# MATHEMATICAL KNOWLEDGE TRANSFERENCE

This research is meant to influence university studies where mathematics is not a goal in itself. Due to the mathematical richness that prevails in engineering, the research is of interest particularly to these areas of study. An engineer requires to work with mathematical modeling. In fact he needs an interdisciplinarity work, he requires mathematical knowledge transference.

It is important to mention that mathematical modeling and knowledge transference are two concepts which are indeed related (Camarena, 2000). The first one is conceived, in Mathematics in the Context of Sciences theory, as the cognitive process that has to be carried out to construct the mathematical model of an event or an object of the context area (Camarena, 2000). While knowledge transference refers to the cognitive process which allows transfer of knowledge from one science to another (Camarena, 2004); that is to say, the knowledge transference needs the knowledge already learnt to be used in new situations.

The mathematical knowledge transference is a superior ability, it is part of the hidden curriculum of university careers. This problematic situation is undertaken by the international investigation net MaCoCiencias (Mathematics in the Context of Science in Spanish). Among the research being done to tackle the described problematic situation is the research reported in this paper.

The research objective is: To investigate if students, who had never modeled mathematically, (a) can tackle successfully each step of the contextualized event resolution process to transfer the knowledge, as well as, each stage of the mathematical modeling cognitive process when they undertake a contextualized event, and (b) how this is correlated with their cognitive resources in terms of mathematical content knowledge.

This is an exploratory type research. It is a case study, where well trained engineering students are investigated when they have to transfer knowledge to solve a vibrating string event. This task develops in one of the most complex mathematics area in engineering careers: multi-variable functions. This point guarantees that the knowledge transference indicators are inside of cognitive structure of the students.

For this purpose the research is founded in the Mathematics in the Context of Sciences theory, particularity in the knowledge transference indicators of the didactic phase of the theory are taken into account, as well as the steps of the contextualized event resolution process and the cognitive process of mathematical modeling. It is shown the problematic when students have not worked contextualized events, as the mathematics in context didactic strategy is, so the mathematical knowledge transference can not be achieved.

While searching, it was founded that with bigger mathematical cognitive resources there is a tendency to transfer the knowledge. Also, when the student knows about mathematics concepts and discipline context concepts involved in the event it will be easier to develop his abilities for the contextualized event resolution process and the mathematical modeling cognitive process, so then the mathematical knowledge transference is obtained. Another result is that the abilities for the mathematical modeling cognitive process, in fact, the abilities for knowledge transference, are helped when different contexts for one mathematical concept are introduced in the classroom.