The Bhutanese Leading the way.
Don’t let Marcus du Sautoy’s title of Mathematics Professor at Oxford University throw you off as Marcus has also built quite the opposite international reputation of doing unprecedented work through his books, TV programs, public appearances, popular culture and work with teachers and students to popularize maths. Though a brilliant mathematician and the winner of many awards, Marcus’s main interest is to make sure that everybody gets Math as a fun subject too. The Bhutanese Editor, Tenzing Lamsang, sat for a chat with Marcus over popularizing the subject in Bhutan and on what we can do right. Marcus was in Bhutan for a short visit on the invitation of the Royal Tutorial Project under His Majesty’s Secretariat.
What are the educational programs and activities that you have done during your stay in Bhutan?
Marcus : The primary thing is to talk to the teachers as they are ones who will excite the students about mathematics and it is actually a model I have used in England. I am an ambassador for ‘The Prince’s Teaching Institute’ which Prince Charles set up, so a little bit like His Majesty The King here is very concerned for Education which is at the forefront of society. Prince Charles is as well and he believes that if you excite the teachers then they will in turn excite their students and if talk to a hundred teachers each one of them will talk to several hundred children.
I can only be here for a week, though I hope to come back. So the next best thing is to leave a record for those teachers who could not come for teachers to also be reminded of what they have just seen. So we are making these five TV programs with the Royal Tutorial Project and each of them will be about a different topic like symmetry, shapes, numbers, prime numbers, logic and winning games.
We will also leave videos of the sessions that we have done with the teachers in Punakha, Paro, Thimphu and also the sessions in RIGSS. We also met a group of very bright students from Thimphu and that was very great as well. I was very encouraged that there were a couple who were very bright and sharp getting my questions very quick.
Many students find maths hard in Bhutan. In your limited stay and interaction with both teachers and students what would you ascribe this reason to?
Marcus: I think there are two things to keep distinct here. One is that people find maths hard and the second is that people don’t enjoy maths. People across the world and not just in Bhutan find maths hard and I must admit that I find maths hard so they should not despair. Actually I think that sometimes we should actually value the fact that it is hard because if something is hard it is rewarding.
Meditation is hard and you have to work at it but the rewards are great if you can do it and with mathematics it is hard but students don’t understand that the rewards are many if you achieve mathematical enlightenment.
So I think what we are missing is giving students the enjoyment of the subject and I think that is the more worrying thing when students say, ‘ I don’t enjoy the maths,’ because I think we all enjoy a puzzle and if a puzzle is hard and yet we can solve it then we feel very good about ourselves. I would not worry about students finding Maths hard but I do worry if they don’t like it and that is not just the case in Bhutan but we have the same problem in Britain too.
So what would I ascribe this too ? I think it is to do with the curriculum. The curriculum in the past has been about rules and nobody likes being told what to do. We want to understand ‘why am I having to do this.’
I was very encouraged when I was here a year and a half ago I met the Prime Minister and the Education Minister and they said, ‘would you look at our curriculum, we have changed it and we think that the old system based very much on the Indian model wasn’t giving our students understanding and they were just learning rules’.
If you just learn rules it is very easy to forget a rule and so this is not the way to teach mathematics and it is not the fun of mathematics either. So I took the curriculum away from year one to 10 and I read through the curriculum. I was very encouraged by what I saw because there is a change of emphasis from rote learning and rules to a deeper understanding of why something is like it is. Not only that, the curriculum has exploration of connection to other subjects like to the history of the subject, to technology, to games and so it has been one of the things that I think is missed in many education systems, which is the connections between subjects.
So the reason why children were not enjoying it is partly because they were not given the full story. It is like being told a story and you are missing half of it. It is also like learning musical instruments where you do all the technical stuff and you never hear the music. I think your curriculum is getting closer to allowing students to hear a bit of the music.
How can teaching maths be made more fun in Bhutan ?
Marcus: In the teacher sessions I have called it mathematic connections. Look, we all love stories, and I think maths has great stories and so what I have been trying to give them is some of the stories that I enjoy.
So we talked a lot about Prime numbers and its connection to nature, music, technology and so I think that it’s trying to find ways to embed the maths in a richer educational environment and I think one of the challenges, is that teachers have been used to the old system and that is what they are used to teaching and so this is a little bit of a change.
However, I have been very encouraged talking to the Teachers. I asked how they are coping with it and I actually think they are really enjoying the chance to explore the underlying reasons. So I think this curriculum is giving them more space to tell the mathematics they love. I think it is about understanding why certain things are rules.
For example what is algebra about? It is about understanding the grammar underlying how numbers work. What you don’t want to do is having to keep reinventing or redoing something every time. If you can spot a pattern underneath there – it is very close to what an algorithm is as algorithms run the modern world. Algorithm is just a mathematical rule that it does not matter what you feed in but it will give you an answer, Google is an algorithm that can give an answer for whatever I or you ask. Mathematics is very good at finding the underlying structure so that you don’t have to keep doing the same think over and over again.
As you said curriculum is key, so what would your broad recommendation be on a student friendly maths curriculum for Bhutan?
Marcus: I think continuing this idea of finding connections with other things that people enjoy. It is already there, the seeds of it in the curriculum, and I think it can be expanded. For example there is an interesting section exposing the students to Fractals and it is a little bit of a start and explains what a fractal is but I think you can explore a little bit as I did in the lecture how fractals are actually used by Pixar animation for creating their movies. That is one thing that can be expanded. It is about broadening the connections and it is like a growing tree and the branches are beginning to connect and I think it can grow more and more. It is a good start and it really helps students to then do the hard work.
