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Digital Manipulatives


      They are the 21st century version of tokens, a computing tradition older than cuniform writing. Digital manipulatives permit one to move pictures on a spread sheet as one might move tokens on a board. They also permit one to neatly record the work, make comments, and create.
      Open a spread sheet. Right click on an image at the left. Copy it and paste it in the spread sheet. Repeat the process for the other image. You've just created your first digital manipulatives, a set of negative and positive tiles for signed number computation.
      Distinct from paper and pencil mathematics, different from concrete manipulative mathematics, this is about digital expression, represention, manipulation (MOVEMENT!), and CREATION.
      Ready-made, free, non-Java-Script, sample digital manipulative spread sheets are examined and the theory that inspired them is considered.
Click, Drag, Select, Copy, Paste, & A Bit of Experimentation
      Nothing moves unless the user makes it move. In some cases the digital manipulative spread sheet contains only tokens, pictures to be moved. In other cases it has instructions and "hot" cells which self-compute and enhance the learning environment. In some cases, the digital manipulative is ready for a teacher to present class-wide instruction. In some cases, it is simply a game or an abacus.
      Faciltiy with basic computer commands (Azzolino, 2009) of select, click, drag, select, copy, and paste speed the movement of the pieces and may easily be acquired while performing digital manipulations.
Spreadsheet required.
Click. Select.
Delete or Copy.
Edit, create text, assign task.
Complete task.
Summarize, document.
Insert automatic computation.
      It is not possible for the "digital hand" to achieve the speed of the hand which moves a concrete manipulative, especially with a thing such as an abacus. Use of these commands does greatly increases speed of manipulation.
      Consider a quick select/copy/paste of the graphic at the right into the digital manipulative spread sheet until your speed increases through practice.
      Newer versions of Excel® have spinning and line drawing capabilities. Even old versions have stretching and shrinking capabilites (Azzolino, 2009).
Digital Manipulatives as a Math Class Language
      "Math Class Languages" (Azzolino, 2009) is the theory that forced the creation of digital manipulatives. In brief ...

The Languages of the Math Classroom
'98, '08, '09 Agnes Azzolino

Most Sophisticated and also the Most Basic

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

      Digital manipulatives were created to:
      Because of them teachers/students might:
Come play. Come create.
      Digital manipulatives easily permit movement of pictures. Abstract ideas and symbols become almost concrete. One might:

    Download digital manipulatives at www.mathnstuff.com/math/xls/xls.htm#digitalm.

Azzolino, 2009, "DIGITAL MANIPULATIVES" at
Azzolino, 2009, "DIGITAL MANIPULATIVES" at
Azzolino, 2009, "MATH SPOKEN HERE! Classes - Taking Notes" at
Azzolino, 2009, "MSH! DIGITAL MANIPULATIVE -- Use and Creation Spread Sheet Pg. b" at
Azzolino, 2009, "The Languages of the Math Classroom" at

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