At this level, children can classify to some extent and can discern some characteristics. They still cannot see interrelationships between figures. Simple proofs can be followed but not understood completely. Students at this level understand the significance of deduction and the role of postulates, theorems, and proofs. They can write proofs with understanding.
Students understand how to work in an axiomatic system.
They are able to make abstract deductions. Non-Euclidean geometry can be understood at this highest level At the elementary and middle school levels children operate at the first and possibly the second levels of the van Heile model. Geometry classes at the secondary level are taught at level three of the van Heile model. Fuys et al. Most work involved naming shapes and relations like parallelism, and students were only infrequently asked to reason with the figures.