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

Status Quo Theses Enrichment Program GCT Experimentation Conclusion

Thank you very much!

Mohamed El-Demerdash Doctoral Dissertation Disputation