Here are some common situations where misunderstandings and difficulties can occur.
Recognising plane shapes in different orientations
Students who regularly encounter plane shapes in one specific orientation may have difficulty in classifying shapes correctly and recognising their properties when they look 'different'. For example, a student may not realise that the height of an obtuse-angled triangle can be 'outside' the triangle or recognise that an irregular five-sided shape is a pentagon.
Correctly identifying and naming corresponding sides and angles
For example, not understanding the importance of correctly identifying the matching sides in a triangle when establishing similarity may result in a student reaching incorrect conclusions about proportions.
Understanding specific geometrical terms
Students meet very many new terms in geometry which adds to the cognitive load of their learning. In addition, there can be confusion between the everyday meaning of the words used and their geometric meaning (e.g. 'similar').
Visualising relationships in diagrams
Many problems in geometry require the analysis and/or construction of a diagram, and the recognition of the relationships within it. Sometimes the relationships can be difficult to visualise without the addition of a construction line; the placement of that line is often not immediately obvious.
In complex diagrams sometimes students need to be able to focus on a particular part whilst ignoring others. It can be difficult to know what information is necessary and useful.
These types of misunderstandings and difficulties can be overcome by providing appropriate activities in a carefully sequenced learning plan.
Many students form fixed images of plane shapes that can hinder their progression in later years.
Similar or congruent?
Students can experience difficulty in knowing which test to use when determining triangles to be either similar or congruent.
The language of geometry
The purpose of the formal language of geometry is to communicate spatial ideas accurately and succinctly. Geometric language is composed of a broad vocabulary which includes both symbols and words.
Revealing the invisible
Adding construction lines to a diagram is often necessary when solving problems in geometry. Knowing when and where to add auxiliary lines is difficult for many students.