Lenguaje, escritura y conceptualización matemática

• Autores: Alfonso Javier Bustamante Santos
• Directores de la Tesis: Jorge Vaca Uribe (dir. tes.), Rosa del Carmen Flores Macías (codir. tes.), Gustavo Martínez Sierra (codir. tes.)
• Lectura: En la Universidad Veracruzana ( México ) en 2014
• Idioma: español
• Enlaces
  • Tesis en acceso abierto en: cdigital.uv.mx
• Resumen
  • español

    La didáctica de las matemáticas, en el contexto de la educación básica mexicana, se ha orientado principalmente haciala enseñanza misma, a través del diseño y aplicación de situaciones didácticas cada vez más afinadas sobre los diferentes contenidos matemáticos. Consideramos que esta didáctica podría complementarse con el tipo de trabajo que proponemos, más centrado en la psicología del aprendizaje. Nuestros resultados muestran la necesidad de explicitar las ideas que los estudiantes construyen sobre los contenidos matemáticos, sobre sus representaciones simbólicas y sobre sus procedimientos que podrían ser útiles para mejorar el diseño y desarrollo de las situaciones...

  • English

    Teaching mathematics, in the context of the Mexican basic education, has been primarily oriented toward teaching itself, through the design and implementation of increasingly refined teaching situations on different mathematical contents. We sustain that this approach could be enriched by the kind of work we propose here, more focused on the psychology of learning. Our results show the need for specialists to become aware of the ideas that students build on the mathematical content, their symbolic representations and procedures, because that could be useful to design and improve mathematical situations.

    In Chapter I the research is introduced and the problem statement is expressed as well as the justification and background. It highlights the work of the program research Written Language and Basic Mathematics: acquisitions, practices and usages, from which this work derives. In recent years, this research group of the Universidad Veracruzana has explored psychological, sociological and anthropological features of the acquisition and use of written language and mathematics in the basic education. This thesis seeks to understand in depth the role of the representations mobilized by students to solve a problem. Finally, in this chapter the competency-based curriculum in basic education is reviewed, as well as problem solving as a hub for the teaching of mathematics and as a tool for evaluation and research.

    In Chapter II we expose the theoretical framework of the research: the theory of conceptual fields, the operational representation theory (La théorie opératoire de la répresentation) and the situated microgenesis approach. Although we recognize that there are multiple research paradigms in the field of mathematical education, we limit ourselves to that conceptual frame.

    In Chapter III we present the research design and methodological tools, which the empirical work was performed with: the experimental design, clinical interview and microgenetic analysis. We describe the empirical referent and the stages and characteristics of the data collection.

    Chapter IV reports the results of the first phase of empirical exploration. These results were the inputs to the publication of a research article (curricular requirement of the doctoral program, Bustamante and Vaca, 2014). In Chapter V we make the microgenetic analysis of a case, which was also the basis for the development of the second article required (Bustamante and Flores, in press).

    In Chapter VI we analyze 30 clinical interviews with a selected group of students who participated in the previous phase. In the last section we present the conclusions and final thoughts. Finally, we annex the PHD student's translation of the last publication that we know about the Theory of Conceptual Fields written by Gérard Vergnaud, in order to divulgate it.

    Results obtained in this research indicate that language and writing help make explicit the concepts and theorems-in-action of the students, to test them and eventually orient their transformation toward more conventional forms.

    The work also identified the need for students to differentiate the representation systems and rebuild their own rules and conventions, in order to use them properly. Only in this way those systems can assume the role of tools that support the reasoning, encourage reflection and help maintain control of the activity during the resolution process, while supporting working memory and finally make the proper communication of the procedures used and the results obtained. Without such clear differentiation and subsequent correspondences, instead of working as useful tools for solutions, the diversity of representations becomes a source of confusion that complicates and blocks those solutions.