Abstract

This thesis is a study of teaching and learning Geometry, and, in particular, angles. The theoretical framework used in the research is a combination of a teaching theory called Realistic Mathematics Education (RME) and a learning theory called the can Hiele Model of Geometric Thinking. These frameworks, backed up by a historical study of geometry, were used in the design, experimentation and evaluation of a lesson where fourth grade students were introduced, for the first time, to the idea of angle and relations between angles of different sizes. The in-class experiment was conducted in two different fourth grade classrooms. The lessons were taught by teachers of the respective classrooms, based on a detailed script and materials prepared by the researcher. At the end of the lesson the students answered, in writing, questions on what they had learned during the lesson. These answers, combined with the classroom observations, provided a basis for the evaluation of the experiment. The written answers were categorized into analytical and narrative statements. The analytical statements were divided into the different levels of the van Hiele Model. The narrative statements were divided into whether or not they mentioned angles. The research findings suggest the usefulness of using lesson plans based on the two theoretical frameworks in helping students develop an analytical conceptualization of mathematics.