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ResumenSe describen los aportes que el estudio de clase brinda a los procesos de formación inicial y cualificación docente en el área de matemáticas. Se explora también las conexiones teóricas plausibles que se pueden generar entre la metodología estudio de clase, la investigación formativa y el conocimiento didáctico del contenido. La metodología empleada se enmarca en el paradigma de investigación cualitativo, privilegiando los alcances descriptivos y exploratorios, mediante la aplicación de la metodología de estudio de clase, con sus fases de indagación-planeación, ejecución-observación y revisión-reflexión. Los resultados evidencian como el estudio de clase favorece ampliamente la cualificación y desarrollo del conocimiento profesional de los profesores, permitiendo establecer una adecuada relación entre el conocimiento disciplinar, pedagógico, didáctico e investigativo. Palabras clave: estudio de clase, estrategia docente, cualificación docente, investigación formativaThe class study, methodology as a strategy and scenario for the mathematics' teacher qualification AbstractThe study describes the contribution that the class study methodology provides to the initial training processes and the teachers qualification in the mathematics area teaching. Also, some valid theoretical connections that can be generated among the class study methodology, the formative research and the knowledge of the educational content are explored. The research methodology can be included in the qualitative paradigm, favoring the descriptive and exploratory scope through the application of a class study methodology and its stages of inquiry-planning, execution-observation and revision-analysis. The results show how the class study favors the qualification and development of the teachers' professional knowledge, allowing establishing an appropriate relation among the academic, pedagogical, educational and investigative knowledge.

This paper introduces a generalization of migrative functions by extending the conditions of the product operation applied in the variables. More specifically, instead of requiring to multiply the variable x by a real number x3B1; in this work we operate this x3B1; number with the variables according to a t-norm. We call such generalization as a t-migrative function with respect to such t-norm. Then we analyze the main properties of t-migrative t-overlap functions and introduce some construction methods.

This paper introduces a generalization of overlap functions by extending one of the boundary conditions of its definition. More specifically, instead of requiring that "the considered function is equal to zero if and only if some of the inputs is equal to zero", we allow the range in which some t-norm is zero. We call such generalization by a t-overlap function with respect to such t-norm. Then we analyze the main properties of t-overlap function and introduce some construction methods.

In this work, using the identification between implication operators and aggregation functions, we study the implication operators that are recovered from overlap functions. In particular, we focus in which properties of implication operators are preserved. We also study how negations can be defined in terms of overlap functions.