1. NCTM Principles & Standards and Mathematics Education

2. The Process Standards Communication Reasoning Problem Solving
Connections
Representation
The Process Standards

3. Communication Two Ways of Communicating
To others what we mean about the mathematics we are doing and using
To use mathematics to communicate about the world around us
Communication

4. Four Types
Inductive
Deductive
Proportional
Spatial
Reasoning

5. Inductive Reasoning 92 – 1 = 80, 112 – 1 = 120 (odd number)2 – 1
32 – 1 = 8, 52 – 1 = 24, 72 – 1 = 48,
92 – 1 = 80, 112 – 1 = 120
(odd number)2 – 1
Inductive Reasoning

6. Inductive Reasoning Observations
Inductive Reasoning – Recognize what is common to a set of examples and the generalize
Inductive Reasoning

7. Deductive Reasoning – Proceed from the general to the specific THM: The difference of the square of an odd number and 1 is divisible by 8.
Deductive Reasoning

8. Proportional Reasoning
Proportional reasoning relies on direct and indirect variation. y = kx Y = k/x
Proportional Reasoning

9. Spatial Reasoning What kind of cross section will produce A square
A rectangle
An isosceles triangle
An equilateral triangle
An isosceles trapezoid
Spatial Reasoning

10. Problem Solving Learning & using strategies
Verifying &interpreting results
Reflecting on solutions and processes
Posing new problems
Generalizing results
Problem Solving

11. Jack is in a race with 15 other boys
Jack is in a race with 15 other boys. At the beginning of the race, he is 5th from last place. At the end of the race, he is in 3rd place. How many boys did he pass?
Problem Solving

12. Connections Two Types Between Math and the Real World (Modeling)
Within Mathematics itself
(a+b)2 b a a b
Connections

13. Connections Area of a regular polygon – Area of a circle
Diagonal of a rectangle – Diagonal of a prism
f(x)=ex – f(x) = ln(x)
Connections

14. Representation Three Types Numerical (Table) Visual (Graph)
Symbolic (Formula/Equation)
Representation