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Geometry can be a particularly frustrating mathematics course, for high school and university level students. Many educators believe, in fact, that only people with right-brain dominance can truly excel in this field of mathematics. Lots of student would agree. It is not unusual for a student to master Algebra without a great deal of effort, only to move on to geometry and meet disaster.
Algebra involves learning rules and algorithms (who does not remember “PEMDAS” for order of operations), and applying those to the solutions of equations. This, of course is a left-brain activity.
Geometry, on the other requires spatial viewpoints and deductive reasoning. To master geometry, then, students need to “see” solutions, not just follow rules. One of the biggest stumbling blocks for students of geometry is the “proof.” One may have certain axioms, such as “parallel lines will never intersect,” or “perpendicular lines always form right angles,” but then they are asked to use the axioms and other preliminary information and to produce step-by-step deductions in order to prove some new geometric axiom. If students cannot “see” the progression, they fail.
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