Las representaciones geométricas para la comprensión de los productos notables (2021)
Eng: This research is part of the area of Mathematics Education, in the line of teacher training, and its purpose is to deepen the teaching of Notable Products (NP). In the study, a historical and epistemological study is carried out as part of the objectives, to show the emergence of the mathematical object in history, which is part of the design of the didactic analysis that is carried out to develop the instructional process of the NP. The didactic analysis is the strategy used to answer the study question: What mathematical and didactic knowledge does the teacher need to enhance in the eighth-grade students of the San Rafael Agricultural Technical Educational Institution, the understanding of the remarkable products, making use of representations and geometric algebra? In this aspect, the didactic analysis is integrated into the subdomains of the teacher's knowledge model for the teaching of mathematics (TKM), which provides tools to design, implement and evaluate the didactic sequences. In the group on Numerical and Algebraic Thinking of the University of Granada - NAT, didactic analysis is defined as the procedure that allows exploring, deepening and working with the different meanings of school mathematical content, for the purpose of designing, putting into practice and evaluate teaching and learning activities. Focused on these two lines (didactic analysis, knowledge of the teacher), the didactic strategy is proposed, which leads to reflection on the TKM model, . based on the design and implementation of the didactic analysis for teaching the NP of eighth grade students giving an answer to the research question: What mathematical and didactic knowledge does the teacher need to empower eighth grade students of the San Rafael Agricultural Technical Educational Institution, the understanding of notable products, making use of representations and geometric algebra? The theoretical and methodological framework that is adopted is the Ontosemiotic Approach to Knowledge and Mathematical Instruction (EOS) that takes up the theory of the Register of Semiotic Representations (RRS), and integrates the didactic analysis and makes operational the components of the Teacher's Knowledge Model for teaching mathematics - TKM. As a result, the document presents an original strategy for understanding the mathematical object of notable products, following a methodology with a qualitative approach and conducting an exploratory-descriptive type of study. The results of the study are presented by means of the elaboration of the didactic analysis for the notable products object. This didactic analysis is structured by conceptual analysis as a first ingredient. Within the didactic analysis proposed by Rico (2013), in which the network of concepts and meanings that articulate the object of notable products is elaborated, providing information for the design and implementation of the didactic strategy and providing elements to achieve compliance with the general objective of the study. It continues with the content analysis, which aims to reach an understanding of the structure and formal analysis of the object Notable products by carrying out a phenomenological study, in this content analysis the semiotic analysis of book II of Euclid's elements is carried out which serves for the design of the didactic sequence in order to identify the partial meanings to be implemented in the process. We proceed with the design of the Cognitive Analysis, in which the dimensions related to learning are studied. It covers the study of educational purposes in its various degrees (guidelines, standards, types of thinking, BLR-Basic Learnings Rights), as well as learning limitations, that is, the difficulties and errors involved in teaching and learning remarkable products. For the cognitive analysis, the diagnostic test necessary for the design of the instruction of notable products is designed, where students' previous knowledge, difficulties and errors are studied to address this mathematical object.