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Using GSP in Discovering a New Theory Dr. Mofeed Abu-Mosa 20-3-2007

Using GSP in Discovering a New Theory Dr. Mofeed Abu-Mosa 20-3-2007. This paper Connects Van Hiele theory and its levels of geometric thinking with the dynamic software program geometry sketchpad.

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Using GSP in Discovering a New Theory Dr. Mofeed Abu-Mosa 20-3-2007

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  1. Using GSP in Discovering a New Theory Dr. Mofeed Abu-Mosa 20-3-2007 • This paper • Connects Van Hiele theory and its levels of geometric thinking with the dynamic software program geometry sketchpad. • 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.

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

  3. 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.

  4. Levels of Geometric Thinking Distributed According to Geometric Skills

  5. reasoning and justification skills, culminating in work with proof in the secondary grades.

  6. Example • 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)

  7. 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).

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

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

  10. A B Ron's Theorem

  11. My Extension

  12. Idea of the proof

  13. Try to discover relation between the area of the origin triangle and the area of trapezoids

  14. the geometric pattern can be converted into algebraic one

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

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