Official documents in several educational systems reflect the importance of integrating Science, Technology, Engineering, Arts, and Mathematics (STEAM) and consider project-based learning (PBL) as a way of integrating such disciplines in the classroom. Although STEAM-PBL has been characterized and evaluated in different ways, its impact on school mathematics teaching remains unclear. Mathematics is recognized as the fundamental basis of other disciplines; however, many students still perceive it as a difficult subject and abandon it. To analyze STEAM-PBL classroom implementation from a school mathematics standpoint, we examined 41 classroom experiences from 11 Spanish secondary education teachers (five in-field mathematics teachers), who participated in a STEAM training program for more than 4 years. To frame this study, Thibaut et al.’s (J STEM Educ 3(1):02, 2018) and Schoenfeld’s (Educ Res 43(8):404–412, 2014) characterizations of well-designed and implemented projects, respectively, were employed. The results showed that in-field mathematics teachers avoided transdisciplinary projects in which school mathematics is difficult to address, while out-of-field teachers tended to overlook the mathematics in interdisciplinary projects. Unlike out-of-field teachers, mathematics teachers often eluded design-based learning processes for deeply exploiting school mathematics. The latter teachers promoted high cognitive demands and positive perceptions about mathematics in projects where formative environments were generated through discussion and a meaningful feedback loop.

Secondary education curricula highlight competence-based learning; however, meaningful school-intervention habits have not yet been observed. The initiatives implemented have focused primarily on promoting the combined development of no more than three key competences. This article presents an international study, under the Erasmus+ and H2020 programmes, for analysing the impact of the STEAM project-based learning approach with KIKS format (Kids Inspire Kids for STEAM) on the interwoven development of key competences. The sample included 267 high school students divided into 53 teams from 29 educational centres in Finland, England, Hungary, and Spain. Each team carried out several projects, for no less than two academic years, by means of the following two approaches: STEAM project-based learning and KIKS format. Data from this qualitative study were collected from observations and interviews with students, teachers, and KIKS trainers. Analyses revealed that the combination of these two approaches facilitated the development of all eight key competences. The project-based learning focus essentially fostered the enhancement of the mathematical competence and competence in science, technology, and engineering, while KIKS format promoted literacy and multilingual competences. The remaining competences were encouraged by the combination of both approaches. It is noteworthy that prolonged participation in the programme, as it was implemented, was crucial to achieving the obtained outcomes. Los currículos de educación secundaria resaltan el aprendizaje por competencias, sin embargo, actualmente no se observan cambios sustanciales en los hábitos de intervención en el aula. Las iniciativas implementadas se han centrado principalmente en impulsar el desarrollo conjunto de tres competencias clave como máximo. Este artículo presenta un estudio internacional, bajo los programas Erasmus+ y H2020, con el objetivo de establecer relaciones entre el aprendizaje basado en proyectos STEAM con formato KIKS (Kids Inspire Kids for STEAM) y el desarrollo global de las competencias clave. La muestra incluye 267 estudiantes de secundaria distribuidos en 53 equipos, pertenecientes a 29 centros de Finlandia, Inglaterra, Hungría y España. Cada equipo elaboró varios proyectos, durante al menos dos años académicos, mediante los siguientes enfoques de implementación: aprendizaje basado en proyectos STEAM y formato KIKS. Los datos de este estudio cualitativo se recabaron por medio de observaciones y entrevistas a estudiantes, profesores y formadores KIKS. Los análisis revelaron que la combinación de ambos enfoques facilitó el desarrollo de las ocho competencias clave. El aprendizaje por proyectos favoreció esencialmente el desarrollo de la competencia matemática y competencia en ciencia, tecnología e ingeniería, mientras que el formato KIKS potenció las competencias en lectoescritura y multilingüe. El resto de competencias se vieron estimuladas por la combinación de ambos enfoques. Cabe destacar que la participación prolongada en el programa de implementación fue determinante en los resultados obtenidos.

