Professor Marcus du Sautoy discusses his vision for teaching the compelling 'literature' of mathematics—and how to banish students' fears of the subject. International Baccalaureate students at Notre Dame take six subject areas: mathematics, English, second language, social studies, experimental sciences and the arts.
“I find mathematics difficult," he says. “It’s like the sort of statement you might expect to hear from a discouraged teenager as they refuse to give a tricky trigonometry problem a second go. It’s not one you expect to hear from the Professor of Mathematics at the University of Oxford (UK), Marcus du Sautoy. But, for him, the complexity of the subject is part of its charm: “I think one needs to address the fact that mathematics is actually quite difficult,” he says in an article published in "IB World" magazine. “If you acknowledge that, the sense of achievement when you actually understand something is that much greater."
A passionate advocate for changing how mathematics is taught in schools, du Sautoy champions the teaching of mathematics “literature,” which would cover the stories behind concepts, such as prime numbers, as well as the technical side, or the “language,” of mathematics. A nautilus hemishell: its chambers form a logarithmic spiral that is closely related to the Fibonacci sequence.
“Children are exposed to big works of English literature throughout school,” he argues. "Students will not always fully appreciate the depth of those pieces, but it's important that they're exposed to these ideas. They're part of our cultural heritage and also help to give context to how powerful and beautiful that culture is.
"You should do the same thing with mathematics. I'm not expecting students to understand every detail of the stories, but I think they are still capable of writing about them and of formulating a few mathematical arguments.”
From future tense to Fibonacci
Growing up, du Sautoy wasn’t always so passionate about mathematics. He originally planned to follow his mother's footsteps into a career in the Foreign Office, taking every language course his secondary school had to offer. He even enlisted his French teacher to help him with an external Russian course. “But I just couldn't get on with these languages because of the irregular verbs and exceptional spellings," he says. “I was really craving a kind of logic that enabled everything to make sense."
One day, in the middle of a mathematics lesson, du Sautoy’s teacher said that he wanted to see him afterwards. Rather than telling him off, the teacher suggested that du Sautoy should “find out what mathematics was really about."
“He exposed me to some big ideas, such as Fibonacci numbers, prime numbers and symmetry," explained du Sautoy. "And that was the seed from which my interest grew."
After completing his secondary education, du Sautoy studied mathematics at the University of Oxford. Still, at Oxford now as well as lecturing in mathematics, du Sautoy is the current Simonyi Professor for the Public Understanding of Science.
The psychology of mathematics
However, just because he’s working with students at a highly respected university doesn't mean that du Sautoy never encounters learners who are nervous or disheartened. “With my PhD students, I think I spend 50 percent of my time on their psychology, giving them the mental strength to tackle areas of research where nobody's been able to find answers,” he reveals.
Students' lack of confidence in mathematics is a long-established problem. A 2012 Program for International Student Assessment (PISA) study found that one in three students in Organization for Economic Co-operation and Development (OECD) countries said they were "put off by difficult problems.”
"Psychology is an extremely important part of teaching mathematics," says du Sautoy. ”Because mathematics tends to have right and wrong answers, we get very frightened of having to give the right answer. The fear of failing is mitigated in other subjects where the line between getting something right or wrong is less clear."
"One of the issues with mathematics is that it is a hierarchical subject,” he says. "Think of it like building a huge pyramid. You need a solid foundation before you move on to next layer. With mathematics, if you’ve a bad year and get a bit lost, it's very hard to build anything on top of that. In contrast, if you struggle with an era in history class, you can move on to the next quite easily."
“If you travel across the world, one really sees that mathematics is successful in the Far East because of the different mentality and attitude towards mathematics,” du Sautoy says. "The parents are encouraging and trying to make their children understand that mathematics will be the passport to economic success.
“It’s very important that children don’t inherit their parents’ own fear of mathematics. It's very easy to say that, but my worry is that this kind of attitude in Europe and North America—where it's acceptable to say, 'I'm rubbish at mathematics' — quickly feeds into students: ‘I can ignore this subject. My parents seem to be doing alright without it.' It’s up to parents, and society at large, to try to manage their own anxiety so they don’t pass it on to their children."
