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

Mobile Math Trails: An Experience in Teacher Training with Mathcitymap

Background: Studies show that the outdoors can be a privileged context to promote positive attitudes towards mathematics. Objectives: We aim to address the following questions: 1) Which pros and cons are pointed out by pre-service teachers of elementary education to the use of MathCityMap (MCM)? 2) How can we characterise the participants’ engagement in a math trail performed with MCM? Design: We followed a qualitative, interpretative methodology. The paradigm choice was because the main goal was to understand the perspective and reactions of the participants to a particular situation. Setting and Participants: The participants were 48 pre-service teachers of elementary education attending the first semester of the 3rd year of an undergraduate course at a public higher education institution in Portugal. Data collection and analysis: Data were collected during the classes of a unit course on Didactics of Mathematics. The pre-service teachers answered a questionnaire, followed by the implementation of a mobile math trail. At the end of this experience, the participants filled out another questionnaire. Participant observation and audio-visual records were also applied. Thus, the analysis involved a qualitative and inductive approach, resorting to content analysis. Results: The pre-service teachers were actively engaged during the math trail, showing interest in solving the tasks, using MCM, and focused on finishing the activity, evidencing persistence and will to be involved in the discussions. We also identified anxiety and frustration related to the outcome of a particular task. Strategies of different nature were used, mainly associated to the level of cognitive demand of the tasks. As pros, they considered the app intuitive, promoting autonomy, spatial orientation and collaborative work and highlighted as cons the inaccessibility to Wi-Fi, younger students’ not having smartphones/tablets, and the limitation of answer formats in task design. Conclusions: Results encourage the use of MCM as a valuable tool in outdoor mathematics education

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