Virtual Manipulatives

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Virtual Manipulatives

• Are they better than their
• concrete counterparts?
• John Meyer
• Governors State University
• University Park, IL

2
Do manipulatives automatically work?

• Manipulative use does not automatically mean
  better learning
• Are they helpful? Yes, but there are no
  guarantees.
• Rote use is not effective
• Teachers must work with students to connect
  manipulation with understanding the notation
  which describes the actions

3
Are virtual manipulatives concrete?

• concrete cannot be only equated with physical
  manipulatives
• Computers might supply representations that are
  just as personally meaningful to students as real
  objects that is, they might help develop
  integrated-concrete knowledge. These
  representations may also be more manageable,
  clean, flexible, and extensible (Clements
  McMillen, 1996).

4
Why use virtual manipulatives?

• Theyre free
• If used in a lab, everyone can have their own
  manipulatives
• Multiple materials are available for each student
• Can individualize for each student

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Why use VM? (contd.)

• Students work can be saved and worked on
  again and again (Clements, 1999, p. 5)
• Work can be saved and printed out
• Shapes are easier to make with software
  manipulativesthey snap to outlines and stay
  where they are put.
• Students control their interaction with the
  mathematics

6
Why use VM? (contd.)

• Actions possible with software model the
  processes we want students to internalize
• Students can change the size of some
  manipulatives and not others. This is not
  possible with physical manipulatives.
• Some tools allow shapes to be glued together.

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Why use VM? (contd.)

• Students make decisions, then see what happens as
  a result of those choices
• Built-in tools such as flips and turns
• In Base Blocks, students can break base 10 rods
  into 10 singles for regrouping. When blocks are
  changed, the numbers are automatically changed to
  reflect the change in the manipulatives.

8
Why use VM? (contd.)

• In LOGO, students connect ideas about
  characteristics of geometric shapes, because they
  must create directions for the turtle which
  reflect angle turns and side lengths.

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Why use VM? (contd.)

• Students using physical manipulatives didnt
  always connect activities with what they wrote on
  paper. They viewed them as separate activities.
• Computer groups linked the base 10 block
  activities to the symbols.
• More grown-upacceptable to middle and high
  school students

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Teaching with computers

• adults play a significant role in successful
  computer use. Children are more attentive, more
  interested, and less frustrated when an adult is
  present (Binder Ledger, 1985). Thus, teachers
  may wish to make the computer one of many
  choices, placed where they can supervise and
  assist children (Clements, 2002, p. 171).

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Teaching with computers (contd.)

• teachers whose children benefit significantly
  from using computers are always active. They
  closely guide childrens learning of basic tasks,
  then encouraging, questioning, prompting, and
  demonstrating. Such scaffolding leads children
  to reflect on their own thinking behaviors and
  brings higher-order thinking processes to the
  fore (Clements, 2002, p. 172).

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Sample Websites
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National Library of Virtual Manipulatives MattiMat
h CD
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Concrete manipulative advantages over VM

• Concrete vs. pictorial
• More natural to manipulate
• If used in groups, can foster discourse
• Dont require computers or Internet access.
• Dont go down as Internet may.

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So which one is better?

• Studies show that a combination of physical and
  virtual manipulatives is more effective than
  either alone. Activities in which children first
  move their bodies, for instance, walking around a
  shape on the floor, and then use commands to
  direct an onscreen turtle to make the same
  motions, improve mathematical understanding and
  problem-solving skills (Clements Samara, 1997,
  1998).

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Resources

• National Library of Virtual Manipulatives for
  Interactive Mathematics Utah State Univ.
  (http//nlvm.usu.edu)
• NLVM CD (www.mattimath.com)
• Interactive math lessons (http//enlvm.usu.edu)
• http//nlvm.usu.edu/en/nav/vlibrary.
• html

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Resources (contd.)

• www.standards.nctm.org/documents/eexamples/index.h
  tm
• http//mason.gmu.edu/mmankus/talks/nctm2000/nctmc
  h00.htm
• http//arcytech.org/java
• www.ies.co.jp/math/java/geo/index.html

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Resources (contd.)

• www.illuminations.nctm.org/Activities.aspx
• http//otec.uoregon.edu/virtual_manipulatives.htm
• www.math.fsu.edu/Virtual/index.php?f4
• www.ct4me.net/math_manipulatives.htm
• www.emints.org/ethemes/resources/S00000592.shtml

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References

• Clements, D.H. (1999). Concrete manipulatives,
  concrete ideas. Contemporary Issues in Early
  Childhood, 1(1), 45-60. http//www.triangle.co.uk/c
  iec/
• www.pbs.org/readytolearn/resources/2005_summer_ins
  titute/Clements_Computers_Math.pdf

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References (contd.)

• Clements, D.H. and McMillen, S. (1996).
  Rethinking concrete manipulatives. Teaching
  Children Mathematics, 2(5), 270-279.

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Want a copy?

• E-mail me at DrMath_at_aol.com
• Put NCTM in the subject line
• I will e-mail you the URL where the presentation
  will be posted
• Thanks for coming!