Semantic knowledge in the representation of problems of differential equations as mathematical models
DOI:
https://doi.org/10.22335/rlct.v7i3.523Keywords:
problem solving, modeling cycles, word problems, external representations, extra mathematical knowledge, mathematical modelingAbstract
This article presents the characterization of the semantic knowledge evidenced by a group of students in the external representation to problems of second order linear differential equations as mathematical models. The work was quantitative exploratory and descriptive using a questionnaire in the collection of information. The theoretical support that gave meaning to the study was the two-stage model proposed by Mayer R. for solving mathematical problems, the modeling cycle under the cognitive perspective according to Borromeo Ferri and the theory of representations of Goldin and Kaput. The research focused specifically on the representation phase of the model. Among the main findings is that each participant makes his own external representation to concepts such as: mass-spring system, weight, mass, equilibrium point, constant of elasticity, equilibrium point, Hooke's law, damping force, external force, law of Newton, among others. Difficulties are also evident in the transition from natural language to mathematical language and the external representation of each of the signs, symbols or mathematical expressions involved in the word problem, because the resolver has to construct a mental model of the real situation and translate it into a mathematical model. This demonstrates the importance of semantic knowledge in the translation stage when trying to solve problems as real situations to be modeled.
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