CHAPTER 2: THE NATURE OF MATHEMATICS

A. PATTERNS AND RELATIONSHIPS

K-2
• Circles, squares, triangles, and other shapes can be found in things in nature...
• Patterns can be made by putting different shapes together or...
• Things move, or can be made to move, along straight, curved, circular...

3-5

• Mathematics is the study of many kinds of patterns, including numbers...
• Mathematical ideas can be represented concretely, graphically...

6-8

• Usually there is no one right way to solve a mathematical problem...
• Logical connections can be found between different parts of mathematics.

9-12

• Mathematics is the study of any patterns or relationships, whereas natural...
• As in other sciences, simplicity is one of the highest values in mathematics...
• Theories and applications in mathematical work influence each other...
• New mathematics continues to be invented, and connections between...
 

B. MATHEMATICS, SCIENCE, AND TECHNOLOGY

K-2

3-5

6-8

• Mathematics is helpful in almost every kind of human endeavor...

 

9-12

• Mathematical modeling aids in technological design by simulating...
• Mathematics and science as enterprises share many values and features...
• Mathematics provides a precise language for science and technology...
• Developments in science or technology often stimulate innovations...
• Developments in mathematics often stimulate innovations in science...

 

C. MATHEMATICAL INQUIRY

K-2
• Numbers and shapes can be used to tell about things.

3-5

• Numbers and shapes--and operations on them--help to describe...
• In using mathematics, choices have to be made about what operations...

6-8

• Mathematicians often represent things with abstract ideas, such as numbers...
• When mathematicians use logical rules to work with representations...

9-12

• Some work in mathematics is much like a game--mathematicians choose...
• Much of the work of mathematicians involves a modeling cycle...