Learning is an active enterprise, where three dimensions stand out, cognitive, social, and physical, and, in addition, not all students learn in the same way. Grounded on these ideas, this article reports a study that aims to understand and characterize the performance of pre-service teachers when experiencing active learning strategies during their mathematics classes. The participants were 48 future teachers of primary education (3-12 years old) that experienced paper folding, a gallery walk, and a math trail as active learning strategies. We followed a qualitative methodology, collecting data though observations, written productions, and photographic records. The analysis involved a qualitative and inductive approach resorting to content analysis. The results of the study show that the participants valued these experiences, due to their potential in the development of a diversity of mathematical concepts and abilities, and throughout them showed traits of cognitive, social, and physical engagement. Active learning provided collaborative work and mathematical communication enabling the emergence of different strategies to solve the proposed tasks. The participants were able to reflect and be aware of their ideas, mistakes, and difficulties, as well as of others, in a non-threatening environment, where movement was highlighted for not being a popular dimension in mathematics classes. Although more research is needed, the results encourage the use of active learning strategies as a valuable approach to teaching and learning.

STE(A)M education (combining science, technology, engineering, art, and mathematics) has globally become a growing concern, being recognized as having the potential to prepare students for the challenges of the 21^st century. However, the levels of integration of the involved disciplines, as well as their relevance, tend to vary. Engineering design (ED) is being used in educational contexts as an ideal STEAM content integrator to solve ill-structured real-world problems, using the practices of engineering as a problem-solving model. The present study aimed to understand how future elementary school teachers can solve an authentic problem that demands the construction of an artifact, using the ED process in the context of 3D printing, focusing on their performance, the perception of the role of the STEAM disciplines, and the potentials and challenges of computer-assisted design (CAD) and 3D printing. We conducted a qualitative exploratory study with 72 pre-service teachers of elementary education. The implementation was based on a didactical experience focused on solving an authentic problem through the ED process using Tinkercad and 3D printing. The research findings revealed that some of the participants did not follow the ED model exactly as it was presented, skipping or merging steps, but all were able to find a solution and reflect about how to improve it. The majority identified concepts associated with all of the STEAM subjects, although they found it easier to refer to mathematics and science topics. They valued the use of Tinkercad and 3D printing, which allowed them to easily build a virtual model and make it tangible, while also recognizing some challenges in the use of these technological resources. This study can contribute to the scarce literature about the interdisciplinary integration of 3D printing technology in STEAM education, promoting awareness of the overlaps in these disciplines and a more equitable disciplinary attention.

A possible pathway to achieve disciplinary integration is through the use of the Engineering Design (ED) process, starting with problems in a real context that enable the mobilization of concepts from various disciplinary areas. The study reported in this paper aims to analyze the performance underlying the use of the ED process in solving authentic problems in a STEAM perspective, with future teachers of elementary education. We adopted a qualitative and interpretative methodology, with an exploratory design, where data were collected through participant observation, documents, artefacts and photographic records. The results are discussed, taking into account previous research and the data collected throughout the classes, where future teachers solved a problem task and created an artefact and a poster. Preliminary results show that the participants valued the experience and were actively engaged, showing persistence and motivation in solving the problem in a collaborative way, through the different steps of the ED cycle. This approach constituted an opportunity to favor the establishment of connections between different areas, such as mathematics, sciences or arts, detecting the possibility of integrating previously learned concepts. Difficulties were evidenced in the identification of some underlying mathematical and physical sciences concepts, particularly in the mobilization of an adequate scientific language while arguing and making decisions, or in accurately justifying the need to improve the designed plan.

This article discusses the importance of visual models in problem solving, in the scope of rational numbers. We seek to highlight the potential of this approach, as a structuring theme in the mathematical development of students in elementary education and the connections it allows to establish. In order for students to be mathematically competent and creative, they must be able not only to solve traditional computational problems but also to use models/visual representations when solving all types of mathematical problems, including those in which the visual component is not evident. We developed a qualitative study based on a didactical experience involving 14 future teachers who were attending a Didactics of Mathematics unit course that included a module about problem solving with emphasizes in visual approaches. The main purpose of the study was to identify the strategies used by the future teachers when solving problems with multiple solutions, before and after that module. Data was collected through observation and the written productions of the participants. It was possible to conclude that they tended to privilege analytical approaches before the intervention and, after the teaching experience, they started to value visual approaches, which generated an increase of the productions involving this type of solutions.

Creativity is a cross-cutting ability that is highly valued in today’s society. Therefore, it should play an important role in education in general and in mathematics in particular. This requires teachers to create appropriate learning opportunities that allow creativity to flourish in students, helping them to develop their mathematical potential. In particular, the use of rich and challenging tasks can encourage fluency, flexibility and originality as three of the essential dimensions of creative thinking. Based on these assumptions, we developed a qualitative study with 19 elementary pre-service teachers to identify the dimensions of creativity revealed by these participants when solving challenging tasks, as well as their ability to recognize these dimensions in written tasks’ resolutions. Ultimately, we aimed to identify potential tasks that contribute to the development of creativity in future teachers. Data was collected mainly through written productions. Preliminary results suggest that the tasks used have creative potential, with participants demonstrating some of the dimensions of creativity. Flexibility was identified as the most challenging dimension for them to identify.