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NCTM Principles & Standards and Mathematics Education

NCTM Principles & Standards and Mathematics Education. Communication Reasoning Problem Solving Connections Representation. The Process Standards. Two Ways of Communicating To others what we mean about the mathematics we are doing and using

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NCTM Principles & Standards and Mathematics Education

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  1. NCTM Principles & Standards and Mathematics Education

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

  3. 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. 32 – 1 = 8, 52 – 1 = 24, 72 – 1 = 48, 92 – 1 = 80, 112 – 1 = 120 (odd number)2 – 1 Inductive Reasoning

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

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

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

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

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