Venn diagrams and basic set theory can serve as a tool for pre-service teachers to grasp complex networks of mathematical concepts, such as different quadrilaterals (Moyer & Bolyard, 2003). Basic set theoretic concepts carry intuitive meanings (Bagni, 2006), and Venn diagrams where the interior of closed plane curves represent sets, are simple and non-controversial, even for children (Freudenthal, 1969). Previous research is inconclusive regarding the benefit of Venn diagrams (Moyer and Bolyard, 2003).
As a reoccurring part of a mathematics course in the primary teacher education, two lectures and associated workshops have introduced basic set theoretical concepts and Venn diagrams to the pre-service teacher. The discovery of objects belonging to several sets seemed unproblematic in the first workshop, the understanding of intersection became an obstacle when working with numerical problems.
We conclude that working with properties of objects is not enough to understand set intersection. In order to support their future students’ mathematical development, pre-service teachers need to be aware of their awareness when working with problems (awareness-in-action), but also of this awareness in turn (awareness-in-discipline) (Mason, 2011).