Abstract
A hypothetical learning trajectory line is described for the assimilation and fixation of the concept of height of a triangle for its treatment in pre-university. The theoretical and methodological basis is based on the processes of assimilation, learning trajectories, problem solving and the use of GeoGebra software. This work provides a didactic proposal aimed at the teacher, different from the classic presentation for the treatment of the concept of height, highlighting that the use of the software favors the processes of assimilation of this concept through the dynamic-visual activity, use of the geometric and numerical resource that this technological tool makes possible.
Highlights
The concept of height is a fundamental concept in the study of plane geometry, in particular, its use is indispensable in the treatment of the concept of area and properties of the triangle
Some historical and epistemological data highlight that this concept is developed at the same time as the classical formula for determining the area of a triangle is constructed, since prior to the generalization of this formula and its application to any triangle, the area of a right triangle was first defined, the justification for this consisted of forming a rectangle and taking half the product of the unequal sides of the rectangle; it is here where the concept of the height of a triangle appears implicitly
Considering the previous references and the justification of the object of research, the objective of this work is the elaboration of a hypothetical line of learning trajectory for the assimilation and fixation of the concept of height of a triangle, in the teaching of geometry in pre-university
Summary
The concept of height is a fundamental concept in the study of plane geometry, in particular, its use is indispensable in the treatment of the concept of area and properties of the triangle. To generalise the definition of the area of any triangle, the concept of height is first defined "as the perpendicular to the opposite side of a triangle from a vertex", the length of the height is the length of the segment that goes from the foot of the height (point of intersection of the height with its perpendicular side) to the opposite vertex. In an exploratory study on errors and difficulties of the triangle's notable lines and points in preuniversity students (Morales and Damián, 2021) identified difficulties associated with mathematical thinking processes in pre-university students: examples of notable lines (height, median, bisector and bisector) emerged in particular cases of triangles, the non-standard representations of the figures are a factor of difficulty for students, which led them to make errors in the representation and construction. The difficulties associated with the teaching processes for learning; were manifested in each answer to the questions of the exploration design, since the equivocal or partially correct answers evidenced the need to contribute in the planning tools to improve the learning of the mathematical content at stake
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