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Abstract

This study explores graduate students’ mathematical sense making through non-routine problems. I consider visualization, gesture and affect as integral cognitive aspects in the solution processes of participants. To analyze them, I introduce a suitable model, a think-aloud protocol coupled with meta-cognitive prompts. The study gives details of the solving of given non-routine problems by participants. It allows focusing on the relationship between visualization and gesture in conjunction with affective states in the process of sense making when solving non-routine problems in the absence of pre-determined mathematical procedures or algorithms. Visual imagery, gesture and particularly affective issues played a role in the solving processes of graduate students. As such these resources are seen as major ingredients in mathematics teaching and learning.