The%20Construction%20of%20Number%20A%20Constance%20Kamii%20Perspective

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The Construction of Number A Constance Kamii
Perspective

• Paterson Public Schools
• Dept. of Early Childhood Education
• Craig Wachsman

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Program Philosophy

• Children are constructivists.
• Children are active learners.
• Children are intrinsically motivated and self
  directed.

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Program Goals

• The construction of Number.
• Cognitive Process Order
• Cognitive Process Hierarchical Inclusion

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3 Stages of Quantification

• Global
• One-to-One Correspondence
• Counting

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Global Stage of Quantification

• Young children are guided initially by their
  perceptions when quantifying.
• At this stage, children make a visual
  approximation of the quantity they are attempting
  to match.
• When asked to take as many objects as are in
  another group, they may create a pile or row that
  looks about the same as the model set.
• (Andre-Anna-Christian-Nicole)

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One-to-One Correspondence Stage

• Children attempt to make an equivalent set by
  taking one object for each item in the original
  set.
• Children may point to an item in the original set
  each time they select a new object for their own
  set.
• They may also line up the materials in rows so
  that each object they take is opposite one item
  in the original set.
• (Omerlyn-David)

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Counting Stage Conservers

• Children understand that the last item they count
  represents the total.
• Children realize that there is a particular order
  to saying the counting words, and each object can
  be counted one, and only one time.

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Conservation Task

• To conserve number means to think that the
  quantity remains the same when the spatial
  arrangement of the objects has been changed.

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Conservers Rationale

• The Identity Argument
• Theres just as many blue ones as red ones
  because you didnt add anything or take anything
  away.

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Conservers Rationale

• The Reversibility Argument
• We could put all the red ones back to the way
  they were before, and youll see that theres the
  same number.

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Conservers Rationale

• The Compensation Argument
• The red row is longer, but theres more space in
  between. So the number is still the same.

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Teachers RoleEntering the Childs World

• Imitating the child as a means of entering their
  world of play
• When playing math games with children, teachers
  or parents can carefully observe a childs level
  of quantification and model the next stage.

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Math Games

• Aiming Games
• Bowling Ball Games
• Hiding Games
• Hide and Seek
• 6 Tongue Depressors
• Races Chasing Games
• Musical Chairs
• Duck, Duck, Goose

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MaterialsMath Games

• Strawberry Game
• Children roll a die to determine how many cloth
  strawberries they can put in their baskets. At
  the end of the game, children can compare
  quantities of strawberries if they chose.

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MaterialsMath Games

• Mail a Letter Game
• Each play has a game board with a short path
  leading from a child sticker to a mailbox.
  Children use a die or spinner to move along the
  path. (A Letter To Amy by Keats)
• Children quantify and create equilvent sets as
  they attempt to move the same number of spaces as
  indicated on the die or spinner.

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MaterialsMath Games

• Balloon (Long Path) Game
• Children move small people along a path made from
  balloon stickers and try to reach the party at
  the end of the game. Younger children should use
  one die, while older children could use two dice
  and add them together.

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Mathematical Opportunities Throughout the Day
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I found all the rough paper.

• Texture

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Andre uses all the triangle blocks and looks for
more.

• Shape

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Michele lines up the blocks from shortest to
longest.

• Seriation

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Do you want the story now or would you rather
finish your collage.

• Order

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Nicole looks at the schedule to see what comes
after group time.

• Sequence

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David breaks the play dough in two pieces and
gives a part to Maria.

• Parts of the Whole

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Stephanie puts cube blocks on her
constructionred, yellow, blue, red, yellow, blue

• Pattern

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Can we have just five more minutes?

• Time

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I need four more bears.

• Number

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These cars are bigger than those.

• Size

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I have a new striped shirt.

• Pattern

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Assessment/Evaluation

• Observation
• Conservation Tasks