María Santágueda-Villanueva

Students’ mathematical problem solving is influenced not only by curriculum and instruction but also by the territorial contexts in which schools operate. This study examines how school typology—Rural, Urban, and High-Diversity Urban—relates to primary students’ performance and cognitive processing in arithmetic word problems. A total of 2,306 students from Grades 1–6 in Castellón (Spain) completed problem-solving tasks for this study using AWPSolver, a digital environment that captures detailed indicators of reading behaviour, problem-solving actions, and efficiency. We analysed success rates, reading and solving times, and efficiency indices using generalized linear models for performance, non-parametric tests for processing times, and correlations between speed and accuracy. Results revealed clear developmental improvements across grades, with older students showing higher success rates and shorter reading and solving times. Rural students tended to show favourable patterns of success and efficiency in several comparisons, particularly in the upper grades, whereas High-Diversity Urban students showed lower estimated success probabilities in some grades and stronger associations between processing time and performance in the upper grades. By integrating outcome and process-based measures, this study provides new insight into how territorial educational contexts are associated with the cognitive dynamics of mathematical problem solving. The findings suggest that school typology relates not only to achievement outcomes, but also to students’ reading and problem-solving processes. These results contribute to research on rural–urban educational differences and offer implications for designing context-sensitive instructional strategies that account for students’ social, territorial, and linguistic environments.

Este trabajo examina las percepciones del profesorado de Educación Secundaria en la provincia española de Castellón sobre la relación entre género, la presencia de las mujeres matemáticas relevantes del pasado y la enseñanza de las matemáticas. Con este propósito, se ha realizado un estudio piloto de carácter exploratorio con profesorado en ejercicio de matemáticas de educación secundaria de la provincia de Castellón, empleando un cuestionario diseñado específicamente para obtener información sobre esta temática. Se destaca la escasa presencia de mujeres matemáticas del pasado en los materiales didácticos, lo que perpetúa estereotipos y limita referentes femeninos. Aunque el profesorado valora la equidad de género y reconoce la importancia de fomentar vocaciones científicas en ambos géneros, se evidencia una falta de formación específica y recursos adecuados. El estudio concluye que es esencial reforzar la formación docente en igualdad y desarrollar materiales inclusivos que integren la historia de las matemáticas desde una perspectiva equitativa.

This study presents “Aula de Apoyo”, a Service-Learning programme in which undergraduate education students provide extracurricular mathematics support to low-achieving Primary learners, particularly those from disadvantaged backgrounds. By applying knowledge from Mathematics Didactics, undergraduates strengthen their teaching skills while helping to reduce educational gaps. A mixed-methods design was used with eight tutor–student pairs. Tutors evaluated their training positively, highlighting the usefulness of the Concrete–Pictorial–Abstract approach, increased responsibility, and the desire for a longer intervention. The findings indicate that Service-Learning supports subject-matter understanding, fosters social engagement, and develops key transversal skills such as empathy and adaptability, thereby contributing to more equitable learning opportunities and aligning with European Higher Education priorities. This study adds to an underexplored line of research by integrating structured extracurricular mathematics support within a Service-Learning framework in initial teacher education. Moreover, the programme helps prepare future teachers to face the challenges of a rapidly changing liquid society, where adaptability and social responsibility are increasingly essential.

Las enciclopedias escolares son una fuente de información fundamental, pero poco explorada, acerca de la enseñanza de las matemáticas en la escuela primaria española durante gran parte del siglo XX. En este trabajo abordamos el tratamiento de un saber aritmético tradicionalmente considerado indispensable: la proporcionalidad. En particular nos centramos en tres focos fundamentales: los aspectos conceptuales, la resolución de problemas de valor perdido y la regla de interés. Nuestro estudio aborda el caso de una importante editorial española, Edelvives, prestando especial atención a su coherencia interna y al impacto que tuvo la publicación en 1953 de los primeros Cuestionarios Nacionales.

