Proceedings of the Annual Meeting of the Cognitive Science Society

Differential calculus provides various ways to conceptualize change, any of which can be employed with applied problems. Experts associated with different academic disciplines (chemistry, physics, mathematics) were asked to think out loud while working on a problem requiring a differential equation for its exact solution. These experts used strikingly different representations in solving the problem. Comparisons between their protocols are based on a historical-cognitive approach that ties present-day representational practices of differential calculus to the history and conceptual development of the calculus. Agency, here defined as the task assigned to the problem solver by the representation, is at the heart of this link between past and present practices. Whereas the agency characteristic of the Leibnizian calculus is choice, the agency characteristic of Newtonian calculus is transformation, and that of the modern function-based calculus may, in applied contexts, be characterized as observation and manipulation.