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Geometry

Geometry. EDN 322. NCTM’S STANDARD FOR GEOMETRY . analyze characteristics and properties of two-and three-dimensional geometric objects and develop mathematical arguments about geometric relationships;

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Geometry

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  1. Geometry EDN 322

  2. NCTM’S STANDARD FOR GEOMETRY • analyze characteristics and properties of two-and three-dimensional geometric objects and develop mathematical arguments about geometric relationships; • specify locations and describe spatial relationships using coordinate geometry and other representational systems; Instructional programs from pre-kindergarten through grade twelve should enable all students to--

  3. NCTM’S STANDARD FOR GEOMETRY Instructional programs from pre-kindergarten through grade twelve should enable all students to-- • apply transformations and use symmetry to analyze mathematical situations; • use visualization, spatial reasoning, and geometric modeling to solve problems.

  4. Goals of Geometry for K-6 Students • Development of useful intuition and knowledge about shapes in the environment • Investigations that are tied to the real world • Analysis of shapes for their usefulness and application to solve real world problems

  5. Why Teach Geometry? • Useful in everyday situations and it is connected to other mathematical and academic content • Allows for orderly representation and description of our world • Children are naturally interested in geometry • Children’s spatial abilities frequently exceed their numerical skills thus providing motivation for number understanding

  6. Van Hiele Levels of Understanding LEVEL DESCRIPTION SAMPLE RESPONSES OF CHILDREN 0 Visualization Children view a Shown a rectangle and asked to identify geometric shape as a it, the child may say, “It is a rectangle whole. They do not because it looks like a book cover.” describe properties of the shape.

  7. Van Hiele Levels of Understanding LEVEL DESCRIPTION SAMPLE RESPONSES OF CHILDREN 1 Analysis Children recognize A child may say that the rectangle has the properties of four sides and square corners. figures. They do not see relations between properties.

  8. Van Hiele Levels of Understanding LEVEL DESCRIPTION SAMPLE RESPONSES OF CHILDREN 2 Informal Students see relations A student may say that since the angles Deduction between properties of a rectangle are right angles, the of a class of shapes. opposite sides are parallel.

  9. Van Hiele Levels of Understanding LEVEL DESCRIPTION SAMPLE RESPONSES OF CHILDREN 3 Deduction Both level 3 (level at which students can use deduction to 4 Rigor prove statements) and level 4 ( level at which students see geometry in the abstract) are beyond the scope of most students in middle school. Level 3 is the level at which a proof-oriented high school geometry course is taught.

  10. Transformations A translation is created by moving an object in a straight line to a new location.

  11. Transformations A reflection is made by picking up the object, turning it over, and sliding it to the new location creating a mirror image.

  12. Transformations A Rotation is created by moving an object around a fixed point.

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