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

Abstract

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.