Patterns and technology: a creative approach to isometries

Abstract

Today’s math education basic syllabus gives an ever increasing emphasis to Geometry and Patterns. Curricula also advocate an approach that allows student to understand the concepts involved supported by dynamical computer tools. However, there is not much research work joining these paradigms. Therefore, a case study was developed, with 9th grade students (14-15 years old), to evaluate the impact of a creative approach to isometries and symmetries—friezes, rosaceas (rosettes) and wallpapers—centered in patterns (reproduction, continuation, completion, description and creation) and using Geometer’s Sketchpad software to solve, mainly in pairs, and discuss, with the whole class, the challenging tasks proposed, involving the formulation of hypothesis, argumentation and justification of the reasoning. The statistical analysis of the quantifiable data and content analysis of the qualitative data, collecting trough enquiry, direct observation and documental analysis (involving questionnaires, field notes, logbook, pre-tests and post-test, other works of the students including those computer related, and internal documents of the school) enable to conclude positively regarding the main research question underlying the study. In fact, it led to the conclusion that the teaching strategy implemented has contributed to deepen the student’s knowledge and skills on geometry, mathematical communication and autonomy as well as to develop a closer relation with the field of geometry itself. This article focuses on one of the cases studied. The pair was selected due to be representative of most students and due to their communication skills.