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http://repositoriodigital.ipn.mx/handle/123456789/11180| Título : | Propuesta didáctica en optimización dinámica: el caso del cálculo de variaciones y la teoría de control |
| Fecha de publicación : | 16-ene-2013 |
| Descripción : | The goal of this research study is to elaborate on and validate a didactical proposal on dynamical optimization. We are going to focus on calculus of variations and control theory. The theoretical background for this study is APOS theory (Action, Process, Objects, Schema). We chose this theory for several reasons. The first being that within its limits the researcher has a frame to observe compare the difficulties the students have when faced to a mathematical concept with the constructions expected from the model. On the other hand, it is important to take into account that this theory has shown to be successful when it has been applied to teaching several concepts. Several research works have demonstrated that students in groups that have followed a teaching sequence based on the genetic decomposition involved in this theory for one or several concepts, show that they have a deeper knowledge of the concepts involved than students who have been taught using other didactical approaches. In this study we present the design of a genetic decomposition. It was based on our experience as teachers of the course to be redesigned, during several years, and on the results of a historical- epistemological study which was carried out at the beginning of this study on the development of dynamic optimization, and in particular, of the Calculus of Variations and Control Theory. The historical research results involved the contexts in which both, Calculus of Variations and Control Theory originated and gave us useful information to include in the above mentioned genetic decomposition. Once we had our genetic decomposition we designed our didactical tools, constituted by a set of seven activities that were designed following the constructions model provided by the genetic decomposition; that is, in each activity opportunities for students to perform actions and interiorize them into processes were provided; to help them construct the mathematical concept of functional and those others linked to it through the idea of variation. These activities are the nucleus of our proposal. Then, validation instruments were designed to be able to assess the didactical proposal presented in this study. Those instruments are three questionnaires and questions for a semistructured interview. These instruments were used with all the students of the pilot group while the course was developed in the semester. Other instruments, as the interviews, were used with a simple of students who were not part of the pilot group and who did not use the didactical proposal. These last students are also in the Economics program but in a theoretical line characterized by more exposition to Mathematics courses. The purpose of interviewing these last students was to obtain some indicators to compare students learning of the concepts and to evaluate the didactical proposal; there was no intention to carry out a statistical analysis of the data. Both the didactical and the evaluation tools’ design were based on the genetic decomposition. Conclusions that can be obtained from the results of this research study are, in general, positive for the didactic proposal. We can mention as some of the most important ones: i) The fact that conceptions of all students in the pilot group regarding all the concepts involved in the proposal related to the concept of functional evolved into richer conceptions, ii) The proposal, in terms of how the course was taught, had a good acceptance by students in the pilot group, iii) The comparison between the pilot group and the Optimization group was favorable to the first one, even though it could be expected the contrary to happen given the curriculum followed by the students in the optimization group. Even though students in both groups seem to show similar conceptions, the numerical results favor students of the pilot group, iv) The teacher of the pilot group, who had a lot of experience teaching these courses, had also a favorable perception of how the didactic proposal worked. Finally we report our results and we come up with some conclusions. The conclusions open up the possibility for further research. |
| URI : | http://www.repositoriodigital.ipn.mx/handle/123456789/11180 |
| Otros identificadores : | http://hdl.handle.net/123456789/696 |
| Aparece en las colecciones: | Doctorado |
Ficheros en este ítem:
| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| campero_2010.pdf | 5.78 MB | Adobe PDF | Visualizar/Abrir |
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