This study presents the design and validation of the P-MATHEX questionnaire, an instrument aimed at assessing preservice primary teachers’ perceptions regarding pedagogical knowledge in mathematics and experimental science education. Initially, a questionnaire comprising 50 Likert-scale items and 10 demographic questions was developed and subjected to a cognitive pre-test with 50 preservice teachers from a Spanish university. The instrument was then validated using a larger training sample of 264 participants. Psychometric validation involved exploratory factor analysis (EFA) and confirmatory factor analysis, item discrimination indices, and internal consistency reliability assessed by McDonald’s omega coefficient. EFA results identified five distinct factors: teacher training improvement, methodological shortcomings, applied teaching methods, trial-and-error approach, and student problem-solving difficulties. The revised questionnaire was further validated with an additional sample of 166 preservice teachers. Results confirmed excellent internal consistency (global ω = 0.95) and robust factorial structure (CFI = 0.986; TLI = 0.985; RMSEA = 0.061). The P-MATHEX questionnaire effectively highlighted preservice teachers’ perceived strengths in practical teaching methods and identified areas requiring further training, particularly inclusive education practices and integration of information and communication technologies skills. This validated instrument provides educators and policymakers a reliable and actionable tool to evaluate and enhance teacher education programmes in mathematics and experimental sciences, ultimately aiming to improve pedagogical practices in primary education classrooms.

O Centro de Recursos de Didática da Matemática Guy Brousseau (CRDM-GB) reúne documentos e bibliografia produzidos pelo Centre d’Observation et de Recherche pour l’Enseignement des Mathématiques (COREM), em colaboração com a Université de Bordeaux-I e o Institut de Recherche sur l’Enseignement des Mathématiques (IREM) de Bordeaux. Este centro, ativo entre 1972 e 1999, foi concebido por Guy Brousseau como uma “escola de observação”, com o objetivo de compreender melhor os fenômenos didáticos no ensino da matemática. Além disso, serviu como laboratório para experimentar a Teoria das Situações Didáticas de Brousseau, facilitando a troca entre professores, alunos e formadores. Este trabalho apresenta o CRDM-GB e seus recursos, utilizando como exemplo uma sequência de ensino sobre a iniciação à multiplicação. Por meio de uma análise histórico-epistemológica dos materiais do ano letivo de 1984-1985, são estudadas as dificuldades e os progressos dos alunos dos níveis CE1 (7 anos) e CE2 (8 anos). No CE1, os alunos utilizaram tanto somas quanto multiplicações para resolver problemas, enquanto no CE2 houve uma melhoria significativa no uso da multiplicação. A capacidade de resolver problemas multiplicativos foi consolidada ao longo do ano, embora alguns erros ainda tenham persistido.

: In this study, we present a didactic experience carried out in a public university with 60 students enrolled in the 2nd year of the Primary Education Teaching Degree. This experience consisted of implementing a teaching and learning sequence in which proportionality problems (mathematics content) and pure substances and mixtures (experimental science content) were addressed together in an ecodidactic garden context. This work presents the results obtained through the analysis of the students' responses. Our findings suggest that pre-service teachers have difficulties similar to those of primary and secondary students in the use of measuring instruments and conversion units, as well as in the calculation of proportions in mathematics and conceptual errors at a microscopic and macroscopic level in experimental sciences. This study highlights the need to design and implement strategies to support students in their formative process in relation to the contents of proportion and matter. As an added value in our work, we emphasize the interdisciplinary connection between mathematics and experimental sciences, offering a more real-life perspective of science.

Introducción: Las clases pospandemia por la Covid-19 representaron un gran desafío para las escuelas, con maestros adaptándose a entornos virtuales, híbridos y presenciales, destacando la flexibilidad, creatividad y apoyo socioemocional. Metodología: Este estudio se centra en la perspectiva del alumnado durante el periodo de prácticas del Grado de Maestro en Educación Primaria e Infantil de la Universitat Jaume I de Castellón sobre los materiales usados en los centros escolares para enseñar matemáticas durante tres cursos pospandemia. Se utilizó un cuestionario revisado por expertos, completado por 264 estudiantes, analizando los resultados con SPSS y QCAmap. Resultados: En el curso 2020/2021, el uso del libro de texto fue significativo en ambos niveles educativos, preferido por su conveniencia en la preparación de sesiones, seguimiento del currículum y refuerzo de conocimientos. Sin embargo, en 2021/2022 y 2022/2023, disminuyó su uso, especialmente en Educación Infantil, sugiriendo una menor dependencia de este recurso. En su lugar, se utilizaron numerosos materiales manipulativos y virtuales, desde figuras geométricas y aplicaciones digitales en Infantil hasta libros en línea y juegos interactivos en Primaria, enriqueciendo la experiencia de aprendizaje. Conclusiones: Según el estudiantado, no hubo cambios significativos en las aulas de Castellón pospandemia.