טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentBershadsky Irina
SubjectLearning the Concept of Locus through Problem Solving in
a Dynamic Geometry Environment
DepartmentDepartment of Education in Science and Technology
Supervisor Professor Orit Zaslavsky


Abstract

The study integrates three main domains: the first is the mathematical nature of the (geometric) concept of locus of points. The second deals with the cognitive processes involved in learning the concept of locus through problem solving sequences; the third is the learning environment that may enhance the learning of such mathematical concepts. The three components are intertwined, leading to the emergence of learning processes that are unique for this particular content in this particular environment, for this particular setup.

The design of the learning environment was heavily influenced by the necessity and advantages of visual-dynamic learning settings, which are of central concern to the community. Special attention was given to the mathematical and didactical considerations regarding the description of the angle bisector as a locus of points, as well as other special loci - some well-known and some less familiar. For the purpose of this study a special learning module was developed consisting of a rich set of problems requiring construction of representations of various loci.

The experimental design was based on a case study involving close ethnographic observations of two pairs of student-teachers while engaged in exploratory learning for fifteen 2-hour sessions. Interventions were minimal. Interactions were video-taped. Inductive-analytical analysis of data in addition to analysis of content and microgenetic analysis were employed.

The main findings point to three strategies that were identified and characterized: a local strategy, a generic point strategy and a global strategy. Analysis of the strategies exposed two phenomena that characterize the learning process of the pairs in this study. The first one is that the thinking process follows zig-zag passages between the different kinds of strategies. The second phenomenon relates to the interconnections between the medium and problem solving strategies. When the participants attempted to find the locus mentally the tendency was to employ a global strategy. When the medium was paper and pencil the tendency was to integrate the global and local strategies. In operating with the dynamic geometry software the tendency was to use the generic point strategy.

The study suggests that the global and local approaches can be considered as two interacting and mutually supporting modes of thinking, rather than two opposite poles as commonly regarded by traditional perspectives.  In addition, the unique set of problems that was designed for the purpose of the study proved effective for learning the concept of locus and for gaining some mathematical and pedagogical insights.