There continues to exist a dilemma about how, why and when geometry should be
taught. The aim of this study was to examine high school mathematics teachers' beliefs
about geometry and its teaching with respect to its role in the curriculum, the uses of
manipulatives and dynamic geometry software in the classroom, and the role of proofs.
In this study belief is taken as subjective knowledge (Furinghetti and Pehkonen, 2002).
Data were collected from 520 teachers using questionnaires that included both
statements that required responses on a Likert scale and open-ended questions. Also an
intervention case study was conducted with one teacher. A three factor solution
emerged from the analysis that revealed a disposition towards activities, a disposition
towards an appreciation of geometry and its applications and a disposition towards
abstraction. These results enabled classification of teachers into one of eight groups
depending on whether their scores were positive or negative on the three factors.
Knowing the teacher typology allows for appropriate professional development
activities to be undertaken. This was done in the case study where techniques for
scaffolding proofs were used as an intervention for a teacher who had a positive
disposition towards activities and appreciation of geometry and its applications but a
negative disposition towards abstraction. The intervention enabled the teacher
successfully to teach her students how to understand and construct proofs.
The open-ended responses on the questionnaire were analysed to obtain a better
understanding of the teachers' beliefs. Four themes, the formal, intuitive, utilitarian
and the mathematical, emerged from the analysis, which support the modal arguments
given by Gonzalez and Herbst (2006). The findings reveal a disconnect between some
high school teachers' beliefs about why geometry is important to study and the current
position of the Standards Movement; and between whether geometry should be taught
as part of an integrated curriculum or as a one-year course
