Maestría en Educación
Hacia un método de análisis del Refinamiento de los Universos Numéricos: articulaciones entre la revisión teórica y los experimentos de enseñanza
In the present document, the research conducted by Mendieta and Henao (2022) on the Refinement of the Numerical Universes of prospective mathematics teachers, hereafter referred to as I1, is revisited. The aim is to extend and improve the analysis of the results and the articulation of certain theoretical relationships through a new study, hereafter referred to as I2. To address the two aforementioned issues, I2 articulated a Documentary methodology together with a Teaching Experiments methodology. The Documentary methodology made it possible to: (1) identify the theoretical foundations supporting the possibility of centering the discussion of mathematics teacher education within a proposal framed in Mathematics Education as a Design Science, which, by considering the activities of the student, the teacher, and the researcher, makes it possible to thematize working tools embedded in these activities; (2) make explicit the relationships among the theoretical elements that enabled the analysis of the data and the development of the results presented in Mendieta and Henao (2022), obtained in I1, with the theoretical elements used in research I2. The Teaching Experiments methodology requires praxis and documentation of its evolution in order to subject practice more reliably to analysis and reflection (León et al., 2017). I2 considered the reflective, methodological, and theoretical elements presented in Mendieta and Henao (2022) as part of the documentation of the evolution of the Teaching Experiment carried out during I1. The theoretical articulations obtained in I2 through the use of the Documentary methodology were tested with data obtained in the Teaching Experiment developed during I1 but not used in Mendieta and Henao (2022). The learning environment designed for I1 took place in a mathematics teacher education classroom, recognizing the importance of task design that stimulates students’ activity, activating some of their prior knowledge and allowing students to generate experience in and of a dual subjective process, both individual and collective (Sáenz-Ludlow & Zellweger, 2016). The process of negotiation of meaning (Wenger, 1998) is articulated with the use of Peircean SIGNS for the understanding of mathematical concepts and as an analytical tool, together with diagrammatic thinking, for the researcher in mathematics educatio
Texto completo 111 páginas con texto de 112
Leer la tesis completa Ficha en el repositorio
Contenido
- Introducciónp. 6
- 2. Planteamiento del Problemap. 8
- 3. Antecedentesp. 11
- 3.1 Formación de Profesores de Matemáticasp. 12
- 3.2 Educación Matemática como Ciencia del Diseñop. 14
- 4. Objetivosp. 19
- 4.1 Objetivo Generalp. 19
- 4.2 Objetivos Específicosp. 19
- 5. Marco Metodológicop. 19
- 5.1 Metodología Documentalp. 19
- Educación Matemáticap. 23
- 5.1.2 Refinamiento como Categoría en Uso en Educación Matemáticap. 23
- 5.2 Metodología de Experimentos de Enseñanzap. 26
- 5.2.1 Fase de preparación del experimentop. 27
- 5.2.1.1 Refinamiento de esquemasp. 28
- 5.2.1.1.1 Esquemasp. 28
- 5.2.1.1.2 Set-beforesp. 29
- 5.2.1.1.3 Met-beforesp. 30
- 5.2.1.1.4 Universos numéricos y sus refinamientosp. 33
- 5.2.1.1.5 Pensamiento Matemático como Actividad Semióticap. 36
- 5.2.1.2 Refinamiento de las Comunidades de Prácticap. 39
- Intra Subjetivop. 39
- 5.2.1.3 Refinamiento de las matemáticasp. 42
- 5.2.1.4 Refinamientos de los Ambientes de aprendizajep. 43
- 5.2.2 Fase de Experimentaciónp. 44
- 5.2.3 Fase de Análisis Retrospectivop. 45
- 5.2.3.1 Resoluciónp. 45
- 5.2.3.2 Debate en Pequeños Gruposp. 45
- 5.2.3.3 Exposiciones de los estudiantesp. 70
- 5.2.3.3.1 Los grupos ven los puntos de forma independientep. 70
- 6.2.3.3.2 Los grupos construyen categorías de problemasp. 75
- 5.2.3.3.3 Los grupos constituyen tipologías de problemasp. 78
- 6. Conclusionesp. 81
- 7. Referenciasp. 88
- 8. Anexosp. 94