Blog Entry 7 - Geometry

The understanding of Geometry takes upon a combination of understanding about shapes and having good spatial sense. "Spatial sense can be defined as an intuition about shapes and the relationship among shapes......They are able to use geometric ideas to describe and analyze their world." (Van De Walle, Karp & Bay-Williams, 2009).

The study of Geometry involves skills that allows individuals to create good connections with the world around them. Everything in the environment is geometric - The Esplanade is oval, the long stretch of road on the highway is rectangular, and the lift buttons are circular. The development ot geometric thinking goes through developmental stages, as described by Van Hiele: He has decribed the levels of geometric thinking according to "what we think and wat types of geometric ideas we think about, rather than how much knowledge we have" (Van De Walle, Karp & Bay-Williams, 2009). Van Hiele's theory of geometric thinking is listed as:

Level 0: Visualisation (classes of shapes)
Level 1: Analysis (Propertities of shapes)
Level 2: Informal Deduction (Relationships among popertities)
Level 3: Deduction (Deductive systems of propertities)
Level 4: Rigor (Analysis of deductive systems).

The child's ability to sort out shapes according to its physical property puts him at Level 1 of Van Hiele's theory: Properties of shapes.

Finding the interior angles in a pentagon:

Finding the interior angles of a pentagon requires that the individual has developed at Level 4 of Van Hiele's theory: Rigor.

A Therefore, the formula of working out an interior angles of a pentagon is:

1. A pentagon is made up of 3 triangles:


2. The interior angles of each triangle in a pentagon adds up to to 180°.

3. Therefore, the interior angles of a pentagon is worked out as:
3 x 180° = 540°

Teaching children geometry requires that they be involved in a variety of critical thinking and making connections with the environment. The reading of the chapter has allowed me to develop a new set of understanding about Geometry, and even better than I did before. I am creating in myself a new set of understanding of the topic, and how I can create more constructive learning opportunities about Geometry. Click here for more information on finding the interior angles of the various geometric shapes.