Characterization of mathematical thinking
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This research is experimental, and qualitative analysis has its origin in the question posed by Wittenberg (1963): What is the mathematical thinking? Its main objective is to characterize mathematical thinking through feedback of empirical observation carried out with elementary students, second graders and undergraduate students from the region of Baviera, Germany. In this process surveys were implemented for a sample of students from the University of Augsburg, which were analyzed with the CHIC program and in other cases, worked with free forms of expression such as mathematical journals and essays, these were analyzed qualitatively using social hermeneutics. As a result a characterization of mathematical thinking was obtained, which considers five dimensions, four of them are: the dimension of perception, strategies and procedures, related to the content and not rational thinking capabilities. A fifth dimension is given by the thinking styles and media, including representations, basic notions and conceptual metaphors.
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