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

Mohamed El-Demerdash (2010): The Effectiveness of an Enrichment Program Using Dynamic Geometry Software in Developing Mathematically Gifted Students’ Geometric Creativity in High Schools. Dissertation, Pädagogische Hochschule Schwäbisch Gmünd.
Betreut durch Ulrich Kortenkamp .
Begutachtet durch Ulrich Kortenkamp und Astrid Beckmann.
Tag der mündlichen Prüfung: 06.05.2010.

Abstract

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 operations necessary. 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 identified principles; third, to investigate the effectiveness 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 identified. Then, a suggested enrichment program based on these identified 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 für Hochbegabte (LGH), a public high school for highly gifted and talented students in Schwäbisch Gmünd – Baden-Württemberg, Germany. The students came from 11th (5), 10th (1) and 9th (1) grade, two of them were male, five female.

In the study, the researcher used a one-group pretest–intervention–posttest pre-experimental 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 first 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 significant differences 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 significantly effective in developing geometric creativity as a whole ability and its four sub-components – fluency, flexibility, 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 firm 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 effectiveness of the suggested enrichment program using both quasi-experimental and true experimental designs.

Other avenues for research may focus on students’ affective and emotional domains (e.g., self confidence, attitudes, and achievement motivation), and might as well include an analysis of gender-related individual differences.

Key Words

• DGS
• Dynamic Geometry Software
• Dynamische Geometrie Software
• Mathematically Gifted Students
• Geometric Creativity