Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials

Abstract

The study that informs this article was undertaken to investigate the benefits and limitations of using pre-constructed,web-based, dynamic geometry sketches inactivities related to deductive proof at the secondary school level. Two distinct themes emerged from analysis of the results– first, the relationship between the activities and the development of geometric thinking skills, and second, the relationship between the design of the materials, and the exploration process. This article focuses on the latter. An analysis of the data showed that task question and sketch provision must work together to create an environment for exploration. It also indicated that explicit attention to visual interpretation and exploration using change is required in order for students to benefit fully from their experiences with pre-constructed dynamic geometry sketches. This article draws attention to the idea that pre-constructed dynamic sketches(whether web-based or not) and accompanying materials are central elements of the learning activity of which they are a part,and therefore, that decisions about their design have the potential to support or impede the development of exploration strategies and geometric thinking skills. An examination of student responses to particular questions in light of visual and dynamic geometry research suggests that through the materials we may be able to improve students' use of the mathematical investigation process in exploring pre-constructed dynamic geometry sketches.