the role of dgs in developing mathematically gifted students' geometric creativity
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Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Role of DGS in Developing MathematicallyGifted Students’ Geometric Creativity
Mohamed El-Demerdash
Mathematics and Computer Science InstituteThe University of Education, Schwabisch Gmund
Dissertation Disputation
May 6, 2010
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Dissertation Working Title and Timeline
The Effectiveness of an Enrichment Program Using Dynamic
Geometry Software in Developing Mathematically Gifted
Students’ Geometric Creativity in High Schools
Dissertation Development Timeline
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Dissertation Working Title and Timeline
The Effectiveness of an Enrichment Program Using Dynamic
Geometry Software in Developing Mathematically Gifted
Students’ Geometric Creativity in High Schools
Dissertation Development Timeline
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Dissertation Working Title and Timeline
The Effectiveness of an Enrichment Program Using Dynamic
Geometry Software in Developing Mathematically Gifted
Students’ Geometric Creativity in High Schools
Dissertation Development Timeline
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Disputation Structure
The Status Quo
Theses (Solution Claims)
The Enrichment Program
The Geometric Creativity Test (GCT)
Study Experimentation Procedures
Conclusion
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Disputation Structure
The Status Quo
Theses (Solution Claims)
The Enrichment Program
The Geometric Creativity Test (GCT)
Study Experimentation Procedures
Conclusion
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Disputation Structure
The Status Quo
Theses (Solution Claims)
The Enrichment Program
The Geometric Creativity Test (GCT)
Study Experimentation Procedures
Conclusion
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Disputation Structure
The Status Quo
Theses (Solution Claims)
The Enrichment Program
The Geometric Creativity Test (GCT)
Study Experimentation Procedures
Conclusion
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Disputation Structure
The Status Quo
Theses (Solution Claims)
The Enrichment Program
The Geometric Creativity Test (GCT)
Study Experimentation Procedures
Conclusion
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Disputation Structure
The Status Quo
Theses (Solution Claims)
The Enrichment Program
The Geometric Creativity Test (GCT)
Study Experimentation Procedures
Conclusion
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Disputation Structure
The Status Quo
Theses (Solution Claims)
The Enrichment Program
The Geometric Creativity Test (GCT)
Study Experimentation Procedures
Conclusion
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Disputation Structure
The Status Quo
Theses (Solution Claims)
The Enrichment Program
The Geometric Creativity Test (GCT)
Study Experimentation Procedures
Conclusion
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
“. . . The student most neglected, in terms of realizing full poten-
tial, is the gifted student of mathematics. Outstanding mathe-
matical ability is a precious societal resource, sorely needed to
maintain leadership in a technological world” (Shefield, 2000)
“. . . many programs for the mathematically gifted students are
inadequate and poorly designed; leaving the classroom teachers
behind, struggling in an attempt to effectively meet the edu-
cational needs of the mathematically gifted” (Rotigel & Fello,
2004)
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
“. . . The student most neglected, in terms of realizing full poten-
tial, is the gifted student of mathematics. Outstanding mathe-
matical ability is a precious societal resource, sorely needed to
maintain leadership in a technological world” (Shefield, 2000)
“. . . many programs for the mathematically gifted students are
inadequate and poorly designed; leaving the classroom teachers
behind, struggling in an attempt to effectively meet the edu-
cational needs of the mathematically gifted” (Rotigel & Fello,
2004)
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
“. . . The student most neglected, in terms of realizing full poten-
tial, is the gifted student of mathematics. Outstanding mathe-
matical ability is a precious societal resource, sorely needed to
maintain leadership in a technological world” (Shefield, 2000)
“. . . many programs for the mathematically gifted students are
inadequate and poorly designed; leaving the classroom teachers
behind, struggling in an attempt to effectively meet the edu-
cational needs of the mathematically gifted” (Rotigel & Fello,
2004)
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
“. . . even though geometric thinking is very important in many
scientific, technical, and occupational fields as well as in study-
ing mathematics, geometry is often neglected in school mathe-
matics especially in most high schools” (Olkun et al., 2005)
“. . . some possible reasons for this negligence would be the lack
of resources, such as concrete materials, computer applications,
and the lack of knowledge and expertise about how to use com-
puters and other materials for instructional purposes” (Olkun
et al., 2005)
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
“. . . even though geometric thinking is very important in many
scientific, technical, and occupational fields as well as in study-
ing mathematics, geometry is often neglected in school mathe-
matics especially in most high schools” (Olkun et al., 2005)
“. . . some possible reasons for this negligence would be the lack
of resources, such as concrete materials, computer applications,
and the lack of knowledge and expertise about how to use com-
puters and other materials for instructional purposes” (Olkun
et al., 2005)
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
The negligence of realizing full potential of the mathemat-
ically gifted.
