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Working on your own mathematics
Working on your own mathematics

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1 Forces for development

Working in mathematics education involves a sense of both past and future, and how the two combine to influence the present. It may seem that, because the past has already happened, it cannot be altered; however, you can alter how you perceive the past, and what lessons you take from it. Each of us has a personal past in mathematics education—the particular events of our personal lives, who taught us, where, what and how they taught us, and what we took from the experiences. Each of us also has a related ‘communal’ past—the general events in mathematics education and their influences on school practices, as well as the perceptions of mathematics and school in the cultures in which we grew up. The past exerts a serious grip on the present, helpfully in terms of maintaining tradition and continuity across generations, and unhelpfully for the same reasons.

A colleague, Christine Shiu, was in China talking with a group of mathematics teachers about problem solving and investigative work in mathematics. One commented ‘Yes, but you must learn from the Ancestors first’. One reason for attending school is to become one of those who know the old ways, and so be part of a ‘community of memory’ and hence an inheritor of traditions. There is perhaps no more fundamental split between a perception of the primary function of schooling as enculturation into traditions, and a perception of schooling as preparation for the future; this is often unfairly characterised as a split between the backward-looking and the forward-looking, with all the connotations of those words.

The future too can exert a strong influence. Again, it might seem strange that the future can exert an influence on the present. But you have a more or less explicitly desired personal future that affects what and how you teach, and part of the work of mathematics education is to envisage possible communal futures for mathematics teaching and learning. A particularly relevant aspect of communal thinking about the future of mathematics education concerns the influence of technologies, especially computers, and their potential to destabilise radically some traditional views of the interactions among teachers, learners and mathematics in a classroom setting.

This section focuses on your own and others’ accounts of their experiences of learning mathematics. It begins to show how such personal experiences can be explored and can inform the shared communal culture of published writing.

Everybody can remember incidents from their own learning of mathematics. Some incidents may be positive and others negative. What influence might such memories have on the teaching and learning of mathematics?

Activity 1 Starting your mathematical autobiography

Think back over your own experiences of learning mathematics, both as a child and as an adult. What stands out for you? It might be particular incidents, particular lessons, particular teachers, or a generalised sense of some sort, or an emotional response, or it might be all of these, and much more.


Wait until you have some spare time and feel willing to be introspective. Start making some notes in response to this task, and continue adding to them. Starting to think about your experiences may produce memories you had forgotten. Be prepared to be surprised, and possibly disquieted or even distressed by some of your recollections. Learning mathematics has seldom been a neutral experience.

Activity 2 Forces for development

Read the chapter Forces for development [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] . This is taken from the book Researching Your Own Practice. In this chapter, John Mason, a member of the ME825 course team, looks at some of the forces for development in mathematics education and introduces reflection as an action. As part of your reading, you are invited to carry out a personal inventory and an inventory with colleagues.