Developing and piloting a DGS based unit for overcoming difficulties faced by grade-9 Lebanese students while learning locus of points. (c2013)

Abstract

The concept of “locus” is often considered confusing to students due to its overly abstract nature. The abstract approach that is used in solving problems involving locus of points in classrooms is probably one of the reasons learners face difficulties in acquiring and understanding “locus”. This paper presents a qualitative research study that is concerned with the use of a constructivist approach where the students have to explore the cases of locus of a point with the integration of Dynamic Geometry Software (DGS), namely Geometer‟s Sketchpad, in the context of open geometry problems requiring conjecturing and proving. The purpose of this study is to explore the difficulties that grade-9 students face in learning locus and solving locus problems. It also aims to investigate whether using DGS can help improving the learning process and better preparing students for solving problems involving locus of points. A series of activities were developed and implemented over seven sessions that integrate the use of DGS, namely Geometer‟s Sketchpad, to teach geometric locus of points. Participants are two classes of grade-9 students (over two academic years), and a group of three grade-9 math teachers, at a private school in South-Lebanon. The total number of students from two classes over two consecutive years is 41 including 18 girls and 23 boys. The students‟ average mathematics scores in grade 8 for each class were considered to determine a base for comparison. The math average of the non-DGS class was found to be 82 out of 100 and that of the DGS class was 73 out of 100. The study involved several stages conducted over two academic years: semi-structured interviews with three grade-9 teachers, classroom observations of grade-9 classes where locus is taught without students‟ use of DGS, open interviews with eight students about the difficulties that they face while learning Locus, classroom observation of a major grade-9 problemsolving session using DGS during the implementation of the unit, clinical interviews with selected pairs of students solving geometric problems using DGS, and paper-pencil test (the same one administered to both, the non-DGS and the DGS groups) to investigate whether the use of DGS enhances students‟ understanding and if the abilities of finding locus of points, developed in a DGS environment, are transferable to a non- DGS environment. Data collected was analyzed according to a framework compiled by the researcher based on frameworks used in the literature and on a primary overview of students‟ work. Results showed that although the two classes were of different levels of achievement, the DGS group performed higher in the paper-pencil test than the non- DGS class. The use of DGS positively impacted students‟ ability to find and formulate conjectures about locus of points. It also gave the DGS group confidence in attempting proofs.