Creating mathematics tasks provide opportunities for students to develop their thinking, reasoning, communication, and creativity. This paper presents a study on teaching pre-service teachers to create realistic mathematics tasks in real contexts and amending them through an iterative process of analysis and refinement. The study was undertaken with pre-service teachers from two university training courses in Spain, undergraduate students from a primary teacher training course, and graduate students from an educational Master’s course. The students worked in groups to collaborate in the creation of the requested tasks and improvement of them based on critical thinking and creativity. The tasks were not only evaluated concerning their level of realism, but also regarding their level of authenticity, the cognitive domains involved, and their openness characteristic. These are the key characteristics related to environmental and sustainability aspects. The outcomes confirmed that the creation of realistic mathematics tasks was a challenge for future primary teachers; however, they were able to create tasks with high levels of cognitive domain, authenticity, and openness. This evidences, on the one hand, the difficulty that future teachers have in understanding the realism of a mathematics task, and, on the other, the possibilities offered by the task’s creation and the revision activity, which has educational implications and opens paths for future research.

This article is aimed at educators concerned with curricular initiatives that foster STE(A)M projects in secondary education to promote mathematics competencies. Research has recently reported that these projects superficially address mathematics content, hampering the development of competencies the consensus deems necessary to prepare citizens for daily life. This study shows that learning goals may be achieved when teachers receive personalised training and sustained assistance in their project experiences. We examine how two Spanish teachers, with advisors’ support, progress in exploiting mathematics competencies within the implementation of a single project each over a period of 3 years. Their evolution was not the result of minor recommendations but of continuous interactions with the advisors. These interactions intended to maintain a balance between teacher confidence and project enhancements, which required commitment and constancy. Four of the five competencies considered in the Spanish curriculum emerged powerfully after sustained refinement. The frequently mobilised competencies were intra-mathematics, representations, as well as collaborative work and positive identity, followed by modelling. The last of which was difficult to address, but when it was, the other three emerged more naturally. Computational thinking was poorly represented mainly because of the advisors’ background and its recent incorporation into the reference curriculum. The teachers’ progress was influenced by the advisor’s academic background, pedagogical expertise, ability to transfer research outcomes into teaching, and experience supporting others.

A suitable mathematics teaching requires the teachers’ knowledge and competence for identifying the variety of objects and meanings involved in solving school tasks. This article describes the design, implementation and retrospective analysis of a formative cycle directed to prospective mathematics teachers, which is focused on developing this onto-semiotic analysis competence. For this, some theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and instruction are used. In this experience, the prospective teachers first solve some visualisation and diagrammatic reasoning mathematical tasks, and then analyse the objects and meanings put at stake in the resolution of each implemented task. In addition, the strategies that students produce in their solutions are discussed and shared in whole-class setting. The data analysis is qualitative oriented to identify significant didactical practices about the initial state of students’ personal meaning, recognition of conflicts, and progress in developing the intended onto-semiotic analysis competence. For this purpose, the students’ written responses, observer researcher’s notes, and audio recordings on the class are used as a data collection instrument. The results reveal the complexity involved in developing this onto-semiotic analysis competence, as well as its relevance to achieve high quality mathematics teaching. Finally, the retrospective analysis of the formative design carried out allows the teacher, and researcher reflecting on each of factors that condition the teaching processes, and thus determining potential improvements for future implementations.

Para comprender las dificultades y conflictos de aprendizaje, es necesario analizar las tareas matemáticas y los diversos modos de abordarlas por los estudiantes. Dicho análisis, que precisa herramientas teóricas específicas para su realización, aporta información útil para el propio diseño de las tareas y la gestión de los conocimientos en el aula. En este trabajo realizamos el análisis de una tarea que requiere la formulación de una conjetura y su demostración haciendo uso de representaciones figurales y algebraicas, aplicando dos herramientas teóricas diferentes: las nociones de registro de representación semiótica y de configuraciónontosemiótica. Los resultados revelan algunas complementariedades que nos permitieron mostrar la potencial utilidad de los análisis epistémico y cognitivo realizados. Se trata de mostrar la potencial sinergia existente entre dichas herramientas y la posibilidad de avanzar en la articulación de los marcos teóricos correspondientes.