Dpto. Ciencias de la Educación

Investigadores y corrientes didácticas, como la Early Algebra, recomiendan introducir el pensamiento algebraico desde los primeros años de la escolarización, incorporando tareas de generalización de patrones, relaciones y propiedades. En este trabajo se estudian las respuestas de 106 estudiantes de Educación Primaria a un problema de generalización de patrones, analizando el nivel de éxito, los grados de desarrollo y la utilización de estrategias y se realiza un estudio de casos. Se ha comprobado que los estudiantes de Primaria están preparados para trabajar la generalización de patrones y que las estrategias más usadas en los cursos inferiores son las aditivas y en los cursos superiores las funcionales.

Background: This research shows how the identification of conceptual advances (CA) that determine the transition between the stages of a progression model in a learning trajectory will help prospective primary teachers (PPT) to develop the teaching competence “professional noticing of students’ mathematical thinking”. Conceptual advances are key moments in the construction of mathematical structures and involve a change in the way students understand mathematical relationships. (2) Methods: A teaching module has been designed in which students of the Teaching Degree will analyze the responses of primary education students to tasks of pattern generalization from the identification and use of conceptual advances. (3) Results: The results of the teaching module show that professional noticing can be developed in suitable teaching environments. (4) Conclusions: The recognition of conceptual advances helps to interpret students’ thinking and learning trajectories which are effective tools to structure and develop professional noticing.

Early algebra proposes to incorporate algebra in primary school from the first years of schooling. The success of this incorporation depends, to a large extent, on the training of teachers, so the objective of this article is to study whether the degree of algebraic knowledge of student teachers at the beginning of their training. To conduct this, 106 preservice teachers were given a questionnaire. This survey is based on two daily life situations. They had to propose tasks to develop algebraic reasoning in primary school students. Most of the participants designed tasks in which they assigned specific values to the indeterminate ones and solved them arithmetically. In this way, they transformed open situations and numerous opportunities to promote algebraic thinking in students through the generalization and representation of relationships and functions into closed single-solution problems that do not promote algebraic thinking. We can see from the results that the participants’ algebraic knowledge is insufficient. Therefore, it is necessary to include in their training process the programs and experiences that will allow them to design tasks in order to detect and promote algebraic thinking in their future students. Sequences of tasks are presented to develop both situations by generalizing and representing relationships and functions, which can serve as a starting point for future training programs and experiences.

Durante el aprendizaje de los números naturales en la Educación Primaria, el estudiante adquiere la concepción de número como cantidad de magnitud con soporte en el mundo físico y concreto. Posteriormente, la generalización de esta concepción a otros campos numéricos supone un obstáculo epistemológico que dificulta su aprendizaje. Este estudio pretende determinar estos obstáculos epistemológicos en el aprendizaje de los números enteros, verificar su presencia en los errores y en las justificaciones que realizan los estudiantes y presentar sugerencias metodológicas que faciliten la ruptura con los obstáculos para mejorar la enseñanza de los números enteros. / During the learning of the natural numbers in Primary Education, the student acquires the conception of number as quantity of magnitude with support in the physical and concrete world. Later, the generalization of this conception to other numerical fields supposes an epistemological obstacle that hinders its learning. This study aims to determine these epistemological obstacles in the learning of the integer numbers, verify their presence in the errors and in the justifications made by the students and present pedagogical suggestions that facilitate the break with the obstacles to improve the teaching of the integer numbers.

El objetivo de esta investigación es estudiar cómo estudiantes para maestro (EPM) proponen acciones para mejorar el proceso de enseñanza‐aprendizaje de alumnos de Primaria a partir del análisis de sus respuestas a un problema de generalización de patrones. Las acciones propuestas por los EPM se clasificaron en tres categorías: actitudinales, genéricas y concretas. Los resultados muestran que algunos EPM se limitan a hacer comentarios sobre la actitud de los alumnos, que los EPM proponen más acciones a los alumnos que tienen dificultades en la resolución de los problemas y que pocos EPM son capaces de plantear acciones de forma concreta especificando una tarea. Como conclusión se reconoce que uno de los aspectos a mejorar en la formación y desarrollo profesional de maestros es la capacidad para proponer acciones adecuadas para mejorar la enseñanza‐aprendizaje de los alumnos. / The aim of this research is to study how Prospective Primary Teachers (PPT) propose actions to improve the teaching‐learning process of Primary students through the analysis of real answers to patterns generalization problems. The actions proposed by the PPT were classified into three categories: attitudinals, generics and concretes. In the results it was observed that some PPTs are limited to commenting on the attitude of the students, that the PPTs propose more actions to the students that have difficulties in the resolution of the problems and that few PPTs are able to plant actions in a concretes way specifying a task. In conclusion, it is recognized that one of the aspects to improve in the training and professional development of teachers is the ability to propose appropriate actions to improve the teaching‐learning of the students.