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 p… Show more
“…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.…”
In this paper, we analyse the results of an experience designed and implemented to evaluate the epistemic and cognitive conflicts identified in the study of proportionality, carried out by a group of 21 students in their last year of primary education. Initially the students exhibit difficulties to recognize situations where proportionality can be applied, to distinguish magnitudes, quantities and proportionality tables, and to identify procedures to solve proportionality problems other than the rule of three. Nevertheless, in the group discussion session, oriented to develop the dialogue and collective justification of the assessment tasks solutions, they are able to justify the methods employed, linking the rule of three with the equivalence of fractions and the proportionality relation.
“…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.…”
In this paper, we analyse the results of an experience designed and implemented to evaluate the epistemic and cognitive conflicts identified in the study of proportionality, carried out by a group of 21 students in their last year of primary education. Initially the students exhibit difficulties to recognize situations where proportionality can be applied, to distinguish magnitudes, quantities and proportionality tables, and to identify procedures to solve proportionality problems other than the rule of three. Nevertheless, in the group discussion session, oriented to develop the dialogue and collective justification of the assessment tasks solutions, they are able to justify the methods employed, linking the rule of three with the equivalence of fractions and the proportionality relation.
“…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 .…”
Background: Research on mathematics teaching in basic science classes within Peruvian engineering degrees was required prior to the identification of alternatives to improve the training of future engineers. Objective: To identify the criteria that guide the practice of professors in Peru when explaining mathematics in basic science classes within engineering degrees, with specific reference to derivatives. Design: Qualitative case-study research that seeks to understand current mathematics teaching through an analysis of and reflection on the participants' practices. Setting and participants: Professors who give classes within engineering faculties in Lima. One of these was selected as a case study. Data collection and analysis: The classes taught by these professors were filmed and the criteria they follow in the design and implementation of their classes were inferred by means of the didactic suitability criteria, which were also used to design a questionnaire to interview the teachers; triangulation was then performed between their words and their actions. Results: This professor was guided by ecological criteria (syllabus and profession) and mediational criteria (time available for classes), although he felt that his practice was based primarily on cognitive criteria (previous knowledge) and ecological criteria (future profession). Conclusion: The criteria that guided his practice help explain why basic science classes within engineering degrees are taught with a lecture-based and procedural approach, and why innovations are not included.
“…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).…”
Section: Theoretical Backgroundmentioning
confidence: 99%
“…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).…”
Section: Theoretical Backgroundmentioning
confidence: 99%
“…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).…”
Background: Many teachers consider the textbook the primary guide for the curriculum materialisation. This work analyses the content of the rational numbers in a textbook used in the 7th-grade of elementary school. For this analysis, the theoretical and methodological tools of the Ontosemiotic Approach to Knowledge and Mathematical Instruction (OSA) are used. Objective: Our goal was to understand the level of didactic suitability of the instruction process in the textbook. Design and setting: Thus, we analysed a section of the textbook about rational numbers using the categories described by OSA. Concepts, procedures, problem situations, definitions and arguments used by the authors were also analysed. Results: From the results obtained, we could infer that there are examples of the concepts worked in class, but without the proper definitions and arguments, hindering generalisation. The analysis also allowed us to highlight didactic-mathematical knowledge that can guide the teacher concerning the textbooks' possibilities and limitations, to achieve more didactic suitability in the process of teaching and learning rational numbers. Conclusions: the book under study should not be considered as planning for an instructional process to meet the current curriculum guidelines.
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