![]() The PROOF is given at the beginning! It is given before the examples that help you understand how the theorem works. The CURRENT PRACTICE of teaching Euclidean Geometry…Įuclidean Geometry is normally taught by starting with the statement of the theorem, then its proof (which includes the diagram, given and RTP – Required To Prove), then a few numerical examples and finally, some non-numerical examples. It is important to see the order of these levels since they will clearly demonstrate the problem with how Euclidean Geometry is taught in most textbooks and classrooms. This level is for post-matric courses generally. This holds if we are looking at normal geometry (planar) however, it does not hold if we are using a rounded surface (spherical). An example of this would be the axiom about the sum of angles in a triangle equalling 180 degrees. The learner should have attained Level 4 by the time they finish Grade 12.Ī learner could challenge axioms in different systems and determine if they would still be valid or not, since in the system in which the axioms are used, these axioms may break down. This means that the learner must be able to structure and write up formal proofs in the Statement-Reason format. This is where formal deduction takes place and the learner can write proofs with understanding. The learner should have attained Level 3 by the time they finish Grade 9. Informal deduction means a learner may be able to follow a given proof, but they will not be able to write and structure it themselves. This means that simple deduction can be followed, but formal proof is not understood. This is a very important stage since it is the beginning of seeing proofs however, this is informal deduction. We must note that a learner has the ideas of the properties however, they are in isolation. ![]() rectangles have four right angles, circles have no right angles, etc. Once a learner progresses from Level 1 to Level 2, they will be able to identify properties of figures, e.g. squares and rectangles seem to be different. It is important to remember that this is a purely visual skill without any deductive or inductive skills. This is where a learner can learn names of figures and recognises a shape as a whole, e.g.
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