Saturday, October 17, 2009

Visualization Plays a Big Role in New Math Standards

The so called "core" standards that only include English and math still have to acknowledge the powerful role visualization plays in learning. Two of the eleven mathematics standards are about the use of images, visual objects, and spaces to learn and express mathematical concepts. Schools and universities, none-the-less, refuse to acknowledge visual communication as a core skill.

Standard 7 is about Modeling.
Modeling uses mathematics to help us make sense of the real world—to understand quantitative relationships, make predictions, and propose solutions.

A model can be very simple, such as a geometric shape to describe a physical object like a coin. Even so simple a model involves making choices. It is up to us whether to model the solid nature of the coin with a three-dimensional cylinder, or whether a two-dimensional disk works well enough for our purposes. For some purposes, we might even choose to adjust the right circular cylinder to model more closely the way the coin deviates from the cylinder.

Standard 8 is about Shape.
From only a few axioms, the deductive method of Euclid generates a rich body of theorems about geometric objects, their attributes and relationships. Once understood, those attributes and relationships can be applied in diverse practical situations—interpreting a schematic drawing, estimating the amount of wood needed to frame a sloping roof, rendering computer graphics, or designing a sewing pattern for the most efficient use of material.

Understanding the attributes of geometric objects often relies on measurement: a circle is a set of points in a plane at a fixed distance from a point; a cube is bounded by six squares of equal area; when two parallel lines are crossed by a transversal, pairs of corresponding angles are congruent.

Students understand that:
Shapes and their parts, attributes, and measurements can be analyzed deductively.
Mathematical shapes model the physical world, resulting in practical applications of geometry.
They can solve problems involving similar triangles and scale drawings and
apply properties of right triangles and right triangle trigonometry to solve problems.

Click on the heading above to see the standards.

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