Behaviorism and Constructivism

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Behaviorism and Constructivism

• What Does it Look Like in a Classroom?

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Behaviorism

• Behavior can be shaped through reinforcement.
• Practice promotes desired behavior.
• Edward L. Thorndike, B.F. Skinner, Robert Gagne

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Constructivism I

• Learners actively create or invent (construct)
  their own knowledge.
•  Students create (construct) new mathematical
  knowledge by reflecting on their physical and
  mental actions.

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Constructivism II

• Learning reflects a social process in which
  children engage in dialogue and discussion with
  themselves as well as others as they develop
  intellectually.
• William Brownell, Jean Piaget, Jerome Bruner,
  Zoltan Dienes

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Similarity in Learning Frameworks

• Active involvement, communication
• Several characteristics and stages of thinking
  Children progress through stages as they mature
• Learning proceeds from concrete to abstract
• Symbols follow conceptualization and meaning

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Procedural Knowledge vs. Conceptual Knowledge

• Procedural Knowledge-based on a series of
  actions, rules,and algorithms
• Conceptual Knowledge-based on meaningful
  connections among existing and new concepts

dividethen multiply
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Which is it?

• To divide 23 candies among four friends, Steve
  knows each must receive an equal amount and there
  may be some left.
• To take 23 divided by 4, Steve knows to take 5 x
  4 and subtract the result from 23.

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Which is it?

• Sara knows when counting, 7 follows 6.
• Sara knows 7 represents 7 objects.

I have painted 6 balls, only one more to go.
9
Which is it?

• Joe knows that to find 25 of a price he can cut
  the price in half, then half again to find
  one-fourth.
•  Joe knows that to find 25 of a price he can
  multiply the price by .25.

to find 25 I must
10
Which is it?

• Nancy knows that to find the area of a rectangle,
  she must find out how much space it covers.
• Nancy knows that to find the area of a rectangle,
  she must multiply the length times the width.

I must multiply
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Principles for Learning Mathematics I

• Actively involve students.
• Learning is developmental.
• Build on previous learning.
• Communication contributes significantly to
  understanding.
• Good questions facilitate learning

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Principles for Learning Mathematics II

• Manipulatives aid learning.
• Metacognition affects learning.
• Teachers' attitudes are vital.
• Experiences influence anxiety.
• Gender aptitudes are equal.
• Retention can improve.

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The Staircase Problem I

• Examine these staircases
• Describe in words a relationship (formula)
  involving the sum of the first 4 counting numbers
  suggested.

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The Staircase Problem II

• Examine these staircases
• Describe in words a relationship (formula)
  suggested. How many counting numbers are
  involved? What is their sum?

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The Staircase Problem III

• Examine these staircases
• The sum of the first n counting numbers is 1 2
  3 4 . . . . n _________