The inadequate of the existing text books and programs.
The elimination of teaching geometry in high schools.
Teachers’ lack of knowledge and expertise in:
Enriching the existing text books and programs.
Using the integrated environments with technology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
The negligence of realizing full potential of the mathemat-
ically gifted.
The inadequate of the existing text books and programs.
The elimination of teaching geometry in high schools.
Teachers’ lack of knowledge and expertise in:
Enriching the existing text books and programs.
Using the integrated environments with technology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
The negligence of realizing full potential of the mathemat-
ically gifted.
The inadequate of the existing text books and programs.
The elimination of teaching geometry in high schools.
Teachers’ lack of knowledge and expertise in:
Enriching the existing text books and programs.
Using the integrated environments with technology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
The negligence of realizing full potential of the mathemat-
ically gifted.
The inadequate of the existing text books and programs.
The elimination of teaching geometry in high schools.
Teachers’ lack of knowledge and expertise in:
Enriching the existing text books and programs.
Using the integrated environments with technology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
The negligence of realizing full potential of the mathemat-
ically gifted.
The inadequate of the existing text books and programs.
The elimination of teaching geometry in high schools.
Teachers’ lack of knowledge and expertise in:
Enriching the existing text books and programs.
Using the integrated environments with technology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
The negligence of realizing full potential of the mathemat-
ically gifted.
The inadequate of the existing text books and programs.
The elimination of teaching geometry in high schools.
Teachers’ lack of knowledge and expertise in:
Enriching the existing text books and programs.
Using the integrated environments with technology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Status Quo
The negligence of realizing full potential of the mathemat-
ically gifted.
The inadequate of the existing text books and programs.
The elimination of teaching geometry in high schools.
Teachers’ lack of knowledge and expertise in:
Enriching the existing text books and programs.
Using the integrated environments with technology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
Thesis #1
The school mathematics textbooks should include open-ended and
divergent-production questions.
Thesis #2
The mathematically gifted students should be given the opportunity
to think like mathematicians do and re-invent mathematics by going
through the process which leads them to the product and not merely
learn the product (theorems and axioms).
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
Thesis #1
The school mathematics textbooks should include open-ended and
divergent-production questions.
Thesis #2
The mathematically gifted students should be given the opportunity
to think like mathematicians do and re-invent mathematics by going
through the process which leads them to the product and not merely
learn the product (theorems and axioms).
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
Thesis #1
The school mathematics textbooks should include open-ended and
divergent-production questions.
Thesis #2
The mathematically gifted students should be given the opportunity
to think like mathematicians do and re-invent mathematics by going
through the process which leads them to the product and not merely
learn the product (theorems and axioms).
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
Thesis #3
Learning and developing creativity, its operations and its skills,
should be taken into consideration and associated with mathemat-
ics curricula while they are designed. Furthermore, it should be a
part of daily lesson plans that mathematics teachers prepare for their
classrooms.
Thesis #4
Special schools or classes should be provided for the mathematically
gifted students at different educational levels and stages.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
Thesis #3
Learning and developing creativity, its operations and its skills,
should be taken into consideration and associated with mathemat-
ics curricula while they are designed. Furthermore, it should be a
part of daily lesson plans that mathematics teachers prepare for their
classrooms.
Thesis #4
Special schools or classes should be provided for the mathematically
gifted students at different educational levels and stages.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
Thesis #5
The use of integrated learning environments with technology, for
instance using Computer Algebra Systems (CAS) and Dynamic
Geometry Software (DGS) is strongly recommended for better learn-
ing outcomes.
Thesis #6
In-service and pre-service teachers of mathematics should be trained
on the ways and techniques that can be used to enrich the math-
ematical content for mathematically gifted students and the tech-
niques of developing creative thinking in the field of mathematics.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
Thesis #5
The use of integrated learning environments with technology, for
instance using Computer Algebra Systems (CAS) and Dynamic
Geometry Software (DGS) is strongly recommended for better learn-
ing outcomes.
