Answer to Question #220669 in Geometry for Sonia

Question

The Van hiele theory on the development of geometric thoughts is very helpful in structuring and teaching geometry. Five levels are identified, in the textbook, these levels are called level 0-4. (Note that in some other sources they are called levels 1-5. Give one example of how a learner on level 1 will define a rectangle. Give one example of how a learner on level 2 will define a rectangle. Discuss its meaning in the context of the classification of quadrilaterals as a lea1 on level 2 would do it. Reflect on how your knowledge of the thought levels of van Hiele will influence your own teaching of geometry.

Answer 1

1) A learner on level 1 will define a rectangle as a shape with one pair of sides longer than the other pair of sides.

(2)A learner on level 2 will define a rectangle as a quadrilateral.

(3) In level 1 the objects of thought are classes of shapes the student learnt to analyze as having properties such as four sides and angles. In level 2 the objects of thought are geometric properties the student learnt to connect deductively. learners recognize the relationship between types of shapes thus rectangle is a quadrilateral because it has four sides.