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- Students will use visual perception and nonverbal thinking.
- They recognise shapes as a whole and compare the shapes with real-life objects.
- They don't recognise the shapes' properties.

For example, students will think that a rectangle looks like a book.

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- Students at this level begin to analyze and name the properties of geometric figures
- They describe shapes based on the basis of properties and consider all shapes within a class (If a shape belongs to a particular class, it has the corresponding properties of that class)
- But they do not see the relationships between properties

For example, students will think that squares share the properties of four sides, four right angles, and their opposite sides are parallel

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1. Students can see the relationships between properties and figures and connect them together.
e.g. Square has four equal sides and four equal 90 degree angles.

2. Students are able to give simple arguments to prove their reasonings.
e.g. This is not a square, but a triangle, because it has three sides, three angles, and three vertices.

3. Students would often describe the properties and figures in a more careful and detailed way. They would also include more mathematical vocabulary in their descriptions.
e.g. This is an equilateral triangle. Hence, every angle is 60 degree.

4. Students can draw logical maps and diagrams, mostly using sketches and grid papers.

Keywords for van Hiele's theory of geometrical thinking Level 2:
inter-relationships, connect, link