But is it too late for adults who struggle with mathematics to become more confident? “There is this myth that mathematics is a young person’s game and, if you miss the boat, then it's too late,” comments du Sautoy. “Mathematics is a wonderfully logical subject. You just need to find a place where you understand everything and start the journey from there.
“In later life, we often want to find the shortcuts to knowledge and that’s sometimes difficult in mathematics. It’s much better to build your pyramid in layers and not try to go straight for the top, only to realize you haven’t got a clue to what’s going on. Provided you have a bit of patience, you can learn mathematics however old you are."
Build from the bottom up
Because of the subject's hierarchical nature, du Sautoy thinks that teachers could help struggling students by going back to an area of mathematics that they do understand and rebuild their confidence from there.
Although this level of personal attention isn’t always possible in a classroom environment, du Sautoy has found a solution. "Technology can help hugely because it allows each student to learn at their own pace,” he explains. “I have developed an Internet mathematics school, Manga High, but there are many online tools that work in a similar way. If the program discovers that a student is failing at a certain level, it takes them back down to a level below and gets them secure on that knowledge before it takes them back up a level." Using technology in this way, he says, gives teachers a clear idea of how each individual student is coping.
Whatever the reason, the issue remains that students are not as interested in mathematics as perhaps they should be. In the UK, children aged between 11 and 14 are particularly at risk of becoming bored by the subject, du Sautoy says. "I think that the teaching for this age group could be much more ambitious," he says. "One of the handicaps when developing a curriculum is a government's obsession with utility. They always say, ‘We need to teach mathematics that wi11 be useful.' This really holds us back in the sort of mathematics that we could talk about.”
Du Sautoy thinks that puzzles can belp students become interested in mathematics: "A lot of students enjoy the satisfaction of getting a puzzle right. I mean, why did the Sudoku [a popular logic puzzle that is printed in many newspapers] catch on? Because there’s a real satisfaction in completing the puzzle and knowing that you found the answer! A powerful stimulator of curiosity is to give people that buzz of adrenaline of getting a puzzle or question right."
Storytelling can also be a powerful tool for getting students interested in mathematics. “We all respond to good stories,” du Sautoy says. "If you can put the mathematics within the context of a good story, then I think that’s very powerful." One of du Sautoy’s favorite storytelling subjects is prime numbers (numbers divisible only by 1 or itself), which he calls "our greatest unsolved problem."
"Prime numbers relate to Internet cryptography," du Sautoy explains. “You find them in nature with North American cicadas, which use them for their evolutionary survival. Oliver Messiaen, a French composer, used them in his music. One of the first great theorems of mathematics proved by the ancient Greeks was that these numbers go on forever. So, suddenly, you've related mathematics to nature, music, architecture and technology, to history, to the idea of philosophy and to the idea that you can prove things. Just with that small seed, you can grow the thing into a story, which is exciting."
After all, du Sautoy argues, mathematics has the power to explain the topics that students love and it is this that makes it such a wonderful subject to learn: “Mathematics is absolutely everywhere around you. If something has a meaning or is important, it will have mathematics hiding inside it. If you can understand that about mathematics, it will give you an amazing understanding of those ideas but also the power, perhaps, to change and influence your world. It is nature's language and,
as such, it is probably the most important language you learn at school.”
Professor du Sautoy was one of the presenters at the 2014 Africa, Europe and Middle East International Baccalaureate Conference this October.
NDPMA has been granted permission by the International Baccalaureate organization to republish articles from "IB World" magazine, which is printed and distributed twice a year. This article was published in the most recent issue. Notre Dame is an IB World School.
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Notre Dame Preparatory School and Marist Academy is a private, Catholic, independent, coeducational day school located in Oakland County. The school's upper division enrolls students in grades nine through twelve and has been named one of the nation's best 50 Catholic high schools (Acton Institute) four times since 2005. Notre Dame's middle and lower divisions enroll students in jr. kindergarten through grade eight. All three divisions are International Baccalaureate "World Schools." NDPMA is conducted by the Marist Fathers and Brothers and is accredited by the Independent Schools Association of the Central States and the North Central Association Commission on Accreditation and School Improvement. For more on Notre Dame Preparatory School and Marist Academy, visit the school's home page at www.ndpma.org.