2. Using GSP in Discovering a New Theory Dr. Mofeed Abu-Mosa 20-3-2007 This paper 1. Connects Van Hiele theory and its levels of geometric thinking with the dynamic software program geometry sketchpad. 2.Offers an example of using GSP to discover a theory, which was developed from the Pythagorean Theorem by using GSP as a tool of thinking.

3. Through the study of geometry, students will learn: Geometric shapes and structures. How to analyze analyze shapes. Characteristics and relationships relationships between shapes. Reasoning and justification skills. Through tools such as dynamic geometry software which enables students to model model, and have an interactive experience experience with, a large variety of two-dimensional shapes NCTM 2000

4. How students learn specific mathematical domain or concept? Van Hiele theory a comprehensive theory yet formulated concerning geometry learning The theory claims that when students learn geometry they progress from one discrete level of geometrical thinking to another This progress is discontinuous and the levels are sequential and hierarchical The Van Hiele theory also suggests phases of instruction that help students progress through the levels.

5. Levels of Geometric Thinking Distributed According to Geometric Skills Level skill RecognitionAnalysisDeduction Visual Recognize geometric shapes by its' picture without knowing the shapes prosperities Recognize the relationship between different kinds of geometric shapes Uses information about a geometric shape to deduce more information Descriptive Naming a geometric shape. Explain statements that describe geometric shape Describes the relationships between geometric shapes. Defines geometric concepts clearly. Understand the difference between the definition, postulate and theorem Logical Understand the meaning of shape reservation in different situations. Uses the prosperities of geometric shapes to identify the subset relation Uses logic to prove and being able to deduce new knowledge from given facts

6. Recognize Shapes Recognize relation between Shapes Deduce more information Describe Shapes Describe relation between Shapes Deduce more information reasoning and justification skills, culminating in work with proof in the secondary grades.

7. Example construct a square Using GSP to construct a square. Draw segments (parallel and perpendicular) and try to make them congruent by daggering the points (level (1)). Construct a grid and join between points on the grid level (1)

8. Construct a circle and perpendicular and parallel lines level (2) Using transformations to do the construction level (2). Use the measure tool to justify your work level (3) Do the same construction in other ways level (3) Ask the student to prove the construction in an abstract way level (3).

9. By using the Custom Tool teachers can follow the thinking of every student and assess the level he (she) reaches

10. Suggestion Curriculum experts can maximize the use of dynamic software. Rebuilding the geometric content is needed to change the traditional way curriculums are written.

11. AB Ron's Theorem

12. My Extension

16. Idea of the proof

17. AREA OF TRIANGLETRAPEZOID1TRAPEZOID2TRAPEZOID3TRAPEZOID4TRAPEZOID5 15241155512640 2104823011025280 3157234516537920 42096460220410560 525120575275513200 630144690330615840 735168805385718480 Try to discover relation between the area of the origin triangle and the area of trapezoids

18. the geometric pattern can be converted into algebraic one

19. Thanks Most of old theorem can lead our students to new ones