The structuring of personal example spaces

This paper elaborates the notion of a personal example space as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task. This is different from the conventional space of examples that is represented by the worked examples and exercises in textbooks. We refer to three studies spanning the age range of learners, from school-age learners to pre-service teachers learning maths and professional mathematicians. Their constructions of examples are used as evidence of their personal example spaces. From these, we identify characteristics of such spaces that provide insight into learning mathematics. This perspective informs teaching by giving access to how personal knowledge is structured and what might enhance that structure.

► Contributes to theory about using example spaces to understand learning.
► Phenomenological exploration of the nature of personal example spaces in mathematics.
► Example spaces of school learners, new teachers, and experienced mathematicians.
► Characterises personal example spaces.