mathematical literacy is right – maths is about one’s ability to reason about things so that one can say “I don’t know the answer but I have a way of thinking about it which will allow me to find out for myself,” especially as opposed to “I don’t know the specific rules here, therefore I’m stupid… Or I feel lost because I forgot the rules.” One aspect I loved about maths was precisely this one – I didn’t have remember anything! If I forgot something I would go back to the beginning and figure it out for myself.

*Sorry for the interruption, but – was this perhaps the drive behind your interest in science communication then, namely to engage different audiences to show how powerful and versatile mathematics is? *

I think my main drive was to show the broadness of mathematics: there are subjects (like knot theory) which people do not even realise are part of mathematics. Just because there are no equations or numbers it does not mean it isn’t maths! I was lucky that the subject I was studying is very easy to present to the public – you can get a long way with drawings and intuitive reasoning – although at the same time I can talk about questions in the subject that nobody in the world has ever answered. In fact, this is another drive for me in science communication: to show people (and especially youngsters) that maths hasn’t all been done already, that it is not the case that the only maths which exists is what is written in textbooks. Finally, of course, another motivation for me is simply that I love doing science communication!

*Yes, I realise that mathematics is rarely pictured as a subject where there is still room for discovery. To go back to the choice of showing the applied side of science (and more specifically maths), can you tell me a bit more about your approach to science communication, and the importance you may or may not assign to making science “applied”? *

I think one should care about applications – unless the specific audience to be addressed is explicitly interested in pure mathematics. The vast majority of people need to see an application. Even if I give a talk about pure knot theory, I will save time in order to add that these concepts are useful in different branches of science. In this way, the collaborative nature of mathematics stands out too – mathematicians do not sit in a room on their own, they work across disciplines. Hence it does not close doors to do a degree in maths, it is actually likely to widen one’s horizons.

*Absolutely. I think I might give an additional twist to my previous question and play the devil’s advocate, so to speak. I do see the importance of presenting maths, as abstract as it may be, along with its more practical, every-day-oriented applications… Yet does one then risk to shadow the beauty of its pure and abstract nature, somehow? To rephrase this – is not mathematics fascinating precisely because of its abstractness? What about this aspect then? *

Well, I wouldn’t see it this way. I generally try to get both messages across – in fact, my favourite examples are the ones where at first there is a result in pure mathematics which was developed purely for its own sake, not because anyone ever thought that it would be useful. Often a few hundred years pass before someone finds a use – and suddenly it is the most basic tool which appears in all areas of maths and beyond. But one should not forget that it was never conceived for that purpose! I think it is great when pure maths finds an application somewhere. However, I do believe in studying abstract mathematics for its own sake, because it is a beautiful subject. In this sense, I do not agree with the way the government is trying to push impact statements – where funds should be granted to research which is proved to have an application right here, right now. We don’t know which area of mathematics, for example, may be underpinning – or at least supporting – the new revolution of science and technology. We have to keep a broad field of view, as it is too early to say which bit will be useful in the future. It might turn out to be the bit we didn’t expect!

*And I would add that history has repeatedly confirmed how scientific progress sometimes takes long and winding roads… Now, I saw on your web page that you are truly immersed in science communication: talks, workshops, open studies courses – and you seem to address almost every age group too! I am particularly curious about the undergraduate course *Proofs and Problem Solving* which you co-lecture at the University of Edinburgh. I read online that this course is structured following the principles of peer instruction *(http://en.wikipedia.org/wiki/Peer_instruction)*. What is your opinion on peer instruction, can you tell me a bit about this course? How do such “alternative methods” apply to subjects as rigorous as mathematics – does this make no difference or does this constitute an additional challenge?*

