Gloria Sánchez-Matamoros

Algunos indicadores del desarrollo del esquema de derivada de una función

The aim of this study is to identify some indicators of post-secondary students’ development of derivative schema. In order to identify these indicators we use intra, inter and trans levels of development of a schema provided by Piaget and Garcia. We argue that students’ flexible use of the logical equivalence between mathematical elements when solving a problem is an indicator of the development of the derivative schema. This characterization helps to explain the transition between the levels inter and trans of the development of derivative schema.

Thematization of derivative schema in university students: nuances in constructing relations between a function's successive derivatives

ABSTRACT This study is part of a more extensive research project that addresses the understanding of the derivative concept in university students with prior instruction in differential calculus. In particular, we focus on the analysis of students’ responses to a sequence of tasks that require a high level of understanding of the concept, and complement this information with clinical interviews. APOS (Action-Process-Object-Schema) theory and the configuration of the derivative concept that is characterized by: mathematical elements, logical relations and the representation modes that students use to solve a task were used in the analysis of students’ responses. The results obtained suggest that thematizing the derivative schema is difficult to achieve. In addition, nuances were observed in responses given by those students who succeeded, indicating differences in the construction of relations between the successive derivatives of a function.