Much comparative education-related beliefs research has exploited questionnaires developed in one culture for use in another. This has been particularly the case in mathematics education, the focus of this paper. In so doing, researchers have tended to assume that translation alone is sufficient to warrant a reliable and valid instrument for cross-cultural research, prompting concerns that a number of necessary equivalences are unlikely to have been addressed. In this paper we consider the nature of these equivalences before examining the literature of a different field, healthcare research, to synthesise an approach to instrument adaptation that is pragmatic but rigorous. Finally, we demonstrate how this pragmatic approach, incorporating extensive cognitive interviews, enabled us to adapt and refine a mathematics-related beliefs questionnaire, developed in Flanders, for use with students, aged 14/15, in England and Spain. Analyses indicate that the instrument so developed is multidimensional, reliable and cross-culturally valid. Some implications are discussed.

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.

In this paper, we offer three examples from our research projects on both technological and pedagogical innovations to illustrate the impact of rapid technology changes on research. Members of our research team both developed and used technology applications in their research projects, utilizing design-based research (DBR). During the experiments, we encountered new challenges by the end of the research cycle due to updates in technologies. Although we had an idea of how to redesign the project for the next cycle based on the analyses of data, we noticed that we needed to not only redesign our approaches based on the research results but the changes in technologies were so rapid that materials and pedagogies needed to be altered as well. In our article, we propose an additional aspect to be considered in DBR while researching technology integration or innovative technologies. Moreover, the rapid change in technology raises further challenges to teachers’ professional development and the integration of those innovative technologies in classrooms. We anticipate our work to contribute to the development of technology resources and related pedagogies as well as the refinement of research methodologies in technology environments. Our contributions for the development of technology resources and refinement of research methods in technology-supported learning environments should, among other things, contribute to a less complex and at the same time more sustainable integration of pedagogical innovations into scientific and school practices.

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.