PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Adding explanatory power to descriptive power: Combining Zandieh’s derivative framework with analogical reasoning
Page: 1041
The derivative is an important foundational concept in calculus that has applications in many fields of study. Existing frameworks for student understanding of the derivative are largely descriptive in nature, and there is little by way of theoretical frameworks that can explain or predict student difficulties in working with the derivative concept. In this paper we combine Zandieh’s framework for understanding the derivative with “analogical reasoning” from psychology into the “merged derivative-analog framework.” This framework allows us to take the useful descriptive capabilities of Zandieh’s framework and add a layer of explanatory power for student difficulties in applying the derivative to novel situations.