Meaningful learning in mathematical modeling activities: an investigation using the conceptual maps

Abstract

This paper consists of an investigation on the use of conceptual maps in the search of evidences of meaningful learning during the development of Mathematical Modeling activities. The research is based on theoretical presuppositions of Mathematical Modeling in Mathematics Education, on the Meaningful Learning Theory and on the use of Conceptual Maps. In this context, the work presents Mathematical Modeling as a way of solving problems and investigates how students’ involvement in modeling activities make meaningful learning feasible. The conceptual maps are proposed as a means of negotiation towards meanings and also as tools for checking signs of occurrence of meaningful learning. In order to search for these evidences in the maps constructed by the students we defined the signaling elements: the concepts used by the students and the interrelations established among them; the relations with power of transference; the signals of progressive differentiation and the integrative reconciliation; the extracontent learning; and the modification or complementation of ‘prerequisites’ or ‘anchorage points’. The data which sustains the research was collected from students of a university course in Technology in Mechanical Maintenance in the disciplines of Mathematical Fundaments and Calculus I and of an extra curricular course. Familiarised with conceptual maps and Mathematical Modeling, the students developed modeling activities and designed maps related to them. In these maps and their explanations we looked for evidences of meaningful learning using the signaling elements in them defined. The information obtained reveals students` progress in the continuous memoristic learning – meaningful learning of mathematical concepts which emerged during the Mathematical Modeling activities developed.