The Themes of Trigonometry and Power Functions in Relation to the CAS Tool GeoGebra, 1

Supervisor: Prof. Carl Winsløw, IND

Censor: Prof. Morten Misfeldt, IND

Abstract

In the curricula for the Danish high school as well as for the written examination for mathematics (regardless of the level), it is evident that CAS tools have a significant role in connection with the teaching of mathematics. This thesis investigates the implementation of a CAS tool in a high school and the learning outcome of the students in relation thereto. The teacher’s way of organising and exploiting the CAS tool in his/her mathematics teaching is also considered since it has a great influence on the students’ work with the tool. The findings of the thesis are based on an observation study of high school teaching has been performed, in the two mathematical themes Trigonometry and Power Functions, in two different classes, having different teachers, where GeoGebra (GG) functions as a CAS tool.

For the observation study, four research questions (RQs) have been developed with the Anthropological Theory of Didactics (ATD) and the notions of instrumented techniques and orchestration as theoretical framework. Additionally, a reference praxeological model (RPM) for both of the themes has been established in order to answer the RQs. Each RPM consists of a profile of the theme, involving scholarly knowledge, and a presentation of the curriculum and teaching material. Finally, an a priori analysis of the CAS tool is included in the RPMs.
The CAS tool, GG, is found to be a versatile tool whereof the visualisation and dynamic properties are considered a significant strength, in relation to examining several examples of a mathematical object. This thesis finds that it may however be difficult for the students to relate the praxis performed in GG to mathematical conceptual knowledge in general. The observed students managed to perform techniques in relation to GG to a greater extent than establishing a knowledge block. In relation to GG related work, both teachers were observed to make use of a projector but, apart from this, their orchestrations were very different with regards to how GG could be approached as a CAS tool.