Mathematics in the Classroom: Conceptual Cartography of Differential Calculus
Mathematics in the Classroom: Conceptual Cartography of Differential Calculus

Summary/Abstract: This paper presents the results of a documentary investigation with the intention of substantiate how and why, and the level and depth of the topics used by the teacher in the classroom for the development of the mathematical knowledge on the part of higher level engineering students. The analysis of the mathematical object was made through the construction of conceptual cartography, being the core of the derivative concept. To construct the axes, the socio-formative theory of Sergio Tobón was used, together with the semiotic representation register of Raychmond Duval and Tall's mathematical advanced thought in the engineering context. The topic is a part of the Unit of learning: Differential and Integral Calculus. This corresponds to the first semester. The course lasts for a semester and is intended for students aged between 18 and 20 years. The research shows that by constructing a conceptual cartography involving at least 8 axes of analysis that the socioformation orientates, and taking mathematics in the context of careers offered by the educational institution, the teacher is allowed to place the thematic content in the appropriate level and depth, guiding in a possible treatment of knowledge to be brought into the classroom.

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