12. september 2016

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

IND's studenterserie Nr. 50. Specialerapport. Matematik.

Anne Kathrine Wellendorf Knudsen og Line Steckhahn Sørensen, september 2016.

"The Themes of Trigonometry and Power Functions in Relation to the CAS Tool GeoGebra" [7,4Mb]

Vejleder: Carl Winsløw


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 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 where 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.