To develop a sound understanding of geometry students need opportunities to explore shapes in both physical and virtual environments. These experiences should be carefully sequenced to aid the development of a deep conceptual understanding of relationships rather than memorisation of lists of rules. You can read more in the article Issues in the Teaching and Learning of Geometry (218 KB PDF).
To support the development of geometric ideas, some key understandings have been grouped together into five areas:
- plane shapes
- congruence and similarity
- geometric proof
- circle geometry.
The properties of quadrilaterals are more easily recognised and understood when students have the opportunity to investigate by observing, measuring and folding.
Once the idea of congruence has been established, students need experience in recognising congruent shapes in embedded diagrams, and in drawing them in a variety of orientations.
Looking beyond the lines
Geometrical diagrams can be complex to decipher. Students may experience difficulty separating out shapes when they overlap or recognising angle relationships.
Writing a proof
Writing a deductive proof is very challenging as students not only have to find the mathematical relationships but also provide reasons and explanations, using correct mathematical language.
The angle and chord relationships in circle geometry are more easily recognised and understood when students have investigated the results themselves.