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;

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--

NCTM’S STANDARD FOR GEOMETRY

apply transformations and use symmetry to analyze mathematical situations;

use visualization, spatial reasoning, and geometric modeling to solve problems.

Instructional programs from pre-kindergarten through grade twelve should enable all students to--

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

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

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.

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.

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.

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.

Transformations

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

Transformations

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

Transformations

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