Thesis #6
In-service and pre-service teachers of mathematics should be trained
on the ways and techniques that can be used to enrich the math-
ematical content for mathematically gifted students and the tech-
niques of developing creative thinking in the field of mathematics.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Enrichment Program
The Principles of Developing the Enrichment Program
The Content of the Enrichment Program
The Types of Enrichment Activities
The Appropriateness of the Enrichment Program
The Pilot Experimentation of the the Enrichment Program
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Enrichment Program
The Principles of Developing the Enrichment Program
The Content of the Enrichment Program
The Types of Enrichment Activities
The Appropriateness of the Enrichment Program
The Pilot Experimentation of the the Enrichment Program
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Enrichment Program
The Principles of Developing the Enrichment Program
The Content of the Enrichment Program
The Types of Enrichment Activities
The Appropriateness of the Enrichment Program
The Pilot Experimentation of the the Enrichment Program
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Enrichment Program
The Principles of Developing the Enrichment Program
The Content of the Enrichment Program
The Types of Enrichment Activities
The Appropriateness of the Enrichment Program
The Pilot Experimentation of the the Enrichment Program
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Enrichment Program
The Principles of Developing the Enrichment Program
The Content of the Enrichment Program
The Types of Enrichment Activities
The Appropriateness of the Enrichment Program
The Pilot Experimentation of the the Enrichment Program
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Enrichment Program
The Principles of Developing the Enrichment Program
The Content of the Enrichment Program
The Types of Enrichment Activities
The Appropriateness of the Enrichment Program
The Pilot Experimentation of the the Enrichment Program
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Enrichment Program
The Principles of Developing the Enrichment Program
The Content of the Enrichment Program
The Types of Enrichment Activities
The Appropriateness of the Enrichment Program
The Pilot Experimentation of the the Enrichment Program
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
1 The activities should provide the mathematically gifted students
with opportunities to explore some mathematical ideas using
the DGS in a creative fashion.
2 Activities within the program should provide the mathematically
gifted students with opportunities to reinvent the mathematical
ideas through both exploration and the refining of earlier ideas.
3 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.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
1 The activities should provide the mathematically gifted students
with opportunities to explore some mathematical ideas using
the DGS in a creative fashion.
2 Activities within the program should provide the mathematically
gifted students with opportunities to reinvent the mathematical
ideas through both exploration and the refining of earlier ideas.
3 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.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
1 The activities should provide the mathematically gifted students
with opportunities to explore some mathematical ideas using
the DGS in a creative fashion.
2 Activities within the program should provide the mathematically
gifted students with opportunities to reinvent the mathematical
ideas through both exploration and the refining of earlier ideas.
3 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.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
1 The activities should provide the mathematically gifted students
with opportunities to explore some mathematical ideas using
the DGS in a creative fashion.
2 Activities within the program should provide the mathematically
gifted students with opportunities to reinvent the mathematical
ideas through both exploration and the refining of earlier ideas.
3 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.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
4 Teaching the instructional activities, within the program, should
follow van Hiele phases of learning geometric concepts: Infor-
mation, guided orientation, explicitation, free orientation, and
integration.
5 The program activities should correspond to the students’ skills,
since they should experience success in order to stay motivated.
6 The enrichment activities should challenge students’ thinking,
enhance students’ achievement, and develop students’ geomet-
ric creativity.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
4 Teaching the instructional activities, within the program, should
follow van Hiele phases of learning geometric concepts: Infor-
mation, guided orientation, explicitation, free orientation, and
integration.
5 The program activities should correspond to the students’ skills,
since they should experience success in order to stay motivated.
6 The enrichment activities should challenge students’ thinking,
enhance students’ achievement, and develop students’ geomet-
ric creativity.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
4 Teaching the instructional activities, within the program, should
follow van Hiele phases of learning geometric concepts: Infor-
mation, guided orientation, explicitation, free orientation, and
integration.
5 The program activities should correspond to the students’ skills,
since they should experience success in order to stay motivated.
6 The enrichment activities should challenge students’ thinking,
enhance students’ achievement, and develop students’ geomet-
ric creativity.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
7 The instructional activities, within the enrichment program,
should be designed to be effective in revealing geometric cre-
ativity and in distinguishing between the mathematically gifted
students in terms of the geometric creativity and their responses.
