Many students usually do not reach Levels 4 and 5 until high school or college, but teachers should be aware of these levels nonetheless.
4. Deduction
Students can go beyond just identifying characteristics of shapes and are able to construct proofs using postulates or axioms and definitions. A typical high school geometry course is usually taught at this level.
5. Rigor
This is the highest level of thought in the van Hiele hierarchy. Students at this level can work in different geometric or axiomatic systems and would most likely be enrolled in a college level course in geometry.
