In this work, we will describe the three basic or fundamental dimensions that distinguish the problems of research in Mathematics Didactics when they are enunciated and proposed. In this way, we postulate a first characterization of the object of study of the Mathematics Didactics and, consequently, of this discipline, under the approach of the TAD 1. However, we do not intend to characterize in an absolute way the object of study of the Mathematics Didactics, since this discipline is still in a foundational and, to a certain extent, pre-paradigmatic historical stage.
We will only try to analyze and relate to each other fundamental characteristics of what we consider didactic problems. These three dimensions, which we will describe in some detail and later exemplify with the case of the problem of elementary algebra, should not be taken as properties obtained from a posteriori analysis of previously defined or established didactic problems, but as defining and constitutive characteristics of the notion of didactic problem, according to the point of view of the TAD.
This means that, instead of starting with a complaint, we know what the didactic problems (which are identified, for example, with the problems related to the teaching and learning of mathematics) and then propose a list of characteristics of them, we will act the other way around. We assume the general epistemological principle that states that scientific problems are not given in advance, but that they are generated and evolved together with the discipline that constructs in our case, we will construct and enunciate the didactic problems with the tools that the TAD provides us in its current state of development.
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Undoubtedly, the resolution of problems is the line on which the greatest number of efforts has focused, both for what has been written on the subject and for the development of research projects in the last 30 years and, consequently, the one that Momentum has provided to mathematics education. Perhaps the reason is that it is nourished by the essential aspects of the mathematical task: the problems and the typical actions of thought that intervene in the solution process. The study and incorporation of these aspects, as well as the clarification of how to carry out actions that contribute to the resolution of problems, is due to who, due to the customary failure of his students in the learning of mathematics, proposed design a method that could help them learn to solve problems, which he called How to solve it? Thus marking a new direction in the study of problems related to the teaching and learning of mathematics is applied.
Here we highlight two important approaches arising from these studies: the first is related to the design of problems or tasks that are useful in the teaching of mathematics, and the second has to do with the implementation of a form of instruction that combines the workgroup of students, in small groups and throughout the class. In this context, the present work is located; the assignments were designed so that students express what they know and are willing to investigate what they do not know through discussion and exchange of experiences. Some questions that guide the development of the study are:
What forms of mathematical understanding and solution methods appear during problem-solving processes? What forms of instruction favor student learning? What is the role of the teacher during the development of the sessions of application of the tasks? What does it mean for students to learn math?
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It is urgent that students can check superiority of research assignment paper, which is the basis of customer administration, it relies on customer approval and it can help to get more work and can assist in developing great relations. In effect, their theoretical and methodological approaches became the line of research that has advanced the most progress and development in mathematics education. But this did not happen immediately; it was not until the 1970s that work began to be widely recognized, once the emerging community of mathematical educators saw in its method a useful methodology for the teaching and learning of mathematics, establishing a new line of research and development. In addition, it is responsible for the incorporation of heuristic processes and monitoring and control as fundamental ingredients in solving problems and, therefore, in mathematics education.