In the article ‘’Learning Geometry in a Dynamic Computer Environment’’, software programs in geometry can encourage the development of students’ understanding and reasoning about two-dimensional shapes. In traditional elementary and middle school geometry curricula, students must learn list of rules, definitions, theorems and properties of shapes. But in Interactive Geometry Microworld, first of all, students develop personally logical geometric concepts. Moreover, they analyze carefully spatial geometric problems by using this program, instead of memorizing. In a word, this system help to students identify the geometric shapes and understand reasons analytically about them.

In order to understand theories describing mathematics and geometry, first of all students must personally envision these theories by using their current knowledge. According to The Van Hiele Levels, when students’ knowledge increases, they move through several levels of geometric thinking. The first level is Level0 (prerecognition). In this level, students do not know completely and adequately to properties of a shape’s. Then, in Level1 (visual), by thinking visual characteristics of shapes, students can identify and recognize the shapes. But in this level, students do not think any formal geometric concepts. In Level2 (descriptive/analytic), in order to identify and describe spatial relationships between parts of shapes and other shapes, students use formal geometric concepts. Moreover, in this level, students know all properties of all shapes. Then, in Level3 (abstract/relational), for groups and classes of shapes, students know necessary characteristics and properties. In this level, the most important thing is students understand and form abstract definitions. In level4 (formal axiomatic), students logically understand theorems and prove them.

The Shape Makers is also mentioned in the article. Thanks to the Shape Makers, students not only make shapes, but also they changed shapes’ sizes, orientation by dragging its vertices with Mouse. In initial activities, students use shape makers in order to make their own pictures. But now, students make more careful analysis and also formulate and describe geometric properties of shapes. Additionally finding lengths and measuring angles, students can also test parallelism and symmetry. Moreover, in the article, some examples are mentioned. They are related with some students using the shape makers. In episode1, three students were investigating the square maker at the beginning of their work with the Shape Makers. In episode2, students claim that all shapes made by the rhombus maker. Then, in episode3, students try to make some shapes by using rhombus maker. And in episode4, students try to make parallelogram, square, and rhombus by using rectangular in The Shape Maker. Finally in episode5, they realize that they can make only given shape by using shape maker. For example, by using parallelogram maker, they can make only parallelogram.

I think the interactive geometry instructional environment help students to realize that logic behind the shapes. When students do this, the Shape Maker help to student understand reasons about shapes by visually transforming them. Moreover, it encourages students to think about shapes and their properties. I think, because this model fosters the creativity, students learn permanently, not memorizingly. Therefore, that is the point, i think. Hence, I think, because of all these reasons, it is the best way of the learning geometry. But, in order to use this program by all students, all schools should have appropriate tools and technology. For this, government should provide schools to necessary budget.

http://www.questia.com/library/1G1-83032531/learning-geometry-in-a-dynamic-computer-environment

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