A study of concrete and formal operations in school mathematics: a Piagetian viewpoint, by K. F. Collis. Pp 205. $10 Australian. 1975. SBN 0 85563 126 0 (Australian Council for Educational Research)

En el presente trabajo se propone contribuir en el fortalecimiento de los procesos relacionados con la generalizacion, uso de representaciones y el uso de la letra, asociados al pensamiento variacional, en estudiantes de grado 5° a partir del diseno y aplicacion de actividades de aprendizaje basadas en problemas. La metodologia para llevar a cabo este proyecto se apoya en el desarrollo de actividades de aprendizaje basadas en problemas, las cuales se denominan como actividades de iniciacion, actividades de afianzamiento y actividades de profundizacion, construidas con base a los estudios teoricos y didacticos sobre el desarrollo del pensamiento variacional en estudiantes de basica primaria las cuales recomiendan el uso de la funcion, la generalizacion de patrones y los sistemas de representacion. Entre los resultados se evidencia el fortalecimiento de habilidades en el proceso de generalizacion, la necesidad del uso de las representaciones para poder comunicar y plasmar lo visualizado y ademas de darle sentido al uso de la letra para representar cantidades indeterminadas o desconocidas, en la solucion de problemas de variacion y cambio

Desarrollo del pensamiento variacional en estudiantes de primaria, a través de actividades de aprendizaje basadas en problemas

Este trabajo tiene como objetivo general analizar, clasificar e interpretar los errores algebraicos que presenta un grupo de 38 estudiantes matriculados en el curso Matematica General de la Universidad Nacional en Costa Rica, que se oferta a diversas carreras. En este estudio, que constituye una replica de investigacion, empleamos un cuestionario centrado en el uso de las letras con diferentes significados, desde etiquetas a variables. Se desarrollo desde el enfoque cuantitativo durante el periodo 2018-2019. Como resultado del analisis se ha detectado que los errores mas frecuentes en las respuestas de los items responden al uso de la letra como incognita de valor especifico, letra como numero generalizado o en el manejo de la letra como variable.

https://dialnet.unirioja.es/descarga/articulo/7579816.pdf

Errores en la comprensión del significado de las letras en tareas algebraicas en estudiantado universitario

Evaluating competencies is not an easy task since they encompass knowledge, attitudes, and skills. The most realistic approach is through a self-assessment where the person who answers it is aware of its purpose. For the construction of this article, the definition of Perrenoud was considered, who refers to competence as the capacity to act effectively in a situation of a defined type, a capacity that is supported by knowledge. The purpose of this study was to design and validate a reliable and pertinent instrument that allows the self-assessment of mathematics teachers’ competencies, considering the socio-training approach. Content validation was carried out with a group of twelve expert judges, applying Aiken’s V and the degree of relevance with a pilot of twenty-eight participants, determined by Cronbach’s Alpha. As a result, adequate levels were reached with minimal observations and a reliable and relevant instrument was concluded.

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Diseño y validez de la escala autoevaluación de las competencias del docente de matemáticas

The purpose of this work was to diagnose previous knowledge of the parabola in freshmen at a university through the conceptual framework of Duval's semiotic representations, in order to develop a didactic proposal that improves their learning. For this purpose, an instrument was designed to assess whether a student understands the main characteristics of the parabola in its various representations, as well as the ability to perform conversions between verbal, algebraic and graphic registers. It was applied to a sample of 55 engineering freshmen before receiving instruction on the topic. It was found that the most difficult treatment activities were the graphic and algebraic records, while in the Conversion activities the lowest performance was observed from the graphic to the algebraic and from the verbal to the graphic. On the other hand, the Treatment activities in the verbal register, and the conversions from the graphic to the verbal, from the algebraic to the graphic and from the verbal to the algebraic were found to be strengths. Therefore, students' prior knowledge of the parabola was diagnosed which will contribute to support a didactic proposal aimed at improving the learning of this topic.

Diagnóstico de conocimientos previos sobre la parábola en estudiantes universitarios

The present investigation is a study with 194 students of the Centro Universitario de la Costa Sur in Autlan, Mexico. It aims to analyze the most common mistakes that first semester students show in the productions, to operate with different meanings that may have letters in algebra and, based on these results, establish its location within one of the four categories of understanding in the use and meaning of letters in algebra proposed by Kuchemann (1980). The results show that more than half of the students at this level of education do not show difficulties in evaluating letters, handling them as objects or considering their presence, however, it does reveal deficiencies in the discernment to understand the use and meaning of the letters as unknown of specific value, numbers, and variables such as widespread.

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José García Suárez

Papers

El Uso de Las Letras como Fuente de Errores de Estudiantes Universitarios en la Resolución de Tareas Algebraicas