Geometry from a Different Angle – Constructions with Mrs. Walker

Walker 01“Construction” in Geometry means to draw shapes, angles or lines accurately.  This quarter we have spent several  days during the quarter learning how to construct geometric figures using only a straightedge and a compass.  Many schools have abandoned teaching constructions because it is not on standardized tests.  We can all agree that learning how to use the tools of constructions is useful.  Beyond that purpose, it is important that students are able to do freehand sketches of geometric figures, construct them using the tools of geometry , visualize geometric figures and relationships, and interpret geometric diagrams.  Sketching and constructing geometric figures provides opportunities to relate to different learning styles including hands-on learners, kinesthetic and visual learners.  Euclid, the Greek mathematician who wrote the geometry text used for centuries, stated many of his theorems in terms of constructions.  His axioms are closely related to the tools he used for construction.  Just as axioms and postulates let us prove everything with a minimum of assumptions, a compass and straightedge let us construct everything with a minimum of tools.   Each time it is announced that we will be working on constructions, there are cheers from the students!  It is fun to teach, and the kids enjoy it as well.

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