The rules are there for a reason for example you learn in school that minus times minus is a plus. That isn’t just a rule we have decided on but it there is a reason for it and you can explain it but it requires a little bit of work to explain why it is so. I think that is the challenging thing for a teacher. I think teachers would think, ‘I learned it is a rule but why is it a rule,’ and you can use a bit if Algebra to explain it. I think rules make sense when you understand why and in a way it isn’t a rule but it is a logical consequence of the mathematics we know. I think rule is the wrong word because it kind of feels artificial. Of course many of the rules and laws have reasons for being there and we obey a rule or law better if we understand it better.
The ‘why’ is a very challenging question and I think a teacher is sometimes frightened of the question why. I try to encourage teachers today to be open to admitting that ‘I am not sure why but let’s find out together,’ and I think that is very empowering for a student to see a teacher wrestling with the question. I know that for many cultures it is difficult for a teacher to say, ‘I don’t know,’ and they would say ‘it just is because it is’. I would really encourage teachers to be open to exploring with their students why things are the way they are. That is why I am very encouraged the title of the curriculum in Bhutan is called ‘Understanding Mathematics,’ and I think that is a good starting point.
There is a perception among students and even adults that one needs to have a ‘maths brain’ to have an aptitude in the subject or that it is even linked to ethnicity like Indians and Chinese are supposedly better at it. What are your thoughts on the issue ?
Marcus: This is really not true and the other one is that in RIGGS I got asked about men and women. There is a perception that maths is a male subject and this is total rubbish and a bad stereotype. As I have said, everyone has an innate mathematician inside them. Often what happens is we learn a fear of the subject and it is quite hard to undo that.
I think I have told the teachers that part of being a teacher in mathematics is being a psychologist and it is about helping your students to believe that they can do it. Belief is so much part of being a mathematician. I think I became a mathematician because I had this arrogant belief that I can understand everything. When you have doubts it can really cloud your education. Okay, there are some geniuses who have very amazing brains wired for mathematics but I don’t think there are people who can be very good at maths and I think in Bhutan everyone has the potential.
After your presentation in the Banquet Hall a lot of animated students asked you questions on maths which is not usually the norm in Bhutan. How can we inspire students to take up maths?
Marcus: I was encouraged to see so many students. I would have been terrified to ask a question in front of the Royal Family and the Foreign Minister. I think asking questions is half the battle. I think quite a few students have watched my BBS programs on mathematics and I think it is giving things outside of just the school curriculum, so for me, it was a book I read and that is partly why I write the books that I write with a hope that it is a book for another maths teacher.
One book is especially called the Number Mysteries and I write it specifically for the 11 to 16 age group when I think it is a time that students that get bored of maths. I think the curriculum most of the time is deadly boring doing the same things over and over again. This book in a way is my manifesto for what I wished the curriculum would be.
I think there are so many scientists who will say it was a teacher that turned me on. So I think you can’t underestimate the power of a teacher to just perhaps take one individual. This teacher took me individually aside and that was the spark and well let’s challenge every teacher and try and see whether if you can light a spark and explore outside of the classroom.
Your advice for students who find maths particularly difficult?
Marcus: Mathematics is slightly different from all of the other subjects in school, because you are sort of building a pyramid and each year you use the things you have done before, and I think what happens is that students, when they don’t get one thing to build on top of the other that the pyramid starts crumbling and you just can’t get higher.
So, I think sometimes the best thing to do if you are finding something difficult go back to something you find a little bit easier. Get your confidence again and come back to the thing you find difficult. I think that very often when you see something the first time it is a bit like being an animal facing the headlights. I think when you come back to something the second time it can be a little bit easier. So I think it is about not giving up, going back to the things that you can do, building confidence.
In the mangahigh.com website we have created for math games we have built in this idea and we can see a student who is just failing and the mechanism takes you back down to a level where you build your confidence and it then takes you back to the place. It is a pyramid so each thing is understandable from a thing before.
I was encouraged by students asking questions because they were not afraid of asking. I think it is on both sides as a teacher is also afraid of being challenged on a things maybe they would find difficult to explain. I think it is a partnership where the students should not be afraid to ask and the teacher are there to help students as it is very rewarding to see a student go forward.
How can Bhutan learn from the western system of education ?
Marcus: You know what I think, we can learn from you as well. I am working at the moment with a Finnish education company and we are looking to develop some new games which help students to be exposed to particle physics and so it is a fun little kind of Angry Birds game. I think Finland has got some of the most innovative ideas about education. I was asked by Wired Magazine a few years to think 10 years ahead and send post card back on what I hoped what education would be. The choice was anything but I choose education. I said I wish we come to a time when schools don’t divide their curriculum. I think curriculum to too divided up. Then I learnt that Finland is proposing a more horizontal view of education. You know students should study what the music, science and literature was during the French Revolution. Look at the interconnected nature of anything and that will give you a much more holistic view. I think Finland is starting an experiment with my dream for education.
I mentioned to the teachers that I also have an internet maths school that I created called mangahigh.com like a high school. Look kids love playing games and they all try a level over and over again and until they get through. Well that’s what we want in education. We want them to keep trying when they are stuck until they get through. So we have made the maths curriculum into one big video game. It was quite fun to do. Solving quadratic equations, doing things about symmetry, angles and it is all there made into a game. You know the games have to be fun as there is no point making it a boring game. We have found this has encouraged children who usually don’t like maths. Suddenly there are students saying ‘can we have more homework’. They are enjoying playing the game. I am not worried about the top one percent. It is the rest who just give up. The idea of using games is an innovative new way in education.
