The document proposes an enrichment program to develop geometric creativity in mathematically gifted high school students using dynamic geometry software. The program aims to have students construct dynamic figures in many ways, come up with construction and problem solving methods, make conjectures and generate proofs. It would include student handouts, a teacher guide, and activities involving problem solving, redefining problems, geometric constructions, and problem posing. The activities are designed following principles of developing creativity and addressing math standards.

1. Suggested Enrichment Program
Using Cinderella (DGS) in
Developing Geometric Creativity
Mohamed El-Demerdash
The University of Education - Schwaebisch Gmuend
Sept. 26th 2008

2. Working Title
The Effectiveness of an Enrichment Program
Using Interactive Dynamic Geometry
Software in Developing Mathematically
Gifted Students' Geometric Creativity in
the High Schools

3. 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

4. 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.

5. 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.

6. 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.

7. 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.

8. Aims
1. 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.

9. 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.

10. Content
lStudent’s Handouts
lTeacher’s Guide
lCD ROM

11. Enrichment Activities
1. Problem Solving Activities
2. Redefinition Activities
3. Construction Activities
4. Problem Posing Activities

12. 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).

13. 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).

14. 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).

15. 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).

16. Questions

17. Thank you very much!