If you are a Star Trek fan, then you are familiar with Holodeck—a three dimensional computer simulation "room" in which humans can move around and interact with computer-generated simulations of people and objects. This science fiction is a target that today's generators of computer simulations hope to someday reach.

Recently I read the article and viewed the video (17:36) about a state of the art (experimental) war game simulator. It’s not quite Holodeck, but to me it was truly amazing (MacManus, C., October 27, 2011).

Computer simulations are now routinely used in a number of different training/education situations. Examples include simulators used by airplane pilots, car drivers, surgeons, and military personnel (Moursund, 1/5/2011). We have long had simulations that are sufficiently well-developed that their use is a good substitute for using the “real thing.” Use of simulators is both effective for training and cost effective. In addition, one can practice dealing with really dangerous situations without fear of getting killed or destroying very expensive equipment.

Modeling and simulation are now standard tools in the sciences. The "computational" in Computational Biology, Computational Chemistry, Computational Physics, and so on refers to computer modeling and simulation (IAE-pedia, n.d.).

There are many less expensive and less sophisticated simulations that are adequate for use in schools. Math manipulatives provide a good example. My new book, Expanding the Science and Technology Learning Experiences of Children, discusses math manipulatives and a variety of modeling and simulation topics from other disciplines (Moursund, 2011). The book is available as a free download from http://i-a-e.org/downloads/doc_download/207-expanding-the-science-and-technology-learning-experiences-of-children.html. Here are two math manipulative quotes from the book:

Students who use manipulatives in their mathematics classes usually out-perform
those who do not, although the benefits may be slight. This benefit holds across
grade level, ability level, and topic, given that use of a manipulative "makes
sense" for that topic. Manipulative use also increases scores on retention and
problem solving tests. Attitudes toward mathematics are improved when students
have instruction with concrete materials provided by teachers knowledgeable
about their use (Clements, 1999).

Individual students learn in different ways. When manipulatives are used, the
senses are brought into learning: students can touch and move objects to make
visual representations of mathematical concepts. Manipulatives can be used to
represent both numbers and operations on those numbers. In addition to meeting
the needs of students who learn best in this way, manipulatives afford the teacher
new ways of visiting a topic (The Math Forum @ Drexel, n.d.).

My Web search of virtual math manipulatives returned about 74,000 hits. Many seem to be just glorified drill-and-practice programs that I do not regard as math manipulatives. Here are three sites that I consider to offer true math manipulatives:

• National Library of Virtual Manipulatives. See http://nlvm.usu.edu/en/nav/vlibrary.html. A free trial version can be downloaded. Notice that materials are available for the full grade range of precollege math, Pre-K to 12. The materials are available in English and Spanish. See http://nlvm.usu.edu/en/nav/grade_g_1.html for a large collection of Pre-K to 2 math manipulatives that can be used online. See http://nlvm.usu.edu/en/nav/grade_g_2.html for a large collection of grades 3-5 math manipulatives that can be used online.
• Tangrams. See http://nlvm.usu.edu/en/nav/frames_asid_268_g_1_t_3.html?open=activities.
• Function Machines. See http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_2.html and http://www.mathplayground.com/functionmachine.html.

Suggested Readings from IAE and Other Publications

You can use Google to search all of the IAE publications. Click here to begin. Then click in the IAE Search box that is provided, insert your search terms, and click on the Search button.

Click here to search the entire collection of IAE Blog entries.

Here are some examples of publications that might interest you.

IAE-pedia (n.d.). What is science? Retrieved 10/27/2011 from http://iae-pedia.org/What_is_Science?

Moursund, D. (4/3/12). New free math education book by David Moursund. Retrieved 10/27/2012 from http://i-a-e.org/iae-blog/new-free-math-education-book-by-david-moursund.html.

Moursund, D. (10/3/2011). Simulations using a Super Computer. Retrieved 10/27 2011 from http://i-a-e.org/iae-blog/simulations-using-a-supercomputer.html.

Moursund, D. (2/16/2011). Artificial intelligence and artificial muscle. Retrieved 10/27/2011 from http://i-a-e.org/iae-blog/artificial-intelligence-and-artificial-muscle.html.

Moursund, D. (2/9/2011). Game of Jeopardy: Computer versus humans. Retrieved 10/27/2011 from http://i-a-e.org/iae-blog/game-of-jeopardy-computer-versus-humans.html.

References

IAE-pedia (n.d.). Computational thinking. Retrieved 10/27/2011 from http://iae-pedia.org/Computational_Thinking.

MacManus, C. (10/ 27/ 2011). A gaming simulator like no other. Retrieved 10/27/2011 from http://news.cnet.com/8301-17938_105-20126227-1/a-gaming-simulator-like-no-other/?tag=rtcol.

Moursund, D. (2011). Play together, learn together: STEM. Retrieved 12/14/2012 from http://i-a-e.org/downloads/doc_download/212-play-together-learn-together-stem.html. Eugene, OR: Information Age Education.

Moursund, D. (1/5/2011). Modeling and simulation in science. Retrieved 10/27/2011 from http://i-a-e.org/iae-blog/modeling-and-simulation-in-science.html.

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