Concrete and Numerical Imagery Strategies

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Concrete and Numerical Imagery Strategies

• F. D. Rivera, Ph.D.
• Department of Mathematics
• San Jose State University
• Module 15, Session 6

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Building Mental Images of Concepts

• The idea behind asking students with learning
  disabilities in math to build mental images of
  concepts and processes is that the images could
  assist them associate the appropriate actions
  necessary for thinking and working with the
  concepts and processes.

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Building Mental Images of Concepts

• 1. Ask students with learning disabilities in
  math to find suitable, personal mental images for
  the following concepts
•  
• Least Common Multiples
• Polynomials
• Rationals
• Radicals
•  
• Example Algebra tiles for polynomials
• Unifix cubes for least common multiples
•  
•  

4
Building Mental Images of Concepts

• 1. Ask students with learning disabilities in
  math to find suitable, personal mental images for
  the following concepts
•  
• Least Common Multiples
• Polynomials
• Rationals
• Radicals
•  
• Example Algebra tiles for polynomials
• Unifix cubes for least common multiples
•  
•  

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Building Mental Images of Processes

• 2. Ask students with learning disabilities in
  math to find suitable mental images for the
  following processes
•  
• Addition and subtraction of signed numbers
• Multiplication and division of signed numbers
•  
• Example A man or a woman that is walking along
  a number line

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Using Gestures to Convey a Mental Performance

• Some students with learning disabilities in math
  are successful in using concrete tools to perform
  some computation but then fail when they are
  asked to do similar tasks without the tools. What
  can be done to remedy this problem?

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Using Gestures to Convey a Mental Performance

• First, ask them to carry out a process concretely
  using a manipulative or some concrete device.
•  
• Second, ask them to carry out the same process
  mentally and then to show how it is done using an
  appropriate gesture.
•  
• Third, repeat the second step above continuously
  until they obtain success in performing a
  computation mentally.

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Using Gestures to Convey a Mental Performance

• Example
• In adding two signed integers, students with
  learning disabilities in math could do the
  following
•  
• 1. First, use a number line to show what 3 -4
  means They draw a man facing the positive side
  of the number line. Then the man moves 3 steps
  forward and then moves back 4 steps. The man
  ends up standing on the point corresponding to
  1.
•  
• 2. Second, they imagine a number line. Then
  using their fingers, they explain what 3 -4
  means. Initially, the teacher may need to model
  this process and students with learning
  disabilities in math may be asked to think aloud.
  Eventually, they should be able to count either
  or with the use of their fingers.
•  
• 3. Third, they are assigned the task of
  performing the following computations using only
  gestures 5 -7, 3 -2, 4 -6, 7 -9, etc.

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Using a Keyword with a Referent

• Using a keyword pictured with a referent is a
  very effective mnemonic strategy for enhancing
  memory of terms or concepts. This strategy
  requires the use of auditory and visual image
  cues.

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Using a Keyword with a Referent

• Example
• To remember the word commutativity
• the word commute is a good keyword.
• The keyword is then associated with its
  referent, say, a picture of two people boarding a
  bus with a bi-directional arrow showing the order
  in which they enter is not important.
• The teacher should provide direct
  instructions on how to use this strategy
  properly.