On Transitions Between Representations: The Role of Contextual Reasoning in Calculus Problem Solving

ABSTRACT

This article argues for a shift in how researchers discuss and examine students' uses and understandings of multiple representations within a calculus context. An extension of Zazkis, Dubinsky, and Dautermann's (1996) visualization/analysis framework to include contextual reasoning is proposed. Several examples that detail transitions between modes of reasoning and how these transitions inform students' reasoning in a calculus context are discussed. These examples are used to provide evidence for the usefulness of the model for unpacking student reasoning.

RÉSUMÉ

Cet article propose qu'on change la façon dont les chercheurs analysent l'utilisation et le niveau de compréhension, de la part des étudiants, des représentations multiples en contexte de calcul différentiel et intégral. Nous proposons d’élargir le cadre de visualisation/analyse proposé par Zazkis, Dubinsky et Dautermann (1996) de façon à inclure le raisonnement contextuel. Plusieurs exemples de transitions entre les modes de raisonnement et les façons dont ces transitions influencent le raisonnement des étudiants dans un contexte de calcul différentiel et intégral sont expliqués en détails. Ces exemples servent à démontrer que le modèle s'avère utile si on veut comprendre le raisonnement des étudiants.

Notes

1. These are gestures that accompany “moving” one part of an equation to another place. As an example, subtracting a constant from both sides of an equation moves its location from one side of an equation to another. Gameboard gestures treat this moving of terms as an allowable move in a game where solving the equation is the goal of the game (Wittmann, Flood, & Black, 2013).

2. Although this ambiguous/verbal code is not used in this specific paper, it is included here for completeness. This code plays an important role in identifying representation related phenomena in VAC-related work currently under preparation.