The Role of the Teacher in Supporting Imagery in Understanding Integers

This paper presents the results of a design experiment conducted in a 7th grade mathematics classroom aimed at improving students\u27 understanding of integer concepts and operations. The study particularly focuses on an expert teacher\u27s role in helping students develop meaningful imagery which students can use as a foundation to fold back and rely on as they engage in further mathematical activities. Toulmin\u27s model of argumentation is used as an analytical tool to document when an image becomes taken-as-shared by the classroom community. The results suggest that the practices of the teacher played an important role in students\u27 development of various images in understanding and solving integer problems meaningfully as well as communicating their ideas effectively