Análisis didáctico de una lección sobre proporcionalidad en un libro de texto de primaria con herramientas del enfoque ontosemiótico

Abstract

Resumen El libro de texto es un recurso ampliamente usado en la práctica de la enseñanza y, en consecuencia, es objeto de investigación educativa, aplicando diversas perspectivas teóricas. En este trabajo se ejemplifica el uso de las herramientas teóricas del Enfoque Ontosemiótico del conocimiento y la instrucción matemáticos para realizar el análisis didáctico de una lección sobre proporcionalidad de sexto curso de primaria (11-12 años de edad). Se considera que una lección refleja el proceso de instrucción planificado por el autor como medio para lograr el aprendizaje del contenido por parte de los estudiantes potenciales del mismo. En consecuencia, se plantean las siguientes cuestiones que guían el análisis: 1) ¿Cuál es el grado de idoneidad didáctica del proceso de instrucción planificado? 2) ¿Cómo gestionar el uso del texto para incrementar la idoneidad del proceso? El método de análisis implementado permite obtener conocimientos didáctico-matemáticos que pueden ayudar al profesor a tomar decisiones sobre las posibilidades y limitaciones de los libros de texto cuando se asumen los postulados socioculturales sobre el aprendizaje matemático.

Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education

“…The intervention was developed after the students had finished the study of proportionality with a methodology based on the use of the textbook. The lesson used as an instruction guide was the same analysed in Burgos, Castillo et al (2020). This allows us to reveal some conflicts of meaning that should be taken into account when it is intended that students develop proportional reasoning, which requires, on the one hand, that procedural knowledge be enriched with the understanding of the concepts and properties involved, and by another, that the justification of the answers to the proposed tasks be favoured.…”

Criteria That Guide the Professor's Practice to Explain Mathematics at Basic Sciences Courses in Engineering Degrees in Peru. A Case Study

“…The notion of didactic suitability is a tool that is widely used, firstly, to analyse didactic sequences (and their redesigns) that have been designed and implemented by teachers with a view to improving mathematics teaching (Breda, 2020;Morales-López & Font, 2019;Sousa, Gusmão, Font & Lando, 2020), and, secondly, to organize the reflections of future or active teachers on their own practice in teacher training programmes (Esqué & Breda, 2021;Giacomone, Godino & Beltrán-Pellicer, 2018;Morales-Maure, Durán-González, Pérez-Maya & Bustamante, 2019;Seckel & Font, 2020), since it allows teachers to engage in systematic reflection on the complexity of the mathematical objects they teach and the factors involved in studying these. This tool has also been used for the analysis and assessment of textbook lessons (Burgos, Castillo, Beltrán-Pellicer & Godino, 2020) and for the design and assessment of mathematical tasks .…”

Textbook: an Analysis in the Light of the Ontosemiotic Focus on Rational Numbers

“…In this sense, the onto-semiotic configurations guide the identification of epistemic conflicts related to the meanings and institutional objects that come from the lesson and cognitive conflicts related to previous knowledge required in the development of the section. They also consider the various meanings of mathematical objects and the identification of objects and processes that emerge from the required mathematical practices (Burgos et al, 2019).…”

“…The didactic suitability, according to Burgos et al (2019), helps formulate the problem of didactic analysis of books in terms of characterising the suitability of the didactic trajectories proposed and identifying possible changes to improve student learning. The epistemic, cognitive, ecological, affective, mediational, and interactional dimensions, which are part of the didactic suitability, and their coherent and systemic articulations, allow us to evaluate a suitable instructional process, so we can adapt the personal meanings achieved by the students, and the meanings intended by the teacher, according to the context and resources available (Godino, 2017).…”

“…The epistemic dimension refers to the degree of representativeness of the institutional meanings implemented or intended, regarding a meaning of reference; the cognitive dimension refers to how close the personal meanings achieved are of the meanings intended or implemented; the ecological dimension refers to the degree to which the study process adjusts to the educational project of the school and society and the conditioning of the environment in which it develops; the interactional dimension refers to the didactic trajectories that allow us to identify the semiotic obstacles and allow us to overcome the difficulties that appear during the instruction process; the affective dimension refers to the interest of students in the study process, and the mediational dimension refers to the degree of availability and adequacy of the material and temporal resources necessary for the development of the teaching-learning process. All these dimensions can serve as a basis for the organisation of a textbook analysis guide that reflects the many variables that should be considered (Burgos et al, 2019).…”