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## Using a Dynamic Software as a Tool |

AREA OF | |||||

Triangle | Trapezoid1 | Trapezoid2 | Trapezoid3 | Trapezoid4 | Trapezoid5 |

1 | 5 | 24 | 115 | 551 | 2640 |

2 | 10 | 48 | 230 | 1102 | 5280 |

3 | 15 | 72 | 345 | 1653 | 7920 |

4 | 20 | 96 | 460 | 2204 | 10560 |

5 | 25 | 120 | 575 | 2755 | 13200 |

6 | 30 | 144 | 690 | 3306 | 15840 |

7 | 35 | 168 | 805 | 3857 | 18480 |

The previous table shows the areas of the origin triangle in different situations and how it relates to the areas of trapezoids. I don’t have the time to finish the work so I do it by excel and fin the best fit polynomial that represents the relation.

It can be seen easily that the geometric pattern can be converted into algebraic one.

The paper suggests a method of using dynamic software (GSP) as a tool of developing geometric thinking which can be summarized by the following steps:

- Find an old theory in geometry.
- Use GSP to revisit the theory.
- Ask your self " WHAT IF" and start using GSP to discover.
- Justify your thinking.
- Prove your conclusion.

Most of old theorems can lead our students to new ones.

1. Chanan, Steven & others (2002). Geometer's Sketchpad Workshop Guide. Key Curriculum press 2002.

2. Evan, Ruhama & Tirosh, Dina, 2003. Teacher Knowledge and Understanding of students' Mathematical Learning. Hand Book of International Research in Mathematics Education. Lawrence Erlbaum Association 2002.

3. Hoffer, A. (1981). Geometry is more than proof, Mathematics Teacher, 74, 11-18.

4. Hollebrands, Karen F, 2007. The Role of a Dynamic Software Program for Geometry in the Strategies High School Mathematics Students Employ. Journal of Research in Mathematics Education. Vol 38, No. 2, 164-192.

5. Jackiw, Nicholas, The Geometry's Sketchpad. Emeryville, Calif: Key Curriculum Press, 1995.

6. MeAlister Ron, Martinez-Cruz Armando and Gannon Gerald (2004). Ron's Theorem and Beyond: a True Mathematician and GSP in Action. Mathematics Teacher. Vol. 97, No. 2. Feb 2004. PP 148- 151.

7. خصاونة، أمل (1994). مستويات التفكير في الهندسة لدى الطلبة المعلمين، **أبحاث اليرموك**، المجلد العاشر، العدد الأول، ص ص

439 – 481.

**Mofeed A. Abumosa**, PhD Curriculum & Instruction- Math Education

Faculty of Education, Arab Open University- Jordan Branch,

Jordan, Amman, P.O Box 240872, code 11121

**Technical Note**:

GSP stands for The Geometer's Sketchpad®. It was used in conjunction with Dynamic Geometry® Software for Exploring Mathematics, Version 4. Visit http://www.keypress.com/x5521.xml for information about the software

According to Dr. Abumosa: “I purchased the software last year and started training on it . Readings in* Mathematics Teacher* (NCTM) led me to use the software to explore new math ideas for both math and math education. This software is dynamic. It enables the user to measure length, area, etc…, it enables construction of geometric objects based on the idea of the father and child, so it gives the mathematician, the math teacher and students an opportunity to discover new concepts in mathematics and employ new techniques in teaching geometry.”