Metaphor or Met-Before? The effects of previouos experience on practice and theory of learning mathematics

While the general notion of ‘metaphor’ may offer a thoughtful analysis of the nature of mathematical thinking, this paper suggests that it is even more important to take into account the particular mental structures available to the individual that have been built from experience that the individual has ‘met-before.’ The notion of ‘met-before’ offers not only a principle to analyse the changing meanings in mathematics and the difficulties faced by the learner—which we illustrate by the problematic case of the minus sign—it can also be used to analyse the met-befores of mathematicians, mathematics educators and those who develop theories of learning to reveal implicit assumptions that support our thinking in some ways and act as impediments in others.

Research highlights▶ How experiences ‘met-before’ affect learning in new contexts. ▶ How experiences ‘met-before’ affect learning in new contexts. ▶ Mathematicians build on their own met-befores to produce new theories. ▶ Mathematics education theories are affected by the met-befores of their creators.