Abstract:

The concept of function is one of the fundamental concepts in mathematics, but also it is one in which students struggle to develop a satisfactory understanding. The reasons why students have difficulty with this concept seem to be focused on its complexity and generality, because it has many facets and contains a multiplicity of representations, along with a variety of related concepts that manifest with different levels of abstraction (Díaz, 2008).

In this research we report the results of our study of the comprehension of linear function through its parameters: Slope and y-intercept, in environments where educational software plays an important role.

We present some activities developed for the visualization during experiments with linear functions realized with software of dynamic geometry Geogebra, which permit the students to achieve the comprehension of linear models.

The benefits of this software, allow students to build and explore the construction of the linear function, then to observe and draw mathematical properties from the interpretation of the changes in the parameters of the algebraic expression, slope and y intercept. We consider that the software allows students to carry out a process of visualization during the experimental activity performed with representations of the linear function. Furthermore, the solution of problems is used in this proposal as a heuristic instrument allows to discover and interrelate critical and reflective thinking with creativity and inventiveness needed to implement the transformation and facing problematics. The design of the sequence for its use was conducted during a school semester. The participants were a group of students of Upper Secondary education in their first semester of the College of Sciences and Humanities of the National Autonomous University of Mexico, CCH-UNAM aged between 15 and 16 years. The theoretical posture of this research is supported by the Ontosemiotic Approach of Mathematics Cognition (Godino, Batanero and Roa, 2005; Godino, Contreras and Font, 2006; Godino 2007, Font et al 2007), as a research methodology, we use the epistemic and cognitive configurations, to interpret the production of students in different problems and contexts.

From the analysis of the results, after the activities, we observed that students inclined in the first instance to represent the phenomenon graphically, some students who do not have graphics when they were interviewed, showed they have in mind the image of the graphic associated with the phenomenon and only present an algebraic representation of the situation, and in second term there are algorithmic processes that were the way to solve problems of linearity. In addition they were able to establish a graphic relating the studied phenomenon before identifying the algebraic operations that should be performed.

Keywords:

Mathematical Cognition, Software Geogebra, Linear function.