Diseño de un proyecto de aula que contribuye a la enseñanza de la operación división mediante la resolución de problemas en el pensamiento numérico en expresiones algebraicas en el grado 8

Toda actividad matemática necesaria para la enseñanza, busca fundamentar el aprendizaje de enfoque significativo desde los conceptos que soportan el conocimiento de objetos abstractos, que permitan definir y luego redefinir los entornos y contextos que conforman la realidad de un ser social. En la enseñanza, el error es un elemento que puede tener facetas que dificultan o favorecen el aprendizaje. El significado que se le dé al error por parte del docente, define la estructura del aula de clase, su metodología, herramientas didácticas y pedagógicas, planificación de tiempos y actividades de evaluación de competencias o desempeños. En matemáticas, el error presenta algunas características que se vuelven repetitivas en los estudiantes, que por obligación o decisión, inician el recorrido que propone un área del conocimiento de objetos abstractos como lo son las matemáticas. Para que el error en el proceso enseñanza-aprendizaje se convierta en posibilidad para un proceso de comprensión, es necesario diseñar situaciones problema y didácticas que muestren el proceso de construcción de un concepto y no entregar el concepto terminado, absoluto, inmutable a través de los contenidos. Lo anterior se soporta en el hecho de que saber la definición memorística de un concepto, no es garantía de que el concepto se comprenda, y si no se comprende, no es significativo; se convierte en un conocimiento momentáneo, fugaz, reciclable. De forma general, no es la definición de un concepto lo que se recuerda, es la imagen conceptual que el individuo ha construido del concepto por medio de la experiencia o la razón.Abstract. All mathematical activities necessary for teaching seek to base the learning of a meaningful approach from the concepts that support the knowledge of abstract objects, that allow to define and then redefine the environments and contexts that make up the reality of a social being. In teaching, error is an element that may have facets that hinder or favor learning. The meaning given to the error by the teacher, - 7 - defines the structure of the classroom, its methodology, didactic and pedagogical tools, time planning and assessment activities of competencies or performances. In mathematics, the error presents some characteristics that become repetitive in the students, that by obligation or decision, they initiate the route that proposes an area of the knowledge of abstract objects as they are the mathematics. In order for the error in the teaching-learning process to become a possibility for an understanding process, it is necessary to design problem and didactic situations that show the process of constructing a concept and not delivering the finished, absolute, immutable concept through the Contents. The above is supported by the fact that knowing the memoristic definition of a concept is not a guarantee that the concept is understood, and if it is not understood, it is not significant; It becomes a momentary, fleeting, recyclable knowledge. In general, it is not the definition of a concept that is remembered, it is the conceptual image that the individual has constructed of the concept through experience or reason. It is understood by conceptual image, "something" nonverbal that is associated in our mind that identifies the concept. The division operation into algebraic expressions requires a rigorous and dense conceptualization, since the process of division in general is a simultaneous process of addition, subtraction and multiplication. This is why the conceptual image of the division operation in algebraic expressions is a didactic and pedagogical strategy proposal that allows to collect isolated concepts of addition, subtraction and multiplication in algebraic expressions, to construct the proper concept of the division operation in Algebraic expressions, through a proposed classroom project. A classroom project, bases its structure on three moments: contextualization, methodological and evaluative. Each moment is made up of elements that allow to systematize the teaching-learning exercise. In contextualization, the problem, the object, the objective and the knowledge are fixed. The methodological is shaped by the method, the group and the media. And finally, the evaluation evaluates the - 8 - achievement of the objective, by solving the problem that directs the design of the project