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Constructing rates of change through a units coordinating lens: The story of Rick

In this research report, we describe the results of a paired-student constructivist teaching experiment with introductory calculus students focused on supporting their understanding of the derivative as rate of change. We focus on one student, Rick. We connect analyses of Rick’s ways of assimilating and operating with numerical units with analyses of ways of conceptualizing rates. The results are conjectures about the relationships between levels of units students coordinate and their ways of quantifying rates.