Abstract:

The present work has been resulted due to the Program of Multimodal Education offered to the professors at the Morelos State University with the objectives to facilitate the implementation of the traditional courses in the non-conventional learning modalities.

As well since 2010 the University Model is supposed to be focused on the competences.

The linear algebra course is very abstract and highly structured: it consists of 5 modules which development is based essentially on the preceding ones.

The first module is devoted to the fundamental concept of modern mathematics: Linear (Vector) space, which is reported to be the most difficult to grasp in the process of learning due to its abstract nature. This is the highest level of abstraction supposed to be acquired by students in this course.

Thus we design the Forum activities in order to develop such competences as the capacity of abstract thinking and social interaction skills.
The Forum scenery is more adequate for continuous assessment, in our case because every further modules provide more examples of the structure of Linear space in another more abstract context, and also helps to participants to develop critical and reflexive thinking, capacity of communications and auto-expression in new situations as virtual ambient, as well as to organize and plane their own time.

To evaluate the operational skills of computation with algebraic expressions we choose the peer-to peer assessment because there is a sequence of standard problems in the first module which require only applications of algorithms, whose origin and justifications should be understood properly. The Peer Learning within the face-to-face sessions helps to participants to overcome difficulties of symbolic operations and to achieve a deeper comprehension of the significance of the algorithms. The final qualitative evaluation is resulted on the base of diagrammatic representations using software for conceptual maps elaborated by a small group of 3-4 students.

The next two module are devoted traditionally to linear transformations and the theory of systems of linear equations, considered as the crucial algorithmic tool, so that there should be evaluated the competences of Problem solving skills including evaluation of the thinking processes as well as the products: exploration, analyzing and processing the information and the final presentation of results.
Here we have been inspired to use the theoretic framework of Ontosemiotic Approach (OSA) in order to apply the epistemic configurations Malaspina y Font (2010) rather than the so-called solved problem method.


The 4th module concerned another abstract concept, determinants, is short and rather technical, so that we choose the WEBQUEST in order to involve the students in the explorations activities
.
The last module is devoted to the principal objective of the course: to find the simplest representations of a linear transformation constructing the specific base elements in the set of the solutions of some characteristic linear system.
Thus the final exam is realized at present session and is evaluated by external group of professors.

Guiding the adequate presentation of solutions we suggest epistemic configurations to the sequence of problems with increasing complexity.

More information concerned to online-assessments will be communicated.

Keywords:

Online assessment, Epistemic configurations, Linear Algebra.