I would like to express here a personal complaint, which will also answer your question: as a child I learnt to work with a compass and straightedge, but there was a great drawback: I learnt that a compass is used to draw circles. These are just a few specific ideas that came to mind - the general idea is to use the constructions as a tool to teach logical and geometric reasoning.įor a case study in how not to teach geometric constructions - which may highlight some pitfalls to avoid - see Schoenfeld 1988, 'When Good Teaching Leads to Bad Results: The Disasters of "Well-Taught" Mathematics Courses'. This could also be used to illustrate how subtle changes to axioms can have a major impact on what's provable/constructible (like how doubling the cube is impossible with compass and straightedge, but becomes possible as soon as you can mark lengths on the straightedge). However, geometric constructions can still serve useful educational purposes now, because it's a simple axiomatic system that can be a good way for students to learn to connect geometric intuition with careful, precise reasoning.įor example, once students have learned how to construct bisections of angles, one can ask them to try to trisect an angle, and use this to introduce the concept of an impossibility proof. This method of axiomatic construction was first studied for historical reasons that perhaps aren't as relevant now - having to do with the "synthetic" style of axiomatic geometry used by the Ancient Greeks, as opposed to the "analytic" style more popular in modern mathematics (e.g., Cartesian coordinates). The accuracy of the actual drawings is basically irrelevant (as long as it's not so sloppy that it impedes visualization) - the point is that they can prove the accuracy of the idealized constructions. The point of compass-and-straightedge constructions is for the students to get experience reasoning about axiomatic systems.
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