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.

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.

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.

This article discusses a review of the relationship between art and mathematics in Spanish secondary school mathematics textbooks. The art-mathematics connection identified in the textbooks was analyzed under six dimensions: (1) art for ornamental purposes; (2) art in calculation and measurement; (3) art to master concepts; (4) art to use technological resources in mathematics; (5) mathematical analysis of art; and (6) creating art with mathematics. Dimensions 1, 2 and 3 clearly prevailed over dimensions 4, 5 and 6, which called for more active participation and analytical reflection. Most of the activities attempted to illustrate the mathematics-art connection with real-world examples, but rarely entailed verifying a hypothesis or assumption nor did they encourage critical thinking for analyzing and creating art with mathematical or technological tools

This paper aims to clarify the inconsistencies present in the field of student mathematics-related beliefs. Despite the general agreement about the important role that beliefs play in the learning of mathematics, the study of student mathematics-related beliefs has resulted in a body of uncoordinated research. The lack of consensus on defining and classifying beliefs has generated much confusing terminology, preventing a consistent conceptualization of the phenomenon. To identify the problem underlying existing inconsistencies, we have undertaken a systematic review of the literature to analyse the belief conceptualisations proposed by the most cited authors in this field of research. Our analysis suggests that authors often fail to conceptualise beliefs in four important ways: existing theories related to the phenomenon under research are normally not considered; definitions are often too broad and do not clearly confine the construct under evaluation; and existing beliefs sub-constructs are rarely defined and thus not explicitly distinguished. Our study has also revealed that some of the scales developed to measure the belief constructs lack of content and internal validity. We believe that these findings open new lines of research that may help to clarify the field of student mathematics-related beliefs.

We apply theoretical tools from the onto-semiotic approach to present skill levels on tasks requiring visualization and spatial reasoning. These scales are derived from the analysis of visualization and spatial reasoning skills involved in solving a questionnaire supplied to 400 pre-service primary teachers. In order to set skill levels, we describe different types of cognitive configurations considering the network of mathematical objects involved in solving the items. The results show that there may be several configurations at each level and the levels depend on both certain conditions of the task and the visualization skills required. In most cases, the ratio of students expressing high level is significantly below than those of exhibiting low level. The analysis manifests that students put into play variety and quantity of visual objects and processes; however, most did not reach the solution successfully. This leads to the need for specific training actions.

To help meet an educational and societal requirement for all students to enjoy, have confidence and ability in creativity and technology, the “Kids Inspiring Kids in STEAM” (KIKS) EU project adopted an intensive Hothousing process challenging students in Finland, Spain, Hungary and the United Kingdom to engage in collaborative problem solving to develop solutions to: “How would you get your schoolmates to LOVE STEAM?” The project provided a process and technology toolkit for students, including those with special educational needs, to achieve their solutions.A completion rate of 90% suggested that all schools and students could cope with and enjoy the process and associated technology toolkit, which featured social media plus Micro:bit, Tracker and GeoGebra for data collection and modelling.We have extended the toolkit with simulation software and a graphical programming environment to produce realistic animations of objects in motion. Thus students will have a creativity and technology toolkit to experience the kinds of techniques and skills used by software engineers in the video, games and special effects industries. The toolkit will be on the GeoGebra platform which, in addition to mathematics, embraces STEAM and social media.