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A Walk Down The Hall To Introduce The Language Families

The Languages of the Math Classroom
© '98, '08, '09 Agnes Azzolino
 
MOTHER TONGUE & OTHER TONGUE(S)
Most Sophisticated and also the Most Basic
 
MOSTLY MATH TONGUES
Most Sophisticated, Most Basic
 
VERBAL / Auditory WRITTEN / Symbolic     PICTORIAL / Visual     CONCRETE / Kinesthetic    
  formal spoken mathematics   written word   DIGITAL MANIPULATIVE     object
  informal spoken mathematics       written symbol   moving picture   model
  spoken symbol   semisymbolic   static picture   manipulative/token
  symbol speak   calculator symbol   numeral
  calculatoreze/computereze   graph
  web speak   nonverbal body language


    Verbal (Not Face-to-Face)

  • Most Abstract
  • Most Linear
  • Easiest to Lose Thread of Discourse
  • No Mention of Anything Concrete
  • Very Possibly Listener Passive
 

    Verbal (Face-to-Face)

  • Most Abstract
  • Most Linear
  • Easy to Lose Thread of Discourse
  • Something Concrete Mentioned
  • Possibly Listener Passive
 

    Written & Verbal

  • Less Abstract
  • Symbols & Words
  • Chalk & Talk
  • Two Paths of Input to Listner
  • Still May Be Listner Passive
 

    Written

  • Less Abstract than Verbal
    (Because Reader Controls Speed)
  • Symbols or Words
  • Chalk
  • One Path of Input to Listner
 

    Pictorial & Verbal

  • "Worth A Thousand Words"
  • Non-Linear
  • Precurser to Written?
  • The Better the Picture, The Better the Picture
  • Not Only in Listener's Hand
  • Listener Has Some Control
  • Two Paths of Input to Listner
 

    Concrete (Modeled)

  • Not in Listener's Hands --
    In Speaker's Hands & Voice
  • Movement if Focus --
    Speech is Secondary
  • Model - Speaker Moves
  • Tokens
 

    Concrete (Listener Manipulated)

  • Learner Centered
  • Manipulative - Listener Moves & is
    No Longer A Listener
  • Most Basic
  • Active


    Mother Tongue(s) Speech

  • W/Concrete Reference -
    Most Concrete & Abstract
  • Easiest Way to
    Make Things Concrete
  • Abstractly Make Things Concrete

    Mother Tongue(s)
    Speech w/Questions

  • Most Concrete & Abstract
  • Easiest Way to
    Make Things Concrete
  • Abstractly Make Things Concrete
  • Conversation Reinforces Communication
  • Less Likely to Be Listner Passive

    Mother Tongue(s) (Conversation)

  • Most Concrete & Abstract
  • May Be Spoken Math
    Rather Than Mathematics
  • Conversation Reinforces Communication
  • Non-Linear
  • Least Likely to Be Listner Passive


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  © 2011, A. Azzolino