Abstract
This study is about student teachers’ conceptual understanding of shapes. While the National Curriculum Statement stipulates that by the time learners exit high school they should have grounded knowledge of basic geometry and know shapes such as polygons and polyhedrons and their properties, this study finds that the majority of student teachers have limited knowledge of basic geometry and require not remedial, but re-learning of these basic concepts. The Van Hiele levels of geometric thought model is used as a lens to gauge and understand students’ knowledge of geometry. A cohort of 128 first-year students registered for a foundation phase programme took part in the study. It was found that while Grade 12 learners are expected to operate at levels 3 and 4 of the Van Hiele’s levels, the majority of the participants in the study were operating at level 1, the level of the learners they will be teaching when they complete the course. Suggestions are made for how to address this problem.
Highlights
Geometry – the “study of shapes, their relationships, and their properties” (Bassarear 2012:463) – has a long history arising from the practical measurement of land in ancient Egypt and the study of the properties of shapes in Greek geometry (Cooke 2007)
Spatial sense consists of two important components of geometric knowledge, namely spatial visualisation (the ability to visually compare shapes that have changed position on the plane or in space), which is essentially transformation geometry (Bassarear 2012), and spatial orientation, which operates when a fixed object is viewed from different points or when the position of an object is acknowledged (Battista 2007)
The objective of the study was to establish the level of basic knowledge of geometry that foundation phase students bring to the programme at university
Summary
Geometry – the “study of shapes, their relationships, and their properties” (Bassarear 2012:463) – has a long history arising from the practical measurement of land in ancient Egypt and the study of the properties of shapes in Greek geometry (Cooke 2007). One of the main reasons for this is that teachers and learners operate and communicate at different Van Hiele levels of learning, which impairs the latter’s understanding of critical concepts in geometry (Pusey 2003). According to Frobisher, Frobisher, Orton and Orton (2007:19), “in their learning of shapes and space children experience and understand the connections between knowledge, concepts and skills in the different facets of geometry” This means that teachers should be mindful of a child’s environment and adapt their instructional. Spatial sense consists of two important components of geometric knowledge, namely spatial visualisation (the ability to visually compare shapes that have changed position on the plane (for two-dimensional shapes) or in space (for three-dimensional shapes)), which is essentially transformation geometry (Bassarear 2012), and spatial orientation, which operates when a fixed object is viewed from different points or when the position of an object is acknowledged (Battista 2007). Van Hiele’s theory of geometric thought is regarded as the best framework known for teaching and learning geometry (Mayberry 1983; NCTM 2000; Wu & Ma 2006)
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