8 The enrichment program activities should address standards for
school mathematics, for example the ones recommended by
(NCTM) as it is one of the most popular standards in the field
of teaching and learning mathematics.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Principles
7 The instructional activities, within the enrichment program,
should be designed to be effective in revealing geometric cre-
ativity and in distinguishing between the mathematically gifted
students in terms of the geometric creativity and their responses.
8 The enrichment program activities should address standards for
school mathematics, for example the ones recommended by
(NCTM) as it is one of the most popular standards in the field
of teaching and learning mathematics.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Content
Student’s Handouts
English Version
German Version
CD-ROM
English Version
German Version
Teacher’s Guide
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Content
Student’s Handouts
English Version
German Version
CD-ROM
English Version
German Version
Teacher’s Guide
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Content
Student’s Handouts
English Version
German Version
CD-ROM
English Version
German Version
Teacher’s Guide
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Content
Student’s Handouts
English Version
German Version
CD-ROM
English Version
German Version
Teacher’s Guide
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Content
Student’s Handouts
English Version
German Version
CD-ROM
English Version
German Version
Teacher’s Guide
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Content
Student’s Handouts
English Version
German Version
CD-ROM
English Version
German Version
Teacher’s Guide
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
1 Problem Solving Activities
2 Redefinition Activities
3 Construction Activities
4 Problem Posing Activities
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
1 Problem Solving Activities
2 Redefinition Activities
3 Construction Activities
4 Problem Posing Activities
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
1 Problem Solving Activities
2 Redefinition Activities
3 Construction Activities
4 Problem Posing Activities
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
1 Problem Solving Activities
2 Redefinition Activities
3 Construction Activities
4 Problem Posing Activities
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
1 Problem Solving Activities
2 Redefinition Activities
3 Construction Activities
4 Problem Posing Activities
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
1 Problem Solving Activities
2 Redefinition Activities
3 Construction Activities
4 Problem Posing Activities
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
1 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.
Activity 1
Activity 5
Activity 6
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
2 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.
Activity 2
Activity 4
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
3 Construction Activities
. . . the student is asked to come up with as many various and differ-
ent methods as he can to construct a geometric figure (e.g., parallel-
ogram) using constructing facility of Dynamic Geometry Software.
Activity 7
Activity 8
Activity 9
Activity 10
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Enrichment Activities
4 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.
Activity 11
Activity 12
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Appropriateness
Subjects
. . . were 8 experts in teaching and learning mathematics.
1 . . . of the program to the level of the mathematically gifted
students in high schools.
2 . . . of the enrichment activities to develop the mathematically
gifted students’ geometric creativity.
3 . . . of Cinderella to the program’s learning actions.
4 . . . of the teacher’s guide to mentor the program’s teaching
and learning processes.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Appropriateness
Subjects
. . . were 8 experts in teaching and learning mathematics.
1 . . . of the program to the level of the mathematically gifted
students in high schools.
2 . . . of the enrichment activities to develop the mathematically
gifted students’ geometric creativity.
3 . . . of Cinderella to the program’s learning actions.
4 . . . of the teacher’s guide to mentor the program’s teaching
and learning processes.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Appropriateness
Subjects
. . . were 8 experts in teaching and learning mathematics.
1 . . . of the program to the level of the mathematically gifted
students in high schools.
2 . . . of the enrichment activities to develop the mathematically
gifted students’ geometric creativity.
3 . . . of Cinderella to the program’s learning actions.
4 . . . of the teacher’s guide to mentor the program’s teaching
and learning processes.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Appropriateness
Subjects
. . . were 8 experts in teaching and learning mathematics.
1 . . . of the program to the level of the mathematically gifted
students in high schools.
2 . . . of the enrichment activities to develop the mathematically
gifted students’ geometric creativity.
3 . . . of Cinderella to the program’s learning actions.
4 . . . of the teacher’s guide to mentor the program’s teaching
and learning processes.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Appropriateness
Subjects
. . . were 8 experts in teaching and learning mathematics.
1 . . . of the program to the level of the mathematically gifted
students in high schools.
2 . . . of the enrichment activities to develop the mathematically
gifted students’ geometric creativity.
3 . . . of Cinderella to the program’s learning actions.
4 . . . of the teacher’s guide to mentor the program’s teaching
and learning processes.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Appropriateness
Subjects
. . . were 8 experts in teaching and learning mathematics.
