When learning Geometry, students may tend to memorise properties, relationships, and formulae and may even attempt to solve problems mechanically. However, Geometry provides students with opportunities to engage with logic and reasoning beyond only symbols, but within spatial contexts as well. There is a tendency that Geometry, as it stands in the curriculum, is interpreted and subsequently taught as a list of separate, unrelated bullet points. Secondly, Geometric elements tend to be memorised according to their appearance, or their definitions are simply memorised without understanding. This qualitative case study underpinned by the Van Hiele theory aimed to explore the “big ideas” that permeate the effective teaching of Geometry, and how these “big ideas” promote an understanding of the connectedness between concepts in Geometry, Measurement, Number, and in the environment. Data were collected from 15 mathematics teacher educators across 10 Higher Education Institutions in South Africa that participated in a Primary Teacher Education project, which focused on developing new teacher graduates’ ability to teach Geometry and Measurement. Data was collected via document analysis, questionnaires and focus group interviews. The study found that geometrical properties, measurement, transformations, invariance and visualization are the big ideas that permeates the teaching of geometry and measurement. These “big ideas” has the potential to influence how mathematics teacher educators re-organize and sequence their teaching and learning activities on geometry in pre-service mathematics teacher education curricula in connected ways. Furthermore, pre-service mathematics teachers must consider the ‘big ideas’ in the design of their lessons for work-integrated learning practices.

Authors:
Rajendran Govender, University of the Western Cape, South Africa

About the Presenter(s)
Professor Rajendran Govender is a University Professor/Principal Lecturer at University of the Western Cape in South Africa

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