Mathematical Modeling of isovolumetric transformations: goal-conciliation-theoretic analysis

Abstract

We analyze the pertinence of goal-conciliation-theoretic abductive-deductive architecture to describe and explain cognitive processes in Mathematical Modeling tasks. In achieving this objective, we observed the performance of a group of second-year students in the Technical Course of Chemistry Integrated to High School at the Federal Institute of Santa Catarina of Criciúma campus in the task of modeling isovolumetric transformations with a gas properties simulator. Evidence shows students were able to model the transformations, negotiating collaboratively smaller action plans associated with different modeling phases and cognitive actions, with which, relating Mathematics and Physics-Chemistry, they mobilized the suitable mathematical object from their didactic repertoire; proposed a model; interpreted and validated the results; and reflected on the limitations and potentialities of the model. The study suggests the architecture can contribute to describe and explain cognitive processes in Mathematical Modeling activities, providing the teacher with tools to generate and evaluate didactic interventions.

Keywords

• mathematical modeling
• cognitive pragmatics
• plans of intentional action