1 . . . of the program to the level of the mathematically gifted
students in high schools.
2 . . . of the enrichment activities to develop the mathematically
gifted students’ geometric creativity.
3 . . . of Cinderella to the program’s learning actions.
4 . . . of the teacher’s guide to mentor the program’s teaching
and learning processes.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Pilot Experimentation
Voluntary Sessions
Subjects were 11 pre-service student teachers of mathematics, 7
male and 4 female, in the PHSG at the beginning of the summer
semester 2008.
In-seminar Sessions
Subjects were 30 pre-service student teachers, 15 male and 15 fe-
male, in the PHSG during the seminar of “Computer im Mathe-
matikunterricht” summer semester 2008.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Pilot Experimentation
Voluntary Sessions
Subjects were 11 pre-service student teachers of mathematics, 7
male and 4 female, in the PHSG at the beginning of the summer
semester 2008.
In-seminar Sessions
Subjects were 30 pre-service student teachers, 15 male and 15 fe-
male, in the PHSG during the seminar of “Computer im Mathe-
matikunterricht” summer semester 2008.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Pilot Experimentation
Voluntary Sessions
Subjects were 11 pre-service student teachers of mathematics, 7
male and 4 female, in the PHSG at the beginning of the summer
semester 2008.
In-seminar Sessions
Subjects were 30 pre-service student teachers, 15 male and 15 fe-
male, in the PHSG during the seminar of “Computer im Mathe-
matikunterricht” summer semester 2008.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6-step process
1 Specification of the Aim of the Test
. . . is to obtain a validated and reliable instrument to measure
geometric creativity.
2 Specification of the Components that the Test Measures
Fluency
Flexibility
Originality/Novelty
Elaboration
3 Creation of a Preliminary Version of the Test
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
4 Setting-up of a Grading Method for the Test
5 Content Validity Check
Subjects
. . . 13 judges from China, Egypt, and Germany.
. . . clarity and readability of test items.
. . . test items are appropriate to measure what they are
designed to measure.
. . . test items are appropriate to the level of the mathematically
gifted students in high schools.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
4 Setting-up of a Grading Method for the Test
5 Content Validity Check
Subjects
. . . 13 judges from China, Egypt, and Germany.
. . . clarity and readability of test items.
. . . test items are appropriate to measure what they are
designed to measure.
. . . test items are appropriate to the level of the mathematically
gifted students in high schools.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
4 Setting-up of a Grading Method for the Test
5 Content Validity Check
Subjects
. . . 13 judges from China, Egypt, and Germany.
. . . clarity and readability of test items.
. . . test items are appropriate to measure what they are
designed to measure.
. . . test items are appropriate to the level of the mathematically
gifted students in high schools.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
4 Setting-up of a Grading Method for the Test
5 Content Validity Check
Subjects
. . . 13 judges from China, Egypt, and Germany.
. . . clarity and readability of test items.
. . . test items are appropriate to measure what they are
designed to measure.
. . . test items are appropriate to the level of the mathematically
gifted students in high schools.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
4 Setting-up of a Grading Method for the Test
5 Content Validity Check
Subjects
. . . 13 judges from China, Egypt, and Germany.
. . . clarity and readability of test items.
. . . test items are appropriate to measure what they are
designed to measure.
. . . test items are appropriate to the level of the mathematically
gifted students in high schools.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
4 Setting-up of a Grading Method for the Test
5 Content Validity Check
Subjects
. . . 13 judges from China, Egypt, and Germany.
. . . clarity and readability of test items.
. . . test items are appropriate to measure what they are
designed to measure.
. . . test items are appropriate to the level of the mathematically
gifted students in high schools.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6 Test Piloting
Subjects
. . . were 30 pre-sevice student teachers, 15 male and 15 female,
in the PHSG during the summer semester 2008.
The Reliability Coefficient
Item-internal Consistency Reliability
Experimental Validity
Determining a Suitable Time-range
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6 Test Piloting
Subjects
. . . were 30 pre-sevice student teachers, 15 male and 15 female,
in the PHSG during the summer semester 2008.
The Reliability Coefficient
Item-internal Consistency Reliability
Experimental Validity
Determining a Suitable Time-range
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6 Test Piloting
Subjects
. . . were 30 pre-sevice student teachers, 15 male and 15 female,
in the PHSG during the summer semester 2008.
