Si bien la evaluación de aprendizajes y el diseño e implementación de estrategias necesarias para ésta son tareas cotidianas del profesorado, cierto es que se carece de conocimiento sobre los criterios empleados por los profesores al momento de llevar a cabo una evaluación, más aun, se desconocen los lineamientos que siguen para el diseño de pruebas escritas y la confiabilidad o alcances de los mismos. En este sentido se presentan los resultados de un estudio sobre la forma en que profesores de educación superior conciben y realizan la evaluación de aprendizajes matemáticos en un curso de Álgebra Superior I. La idea central consistió en asumir a la prueba escrita como componente de un sistema de evaluación.
This paper reports on the characterization of the inductive reasoning used by middle school mathematics teachers to solve a task of generalization of a quadratic pattern. The data was collected from individual interviews and the written answers to the generalization task. The analysis was based on the representations and justifications used to move from particular cases to the formulation of the general rule. Three processes characterize the inductive reasoning of the mathematics teachers to obtain a general rule: observation of regularities, establishment of a pattern and formulation of a generalization; while some teachers revealed problems in moving from the observation of regularities to the formulation of a generalization. Therefore, some difficulties in generalizing associated with these processes are also mentioned.
This article examines the development of professional knowledge in pre-service mathematics teachers. From the discussion of a task associated with the multiplication of consecutive integer numbers, generalization is recognized as a process that allows to explore, to explain, and to validate mathematical results, and as an essential ability to develop in the teaching of arithmetic, algebra, and geometry by using various representations. The study was conducted during three sessions of a didactic mathematics course, in which the instructor and ten students participated. The conversations of each session were recorded on audio and video. It was found that the reflective conversation fosters this knowledge from questions about the nature and processes of construction of mathematical concepts from a mathematical and didactic point of view.
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