Using the K5Connected Cognition Diagram to analyze teachers’ communication and understanding of regions in three-dimensional space

This paper reports on a study that introduces and applies the K5Connected Cognition Diagram as a lens to explore video data showing teachers’ interactions related to the partitioning of regions by axes in a three-dimensional geometric space. The study considers “semiotic bundles” ( Arzarello, 2006), introduces “semiotic connections,” and discusses the fundamental role each plays in developing individual understanding and communication with peers. While all teachers solved the problem posed, many failed to make or verbalize connections between the types of semiotic resources introduced during their discussions.

► The K5Connected Cognition Diagram is used to explore semiotic resource use.
► We examine teachers’ responses to the number of regions in 3-space.
► Teachers used multiple semiotic resources when reasoning in three dimensions.
► Some teachers failed to connect representations of the problem.
► Teachers’ communication and comprehension of representations varied.