The solution presentation will help students construct a reliable solving process. Several points should be noted.
It is important to ignore the given material in constructing the solution of a problem. Delay using given material untill the equations demand it. Building a problem solution around the givens, instead of ideas and concepts, is a habit students acquire from early training in mathematics. As a result these inadequate habits become more and more of a handicap as they progress in grade level.This problem provides a particularly good example of the distracting effect of the givens. The given fact that the triangles are similar is irrelevant to constructing the problem solution. It only comes into play in the final steps when numbers are needed.The animated measurement of the lengths of the sides was constructed using a standard computer drawing program. Most of the figures in these web pages were created using draw and paint programs. The algebra was done using a symbolic algebra program. Other computer-based resources have been used for some special effects.
Breaking the habit of trying to solve a problem by manipulating the givens is a primary step toward learning to solve problem reliably.This demonstrates the extensive range of computer-based resources available to the student studying algebra, geometry, physics, chemistry or whatever. Using them provides the student with experience with tools that will be of permanent value as well as developing deeper insight into the subject matter.
This problem was adapted from an example from the Mathematics Projects of the Curriculum Research & Development Group, University of Hawaii at Manoa. The group has developed extensive research-based, materials for the K-12 curriculum.
The animations were produced using Gif*gIF*giF from Pedagoguery Software.
Copyright by Howard C. McAllister, 1997