Answer to Question #204615 in Geometry for Khomotso

Question

The van heile theory and development of geometric thought is very helpful in structuring and teaching geometry.

1. Give an example of how a learner on level 1 will define a rectangle.

2. Give one example of how a learner on level 2 will define a rectangle.

3discuss it's meaning in the context of the classification of quadrilateral as a learner on level 2 would do it.

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.