Abstract:

This contribution aims to study the progressive implementation of a teaching-learning methodology in a mathematical laboratory, applied to a basic algebraic topic in mathematics: the LU decomposition of a matrix. The methodology used is that of the inverted or flipped classroom (see [2]), a class that relates the work previously done at home using various materials including videos with group activities and classroom projects. This approach combines direct instruction with the perspective of constructivism, and specifically with the theory called Zone of Proximal Development (ZPD, see [1] and [3]), since it can provide meaningful learning situations, oriented towards contexts of engineering and science in general.

The above-mentioned postulates are used because they provide a framework directed to analyzing, explaining and understanding the learning process.This framework is based on psychological and cultural approaches, and it has been adopted in the international agenda on education reform processes, in the case of constructivism, from the 1990s.

The educational intervention focused on the ZPD—ie. at the level of potential development that can reach a subject with the help of other subjects--involves the careful forward planning of teaching. So the teacher becomes a reflective practitioner who takes decisions, implements, evaluates and adjusts progressively according to the subjects knowledge and professional experience.

The main assumptions to test this methodology can be summarized in three phases:
(a) the construction of meanings, in order to present some basic theoretical concepts;
(b) the use of instruments for cognitive development, to show the main ideas on specific examples;
(c) the attention to the ZPD, to structure the knowledge and attitude of the student.

In this third aspect according to Vygotsky’s theory, the capacities to confront different situations and solve problems can be of three types: those that allow the student to solve problems independently (a fundamental part of their work at home); those that do not allow students to solve a problem even with help (because they require other previous learning), and finally those that allow to solve problems but with the help of other subjects (a strategy characteristic of the inverted classroom).

The proposed methodology is addressed to the field of Topography and Geodesy by focusing on the problem of least squares. A brief theoretical approach accompanied with case resolution is proposed first with material offered to the student to work at home. Then it is verified how learning of the algebraic topic takes place with supplementary classroom activities and exercises solved using the software Mathematica, emphasizing the contrasting results with the development of the theoretical and practical process performed. Finally, conclusions about the educational and scientific value of the process carried out are obtained.

References:
[1] Coll, C. et al. (1997). El constructivismo en el aula. Ed. Graó.
[2] Talbert, R (2012). “Inverted Classroom”. Colleagues 9.1
[3] Vygotsky, L. S. (1973). Pensamiento y lenguaje, Ed. La pléyade.
[4] Vygotsky, L. S. (1979). El Desarrollo del los procesos psicológicos superiores. Barcelona, Crítica.

Keywords:

Teaching-learning methodology, meaningful learning, inverted/flipped classroom, constructivist theory.