Salinas, P. (2010). - Repositorio Digital - Instituto Politécnico Nacional

considered a systemic action of the four dimensions of knowledge: cognitive, didactical,
epistemological and social, assuming that the latter, social, restates each of the above
dimensions and incorporates social practices and with them, the human activity so
intentionally.
Based on appropriate frameworks are made Epistemological, Didactic and Cognitive
Analysis, outlining a method for addressing the research problem. Within the Cognitive
Epistemological Analysis is included the review of studies that report historical items
related to the numerical procedure under consideration, and the related cognitive
difficulties, as well as reports dealing with the Euler's method in connection with the study
of change. In the Didactic Analysis lies the role of this procedure in the current curriculum,
in particular, Differential Equations, the interest is to distinguish the role of this method in
the structure of the proposal to introduce the Newtonian approach. Finally, the core of
this work is on the Cognitive and Didactic Analysis, where qualitative research is
conducted that includes the monitoring in three semesters in the fall (August-December)
of the appropriation process of the Euler's method located in the classroom and guided by
activities that are refined during this process so that eventually becomes the teaching
sequence, as the product of this research.
As a result we have the teaching sequence for introducing the Newtonian approach in the
teaching of Calculus. The establishment of the applicability conditions that allow its
implementation and analysis of the cognitive difficulties in this process likely accompany
this result.
With the above is provided a didactic material that supports innovation in teaching and
learning Calculus, acting under the belief that educational research must be assumed as a
leading activity of teaching practice, which commits the decision-making and supports
innovation.
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