Narrative in teaching mathematics
Posted on 28 February 2008 by Phil Wilson
Bob has yet another fascinating post over at Heroes Not Zombies, this time explaining how writing about their experience of the disease helped cancer patients to change their thinking of the illness.
In the face of suffering and death, mathematics seems very trivial. But I have noticed that many of the best moments in a lecture theatre, those wonderful times when the audience seems rapt and suddenly there is a collective “a-ha!” look which sweeps the rows, are when I set the dry theory in the context of a story, or at least a concrete situation which can be held in the student’s mind. Moreover, I consciously try to link new ideas or results to early work, to build up a web of connections between the things we learn, and indeed the things we may know and learn from other areas of life. I explain that this strange mathematical symbol is named after an ancient Hebrew harp, or that this result is like walking into a cave at the same moment that someone pelts you with a snowball.
These images, and the tale which weaves them together, seems to lead to a more rewarding learning experience for the students. The jury is still out on whether it helps them to pass with a better mark. But the idea of narrative in mathematics is even being explored at the research level.
Filed under: creativity, education, mathematics | Tagged: bob leckridge, education, heroes not zombies, lecture, lecturing, math, mathematics, maths, nabla, narrative, university
Well, Phil, I never knew narrative was being explored in mathematics. How I wish I’d had someone like you to teach me maths at school! I was always good at school maths, easily gaining the top band of marks in exams and I had a group of friends in the same class who were at the same ability level. One day, after discussion, we realised we all shared the same view of maths - we could do it, but it really wasn’t fun because we often couldn’t see the point of it - so we decided to approach the teacher privately and explain our problem.
We said to him that we understood what he was teaching and he could see we were getting the answers to his questions correct but we couldn’t see how things like differential calculus and so on had any relevance to real life. Could he please put the maths into context so we could see its relevance?
He told us to stop playing silly asses, sit down and be quiet. And if we didn’t he’d belt ALL of us!
Kind of lost something in my education that day!
But niggling away in there, I still have a real fondness for mathematics. So can I ask you a question?
Is there a book you’d recommend of me at this point in my adult life, which might reignite the joy I used to have for mathematics? I’d be especially interested in anything which took the narrative approach you describe here
Thanks, Phil
Bob
Oh, I’ve just clicked on that link in your post - looks incredibly like exactly what I’m looking for! Is it?
Urgh, not the most inspiring teaching story!
The intriguing thing is that the “relevance to real life” of mathematics which you sought really depends on your own approach to life, but in all cases maths seems central to life. At one end of the scale are the Platonists who believe that pure mathematical forms, such as the triangle or the number 3, exist “out there” somewhere in a realm of perfection. And yet our minds can touch these perfect forms. I talked about this a little bit when I described Roger Penrose’s brilliant book The Road to Reality, over here.
At the other end of the scale are people who apply maths to the real world. These people are not so concerned with lofty ideals of what it all means, or of whether we can touch the realm of the gods. Rather, such applied mathematicians want to figure out how the weather works, how blood flows, how proteins fold, how mobile phones can be made more secure, how a partial footprint can nab a criminal, how lung tumours move as a patient breathes, how genes spread through a population, how weeds spread from farm to farm, and how planes can be boarded more efficiently (by row from the back is not the best way, it seems).
As for narrative, I think the Thales and Friends conferences look very interesting, and they have produced some intriguing ideas.
Let’s tie al this together, in the person of David Corfield, who has posted here. He is heavily invoved in the Thales and Friends conferences. I mention Corfield over here
where you will also find some other links just perfect for you. The first is to Corfield’s book about “Why do people get ill?”. The second is to my recommended book for you, The Mathematical Experience, by Rueben & Hersh. The book covers all of what I’ve rambled about above, and much more. It has a readable and engaging style, lots of diagrams, and is broken into bite-size chunks. But it is written by two mathematicians at the top of their game, exploring the meaning and application of maths in a scholarly and enlightening way.
Hope you enjoy, and feel free to come and chat here about it!
Thank you Phil - sorry to post that horrid story - but, hey, that’s what happened! I don’t have great memories of my education overall!
Were you luckier than me?
Thanks for this great reply. I really appreciate. I am a huge admirer of David Corfield’s work and posted about it http://heroesnotzombies.wordpress.com/2007/04/02/why-do-people-get-ill/
I have just ordered a second hand copy of The Mathematical Experience and parked the Roger Penrose book in my Amazon wish list (that’s where I keep the things I hope to get round to one day! Oh, and I always DO get round to them!)
I’ll certainly be back to discuss these. Thanks for your continually inspiring blog, Phil
Hi Bob, and no apology needed! I imagine that things are getting worse in this respect in many “developed” countries, simply because children are being reduced to a number which acquires magic properties once it becomes attached, almost indelibly to their lives. Since teachers and schools are also essentially reduced to a number, such as their position in a league table, there is no driving market force for an inspirational teacher, one who would make a love of learning the greatest gift of childhood education, only for the teacher who can crank out high-scoring students.
I think I was luckier, in the sense that several of my teachers took the long view of their subjects, and saw the human and fun side of them all. But we shouldn’t be too harsh on teachers today who don’t do so. A friend of mine recently qualified as a teacher in the UK but quit within a year because she was working 70 or 80 hours a week. On the other had, there is an increasing amount of research which shows that fun and engagement improve learning. Take this work, for example.
Thanks for the link to your discussion of Corfield’s book. I really must try to get hold of it. Books are so expensive here in New Zealand, and the libraries haven’t got hold of it yet.
OK, good luck with those books! (Penrose’s is very heavy going - brilliant, but a real challenge. I haven’t come close to finishing it. I must say that if you read it through you will probably have learned, or at least touched on, all of the material from a joint physics and maths degree!)
Thanks for the compliment, which really means something coming from the author of such a wonderful blog.