The Reliability Coefficient
Item-internal Consistency Reliability
Experimental Validity
Determining a Suitable Time-range
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6 Test Piloting
Subjects
. . . were 30 pre-sevice student teachers, 15 male and 15 female,
in the PHSG during the summer semester 2008.
The Reliability Coefficient
Item-internal Consistency Reliability
Experimental Validity
Determining a Suitable Time-range
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6 Test Piloting
Subjects
. . . were 30 pre-sevice student teachers, 15 male and 15 female,
in the PHSG during the summer semester 2008.
The Reliability Coefficient
Item-internal Consistency Reliability
Experimental Validity
Determining a Suitable Time-range
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
The Geometric Creativity Test
Test Design
6 Test Piloting
Subjects
. . . were 30 pre-sevice student teachers, 15 male and 15 female,
in the PHSG during the summer semester 2008.
The Reliability Coefficient
Item-internal Consistency Reliability
Experimental Validity
Determining a Suitable Time-range
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Subjects
. . . were 7 mathematically gifted students in Landesgymnasium
fur Hochbegabte (LGH).
. . . were 5 eleventh graders, 1 tenth grader, and 1 ninth grader
(2 male, 5 female).
. . . have IQ > 130, 14/15, and high interest in solving
mathematical problems.
Experimental Design
The pre-experimental one-group, pretest – intervention – posttest
design was used to investigate the effectiveness of the enrichment
program in developing the mathematically gifted students’ geometric
creativity.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Subjects
. . . were 7 mathematically gifted students in Landesgymnasium
fur Hochbegabte (LGH).
. . . were 5 eleventh graders, 1 tenth grader, and 1 ninth grader
(2 male, 5 female).
. . . have IQ > 130, 14/15, and high interest in solving
mathematical problems.
Experimental Design
The pre-experimental one-group, pretest – intervention – posttest
design was used to investigate the effectiveness of the enrichment
program in developing the mathematically gifted students’ geometric
creativity.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Subjects
. . . were 7 mathematically gifted students in Landesgymnasium
fur Hochbegabte (LGH).
. . . were 5 eleventh graders, 1 tenth grader, and 1 ninth grader
(2 male, 5 female).
. . . have IQ > 130, 14/15, and high interest in solving
mathematical problems.
Experimental Design
The pre-experimental one-group, pretest – intervention – posttest
design was used to investigate the effectiveness of the enrichment
program in developing the mathematically gifted students’ geometric
creativity.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Subjects
. . . were 7 mathematically gifted students in Landesgymnasium
fur Hochbegabte (LGH).
. . . were 5 eleventh graders, 1 tenth grader, and 1 ninth grader
(2 male, 5 female).
. . . have IQ > 130, 14/15, and high interest in solving
mathematical problems.
Experimental Design
The pre-experimental one-group, pretest – intervention – posttest
design was used to investigate the effectiveness of the enrichment
program in developing the mathematically gifted students’ geometric
creativity.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Subjects
. . . were 7 mathematically gifted students in Landesgymnasium
fur Hochbegabte (LGH).
. . . were 5 eleventh graders, 1 tenth grader, and 1 ninth grader
(2 male, 5 female).
. . . have IQ > 130, 14/15, and high interest in solving
mathematical problems.
Experimental Design
The pre-experimental one-group, pretest – intervention – posttest
design was used to investigate the effectiveness of the enrichment
program in developing the mathematically gifted students’ geometric
creativity.Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Administering the Pretest
Administering the Enrichment Program
Administering the Posttest
Experimental Results
There are statistically significant differences at the level 0.05
between the mean ranks of the subjects’ scores on the pre-
post measurements of the geometric creativity and its four sub-
components in favor of the post measurement.
The enrichment program using DGS has a suitable level of
effectiveness in developing the mathematically gifted students’
geometric creative potential and its sub-components.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Administering the Pretest
Administering the Enrichment Program
Administering the Posttest
Experimental Results
There are statistically significant differences at the level 0.05
between the mean ranks of the subjects’ scores on the pre-
post measurements of the geometric creativity and its four sub-
components in favor of the post measurement.
The enrichment program using DGS has a suitable level of
effectiveness in developing the mathematically gifted students’
geometric creative potential and its sub-components.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Administering the Pretest
Administering the Enrichment Program
Administering the Posttest
Experimental Results
There are statistically significant differences at the level 0.05
between the mean ranks of the subjects’ scores on the pre-
post measurements of the geometric creativity and its four sub-
components in favor of the post measurement.
