There are various literatures and articles write-up about the teaching of mathematics with technology. One of the topics that has been discussed recently and need to be acquainted with teacher is ‘Virtual Manipulatives’. To help teachers having a clear overview on Virtual Manipulatives, this section started off with giving definition on Virtual Manipulatives from the discussion available in the web-sites and later went on to talk about:
The Characteristics of Virtual Manipulatives.
Roles of Virtual Manipulatives (choosing good Virtual Manipulatives and how they can be used effectively in the classroom).
Pessimistic Views on Virtual Manipulatives.
What is Virtual Manipulatives?
There are various definitions of Virtual Manipulatives stated in the web-sites. Bolyard, et. al. in Deubel, P. (2008) clarified that there are Static Virtual Manipulatives and Dynamic Virtual Manipulatives found on the Web. However, they commented that static models are not true virtual manipulatives because static models look like physical concrete manipulatives that have traditionally been used in classrooms, but they are essentially pictures and learners cannot actually manipulate them. They consider that the authentic definition of Virtual Manipulatives matches with the definition of the Dynamic Virtual Manipulatives as an interactive, web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge.
On the other hand, Leatham (2007), defined the dynamic virtually manipulatives as hands on technology instruments. This means basically that the person using the computer is controlling what is on the screen instead of watching it like you would a television.
Characteristics of Virtual Manipulatives
Virtual manipulatives have a range of characteristics, such as pictorial images only, combined pictorial and numeric images, simulations, and concept tutorials, which include pictorial and numeric images with directions and feedback (Bolyard, J.J., Moyer-Packenham, Salkind, 2008).
Deubel, P. (2008) stated that virtual manipulatives are currently modeled after concrete manipulatives such as base ten blocks, coins, pattern blocks, tangrams, spinners, rulers, fraction bars, algebra tiles, geoboards, and geometric plane and solid figures, and are usually in the form of Java or Flash applets.
Roles of Virtual Manipulatives
In order to help teachers to choose good Virtual Manipulatives which are abundant in the web and to know how they can be used effectively in the classroom, the following points that I summarized from Bolyard, et. al. (2008), Clements. D. H. (2000), Dement, A. (2009), Deubel, P. (2008), Moyer & Reimer (2005), National Mathematics Advisory Panel (2008) and Spicer, J. (2009) might be helpful to teachers.
Good Virtual Manipulatives
Basic characteristics by Dement, A. (2009):
no cleaning needed;
no limited number of resources;
work can be save;
have links to other resources;
can access anywhere there is computer;
- allow formatting (potential to alter and add color, etc..).
Virtual Manipulatives are those that can be used:
to address standards and to assist with those goals;
to keep with the progressive movement of discovery and inquiry-based learning;
to focus on investigation and skill solidification;
as an additional tool for helping students at all levels of ability to develop their relational thinking and to generalize mathematical ideas;
to provide control and flexibility to the learner and serving as a catalyst for the growth of integrated-concrete knowledge;
easily and faster compared to using paper-and-pencil;
to provided enjoyment for learning mathematics especially for older students (rather than pattern blocks);
to cater pupils with different ability, ranged from lesser ability to those of greatest ability. This allows pupils to remain engaged with the content, thus providing for differentiated instruction;
to record and replay students’ actions;
to link the concrete and the symbolic with feedback;
to encourage and facilitate complete, precise, explanations;
can expand the horizons of what mathematics pupils can see. (explore concepts not readily accessible in other mediums/ make visible that which is hard to see and impossible to imagine).
How Virtual Manipulatives can be used effectively in the classroom.
Teacher may use virtual manipulatives alone or use physical manipulatives first, followed by virtual manipulatives;
Virtual Manipulative with other instructional strategies that combine "see-hear-do" activities because pupils/ students learnt best this way'
By combining visual (i.e., pictures and 2D/3D moveable objects) and verbal representations (i.e., numbers, letters, words) of concepts and is in keeping with Paivio and Clark's Dual Coding Theory .[ http://tip.psychology.org/paivio.html];
Teachers must have an understanding of how to use representations for mathematics instruction as well as an understanding of how to structure a mathematics lesson where students use technology;
Teachers must also be comfortable with technology and be prepared for the technical problems;
Evidence regarding the usefulness of Virtul Manipulatives in helping children learns geometry is tenuous at best. However, concrete (hands-on) experiences must be done before they eventually transit to internalized abstract representations;
Teacher may use virtual manipulatives, either alone or in combination with physical manipulatives because the overall results from classroom studies and dissertations have indicated that students gains in mathematics achievement and understanding in both ways.
