El Instituto Politécnico Nacional
Contribuye al desarrollo económico y social de la nación, a través de la formación integral de personas competentes; de la investigación, el desarrollo tecnológico y la innovación. Además tiene reconocimiento internacional por su calidad e impacto social.
Por favor, use este identificador para citar o enlazar este ítem:
http://repositoriodigital.ipn.mx/handle/123456789/11201| Título : | El papel del contexto en la asignación de significados a los objetos matemáticos. El caso de la integral de una función |
| Fecha de publicación : | 16-ene-2013 |
| Descripción : | This work presents the results of a research about the role of the context in the assignment of meanings to the mathematical objects. We focus the attention in the integral of a function. In different works is admitted that the knowledge generated by the human activity is always contextual but little is deepened in the form in which occurs this process. This vision is tied to a not realistic conception of the mathematics, in which there is not conceived the preexistence of the objects that is necessary "to discover". The mathematical objects are constructed like a product of the human activity in the resolution of certain kind of problemic situations. Nevertheless, multiple versions exist about what can be the meaning of the context by an expert and, in this sense, this work tries to reach elements that allow to characterize the context in which the mathematical work develops, as well as its teaching and its learning and to show the determinant role that this one plays in the construction of meanings. The study is realized with the ontosemiotic approach of the mathematical cognition, a pragmatic conception of the meanings, assuming the mathematical practices developed by the individuals and the communities when they face a certain type of problemic situations like the meaning of the object. In the majority of the works realized in the ontosemiotic approach, the context is associated with the problemic situations that generate the practices system. In our thesis we assume a more general vision of the context, composed for the elements of the meaning (components of the meaning) or the mathematical primary objects, that is, the problemic situations self, the language, procedures, properties or propositions, arguments and conceptions that are constructed about the mathematical objects. In our research gets elements, inside of the ontosemiotic approach, about the principal role of the context in the construction of meanings for the mathematical objects, exemplified with the integral of a function. The work is realized to two levels: On one hand a historical and epistemological study of the development of the object "integral of a function", departs from Leibniz's contributions up to Riemann's developments. In this part the study is realized in the frame of the objects and institutional meanings, centering the attention on the experts' community on mathematics. On the other hand, a study is done among some teachers and students of calculus of the school superior levels top of our region, attending the construction of personal meanings of the mathematical objects. Both cases we show the meanings of the mathematical objects of calculus linked to the integral of a function and study its relations with the correspondent context. We use methodological resources of the ontosemiotic approach, mainly the construction of epistemological configurations, cognitive dualities of the mathematical knowledge and the theory of the semiotic functions. |
| URI : | http://www.repositoriodigital.ipn.mx/handle/123456789/11201 |
| Otros identificadores : | http://hdl.handle.net/123456789/834 |
| Aparece en las colecciones: | Doctorado |
Ficheros en este ítem:
| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| grijalva_2008.pdf | 10.48 MB | Adobe PDF | Visualizar/Abrir |
Los ítems de DSpace están protegidos por copyright, con todos los derechos reservados, a menos que se indique lo contrario.