This study aims to understand how teachers used their existing knowledge about proportions to make sense of a representation that was new to them and the ways in which their existing knowledge proved to be helpful or unhelpful.
The authors identified two knowledge components that were important to the participants’ sense-making activities.
The first necessary component of knowledge for making sense of the DNL was coordination.
Partitioning was the second critical concept for reasoning with the DNL.
They also identified three components that impeded sense-making with the DNL representation.
The authors also found three knowledge components participants invoked in these tasks that prohibited effective reasoning with the DNLs.