Abstract:

Geometric transformations have undeniable applications in daily life, allowing the establishment of rich mathematical connections. However, it is not only outside mathematics that this happens, opportunities can be created to identify relations with other areas of mathematics, contributing to the development of a more sustained knowledge. This theme allows students to explore/create patterns, solve problems and think spatially, fundamental abilities in the scope of geometric transformations, Geometry, and Mathematics in general. Taking these ideas into account, we should be concerned with the fact that students generally show a low level of learning regarding geometric transformations. This scenario reflects on the known difficulties with the teaching and learning of this theme since elementary school levels. Research suggests that the approach to this theme should be based on concrete experiences of observation and manipulation, since the underlying thought is linked to the understanding of the properties of the figures. Classes should be of exploratory nature, privileging the use of resources that promote the understanding of concepts/procedures. Research also supports the assumption that appropriate technology/media-supported instruction can help with learning in a variety of domains, including geometric transformations. So, technological tools may be useful to develop visual skills and overcame some difficulties.

With this study we intend 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 conduct this investigation, we followed a qualitative approach. The participants were 14 future teachers enrolled in a Masters Course. Data was collected during the classes of two unit courses through: observation, written productions and photos. 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. The most used functions of the software were: Search for symmetries, Classify/Generate Friezes and Rosettes.

Results show that these pre-service teachers easily identified symmetries with both resources (paper and pencil; Gecla) and were comfortable with the construction/generation of friezes and rosettes, since it is a step-by-step process. They exhibited difficulties in identifying the motif/module that generates some friezes/rosettes, in both environments. Gecla allowed them to develop an intuition in some of these cases and increased their motivation due to its dynamic features, being able to test their conjectures. In spite of valuing the potential of the software, sometimes they felt the need to recur to paper and pencil to support their reasoning. The main difficulties evidenced, either with paper and pencil or with Gecla, were related to the characterization of some friezes, in particular of the rotational symmetry.

Keywords:

Geometry, Digital resources, Non-digital resources, Pre-service teacher education