John writes about elastic multiplication: "It is often said that 'multiplication is repeated addition' when what is meant is that 'repeated addition is an instance of multiplication'. I have been developing some tasks which present 'scaling as multiplication' based around familiarity with elastic bands. Participants would benefit from having an elastic (rubber) band to hand which they have cut so as to make a strip; wider is better than thinner if you have a choice."

About John Mason

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 high school 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 (translated into four 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.

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, and ways of working on and with mental imagery in teaching mathematics. The book Practitioner Research Using The Discipline of Noticing is one manifestation of a lifelong collection of tactics and frameworks for informing the teaching of mathematics. Along the way he has articulated a way of working developed at the Centre which provides methods and an epistemologically well founded basis for practitioners to develop their own practice, and to turn that into research.

## Recording: voice, video, interactives, chat, web tour

During the event, John Mason will lead a conversation about multiplication as scaling, and answer questions about his books, projects and communities.

All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events

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## Event challenge!

What good multiplication tasks about scaling do you know?

Share links and thoughts at these places:

Math Future wiki:http://mathfuture.wikispaces.com/message/list/JohnMasonLinkedIn:http://www.linkedin.com/groupItem?view=&gid=33207&type=member&item=95717990&qid=81c95d43-170c-4b4e-9137-0095b84f4a8aJohn writes about elastic multiplication: "It is often said that 'multiplication is repeated addition' when what is meant is that 'repeated addition is an instance of multiplication'. I have been developing some tasks which present 'scaling as multiplication' based around familiarity with elastic bands. Participants would benefit from having an elastic (rubber) band to hand which they have cut so as to make a strip; wider is better than thinner if you have a choice."

## About John Mason

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 high school 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 (translated into four 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.

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, and ways of working on and with mental imagery in teaching mathematics. The book Practitioner Research Using The Discipline of Noticing is one manifestation of a lifelong collection of tactics and frameworks for informing the teaching of mathematics. Along the way he has articulated a way of working developed at the Centre which provides methods and an epistemologically well founded basis for practitioners to develop their own practice, and to turn that into research.

You can learn more about collaborating with John Mason at his site http://mcs.open.ac.uk/jhm3/