A visual approach for solving problems with fractions

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.0D1E-4824-1244 | Ana Cristina Coelho BarbosaN/

Math trails: meaningful mathematics outside the classroom with pre-service teachers

This paper presents a study about the potential of the construction of math trails as a non-formal context in the teaching and learning of mathematics. This research is of qualitative nature and was developed with future teachers of basic education. It can be said that these future teachers showed a more positive attitude towards mathematics, broadening their perspective about the connections that can be established between mathematics and everyday life. Results suggest as well that despite the construction of the trail not being easy, as well as the process of designing the tasks that focused mainly on geometry, it was possible to identify traces of originality and involvement on the part of the participants.0D1E-4824-1244 | Ana Cristina Coelho Barbosainfo:eu-repo/semantics/publishedVersio

The exploration of friezes and rosettes through digital and non-digital resources in a teacher education program

This paper describes a study that aims to analyse the performance of future teachers of primary education (6-12 years old) in identifying and constructing symmetries, especially friezes and rosettes, with different resources (paper/pencil; software). To carry out this investigation we followed a qualitative methodology and collected data through observation, written productions, artifacts and photographic records. The participants were fourteen pre-service teachers that attended a Master’s Degree Course in Primary Education (6-12 years old). These pre-service teachers had a unit course about geometric transformations, refining their knowledge about the theme, through the analysis and exploration of each transformation, resorting to examples of applications in mathematical contexts or in other areas. The participants were also motivated to identify/construct friezes and rosettes using paper and pencil. After a period of appropriation, they explored the same aspects of geometric transformations in a dynamic environment provided by the software Gecla, doing it in the classes of another unit course. Results show that the pre-service teachers valued this experience, considering it useful and effective in the development of mathematical knowledge concerning geometric transformations and symmetries. They easily identified symmetries with both resources and were comfortable with the construction/generation of friezes and rosettes. They exhibited difficulties in identifying the motif/module that generates some friezes/rosettes, in both environments. The main difficulties evidenced, either with paper and pencil or with the software, were related to the characterization of some friezes and rosettes.0D1E-4824-1244 | Ana Cristina Coelho Barbosainfo:eu-repo/semantics/publishedVersio

Mathematics creativity in elementary teacher training

Creativity plays an important role in mathematics learning, so teachers must provide students with appropriate learning opportunities. This means using tasks, in particular those with multiple solutions and/or multiple resolutions, that usually require creative thinking and it could be a possible way to promote creativity in students. In this paper, we identify some traits of creativity in elementary pre-service teachers through tasks productions used during math classes.0D1E-4824-1244 | Ana Cristina Coelho Barbosainfo:eu-repo/semantics/publishedVersio

Visualization in pattern generalization: potential and challenges

This study tries to understand how pre-service teachers, for basic education, solve problems involving the generalization of visual patterns, identifying: the strategies used; the difficulties presented; the role of visualization in their reasoning; the factors that influence their generalizations. We followed a qualitative methodology. The participants were 80 pre-service teachers. During the classes of a Didactics of Mathematics unit course, they solved a sequence of tasks involving growing visual patterns. Results showed that students were able to use different strategies, but also that some dimensions of the tasks can have impact in their reasoning, provoking, sometimes, a shift on the strategies used and the emergence of difficulties of different kind.0D1E-4824-1244 | Ana Cristina Coelho Barbosainfo:eu-repo/semantics/publishedVersio

Feedback and written mathematics communication: a pen pal exchange

This paper describes a study that aims to understand and characterize the written communication of future primary education teachers in a context of a pen pal exchange with 3rd grade students (8 years old), in particular the nature of the feedback. We followed a qualitative methodology, where data were collected through observation, written productions (letters) and an interview with the participants. Each future teacher was paired with two students, and four letters were written by the participants over the course of ten weeks. The first letter had the intent of presenting themselves and knowing the recipient. In the following letters the dialogue was continued and the pre-service teachers posed challenging mathematical tasks for the students to solve and for them to give feedback. We focused our analysis in the quality of written communication/feedback, the perceptions of future teachers about the potential of this experience and difficulties experienced. The dynamics of the correspondence exchange allowed the records to be prepared with great commitment. When selecting the tasks, they realized the importance of knowing the curricular guidelines, as well as the contents that the students were addressing. The tasks posed varied from exercises/problems centred on contents addressed by the students. The feedback sent was quite diverse. In some cases, it was not informative, and was even quite superficial; in other situations, the comments provided indicated hints for future action, seeking to promote learning. The exchange of correspondence by letter enabled the sharing of ideas, access to mathematical knowledge, the formulation of tasks, promoting the development of written communication.0D1E-4824-1244 | Ana Cristina Coelho BarbosaN/