From Geometry to Algebra and Vice Versa: Realistic Mathematics Education Principles for Analyzing Geometry Tasks

In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.