‘It sometimes happens that during an arithmetic lesson, when the very atmosphere seems heavy with tedium, a butterfly will flutter into the classroom from out of doors. Then the urchins will all crane their necks and follow its flight with curiosity, as if they saw before them something strange and new and not simply a butterfly.’
So wrote Chekov in his short story Champagne. It is an uncomfortable question to ask: whether the perception of maths lessons has changed all that much in the 130 years since Chekov’s story was written. Many people who are passionate about mathematics and about teaching argue that it is a creative discipline, but I would suggest that Chekov’s description persists in the imaginations of many. There are also fears that an increased focus on arithmetic skills, and a push for ‘mastery’ teaching—taking slower steps through learning, perhaps with children sitting in rows facing the front—might actually be rewinding the clock to those lessons heavy with tedium.
To communicate just what we mean when we say that mathematics is a creative discipline requires more than just showing the pretty pictures of the Mandelbrot fractal or the tessellations and paradoxes of Escher’s etchings. If anything, these only confirm the sense that mathematics is, at its core, incomprehensible to most of us. Even where the message has been communicated in part, there is an entrenched cultural norm: mathematics is something a very few unusually clever people can do, for whom it might indeed be creative though abstruse and abstract, but that most people cannot do, and for whom it is alienating, frightening or just plain dull.
A student who has success in maths and shows an interest in the subject is not usually described as creative. Logical, perhaps. Clever, bright or intelligent maybe, but creative is hardly ever heard. The student who paints portraits or writes poetry with a good grasp of rhythm and metaphor, or strums a guitar soulfully—this student is deemed creative. In this short article I have picked out some of the ways in which doing and learning maths require such facets of creativity as intuition, revelation and the construction of meaning in the world. Rather than showing how these are present in the higher mathematics of academia, I have used examples that will be familiar to any teacher or pupil from primary school.
Story and making meaning
‘A class of 25 children needs to be in groups of 4 for their tennis lesson.’
This is a pretty standard setup for a word problem in a lesson on division with remainders and will likely result in the calculation: