Unbalanced and Balance Reasoning: a study in design of task-sequences to introduce underlying principles

28th May 2020 : 15:30 - 16:30

Category: Webinar

Research Group: Subject Pedagogy

Speaker: John Mason, Senior Research Fellow

Location: Online

Convener: Karen Skilling

Audience: Department Staff and Students

We are very pleased that John Mason has agreed to deliver his presentation which was originally planned for March in a remote format.

The seminar will be delivered via Zoom and we will provide the access details closer to the date and we hope that many of you can join.


Seminar Abstract


The metaphor of balance if often used when solving equations in Secondary School. Participants will be invited to engage in a sequence of tasks which make it possible for Primary pupils to make use of their natural sense of balance to move to abstract thinking concerning strict inequalities, and for Secondary students to further develop this in order to resolve equations. I may report on some of the challenge in developing programmes to display balance-configurations and the corresponding inequalities or equalities.

About the  Speaker


John Mason was retired as Professor Emeritus from the Open University in 2009 where he had worked for 39.5 years. He continues an active interest in and concern for the teaching of mathematics in schools in each and every phase, from kindergarten to university.

He conducts numerous workshops for teachers in the UK and abroad, leads seminars, and presents plenary lectures, always stressing the dimension of lived-experience rather than theoretical stance.

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.

He is perhaps best known for being the principal author of Thinking Mathematically (with a new augmented edition published in 2009), joint author of Mathematics as a Constructive Enterprise: learner generated examples with his wife, Prof. Anne Watson, for his uncompromisingly experiential stance to research methods in Researching Your Own Practice Using the Discipline of Noticing and for his contribution to practical suggestions for teachers such as Questions & Prompts for Mathematical Thinking, and Thinkers, both written with colleagues.