Mathematical Tools

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Mathematical Tools

• Jessica Hoilman
• Heather Respass
• Jaime Wilson
• Debbie Winters
• Justina Wright

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Representations

• Realistic
• Concrete
• Abstract
• Teacher moves from realistic representations
  toward abstract representations over time.

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Realistic Representations
Illustrations / Pictures

• Creates interest
• Closer to reality
• Connect with the world around them
• Visual learners

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Use with stories and math sentences
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Concrete Representations

• Dots
• to represent pumpkins
• (builds on childrens experience)
• Tiles
• Fingers

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Subitizing

• Dot Flash
• Different patterns flashed on screen
• Short time forced students to subitize
• Students became familiar with patterns that made
  it easier for them to subitize

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Abstract Representations

• Teacher writes number sentences that represent
  students thought processes

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Organizing ThinkingCharts Grids

• Monkeys Trees
• Two-column chart
• 10-Frame
• Double 10-Frame

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Two-Column Chart

• Placed between trees to transition children
  realistic ? abstract
• Organizes ideas of students
• Students explore fact families
• Different combinations that form the same result

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10-Frame Double 10-Frame

• Encouraged grouping of numbers, especially by
  fives and tens
• Children worked with facts instead of counting
• Short exposure forced children to subitize and
  then add subitized groupings
• Students solved algebraic problems
• (has six pumpkins, how many more does he need to
  fill the crate of 10 pumkins?)

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Manipulatives

• Engage the psychomotor domain
• Tiles
• Fingers
• Bodies

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Tiles

• Create a visual representation of quantity they
  (as individuals) find easy to subitize
• Create and work with patterns

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Finger Play

• Do it- Think it-Say it
• Clumping
• Hands naturally group numbers by fives
• Students compose big numbers with different
  combinations of little numbers
• Working with facts (not counting!)

14
Games

• Simon Says
• Children had to pay close attention to teacher
• Opportunity to introduce and practice facts
• Engaging The children enjoyed it!

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Stories

• Monkeys in trees, Bus passengers, Farmer Earl and
  his pumpkins
• Help relate problems to real life
• Create Interest
• Helps auditory learners

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Drama

• Acting the story out is a concrete way to present
  math concepts
• Physical manipulation
• Something different than the usual class setting
• Good for children to be active
• Visual Bodily-Kinesthetic learners

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Dont Forget the Affective Domain!!

• Students must be interested to attend.
• Students must attend to learn.