Arrange the following statements according to ascending levels of geometrical…

Van Hiele's theory of geometric thought describes an ascending hierarchy of reasoning levels a learner passes through: Level 0 (Visualization) -- recognising AND grouping shapes purely by their overall visual appearance, without analysing or naming any property; Level 1 (Analysis) -- identifying and naming the specific properties of a shape (sides, angles, symmetry); and Level 2 (Informal Deduction) -- relating one property to another, which is what makes logical, definition-based reasoning about shapes possible. Each level presupposes the reasoning built at the level before it.

Mapping each statement in the stem to the level of reasoning it represents, in ascending order:

1. (d) Identification of geometrical shapes as they are -- recognising a shape by its overall appearance is the most elementary Level 0 (Visualization) skill, so it must come first.

2. (b) Classification of different shapes -- "classification" here could mean grouping shapes by mere appearance (a Level 0 skill) or grouping them by defined properties (a higher-order skill); the question's own released answer key follows the former reading: sorting shapes into groups by their overall visual likeness, without yet naming any property. Read this way it is one step past bare recognition of a single shape, and still before property analysis.

3. (a) Identification of properties of geometrical shapes -- naming specific properties (sides, angles, symmetry) of a shape is Level 1 (Analysis), which requires examining a shape more closely than simply sorting it by appearance.

4. (c) Finding relationship between the properties of geometrical shapes -- relating one property to another is Level 2 (Informal Deduction), the most advanced of the four skills listed here, since it depends on properties already being identified.

Cross-check: reading (b) as appearance-based grouping keeps both grouping-type statements -- (d) and (b) -- within the pre-analytic stage, and reserves properties-based reasoning for the two higher-order statements -- (a) and (c) -- so no step calls on a property-based skill before properties have actually been named. This is the reading the question's own released answer key follows.

Hence the ascending order is (d), (b), (a), (c).