As a lecturer, I think that peer instruction is much more fun than traditional lecturing. Let me tell you the way the course works in Edinburgh: the students have to read the relevant chapter from the course textbook before the lecture. There is an online multiple-choice test which allows us to check that they did read the material; importantly, the last question on the test is “What did you find difficult about the reading?” Therefore, one could say that in the lecture there is no lecture – what we want to do is address the problems of the students further to their reading. In order to do so we ask a series of questions; the students have clickers, just like the ones you see on television, so that when they are asked a question they can “vote” anonymously. Ideally one should ask a question on something which they might have a misunderstanding about! The students vote individually and the lecturer can then see whether the majority of the class gave the right answer or a wrong one. After the vote, the students have a few minutes to talk to each other; then they are asked the same question again. The optimal scenario is to initially have half to two thirds of the class with the wrong answer, along with a few people in the classroom who understand what is going on, so that when they talk to each other they are able to work out the right answer by reasoning with each other, as well to realise where they were wrong. This is a much more effective way of learning than me trying to explain to them some fact when I don’t know what problems they might have, and I am not at the level where I can explain it in a way they can understand. Most importantly, it often turns out that the misconception, when there is one, is not what the lecturer thought it might be: it is some peripheral aspect which one would never have imagined could be a problem – and this does not show until one asks. Facilitating people to teach each other, this is the key. Here is an insightful example: one of the questions that we ask, which usually scores a big wrong response, is “Do you believe that 2 is less than or equal to 3?” Half of the class would answer “No, 2 is less than 3.” They do not understand a symbol which one would think that they studied in school already (3). Without a direct question we might never pick up on such problems. Of course, it is not easy lecturing – one has to come up with the right questions, so to speak. If the question is too easy the entire approach becomes pointless, yet it shouldn’t be too hard either… It is important to find a trade-off. And this is not straightforward – I am still learning, but it is very stimulating and I like to interact with the students to see how they reason. As for the students, they seem to enjoy the lectures, and they cannot fall sleep as every five minutes there is a question which needs to be answered!

*This is a first-year course – basic maths. Would you see peer instruction applied to other courses too, even more advanced ones? *

I would like to believe that peer instruction could be applied to any science subject and at pretty much any level. I know that it works really well in physics (4), where people seem to have misconceptions starting from the very basics… For example, in Harvard they ask their undergraduates “You have a light car and a heavy truck and they are colliding with each other – in the moment of collision, does the truck exert more force on the car or the car on the truck?” It turns out that the students ask questions such as “Do you want me to answer according to what I actually believe or the way you taught me?” There is something deeply wrong here, right? They know Newton’s laws of motion, but they don’t believe that they actually work (5)! It is very important to identify this kind of issues before going onto more complex subjects – if there is a problem there, what is the point of teaching them the rest of physics? And these students are bright – the point is that the lecturer must ask themselves “What shall I do to convince the students that something is true?” rather than just saying “Believe it.”

*I understand why physics is particularly well-suited (having studied physics myself!). Mathematics seems trickier to me as I would think that there are a few techniques and ways of reasoning which the students have to become familiar with, maybe in the “old way”… *

Well, I should add that there are different parts to a course like ours – there are lectures and tutorials. Lectures are about giving facts, proofs and understanding of basic concepts, while tutorials are for solving problems and working on the students’ reasoning skills in a different context. So I think that eventually one could have both approaches, the “reason on your own” one together with a more “traditional” one. An additional, novel aspect of our course is that exams are open-book. The students can use whatever they want except for the internet – they can print hand-outs and bring the course textbook, for instance. This means that the exam is not a memory test anymore: the students need a genuine understanding of the subject to be able to pass the course.

*It will be interesting to follow these students throughout their degree, I would imagine? *

The first students who started with this course are now in year 3 – and this is a brand-new course, we structured it ourselves. Give us maybe five years, and hopefully we will have some statistics by then.

*Thank you very much and good luck with all your projects! *

I am extremely grateful to Dr Julia Collins for accepting to be interviewed after a one-hour talk and for patiently answering my questions – please have a look at the notes to the interview if you wish to know more about a few topics.

(1) See also https://dubitareaude.wordpress.com/2013/11/01/stereotypes/

(2) http://www.oecd.org/pisa/pisaproducts/PISA%202012%20framework%20e-book_final.pdf

(3) “2 is less than or equal to 3” can be rewritten as “2 ≤ 3” (whereas “2 is less than 3” is translated as “2 < 3”) – as for the correct answer to this question, the key word is “or”…

(4) See also “Confessions of a Converted Lecturer” by physicist Eric Mazur at http://www.youtube.com/watch?v=WwslBPj8GgI (thanks to Julia for this link!) or, for an abridged version of it, at http://www.youtube.com/watch?v=rvw68sLlfF8&feature=youtu.be

(5) http://van.physics.illinois.edu/qa/listing.php?id=92 or https://hh-honors-physics.wikispaces.com/Newton%27s+Laws might shed some light on this problem…

** The image associated with this post was taken from the Wikimedia Commons

Interesting interview. I find the concepts of peer instruction and the flipped classroom quite compelling.