R. Ramos, A. Aguilar, F. León, O. García León

Universidad Nacional Autónoma de México (MEXICO)
Problem Statement
This investigation aims to prove that a student can achieve to build their own structures to make the apprehension of a mathematical object.

Description of the mathematical object
In the area of numerical computing, interpolation is understood as obtaining new points based on a set of data, usually obtained from some engineering or science experiment which can be viewed as a graph in the plane, so the problem to be solved is: what is the best curve that fits the given set of data?
There are several methods for interpolation or approximation to a function by polynomials, some of which are treated as curve fitting, among them one can mention the Newton polynomial interpolation, Lagrange interpolation polynomials, last squares of linear, quadratic or parabolic, polynomial and geometric curves, Chebyshev polynomials and spline technique (Madhumangal, 2007) or set of curves with segmental or interpolation cubic polynomials of various kinds, among other methods for curve fitting or numerical modeling.

The purpose of this research focuses on learning the Newtonian model, using the mediators of the Zone of Proximal Development, as proposed by Lev S. Vygotsky (Vygotsky, 1979) which argues that both processes, development and learning, interacting considering learning as a factor of development. It is this close relationship between development and learning that stands out and leads Vygotsky to formulate his famous theory of "Zone of Proximal Development" (ZPD). It also stresses that the learning engine is always the subject's activity. In our experiment we seek to foster the development of psychological skills by proposing a set of activities to enable the student to solve problems using Newton's model, assuming that, to achieve just need some structure. Also Vigotskyana theory states that our thoughts, our experiences, our intentions and our actions are culturally mediated, that is the central fact in the theory, which postulates that the human being as a subject who knows, have no access direct objects, and access is mediated through psychological tools, available, and knowledge is acquired, constructed through interaction with others mediated by culture, historical and social development.

It has been observed, the attainment of skills and positive habits that favor the student's apprehension of learning through continuous development. Also it has been to reorient the teaching under these theoretical principles. Thus concludes that it is necessary to promote the formation of habits and attitudes that shape a human kind capable of becoming conscious agent of development, thereby encouraging creativity, capacity for independent learning, critical thinking, discipline and organization in the work, sense of personal and social responsibility.

Vygotsky, L. S. (1979). Desarrollo de los procesos psicológicos superiores. Barcelona, España: Grijalbo-Critica.
Madhumangal P. (2007). Numerical Analysis for scientists and enginners. Theory and C programs. Londres. Inglaterra: Alpha Science.