Estudio numérico de la gráfica para construir su expresión algebraica: El caso de los polinomios de grado 2 y 3

exploring the graphical representation by means of the global interpre-tation allows to establish modifications in the algebraic expression to identify the corresponding visual variable in the graphic, allowing the association of a visual variable within the algebraic expression, contributing to the articulation between such variables. however, developing the global interpretation in polynomials of higher degree than two seems to be a complex task because of the behavior of the trace which makes difficult to identify and interpret the corresponding visual variables that experiment multiple variations. to overcome this problem an alternative was proposed oriented to explore in a qualitative and quantitative way traces to identify the "visual characteristics", information that is enriched with the numerical representation; this allows to identify the content of the parabola and the cubic trace. this proposal was applied in two high-school groups, where students were studying an algebra course (15 to 16 year-old students). the objective of this research is the analysis of the strategies that the students employed when they have had the experience to explore the graphic, numeric and algebraic representations using the global interpretation in situations that demand the construction of the algebraic expression in a graph (straight line, parabola and cubic). during the experience, the students employed the dynamic software cabry géomètry to do the designed tasks.