Katha 2014: Teaching Geometry

Minutes of the Workshop transcribed. Speaker Mr. Robert Contreras

KATHA: DAY 5

Teaching Geometry

Mr. Robert Contreras

University of the Philippines Diliman

August 16, 2013

Minutes of the Workshop

 1. Introduction. Conceptual understanding in Geometry is essential for the students to understand and comprehend the subject better. There are necessary conditions on the different jargons and terms to be used in Geometry.

2. Geometry. The speaker said that Geometry is a tool for understanding and interacting with space. It also describes the world we live in and are axiomatic; that is it is rule-based.

2.1. Deductive System. This may be an analogy for a building where postulates are the base of the foundation of geometry.

2.2. Van Hiele Model. This model is learner-centered and is proposed in high school geometry in 1957 by teachers in Netherlands. It is a learning model with a holistic perception and develops a geometric thinking. It also refines the understanding of geometrical proofs.

There are three levels of the Van Hiele Model which are a validation of the CPA model: 1) Level 0 or Visualization. This is where the students perceive geometric shapes as total entities without attributes. This means that they are only aware of space as it is. 2) Level 1 or Analysis Model. This is where parts of the shape are already recognized by the students and they can discern characteristics of the shapes.  3) Level 2 or Abstraction. This is where figures are identified as having parts and are recognized by parts. Students can already discern the properties of the shapes and establish and analyze figures. Finally they can also subset classifications. 4) Level 3 or Deduction. This is the level where there is already the significance of deducing the figures to prove something and construct proofs based on the figures.  5) Level 4 or Rigor. This is where geometry is seen as an abstract form, i.e. in spherical geometry where parallel lines do not meet. Postulates are also recognized as usual functions of the body. These are the major characteristics of the Van Hiele Model, where it is sequential and in a reduction of level.

3. Implications to Teaching. This model entails mastery of polygons, grasping shapes as in CPA approach and the basis for each one. This can also be improved into shape teaching where teachers can create robots, counting how many are used, hopscotch, sorting cut out shapes and letting the students list the properties. The speaker illustrated different examples on how teachers can improve teaching Geometry through discovery games. He also provided samples on properties of shapes of everyday objects and property cards (What am I (shape)).