En el marco del enfoque ontosemiótico del conocimiento y la instrucción matemáticos se ha propuesto una caracterización del razonamiento algebraico en Educación Primaria basada en la distinción de tres niveles de algebrización. Tales niveles se definen teniendo en cuenta los tipos de representaciones usadas, los procesos de generalización implicados y el cálculo analítico que se pone en juego en la actividad matemática correspondiente. En este trabajo ampliamos el modelo anterior mediante la inclusión de otros tres niveles más avanzados de razonamiento algebraico que permiten analizar la actividad matemática en Educación Secundaria. Estos niveles están basados en la consideración de 1) el uso y tratamiento de parámetros para representar familias de ecuaciones y funciones; 2) estudio de las estructuras algebraicas en sí mismas, sus definiciones y propiedades.Asimismo, se analizan las concordancias y complementariedades de este modelo con las tres etapas del proceso de algebrización propuestas en el marco de la teoría antropológica de lo didáctico.

A multidisciplinary team collaborated on the development of a learning experience involving 10th grade students using a Science, Technology, Engineering, Arts, and Mathematics (STEAM) approach. The experience was based on the development (conception, implementation, and evaluation) of a science cartoon that aimed to highlight different scientific and technological dimensions related to the diversity of marine worms (Phylo Annelida, class Polychaeta) present in the continental shelf off the coast of Aveiro, Portugal (NE Atlantic coast). The study was implemented in a Portuguese high school in the Aveiro region, involving 24 10th grade students, emphasizing a social context close to the students’ lives. All pedagogical interventions occurred in face-to-face sessions during the 2020/21 school year and were oriented by the following research question: What is the role of science cartoons in establishing STEAM connections for solving real-world problems presented to 10th grade students? Following a qualitative and interpretative research methodology, with a design-based research focus, data were collected through a questionnaire, observations, and students’ written records. The content analysis shows that most students learned new concepts related to STEAM areas. Evaluating the impact of the science cartoon reveals that it can be considered an innovative science communication resource due to its educational potential in stimulating a STEAM approach within the students’ learning process.

La promoción del pensamiento algebraico en alumnos de primaria requiere implementar acciones formativas específicas para los profesores, lo que a su vez implica elaborar instrumentos de evaluación del estado de sus conocimientos didáctico - matemáticos sobre el tema. En este trabajo presentamos resultados del estudio realizado para la construcción de un cuestionario de evaluación de los conocimientos didáctico - matemáticos de estudiantes de magisterio sobre razonamiento algebraico elemental. Describimos las categorías de conocimientos algebraicos tenidas en cuenta (estructuras, funciones y modelización) y las categorías de conocimientos didácticos (facetas epistémica, cognitiva, instruccional y ecológica). Así mismo se describen y analizan las tareas incluidas en el cuestionario informando de la validez de contenido del mismo.

A presente revisão integrativa tem como objetivo conhecer os principais fatores influenciadores dos resultados de estudantes portugueses e brasileiros nas edições do PISA, de 2000 a 2012, de acordo com a literatura publicada. Identificaram-se cinco fatores e dez subfatores. Os fatores mais determinantes nos estudos considerados são o sistema educativo, o contexto socioeconômico dos estudantes e as características das escolas. Esta revisão integrativa evidencia que há uma multiplicidade de fatores que afetam o desempenho de estudantes no PISA, tanto em Portugal como no Brasil. Ressalta também a lacuna significativa de estudos na literatura, havendo fatores que são pouco ou mesmo nada estudados em ambos os países. Existe, assim, uma necessidade de maior investimento em investigação na área, aproveitando o manancial de dados gerados pelo PISA.

This article presents the analysis and discussion of solving geometry tasks by Portuguese Basic Education students, using material from the Poly-UNiverse in Teacher Training Education (PUNTE) project. The teaching experience developed was aimed at testing and disseminating new resources, and innovative and transdisciplinary methodologies in the areas of Science, Technology, Engineering, Art and Mathematics (STEAM). The adopted methodology involved two phases. The first phase was exploratory, followed by a second phase where the exploration of geometry concepts in the plane (namely, the perimeter and the similarity of triangles) was carried out using the Poly-Universe material. The results of the study show that the Poly-Universe materials constituted an important teaching resource in solving the proposed tasks. Its manipulation allowed the visualisation of the situations involved in the tasks, as well as contributed to an implication in the activities developed by the students.

The relevance of data exploration in mathematics programmes at all levels of education led us to develop a learning experience with 1st grade students with the aim of investigating the contribution of investigative activities in the learning of statistics. To achieve this objective, the following research questions were outlined: How do students implement investigative activities when learning statistics? What difficulties do students have in carrying out investigative activities when learning statistics? Adopting a qualitative and interpretative approach, data were collected through students’ written records, the reflections of the teacher, and a written test applied before and after the learning experience. The results obtained suggest that students were able to carry out investigative activities when learning statistics although with some weaknesses, namely defining the topic and research questions, and analysing the data due to the greater complexity of the research proposed by them. Students were able to formulate conclusions, although in some groups the conclusions were underdeveloped. Students were most confident in data collection, organization, and representation activities, with limitations typical of their young age (e.g., written communication). Students also showed difficulties in managing group work and knowledge of statistics, notably concerning strategies of data organization and representation and statistical measures.