Determination of the Relative Positions of Three Planes: Action Research

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Tuba Ada, Aytaç Kurtuluş

Abstract

The purpose of this study was to explore how a more effective lesson plan and teaching environment can be achieved so as to improve elementary mathematics teacher candidates’ achievement in analytical examination of planes in space. In order to improve achievement in expressing the relative positions of three planes not only algebraically but also visually the study used an action research approach as planned by the researchers. In Implementation 1, the teacher candidates were given the equations of three planes and they were asked to determine the relative positions of the planes so that their prior knowledge could be identified. In this stage, the candidate teachers tried to determine the relative positions of the planes in one direction by examining the plane equations in pairs. In Implementation 2, the candidate teachers were asked to find the solution set of the linear equation system consisting of three equations with three unknowns and to come up with geometric interpretation of this solution. In this stage, some of the candidate teachers were able to solve the equation, but they couldn’t interpret it geometrically. In Implementation 3, Maple, a computer algebra system, was used so that the candidate teachers could visualize and observe the relative positions of the three planes by using the plane equations. In this stage, the candidate teachers associated the set of solutions of the plane equations with the three-dimensional images obtained with Maple. The results of the implementation showed that the proposed plan improved the mathematics teacher candidates’ visualization of the relative positions of the three planes.

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