The enrichment program using DGS has a suitable level of
effectiveness in developing the mathematically gifted students’
geometric creative potential and its sub-components.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Administering the Pretest
Administering the Enrichment Program
Administering the Posttest
Experimental Results
There are statistically significant differences at the level 0.05
between the mean ranks of the subjects’ scores on the pre-
post measurements of the geometric creativity and its four sub-
components in favor of the post measurement.
The enrichment program using DGS has a suitable level of
effectiveness in developing the mathematically gifted students’
geometric creative potential and its sub-components.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Administering the Pretest
Administering the Enrichment Program
Administering the Posttest
Experimental Results
There are statistically significant differences at the level 0.05
between the mean ranks of the subjects’ scores on the pre-
post measurements of the geometric creativity and its four sub-
components in favor of the post measurement.
The enrichment program using DGS has a suitable level of
effectiveness in developing the mathematically gifted students’
geometric creative potential and its sub-components.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Procedures of the Experimental Study
Administering the Pretest
Administering the Enrichment Program
Administering the Posttest
Experimental Results
There are statistically significant differences at the level 0.05
between the mean ranks of the subjects’ scores on the pre-
post measurements of the geometric creativity and its four sub-
components in favor of the post measurement.
The enrichment program using DGS has a suitable level of
effectiveness in developing the mathematically gifted students’
geometric creative potential and its sub-components.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Conclusion
The positive impact of the enrichment program can be traced
back to its content and designed enrichment activities.
The effectiveness of the enrichment program can be also traced
back to the use of DGS and its different facilities throughout
the teaching course.
The results can be also ascribed to the characteristics of the
mathematically gifted.
Recommendations
. . . are given in the six suggested theses presented in the beginning
of the disputation.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Conclusion
The positive impact of the enrichment program can be traced
back to its content and designed enrichment activities.
The effectiveness of the enrichment program can be also traced
back to the use of DGS and its different facilities throughout
the teaching course.
The results can be also ascribed to the characteristics of the
mathematically gifted.
Recommendations
. . . are given in the six suggested theses presented in the beginning
of the disputation.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Conclusion
The positive impact of the enrichment program can be traced
back to its content and designed enrichment activities.
The effectiveness of the enrichment program can be also traced
back to the use of DGS and its different facilities throughout
the teaching course.
The results can be also ascribed to the characteristics of the
mathematically gifted.
Recommendations
. . . are given in the six suggested theses presented in the beginning
of the disputation.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Conclusion
The positive impact of the enrichment program can be traced
back to its content and designed enrichment activities.
The effectiveness of the enrichment program can be also traced
back to the use of DGS and its different facilities throughout
the teaching course.
The results can be also ascribed to the characteristics of the
mathematically gifted.
Recommendations
. . . are given in the six suggested theses presented in the beginning
of the disputation.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Conclusion
The positive impact of the enrichment program can be traced
back to its content and designed enrichment activities.
The effectiveness of the enrichment program can be also traced
back to the use of DGS and its different facilities throughout
the teaching course.
The results can be also ascribed to the characteristics of the
mathematically gifted.
Recommendations
. . . are given in the six suggested theses presented in the beginning
of the disputation.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
1 Reforming school mathematics textbooks to include open-
ended and divergent-production questions.
2 Giving opportunities to students to re-invent mathematics.
3 Including creativity skills and operations in every day mathe-
matics lesson plan.
4 Providing special schools and classes for the mathematically
gifted students.
5 Using the integrated learning environment with technology is
strongly recommended for better learning outcomes.
6 Training in-service and pre-service teachers on the ways and
techniques of enriching the current content and the use of tech-
nology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
Status Quo Theses Enrichment Program GCT Experimentation Conclusion
Theses
1 Reforming school mathematics textbooks to include open-
ended and divergent-production questions.
2 Giving opportunities to students to re-invent mathematics.
3 Including creativity skills and operations in every day mathe-
matics lesson plan.
4 Providing special schools and classes for the mathematically
gifted students.
5 Using the integrated learning environment with technology is
strongly recommended for better learning outcomes.
6 Training in-service and pre-service teachers on the ways and
techniques of enriching the current content and the use of tech-
nology.
Mohamed El-Demerdash Doctoral Dissertation Disputation
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