Abstract

In the next sections I shall describe a 2018;dynamic2019; hypothetical learning path (DHLP) for the learning of the concept of parallelogram in geometry, which helped the students of the experimental team to raise their van Hiele levels. The design of the DHLP started with a 2018;thought experiment2019; with which I imagined a learning path for the understanding of the parallelograms, trying simultaneously to predict the reactions of students. I shall also describe the aims I had posed, as well as the points of the research process in which I changed the route of the path in order to introduce a new tool, due to students2019; cognitive conflicts or other obstacles which occurred. Using examples, I will describe the research process and (a) the design and redesign of the DHLP through linking visual active representations and (b) the students2019; competence in the mental or verbal decoding of these representations and in using the tools that affect their development of the thinking levels. Finally, I shall extend the conceptual framework of Linking Visual Active Representations to introduce what arises from the research process.