Van Hiele levels of geometry understanding

What are the van Hiele levels of geometry understanding?

A . There are five levels, which are sequential and hierarchical. They are:

Level 1 (Visualization): Students recognize figures by appearance alone,
often by comparing them to a known prototype. The properties of a figure
are not perceived. At this level, students make decisions based on perception,
not reasoning.
Level 2 (Analysis): Students see figures as collections of properties. They
can recognize and name properties of geometric figures, but they do not see
relationships between these properties. When describing an object, a student
operating at this level might list all the properties the student knows, but not
discern which properties are necessary and which are sufficient to describe
the object.
Level 3 (Abstraction): Students perceive relationships between properties
and between figures. At this level, students can create meaningful definitions
and give informal arguments to justify their reasoning. Logical implications
and class inclusions, such as squares being a type of rectangle, are
understood. The role and significance of formal deduction, however, is not
understood.

Level 4 (Deduction): Students can construct proofs, understand the role of
axioms and definitions, and know the meaning of necessary and sufficient
conditions. At this level, students should be able to construct proofs such as
those typically found in a high school geometry class.

Level 5 (Rigor): Students at this level understand the formal aspects of
deduction, such as establishing and comparing mathematical systems.
Students at this level can understand the use of indirect proof and proof by
contrapositive, and can understand non-Euclidean systems.

Clements and Battista (1992) also proposed the existence of Level 0, which
they call pre-recognition. Students at this level notice only a subset of the
visual characteristics of a shape, resulting in an inability to distinguish
between figures. For example, they may distinguish between triangles and
quadrilaterals, but may not be able to distinguish between a rhombus and a
parallelogram.