the effectiveness of an enrichment program using dynamic geometry software in developing...

The Effectiveness of an Enrichment Program Using Dynamic Geometry

Software in Developing Mathematically Gifted Students’ Geometric Creativity

Mohamed El-Demerdash: PH Schwaebisch Gmuend

Ulrich Kortenkamp: PH Karlsruhe

Metz, France: ICTMT 9, July 7th 2009

Purposes of the Study

lTo identify the principles of preparing an enrichment program in Euclidean geometry using DGS to develop the mathematically gifted students’ geometric creativity in high schools.

lTo develop the enrichment program based on the identified principles.

lTo investigate the effectiveness of this program by testing it with high school students.

Presentation Structure

lThe Principles of Developing the Suggested Enrichment Program Using DGS.

lThe Suggested Enrichment Program.lHypotheses of the StudylGeometric Creativity Test (GCT).lProcedures of the Experimental Study.lResults.lConclusion.



lThe Suggested Enrichment Program.lHypotheses of the StudylThe Geometric Creativity Test.lProcedures of the Experimental Study.lResults.lConclusion.

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.

Principles > Principles 1 to 3

Principles

4. Teaching the instructional activities, within the program, should follow van Hiele phases of learning geometric concepts: Information, 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 suggested enrichment activities should challenge students’ thinking, enhance students’ achievement, and develop students’ geometric creativity.

Principles > Principles 4 to 6

Principles

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

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

Principles > Principles 7 and 8



lThe Suggested Enrichment Program.lHypotheses of the Study. lThe Geometric Creativity Test.lProcedures of the Experimental Study.lResults.lConclusion.

Content

lStudent’s HandoutslTeacher’s GuidelCD ROM

Enrichment Program > Content

Enrichment Activities

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

Enrichment Program > Content > Activities



Enrichment Program > Content > Activities > Problem Solving

Problem Solving Activities

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

Enrichment Program > Content > Activities > Problem Solving



Enrichment Program > Content > Activities > Redefinition

Redefinition Activities

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

Enrichment Program > Content > Activities > Redefinition



Enrichment Program > Content > Activities > Construction

Construction Activities

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

Enrichment Program > Content > Activities > Construction



Enrichment Program > Content > Activities > Problem Posing

Problem Posing Activities

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

Enrichment Program > Content > Activities > Problem Posing



lThe Suggested Enrichment Program.lHypotheses of the Study.lThe Geometric Creativity Test.lProcedures of the Experimental Study.lResults.lConclusion.

Hypotheses of the Study

There is a statistically significant difference at the level 0.05 between the mean ranks of the subjects’ scores on the pre-post measurements of the geometric …

1. Fluency Component2. Flexibility Component3. Originality/Novelty Component4. Elaboration Component5. Geometric Creativity as a Whole Ability

… measured by the designed geometric creativity test, in favor of the post measurement.

Hypotheses > Hypotheses 1 to 5

Hypotheses of the Study

The suggested enrichment program using dynamic geometry software has a suitable level of effectiveness in developing the mathematically gifted students’ geometric …

6. Fluency Component.7. Flexibility Component8. Originality Component9. Elaboration Component10.Overall Geometric Creative Potential

Hypotheses > Hypotheses 6 to 10

The Geometric Creativity Test

l Specification of the aim of the test.l Specification of the components that the test

measures.lCreation of a preliminary form of the test.l Set-up a grading method for the test.lContent validity check.lTest-piloting.

GCT > 6-step Designing Process

Subjects of the Study

lThe subjects of the study were 7 mathematically gifted students in Landesgymnasium für Hochbegabte (LGH).

lThe subjects consisted of 5 eleventh graders, 1 tenth grader, and 1 ninth grader (2 male, 5 female).

l Selection criteria of the subjects:IQ > 130, 14/15, and high interest in solving mathematical problems.

Procedures > Subjects

Experimental Design

lThe pre-experimental one-group, pretest –intervention – posttest design was used to investigate the effectiveness of the prepared enrichment program in developing the mathematically gifted students’ geometric creativity.

Procedures > Experimental Design

Administering the Pretest

lThe designed GCT was administered to the subjects as a pretest at the beginning of the experimental study to assess their geometric creativity before administering the suggested enrichment program.

l It took 100 minutes, which is the suitable time-range calculated for the GCT.

Procedures > Pretest

Administering the Program

lThe suggested enrichment program was administered to the study subjects during the first semester of the academic year 2008/2009.

lThe program administered in approximately 18 hours distributed on 12 weekly 90-minute sessions. The intervention took place in the computer lab of LGH where each student of the subjects had a PC with Cinderella installed on it.

Procedures > Intervention

Administering the Posttest

lThe designed GCT was administered to the subjects as a posttest at the end of the experimental study to assess their geometric creativity after administering the suggested enrichment program.

lThe test administered took 100 minutes, which is the suitable time-range calculated for the GCT.

Procedures > Posttest



lThe Suggested Enrichment Program.lHypotheses of the StudylThe Geometric Creativity Test.lProcedures of the Experimental Study.lResults.lConclusion.

Results of Pretest/Posttest

Mean Scores and SD of the Subjects on the Pretest and Posttest

Results > Pretest / Posttest

Results of Pretest/Posttest

Mean Scores of the Subjects on the Pretest and Posttest

Results > Pretest / Posttest

Results of Testing Hypothesis 1

Geometric Fluency Tests Results

Results > Hypothesis 1


Fluency Scores of the Subjects on the Pretest and Posttest



Geometric Flexibility Tests Results



Flexibility Scores of the Subjects on the Pretest and Posttest



Geometric Originality/Novelty Tests Results



Originality Scores of the Subjects on the Pretest and Posttest



Geometric Elaboration Tests Results



Elaboration Scores of the Subjects on the Pretest and Posttest



Overall Geometric Creativity Tests Results



Overall Geometric Creativity Scores of the Subjects on the Pretest and Posttest



The Effect Size of the Enrichment Program on Geometric Fluency



The Effect Size of the Enrichment Program on Geometric Flexibility



The Effect Size of the Enrichment Program on Geometric Originality/Novelty



The Effect Size of the Enrichment Program on Geometric Elaboration



The Effect Size of the Enrichment Program on Overall Geometric Creative Potential


Conclusion

l The study indicated that the effectiveness of the suggested enrichment program in developing the mathematically gifted students

l The study suggested the effectiveness of the use of DGS in promoting the mathematically gifted students in high schools.

l The results can be traced back to the content of the program.l The results can be ascribed to the use of DGS.l The results can be also traced to the characteristics of the

sample. l Recommendations:l The use of DGS, Promoting creativity with in classroom

subjects.l Suggestions for further research:l Regular students, true and quasi-experimental designs.

Conclusion

Questions

Thank you very much!

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