Abstract:

Using the concepts of sociocultural learning theory, has experimented with college students to prove that it produces satisfactory results in the acquisition of knowledge of numerical objects and professional development

One of the most important aspects in scientific computing is the numerical solutions of mathematical models expressed in terms of differential operators. This research presents a method of solution that, is considered one of basic methods in the literature related to the numerical solution of ordinary differential equations, is to say, the improved Euler method (Madhumangal, 2007), also known as the name of Heun method or Euler-Gauss method. This method is intended to resolve, as do several other methods, the mathematical model of the ordinary differential equation.

Improved Euler's method is one of the methods of solution, step by step, through the operation of integration and the solution can become established through the use of Taylor polynomials, or by using the Newton interpolation polynomials, or using a geometrical construction (B. Rai, 2008).

The object of study of this research focuses on learning the improved Euler method, using the basic concept of the zone of proximal development as proposed in his theory Lev Vygotsky (Vygotsky, 1979), who argues in this theory that the two processes, ie learning and development interact with each other and also believes that learning is 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). In the experiment we seek to foster the development of psychological skills by proposing a set of activities to enable the student to solve problems using Euler's model, assuming that, to achieve just need some structure. Also Vigotskyana theory states 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. Thus, awareness of how you learn, will only be possible when the student was located and interact with the environment in which they live and the university may be considered one of the principal means for individual development. (Labatut, 2004)

It has been observed, the attainment of skills and positive habits that favor the student's apprehension of learning through continuous development. . 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, and discipline and organization in the work.

Keywords:

Numerical Solution, Differential Equations, Zone of Proximal Development.