- 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.
||Delete or Copy.
Edit, create text, assign task.
DRAG & MOVE.
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
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 || |
- Digital manipulatives were created to:
- Introduce in the concrete and debrief in the abstract.
- Increase the number of clear, valuable, graphics to communicate an idea in class.
- Increase visualization as a form of presentation, summary, debriefing.
- Create math experts.
- Restate a mathematical idea in as many math class languages as possible for increased understanding
on the part of both the speaker and the listner.
- Bring a cart load of manipulatives to class without having to bring a cart load of manipulatives to class.
- 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:
- Write, illustrate, print a worksheet or classwork.
- Complete a lab, play a game, "use an abacus."
- Take and store notes.
- Create something beautiful.
- Make a picture with tokens and write text on some mathematical aspect of the picture.
- Create tests, quizzes, or projects.
- Complete homework or teacher-written assignments.
- Divide the circle and generate a parallelogram-like shape to compute its area using
- Verify a 1/4-bar with another 1/4-bar have the same length as a 1/2-bar using fract.xls.
Find a fraction greater than 1/4 and smaller than 1/2 and verify through decimal approximation using
- Make multiples of x+2 to represent 2(x+2) and x(x+2) and (x+2)2 using create.xls.
Simplify algebraic expressions and solve equations using tiles and tokens using
- Expand (x-y)3 using
- Play addition rummy with a deck of cards using
- "Roll" a die or pair of dice using
- Add and subtract fractions, decimals, integers, on a nomograph using
- Add and subtract fractions with multiple strips and fraction bars using
- Complete vector addition using
- Reinforce mental computation and words like multiple, reciprocal, cube, double, and prime using
Download digital manipulatives at
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
www.mathnstuff.com/math/xls/digital.htm © 1/2010 A2