NCTM Principles & Standards and Mathematics Education

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

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

Four Types Inductive Deductive Proportional Spatial Reasoning

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

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

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

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

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

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

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

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

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

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