Suggested Enrichment Program Using Cinderella (DGS) in

Developing Geometric CreativityMohamed El-Demerdash

The University of Education - Schwaebisch GmuendSept. 26th 2008

Working Title

The Effectiveness of an Enrichment Program Using Interactive Dynamic Geometry

Software in Developing Mathematically Gifted Students' Geometric Creativity in

the High Schools

Purpose

Developing an enrichment program in Euclidean geometry to enhance the

geometric creativity of the mathematically gifted students in the high schools using

dynamic geometry software

Bases

l The characteristics of the mathematically gifted students and the nature of mathematical giftedness.

l The nature of creativity and geometric creativity.l General principles of developing enrichment

programs for the mathematically gifted students.l The contemporary trends in planning and organizing

enrichment programs for the mathematically gifted students.

l The characteristics of interactive dynamic geometry software.

Principles

l The program should provide opportunities for the mathematically gifted to explore some mathematical ideas using the IDGS in a creative fashion.

l Activities within the suggested enrichment program should provide the mathematically gifted students with opportunities to reinvent the mathematical ideas through both exploration and the refining of earlier ideas.

l The enrichment activities should be designed and presented in a constructivist way that encourage the mathematically gifted students to make new connections to their prior experiences and construct their own understanding.

Principles

l Teaching the instructional activities, within the suggested enrichment program, should follow van Hiele phases of learning geometric concepts: Information, guided orientation, explicitation, free orientation, and integration.

l The suggested enrichment program activities should correspond to the students’ skills, since they should experience success in order to motivate to continue in the program.

l The suggested enrichment activities should challenge students’ thinking, enhance students’ achievement, and develop students’ geometric creativity.

Principles

l The instructional activities, within the suggested enrichment program, should be designed to be effective in revealing geometric creativity and in distinguishing between the mathematically gifted students in terms of the geometric creativity and their responses.

l The suggested enrichment program activities should address standards for school mathematics, for example the ones recommended by the National Council of Teachers of Mathematics (NCTM) as it is one of the most popular standards in the field of teaching and learning mathematics.

Aims1. Construct dynamic figures. 2. Come up with many construction methods to construct

dynamic configurations for an assigned figure.3. Come up with many various and different construction

methods to construct dynamic configurations for an assigned figure.

4. Come up with novel and unusual methods to construct dynamic configurations to an assigned figure.

5. Produce many relevant responses (ideas, solutions, proofs, conjectures, new formulated problems) toward a geometric problem or situation.

6. Produce many various and different categories of relevant responses (ideas, solutions, proofs, conjectures, new formulated problems) toward a geometric problem or situation.

Aims

7. Generate many unusual ("way-out"), unique, clever responses or products toward a geometric problem or situation dynamic figures.

8. Make new conjectures and relationships by recognizing their experience toward the aspects of the given problem or situation.

9. Investigate the made conjectures by different methods in different situations.

10. Generate many different and varied proofs using the formal logical and deductive reasoning toward a geometric problem or situation.

11. Generate many follow-up problems by redefining (modifying, adapting, expanding, or altering) a given geometric problem or situation.

12. Apply different learning aspects of geometry (concepts, generalizations, and skills) in solving a geometric problem or situation.

Content

lStudent’s HandoutslTeacher’s GuidelCD ROM

Enrichment Activities

1. Problem Solving Activities2. Redefinition Activities3. Construction Activities4. Problem Posing Activities

Problem Solving Activities

… the student is given a geometric problem with a specific question and then invited not only to find many various and different solutions but also to pose many follow-up problems related to the original problem (e.g. activities 1, 5, and 6).

Redefinition Activities

… the student is given a geometric problem or situation and invited to pose as many problems as possible by redefining –substituting, adapting, altering, expanding, eliminating, rearranging or reversing – the aspects that govern the given problem (e.g. activities 2 and 4).

Construction Activities

… the student is asked to come up with as many various and different methods as he can to construct a geometric figure (e.g., parallelogram) using constructing facility of Cinderella application (e.g. activities 7, 8, 9, and 10).

Problem Posing Activities

… the student is given a geometric situation and asked to make up as many various and different questions, or conjectures as he can that can be answered, in direct or indirect ways, using the given information (e.g. activities 11 and 12).

Questions

Thank you very much!