Stages of Geometric Thinking

Question 1

Level 0: Visualization

Answer 1

See geometric shapes as a whole; do not focus on their particular attributes

Question 2

Level 1: Analysis

Answer 2

Recognize that each shape has different properties; identify the shape by that property

Question 3

Level 2: Informal deduction

Answer 3

Can see the interrelationships between figures

Question 4

Level 3: Formal deduction

Answer 4

Construct proofs rather than just memorize them; see the possibility of developing a proof in more than one way

Question 5

Level 4: Rigor

Answer 5

Learn that geometry needs to be understood in the abstract; see the “construction” of geometric systems