Developing Thinking in Algebra by Professor John Mason, Alan Graham, Sue Johnston-Wilder

By Professor John Mason, Alan Graham, Sue Johnston-Wilder

By integrating pedagogy and topic wisdom via experiencing various initiatives for beginners, this book makes it attainable for all inexperienced persons to be triumphant in thinking algebraically.

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THOAN; square it; add 4; subtract four times the number you first thought of; take the (positive) square root; add 2; you’re left with the number you first thought of. You can easily make up your own; the more complicated they get, the more dependent you will become on being able to manipulate the expressions in order to simplify them. One of the features of a good THOAN is that it builds up a complicated expression one way, and then undoes the expression in a non-obvious way. Pause for Reflection Some important arithmetical ideas have passed by along the way to using the expression of generality in order to make sense of those ideas.

Pdf). The pedagogic significance of the chapter lies in becoming attuned to noticing opportunities, within standard topics, to pause briefly and get learners to express generality. R Reflection What struck you about the work in this chapter? What do the following terms mean to you, currently? Try telling someone else, or writing down something about them. Specialising Generalising Expressing generality Conjecturing Algebra What aspects of the tasks gave you some pleasure (even just a tiny bit)?

This provides one important reason that you should actually do the tasks yourself, rather than just thinking about them or imagining yourself doing them – that ‘doing’ is the only means by which you can experience the pedagogic ideas directly for yourself. For example, it has been suggested that manipulating familiar objects that inspire confidence is the beginning of getting a sense of structure, and that the structure eventually emerges in the form of a generalisation or expression. You will learn most from your own first articulations of the emerging generalisation.

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