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 configuración ontosemiótica. Los resultados revelan algunas complementariedades que nos permitieron mostrar la potencial utilidad del análisis epistémico realizado. Se trata de mostrar la potencial sinergia existente entre dichas herramientas y la posibilidad de avanzar en la articulación de los marcos teóricos correspondientes.

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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.

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 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.

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

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