Abstract:

We present some experiences in Undergraduate education at the Morelos State University (México) concerned to the new educational model (Blended learning) which provides flexibility in learning processes and formation of subjects. Our educational innovations have been developed in the frames of the research project “Implementation of the innovation strategies in order to attend the educational programs In Mathematics at the Faculty of Sciences”.

We consider that in the B-learning modality the traditional curricula of Linear Algebra course can be enhanced by problem-situations where students can concentrate on important concepts (instead of tedious algebraic manipulations) as well as on their interpretations of geometric and physics nature so that the visualization of many difficult situations in applications may help to grasp the underlying ideas. This approach creates the necessity to design recourses to be implemented in the MOODLE platform, to serve as useful instructions in the process of independent studies.

Analyzing the traditional teaching practice according to the work “Ontosemiotic tools for the analyzing of our own practice” (V. Font, N. Rubio, 2008), it has been detected that there are various complex mathematical objects in the linear algebra course which are not illustrated in the recommended textbooks and, as a consequence, are not explained in traditional teaching instructions.

In our work we rely upon the theory of Ontosemiotic Approach (OSA), which provides a generalized point of view of mathematical objects and their relations in terms of institutional and personal practices. The onto-semiotic approach to mathematical cognition treats the problem of meaning and the representation of knowledge; knowledge is linked to the activity in which the student should be involved. The mathematical activity plays the central role in OSA theory and is modeled in terms of system of operative and discursive practices.

In the light of this theory we propose some teaching resources which can serve for deeper understanding of basic complex mathematical objects and may help to develop intellectual activities. In order to achieve the significant mathematical activity some extra-mathematical problems have been designed to provide the active engagement of students with the real experience. As well as our guiding instructions should motivate students and create genuine interest to study these complex objects so that their multiple representations in different intra and extra mathematical contexts could be properly distinguished.

In our talk much attention will be paid to the principal trajectories which characterize the efficiency of teaching practice according to OSA Theory.

Keywords:

Efficiency of teaching practice, Ontosemiotic Approach, Linear Algebra, b-learning.