
Re: Technology In Education
Posted:
Nov 26, 2007 12:05 AM


At 05:09 PM 11/23/2007, Richard Strausz wrote (to Haim):
>It is too bad you never tried Sketchpad with the one student you taught.
Why would that be? You still have not addressed the earlier request:
At 11:33 AM 11/20/2007, Richard Strausz wrote:
>Have you ever used the "Geometer's SketchPad?" I now use it in place >of straightedge and compass constructions. It gains me >instructional time and more depth of understanding.
Can you give us an example is to two of concrete settings to reinforce your position here? My impression is that it undermines the whole idea of straightedge and compass; i.e., realization of the axioms. Most explicitly, two points determine a line and a point and a radius determine a circle. Geometer's Sketchpad can trisect angles at will. Is that really a savings of instructional time and does it give more depth of understanding? What point has there ever been to constructions with the Euclidean tools than to then prove that the construction is valid?
As a concrete example at the simplest level, constructing a regular hexagon inscribed in a circle (if the center, hence the radius, is known) using the standard instruction is notoriously inaccurate. Better to use a protractor if the goal is a good hexagon, not the construction and why it is valid. Even bisecting an angle, for that matter.
At a more sophisticated level, watching the angle bisectors determine the incircle as a vertex of the triangle is dragged might lead to a good conjecture but is there any point in making it if it is not then to be proved? And that is really cheating, basically telling them theorem, not some deep training in making conjectures. If you don't believe me, just include the incircle, not the angle bisectors, as you drag a vertex of the triangle. See how long it takes students to make the desired conjecture. Don't measure this in minutes; try years, or maybe decades.
Wayne

