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This paper describes the design, implementation and results of a formative action with 61 students for primary education teachers, oriented to the development of the competence of analysis of the didactic suitability of educational videos about percentages. The a priori analysis of the video made by the researchers revealed important deficiencies in the different facets of didactic suitability, being especially relevant those detected in the epistemic dimension. Most of the students for teacher made quite relevant global assessments of the didactic suitability (70.49% considered it between low and medium) basing their judgment on the precision or degree of fulfillment of the suitability indicators in the different components. However, although the suggestions for improvement indicated are quite timely, not all students who identify weaknesses in the videos are able to explicitly make changes to the resource. [ABSTRACT FROM AUTHOR]

This paper presents the results of a research based on the process of reflection on school mathematics of middle school teacher. For this purpose, a three-component theoretical model was configured, articulated with the Socioepistemological Theory. Specifically, it shows how the process takes place: what and how awareness is acquired, what knowledge is constructed and what is transformed. For the analysis we considered a category of meanings and another on the forms of argumentation related to direct proportionality; both categories allowed us to understand the state of the teacher's knowledge at the beginning and at the end of the ref lective process. Among the results we have that the ref lection of school proportionality gives evidence that the change of relationship to this mathematical knowledge promotes the awareness of responsibility for mathematical education and the development of autonomy over mathematical knowledge (both related to proportionality), two aspects that characterize the professionalization of mathematics teachers. [ABSTRACT FROM AUTHOR]

The study of mathematical knowledge in different contexts has acquired relevance due to the current interest in students' ability to use mathematics in solving real life problems. Thus, the purpose of this research is to characterize the knowledge in use in the measurement of inaccessible distances in Johann Stöffler's Elucidatio Fabricoe Ususque Astrolabii, published in 1513. The theoretical model used considers the study of the constitution of knowledge through the analysis of its genesis, development and transversality. The results reveal in the analyzed work an episteme of the measurement of inaccessible distances that includes both the search for a suitable reason to carry out the measurement and the dynamic analysis of the behavior of the shadows or the visual rays in the estimation of inclinations. This episteme is critical for the understanding of this mathematical knowledge in problem solving. [ABSTRACT FROM AUTHOR]

The importance of the arithmetical proportion is unquestionable from two points of view: school mathematics and its practical application. Its importance is reflected in a series of works in the Mathematics Education field, which is our main topic. In this article we show an historical review of some of the main concepts related to the arithmetical proportion, such as ratio and proportion. Besides its importance, as an historical study, we believe that the conclusions that follow this research may be useful in order to improve the teaching of ideas, concepts and techniques involved. [ABSTRACT FROM AUTHOR]