Mathematics Education Is Not an Enigma - Part 1
Williams, Doug, Mathematics Teaching
Doug Williams uses practical experience working with teachers and learners to prove his point
This article is an edited version of the opening address given by Doug Williams at the ATM Conference 2012. The theme of Conference 2012 was 'Enigmas'.
Setting the Scene
I am a storyteller in mathematics education. It is my job to collect and retell stories of success from classrooms. It is the quantity and quality of these stories, which leads me to the belief that there is nothing mysterious, puzzling, or difficult to understand about mathematics education. We know how to do it, and do it well. Therefore mathematics education is not an enigma.
The theme which weaves these separate stories into an integrated anthology is choosing the core of the curriculum to be learning to work like a mathematician (Working Mathematically), and choosing teaching craft that fascinates, captivates, and absorbs learners. In such classrooms the teacher realises that they are not teaching mathematics and the children realise that they are involved in the process of working like a mathematician in a happy, healthy, cheerful, productive, inspiring classroom.
Mathematics content, the stuff you see listed in systemic curriculum documents, offers very Sttle in and of itself. The amount listed cannot be justified on the basis of you need it to pass an exam', or 'it will help you to get a job one day', or 'you might need this when you grow up'. Worse, content lists set learners up to fail. A contentdriven view of mathematics learning ensures everyone succeeds... to the first level of content that they 'don't get'... and often, having not 'got that', learners decide they 'can't do maths'. Some of these learners later find themselves teaching mathematics with no vision of a mathematics classroom to inspire them other than the contentdriven ones they survived... or escaped from.
A content-driven curriculum also sets teachers up to fail. It encourages us to think about teaching stuff rather than people; whole human people with both integrity and a self-image formed by past experiences and within which they operate.
In 1969, following my degree, I studied a Diploma in Education course at Monash University and, through the wisdom and teaching experience of my lecturers and tutors, in particular David Davidson, my Maths Methods tutor, I began my teaching career believing that it was not my job to teach mathematics. Rather, it was my job to use my mathematics background to help learners to feel better about themselves, to build their self-esteem. This is an objective I have failed to achieve with many of my students through my years of full time teaching in both primary and secondary schools, but it is one from which I have never wavered.
I was fortunate that my attitude was fashioned this way before I qualified. However, it took many more years, many experiences, and the stories told by many colleagues before I recognised there is an alternative framework to traditional mathematics teaching, and that when teachers choose to change their attitude to make this framework the core of their teaching, students learn more mathematics content more quickly and securely and feel successful.
The turning point, for myself, and others, was the clear, concise statement of the work of a mathematician developed by the Mathematics Task Centre Project from the statements of professional mathematicians. This Working Mathematically framework is at www.atm.org/MT230. It helped us move from problem solving being added to the curriculum as a topic, to working like a mathematician being the essence, the core, the raison d' être, that gives all mathematics content its meaning.
When asked about their work, mathematicians began their response with "First give me an interesting problem. "
So, a Working Mathematically curriculum would begin with problems, not add them on at the end of a chapter if there is time, or reserve problems for one period per week, and our teaching craft would call upon us to interest learners in the problems. …