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] [3]
and [4]), 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, since the 1990s.
The educational intervention focused on the ZPDi.e. at the level of potential development that can
reach a subject with the help of other subjectsinvolves 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 and according to
Vygotskys 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 how learning of the algebraic topic
takes place with supplementary classroom activities and exercises solved using the software
Mathematica is verified, 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.