Evaluation of the Knowledge of Future Teachers of Mathematics about the Transformation of the Representations of a Function

Authors: Tulio R. Amaya De Armas, Luis R. Pino-Fan, Antonio Medina Rivilla

Abstract: In this paper the mathematical dimension of the Didactical-Mathematical
Knowledge of the future teachers of mathematics is analyzed when they
transform the representations of a function. A questionnaire was applied to 90
future teachers who were distributed in three groups. The homogeneity of the
answers per group is analyzed, and the primary mathematical objects and
the present process in the mathematics practices they develop trough their
answers are characterized. The results show serious difficulties of the future
teachers with some function topics, such as: indetifying and using their intercepts
without a graphical support; analyzing their extreme values and growth ranges;
making a mathematical model or a graphical draft; indetifying the slope of a
linear function. The primary mathematical objects and present processes in the
practices that the prospective teachers develop are very similar, in spite of the difference
in the number of hours od instruction in each of three gropus.

Keywords: future teachers, function, semiotic representations, mathematical




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