Pessimistic Views (Conc) on Virtual Manipulatives
Deupal, P. (2009) own experience confirms that virtual manipulatives may take a while to download, and in some cases, the wait time might be frustrating. Deupal also stated the arguments by various authors that:
drill and practice may have a disparaging connotation as a pedagogical tool to teach skills and runs contrary to the progressive movement;
computers may not be available or Internet connections are not working properly;
might not work fast enough for learners who are accustomed to playing high speed, interactive video games;
the footprint on the screen might be too small for learners with poor mousing skills or for those with limited dexterity to click on relevant icons or to perform the spins, rotations, flips and turns required;
a reliance might have its roots in the quality of instruction, in part, and failure of the math educator to explicitly state and reinforce the link between the use of the manipulative, and development of concepts for understanding and properties of mathematics to be learned;
though manipulatives are useful for introducing new concepts to elementary students, but, in the higher grades, manipulatives can undermine important educational goals such as in terms of developing skill fluency, conceptual understanding, and mathematical reasoning.
More negative prospect..
Klein, D. (2005) stated that overuse of calculators and manipulatives in that students might come to depend on them and focus on the manipulatives more than on the math.
Spicer, J. (2009) noted that integrating technology into instructional practice requires time to learn and to explore ways to effectively implement the technology into their classroom. To some extend, technical assistance may be needed by teachers to maintain the equipment.
The Dement, A. (2009) listed the weak point of Virtual Manipulation as below:
- Little Gained (little difference from concrete manipulatives);
- programming manipulatives;
- access to computer (not available in every home);
- equity;
- distraction from learning, more time in class (trouble shooting);
- too individualized (not much group work);
- might feel like "do" vs "learn/explore".
References:
Bolyard, J. J., Moyer-Packenham, & P. S., Salkind, G., (2008). Virtual manipulatives used by K-8 teachers for mathematics instruction: Considering mathematical, cognitive, and pedagogical fidelity. Contemporary Issues in Technology and Teacher Education, 8(3), 202-218. Available: http://www.editlib.org/index.cfm?fuseaction=Reader.ViewFullText&paper_id=26057
Clements, D. H. (2000). Concrete' manipulatives, concrete ideas. Contemporary Issues in Early Childhood. Available at: http://www.gse.buffalo.edu/org/buildingblocks/Newsletters/Concrete_Yelland.htm
Dement, A. (2009). Teaching with Technology: Virtual manipulatives [Online]. Available at:
http://sites.google.com/site/matheducation308/Home/virtual-manipulatives
Deubel, P. (2009). Math manipulatives [Online]. Retrieved from Computing Technology for Math Excellence. Availabe at:
http://www.ct4me.net/math_manipulatives.htm#Role%20of%20Manipulatives
Klein, D. (2005, January). The state of state math standards 2005. Washington, DC: Thomas B. Fordham Foundation. Available at:
http://www.edexcellence.net/detail/news.cfm?news_id=338
Leatham, K. (2007). Article Write-up:What are Virtual Manipulatives? [Online]. Brigham Young University. Available at:
http://webpub.byu.net/millsk/article%20write%20up%201.htm
Spicer, J. (2009). Expanding Horizons through Technology [Online]. Retrieved from The Knowledge loom: Panel Discussion. Available at:
http://knowledgeloom.org/forum_read.jsp?t=1&messageid=1393&forumid=1004&location=8&tool=2&bpinterid=1102&spotlightid=1102&testflag=yes
Lesson Plan 1 - POLYGONS MANIPULATIONS
Lesson Plan 2 - TURTLE MAZE CHALLENGE
Lesson Plan 3 - WHAT SHAPE IS THE TURTLE DRAWING?
Lesson Plan 4 - TURTLE STORY 
Lesson Plan 5 - SHOW THE TIME 
