The Effectiveness of an Enrichment Program Using Dynamic Geometry Software in Developing Mathematically Gifted Students' Geometric Creativity in High Schools

TitelThe Effectiveness of an Enrichment Program Using Dynamic Geometry Software in Developing Mathematically Gifted Students' Geometric Creativity in High Schools
Publication TypeThesis
Year of Publication2010
AuthorsEl-Demerdash M
Academic DepartmentUniversität Schwäbisch-Gmünd
Number of Pages523
UniversityUniversität Schwäbisch-Gmünd

It goes without saying that students can learn and develop their creative potential if appropriate programs are used that successfully teach them the creative skills and operationsnecessary. However, mathematics in general and geometry in particular, by their own nature, have a lot of possibilities that can be used in developing creativity. The purpose of the present study was threefold: First, to identify the principles of preparing a suggested enrichment program in Euclidean geometry using dynamic geometry software to develop the mathematically gifted students' geometric creativity in high schools; second, to develop an enrichment program based on the identied principles; third, to investigate the eectiveness of this program by testing it with high school students. By reviewing the prior literature and studies related to the subject of the study, the principles of developing the suggested enrichment program were identied. Then, a suggested enrichment program based on these identied principles using the Interactive Geometry Software, Cinderella was developed. Moreover, within the present study an instrument, a geometric creativity test (GCT), was developed and a grading method for assessing the mathematically gifted students geometric creativity was established. The material was tested with a group of 7 mathematically gifted students in the Landesgymnasium fur Hochbegabte (LGH), a public high school for highly gifted and talented students in Schwabisch Gmund { Baden-Wurttemberg, Germany. The students came from 11th (5), 10th (1) and 9th (1) grade, two of them were male, ve female. In the study, the researcher used a one-group pretest { intervention { posttest preexperimental design. In this context the GCT was administered to students as a pretest at the beginning of the study; then the suggested enrichment program was introduced to them in 12 weekly 90-minutes sessions during the rst semester of the academic year 2008/09. The students retook the GCT as a posttest at the end of the study. 

The results indicated there were statistically signicant dierences between the mean ranks of the subjects' scores on the pre-post measurements of the geometric creativity test and its subscales in favor of the post measurement. The results also revealed that the suggested enrichment program was signicantly eective in developing geometric creativity as a whole ability and its four sub-components uency, exibility, originality, and elaboration. The results of the study suggest that the prepared enrichment program using DGS has a positive impact on the mathematically gifted students' geometric creativity. The positive impact can be traced back to the content of the suggested enrichment program and its open-ended and divergent-production geometric situations and problems. Also, the positive impact can be attributed to the use of DGS along the program sessions that provide the subjects with not only many opportunities to explore, experiment, and make new mathematical conjectures, but also to solve problems and pose related problems. However, the study requires replication and improvements before any rm conclusions can be made. One of the biggest improvements would be to have more subjects so that the results become more generalized and meaningful. Moreover, pertaining to the experimental design, further studies are needed to investigate the eectiveness of the suggested enrichment program using both quasi-experimental and true-experimental designs. Other avenues for research may focus on students' aective and emotional domains (e.g. self condence, attitudes, and achievement motivation, among others), and might as well include an analysis of gender-related individual dierences.

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