Transcript nctm`s standard for geometry

Geometry
EDN 322
NCTM’S STANDARD FOR
GEOMETRY
Instructional programs from pre-kindergarten through grade
twelve should enable all students to--
 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;
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.
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
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.
SAMPLE RESPONSES OF CHILDREN
LEVEL
DESCRIPTION
2 Informal
Students see relations
A student may say that since the angles
between properties
of a rectangle are right angles, the
of a class of shapes.
opposite sides are parallel.
Deduction
SAMPLE RESPONSES OF CHILDREN
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.