Abstract

Representation and justification are two central “mathematical practices”. In the past, each has been examined to gain insights in the functions that they have in students’ mathematical problem solving. Here, we examine the ways that representation and justification interact and influence the development of one another. We focus on the problem solving activity of 12-14 year-old students. Overall, this work highlights that the two practices are tightly connected. Students’ representations impact the way they form generalizations and subsequently justify their work. The work also provides insights in the development of representation and justification within the problem solving process. This work also provides insights where students’ representational practices may hinder the development of advanced justifications, and provides directions for pedagogy and further research.

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