Abstract:

In the process of construction of knowledge by the students in the B-learning modality the role of the professor is the most important although it depends in major part on the Theory of Learning adopted by the institution.
At the Morelos State University, Mexico, much attention is paid to the formations of students as individuals, whereas the role of a professor is considered as accompanying in the construction of knowledge by the persons in the formation process.

We accept the position of the author in [1] that the constructionist activity is the result of the interaction between the professor, expert in the field of knowledge, who provides the adequate influence through arrangement of the learning environment in the virtual space,
and the students whose mental activity guided pedagogically allows to re-construct the content and to form the personal system of knowledge.

Thus the pedagogical guidance through the instructional components of the course puts the tutor as the key element in the process of the construction of knowledge since the simple activity does not guarantee the significant construction of knowledge due to variety of factors, such as the lack of the cognitive recourses previous to realize the development and correct comprehension of the content [1] .

On the other hand in order to produce the adequate instructional components the tutor needs some theoretical background as well as some tools to evaluate the efficacy of teachers’ own practice. In the process of producing of the learning guides we follow the Ontosemiotic Approach [2 ] for the analysis of our own practice.

The study of determinants in the theoretical aspects presents serious problems for the students of the Linear Algebra course in any of its modalities, present o virtual. Being aware of the crucial role which the visualization plays in learning demand to achieve the comprehension of a concept, we suggest some geometric interpretation which may be used to produce images that accompany the mathematical ideas employed in different context.

We offer some instructional guides with a specific pedagogical objectives in order to provide an environment where one could achieve the personal significance of this notion one of the most difficult to grasp in the contexts of matrices as it is usually taught (especially of the formalization of the definition for the nxn case)
As well the matrix environment is also rather abstract for the students, although both concepts are of great importance in applications to economy and administration (as a technical tools) apart from its theoretical value in the mathematical proofs in many adjacent branches of mathematics.

The Technology of b-learning provides the possibility of familiarizing with contents when a student is short of time or when they are interested more in the applications but need the true understanding of the mathematical nature of contents which underlay the implementation

Finally, these instruction materials can be used for the autodidactic learners en which case the student usually have no previous knowledge, serving for the so-called long-life education.

References:
[1] E.Barberá Los fundamentos teóricos de la tutoría presencial y en línea: una perspectiva socio-constructivista.
[2 ]Godino, J. D., Contreras A., & Font, V. (2006). Analysis of teaching processes based on the ontosemiotic approach to mathematical cognition. Recherches en Didactique des Mathématiques, 26(1), 39–88.

Keywords:

b-learning, determinants, OSA-Theory.