@unpublished {403, title = {The Development of an Instrument to Measure Geometric Creativity}, year = {In Press}, abstract = {

There is no doubt that students can learn and develop their creative potential, if we use the
appropriate programs that successfully teach them the creativity skills and its operations.
However, in order to measure the effectiveness of such programs we need an instrument to
assess creativity. This paper presents the development of a test that can be used to assess
geometric creativity and to obtain concrete indicators of creative potential in geometry. The
test was designed as a part of larger experimental study conducted to assess the geometric
creativity among mathematically gifted students, and to develop their geometric creativity
using dynamic geometry software. It uses four components that we consider to be basic
ingredients of geometric creativity: fluency (based on the number relevant responses),
flexibility (based on the number of different categories of the relevant responses), originality
(based on the statistical infrequency of responses in relation to peer group), and elaboration
(based on number of redefined follow-up questions or problems).

}, keywords = {creativity, elaboration, flexibility, fluency, geometric creativity, originality}, author = {El-Demerdash, Mohamed and Ulrich Kortenkamp} } @mastersthesis {402, title = {The Effectiveness of an Enrichment Program Using Dynamic Geometry Software in Developing Mathematically Gifted Students{\textquoteright} Geometric Creativity in High Schools}, volume = {Ph.D.}, year = {2010}, pages = {523}, school = {Universit{\"a}t Schw{\"a}bisch-Gm{\"u}nd}, address = {Schw{\"a}bisch-Gm{\"u}nd}, 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 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{\textquoteright} geometric creativity in high\ schools; second, to develop an enrichment program based on the identi ed principles;\ third, to investigate the e ectiveness 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 identi ed. Then, a\ suggested enrichment program based on these identi ed 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 signi cant di erences between the mean\ ranks of the subjects{\textquoteright} 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 signi cantly e ective 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{\textquoteright} 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 e ectiveness of the\ suggested enrichment program using both quasi-experimental and true-experimental\ designs.\ Other avenues for research may focus on students{\textquoteright} a ective and emotional domains\ (e.g. self con dence, attitudes, and achievement motivation, among others), and might\ as well include an analysis of gender-related individual di erences.

}, url = {https://dl.dropboxusercontent.com/u/5761672/dissertation.pdf}, author = {El-Demerdash, Mohamed} } @conference {El-Kor-EEPUDGSDMGSGC-2009, title = {The Effectiveness of an Enrichment Program Using Dynamic Geometry Software in Developing Mathematically Gifted Students{\textquoteright} Geometric Creativity}, booktitle = {Proceedings of the 9th International Conference on Technology in Mathematics Teaching}, year = {2009}, publisher = {ICTMT-9}, organization = {ICTMT-9}, address = {Metz}, abstract = {

The research work presented in this paper was guided by three goals: First, to identify the principles of preparing an enrichment program in Euclidean geometry using Dynamic Geometry Software to develop the mathematically gifted students{\textquoteright} geometric creativity in high schools, second, to develop an enrichment program based on the identified principles, and third, to investigate its effectiveness by testing it with high school students. The enrichment program was administered to 7 mathematically gifted students in 12 weekly 90-minute sessions. Results of a pre-post measurements revealed the effectiveness of the program in developing the subjects{\textquoteright} geometric creativity as a whole ability and its four sub-components (fluency, flexibility, originality, and elaboration).

}, keywords = {refereed}, author = {El-Demerdash, Mohamed and Kortenkamp, Ulrich}, editor = {Bardini, C. and Fortin, C. and Oldknow, Adrian and Vagost, D.} }