Zapatera Llinares, Alberto

The objective of this research is to study the Scratch programming language as a didactic tool to teach functions. The introduction of didactic tools allowing comprehension in simple and attractive ways is required. Given the traditional teaching/learning system, it is necessary to organize participatory and collaborative dynamic classrooms, which allow the interaction of students in activities where the educator modifies his or her traditional role as an advisor and the students take a more active role in learning through their own effort. In this sense, three activities using the Scratch programming language are proposed: the first one refers to the linear and affine functions, while the second one deals with the quadratic function and the third one is related to the exponential function. The participants in this study were 30 future teachers. The study considers the combination of magisterial lessons and active didactic methodologies as demonstration method, cooperative learning and gamification, also including the applied assessment. The activities, methodologies and assessment were evaluated by the participants with results higher than 4 in 5-point Likert scale for all cases, preferring the active methodologies than magisterial lessons.

Educational robotics has come to the classrooms and is here to stay. STEAM (Science, Technology, Engineering, Arts and Mathematics) learning has put the use of robots in classrooms in vogue, though these are mostly closed products and at a high price. The educational innovation project “Design, implementation and tests of a modular low-cost educational robotics platform” from the University of Las Palmas de Gran Canaria, expects to design an open, modular and low-cost educational robot to make robotics more accessible. One of the challenges which the project hopes to accomplish is for this robot to be able to adapt to any educational level, thanks to its modularity, from pre-school to university levels. This study analyzes the Industrial Design and Product Development Engineering degree students’ level of acceptance. Therefore, an analysis of the currently most used educational robots at any level has been made, comparing them to the project design. Moreover, a survey was passed to a total 78 students from several degrees to compare the level of acceptance, concluding that students show a general interest in the proposal, but not so among those of the study group, probably due to the lack of robotics knowledge. / La robótica educativa ha llegado a las aulas para quedarse. El aprendizaje STEAM (Science, Technology, Engineering, Arts and Mathematics) ha puesto en boga el uso de los robots en las clases pero, en su mayoría, son productos cerrados y a un alto precio. El proyecto de innovación educativa «Diseño, implementación y puesta en práctica de una plataforma modular de robótica educativa de bajo coste» de la Universidad de Las Palmas de Gran Canaria pretende diseñar un robot educativo abierto, modular y de bajo coste para hacer más accesible la robótica. Uno de los retos que pretende alcanzar es que dicho robot, gracias a su modularidad, sea capaz de adaptarse a cualquier nivel educativo, desde infantil hasta grados universitarios. Este estudio analiza el nivel de aceptación por parte de los estudiantes del Grado en Ingeniería en Diseño Industrial y Desarrollo de Productos, realizando un análisis de los robots educativos más usados en la actualidad en todos los niveles y comparándolos con la propuesta del proyecto. Además, se realizó una encuesta a 78 alumnos de ingeniería, concluyendo que muestran un interés general por la propuesta, pero no tanto entre los del grupo de estudio, probablemente debido a la falta de conocimientos de robótica.

Los excelentes resultados obtenidos por Singapur en las últimas pruebas PISA 2015 y TIMMS 2015, han provocado un gran interés por el denominado Método Singapur de aprendizaje de las matemáticas. El marco curricular de Singapur tiene como centro de aprendizaje la resolución de problemas matemáticos y se basa en cuatro aspectos fundamentales: el enfoque CPA (concreto - pictórico - abstracto), el currículo en espiral, las variaciones sistemática y perceptual y la comprensión relacional. Estos aspectos se fundamentan en las ideas de Jerome Bruner, Zoltan Dienes y Richard Skemp. En este trabajo, tras presentar el sistema educativo de Singapur y el marco curricular, se estudian las aportaciones de estos autores y sus concreciones en el Método Singapur y se extraen una serie de conclusiones para su adaptación. / The latest mathematics assessment tests, PISA 2015 and TIMMS 2015 have caused a great interest in the Singapore Method of Mathematics Learning. The Singapore curriculum framework, which has as a learning center the resolution of mathematical problems and which is developed through four fundamental aspects: the CPA approach (Concrete – Pictorial - Abstract), the spiral curriculum, systematic and perceptual variations and relational understanding. The Singapore Method is based on the ideas of Jerome Bruner, Zoltan Dienes and Richard Skemp. In this work, after presenting the Singapore educational system and the curricular framework, the contributions of these authors and their concretions in the Singapore Method of learning mathematics are studied.

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.

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.

New technologies have offered great alternatives for education. In this context, we place robotics and programming as innovative and versatile tools that adapt to active methodologies. With the arrival of COVID-19 and lockdowns, physical resources were kept out of use, and the virtual lectures did not propose to incorporate these elements in a meaningful way. This recent situation raises as an objective of study the need to evaluate if robotics and programming are content that can be taught virtually in these circumstances, without physical resources and without face-to-face lectures. To do this, a mixed methodology consisting of questionnaires and interviews has been incorporated, aimed at primary education teachers, families, and primary education grade students. The results suggest that the virtualization of robotics and programming is a feasible and beneficial alternative for students, which allows the development of digital skills, while it is enhanced with the use of audiovisual materials and online resources. Even though face-to-face classes have other benefits not offered by virtualization, and teacher training needs to be up to the task to face this situation, it is a matter of time to respond to these situations and to guarantee a high-quality distance education.

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.

Tradicionalmente se ha pospuesto el estudio del álgebra a la Educación Secundaria, pero investigaciones en didáctica de las matemáticas han demostrado que el pensamiento algebraico puede ser desarrollado desde edades tempranas. En los últimos años han surgido corrientes como la Early-Algebra que proponen la introducción del álgebra desde los primeros años de escolarización y consideran que una de las vías más eficaces para ello es la generalización de patrones. En este artículo, tras estudiar el proceso de generalización de patrones, se presenta una secuencia de tareas a desarrollar en Educación Infantil y en Educación Primaria. El objetivo de este trabajo es animar a los maestros a introducir el pensamiento algebraico en sus alumnos y proporcionarles una herramienta que puede servirles de referencia en su práctica docente. / Traditionally the study of algebra has been postponed to Secondary, but research in didactic of mathematics has shown that algebraic thinking can be developed from early age. In recent years have been emerging currents such as Early-Algebra that propose the introduction of algebra from the first years of schooling and consider that one of the most effective ways to do this is the generalization of patterns. In this article, after studying the process of generalization of patterns, is presented a sequence of tasks to be developed in Pre-school and Primary Education. The aim of this work is to encourage teachers to introduce algebraic thinking in their students and provide them a tool that can serve as a reference in their teaching practice

This article presents a STEAM project, “Sustainable City”, based on educational robotics whose objective is to bring the problems of climate change closer to primary school students. The participants were 30 students (aged 10–11) from 5th year of Primary Education and the project consisted of 14 sessions in which different active methodologies such as project-based learning, collaborative learning and the flipped classroom were carried out. A pre-test and a post-test were carried out and the results were better in the post-test, which indicates that the students improved their skills and increased their motivation. As a conclusion, this STEAM project, which is adapted to the Spanish LOMCE curriculum, can be a reference for other teachers to bring their students closer to the problem of environmental change through educational robotics and the use of active methodologies.