“Close but not Exact”: An Alternative to Introducing Derivatives
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In this paper, I report on the findings of two students engaged in a teaching experiment on instantaneous rate of change (derivatives). While derivatives are a quantification of how two quantities covary, many students tend to have static images of the derivative (Zandieh, 2000). This teaching experiment was designed to support the students in building a meaning for instantaneous rate of change based in quantitative and covariational reasoning. The results of this study provide empirical evidence of the benefit of alternative teaching methods to the current standard curriculum.