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DYNAMIC MODELING AS A TOOL OF SEARCHING FOR AUXILIARY CONSTRUCTIONS IN SOLVING GEOMETRY PROBLEMS
Abstract
Background: Geometry problems requiring auxiliary constructions are generally challenging for students, and they are traditionally included in Mathematics Olympiad tasks and examinations. Most teachers recommend that students remember basic auxiliary constructions, such as doubling the median of a triangle, inserting an additional circle, constructing the point of intersection of lines on which the segments lie, et?. These recommendations are usually insufficient for successful problem solving. Now students have an opportunity of using dynamical models of situations to solve complicated problems. Various dynamical geometry software such as Cabri, Geometer's Sketchpad, GeoGebra provide them with appropriate tools. Methods: The authors' idea is to use dynamical modeling for finding out relevant auxiliary constructions. We compiled a list of 10 problems used for the State final attestation of school graduates in different years. There were two test groups of 11 grade students: an experimental group consisting of 15 students trained to use GeoGebra, and a control group including the same number of students. After setting the problems, we invited the experimental group to construct dynamical models of the relevant situations and then to solve the problems. Students in the control group solved the problems using a pen and paper only. We were interested in a random value of success in finding out necessary auxiliary constructions. To compare two distribution of this random value we used statistical analysis. Results: We have established that preliminary modeling of a situation is a significant factor for success in detecting auxiliary constructions. We attribute this result to the fact that all key auxiliary constructions are utilized when creating a stable dynamical model. In this case, they are a logical consequence of data. Conclusions: We recommend that teachers use dynamic modeling to teach students how to find auxiliary constructions for geometry problems.
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