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Description of Presentation Appropriate use of technology is an - - PDF document

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NCTM 2012 Presentation no video.notebook April 26, 2012 Preparing Smart Teachers to Teach with SMART TM Technology NCTM Annual Conference April 26, 2012 Philadelphia, PA Mary Lou Metz (mlmetz@iup.edu) Edel Reilly Francisco Alarcon Indiana

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 1 April 26, 2012

Preparing Smart Teachers to Teach with SMARTTM Technology NCTM Annual Conference April 26, 2012 Philadelphia, PA

Mary Lou Metz (mlmetz@iup.edu) Edel Reilly Francisco Alarcon Indiana University of PA

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 2 April 26, 2012

Description of Presentation

Appropriate use of technology is an essential component of preparing pre­ service teachers to teach mathematics. We will share smart technology lessons, activities, strategies, and tools we have used in our work with pre­service mathematics teachers at the elementary, middle school, and secondary levels.

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 3 April 26, 2012

Agenda

  • Example from Geometry
  • Example from Algebra
  • Example from Number Theory
  • Example from Fraction Concepts
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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 4 April 26, 2012

Examples from Geometry

  • Methods Course for PreK ­ 4 Education

Majors

  • Lesson: Teaching Geometry concepts

­ Four NCTM content goals for geometry

Shapes and properties Transformations Location Visualization

­ Five van Hiele levels of geometric thought

0: Visualization 1: Analysis 2: Informal Deduction 3: Deduction 4: Rigor

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 5 April 26, 2012

Shapes and Properties - Level 0

Click here to check your answer.

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Shapes and Properties - Level 1

Back to Geometry Goals

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Transformations - Level 1

Back to Geometry Goals

  • Reflect the shape across the

x- axis.

  • Reflect the shape across the

y-axis.

Click here to check your answer. Click here to check your answer.

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 9 April 26, 2012

Visualization - Level 0 Pentominoes

Using 5 squares, make as many DIFFERENT shapes as you can. Each square must share a side with at least one other square.

Click here to check your answer.

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 11 April 26, 2012

Examples from Algebra

  • Grades 4 through 8 Algebra Course
  • Modeling the simplification of expressions.

Distributive property Adding and subtracting polynomials Multiplying and factoring polynomials

  • Graphing equations
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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 12 April 26, 2012

Distributive Property

Use the same concept that was applied with multiplication of integers, think of the first factor as the counter. The same rules apply. 3(x + 2)

1

x

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 13 April 26, 2012

Addition and Subtraction of Polynomials

  • 1. (x2 + 2x + 1) + (x2 ­ x ­ 4)

x2 x2 x x ­x

1

­1 ­1 ­1 ­1

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 14 April 26, 2012

  • 4. (2x2 + 2) ­ (x2 + 2x ­ 1)

x2 x2

1 1

x ­x

1

­1

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 15 April 26, 2012

Substitution

Algebra tiles can be used to model substitution. Represent original expression with tiles. Then replace each rectangle with the appropriate tile

  • value. Combine like terms.

3 + 2x let x = 4

1

x

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 16 April 26, 2012

Multiplication Binomials­­Using Algebra Tiles x x

1 1 1 1 1

x2 x

1

(x + 3)(x + 2)

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 17 April 26, 2012

Make a collection of 2 big squares, 7 rectangles, and 6 ones. How many ways can they be arranged? Which set looks aesthetically pleasing (in a rectangle)? What are the dimensions of the rectangle? This will lead to factoring.

x2 x

1

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  • 3. x2 + 6x + 8

x2 x

1

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A rational function is a function f that is a quotient of two polynomials, that is, where p(x) and q(x) are polynomials and where q(x) is not the zero polynomial. The domain of f consists of all inputs x for which q(x)≠ 0.

­10 ­5 5 10 ­2 ­1 1 2 x y

f(x) =

p(x) q(x)

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­5 5 10 1 2 x y

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­10 ­5 5 10 ­20 ­10 10 20 30 x y

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Example from Number Theory

  • Introduction to Number Theory for

secondary mathematics education majors

  • Lesson: introduction to divisibility and

proof techniques

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NCTM 2012 Presentation no video.notebook Metz, Reilly & Alarcon 23 April 26, 2012

Some Other Number Theory Magicians

Diophantus of Alexandria

Euclid

Fibonacci

Euler

Carl Friedrich Gauss

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Onto some magic with numbers ...

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Was this really a magic trick?

Is there a pattern you notice?

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Theorem: An integer is divisible by 9 if and only if the sum of its digits is divisible by 9

Definition: An integer b is divisible by an integer a≠0 if and

  • nly if b = a c for some integer c.
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Making a Video of the Class

Class April 18 2011.wmv

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Examples from Fraction Concepts

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Smart Pen background

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Fraction Concepts Task 1:

Video of Task 1

= 1

= ? = ?

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Attachments fractions1.pdf