John Mason

John Mason

Emeritus Professor

John Mason has been teaching mathematics ever since he was asked to tutor a fellow student when he was fifteen. In college he was at first unofficial tutor, then later an official tutor for mathematics students in the years behind him, while tutoring school students as well. After a BSc at Trinity College, Toronto in Mathematics, and an MSc at Massey College, Toronto, he went to Madison Wisconsin where he encountered Polya's film 'Let Us Teach Guessing', and completed a PhD in Combinatorial Geometry. The film released a style of teaching he had experienced at highschool from his mathematics teacher Geoff Steel, and his teaching changed overnight.

His first appointment was at the Open University, which involved among other things the design and implementation of the first mathematics summer school (5000 students over 11 weeks on three sites in parallel). He called upon his experience of being taught, to institute active-problem-solving sessions, which later became investigations. He also developed project-work for students in their second year of pure mathematics. In 1984 he wrote Thinking Mathematically with Leone Burton and Kaye Stacey, which has turned into a classic (considerably extended in 2010 and translated into 6 languages), and is still in use in many countries around the world with advanced high school students, with graduates becoming school teachers, and with undergraduates in courses in which students are invited to think about the nature of doing and learning mathematics. Learning and Doing Mathematics was originally written for Open University students, then modified for students entering university generally.

During his 40 years at the Open University he led the Centre for Mathematics Education in various capacities for fifteen years, which produced the influential Routes-to Roots-of Algebra, and numerous collections of materials for teachers at every level. His principal focus is thinking about mathematical problems, and supporting others who wish to foster and sustain their own thinking and the thinking of others. Other interests include the study of how authors have expressed to students their awareness of generality, especially in textbooks on the boundary between arithmetic and algebra, ways of working on and with mental imagery in teaching mathematics, and the nature and role of attention in teaching and learning mathematics. The book Researching Your Own Practice: The Discipline of Noticing is an articulation of a way of working developed at the Centre which provides a well-founded basis and method for practitioners to research their own practice. The book Mathematics Teaching Practice: a guidebook for university and college lecturers is one manifestation of a lifelong collection of tactics and frameworks for informing the teaching of mathematics.

John continues to respond reasonably well to invitations to work with teachers and teacher educators around the world. With his wife and with Malcolm Swan he runs an annual Institute for Mathematical Pedagogy.

  • Mathematical Thinking: how to promote and support it in myself and in others, and how to support those who want to foster and sustain it in others
  • Nature and role of generalisation in mathematics, including study of how historically authors have indicated or prompted readers to generalise or appreciate the scope of potential generality
  • Nature and role of attention in learning and doing mathematics: not only what people attend to at different times, but how their attention is structured, influenced by their dispositions and by the social milieu
  • Nature and role of mental imagery in learning and doing mathematics, including the use of mathematical animations and applets
  • Supporting those who wish to examine and research their own experience (especially but not exclusively) of mathematics


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