Virtual manipulatives have been defined as an "interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge" (Moyer et al., 2002, p. 373).
Technology in the Classroom
Over the past two decades technology has become increasingly more influential in the world of education. However, education is still behind in the realm of technology. Despite the increasing availability and technological push that the educational world is witnessing, many teachers are still resistant to the use of technology in the classroom. (These reasons are gone over in more depth when the disadvantages of virtual manipulatives are discussed.) Despite the refusal of some teachers to come to terms with technological resources, technology in the classroom has been shown to boast many benefits and "can enrich the learning experiences of students" (Hicks, 2011, p. 188). Today's classroom sees more and more technology use every year and students are becoming ever more tech savvy. "Technology directly affects every aspect of life, and nearly every job option available to Americans today requires the use of some type of technology. Thus, it is imperative that we use technology in the classroom, as the ultimate success of our students depends on this fact" (Hicks, 2011, p. 190). In an article published by Dessoff, students between the ages of 8 and 18 have been found to spend, on average, 7 hours and 37 minutes per day engaged in entertainment media (2010). This is creating an over saturation of technology in our students lives and is shaping the way students "think, learn, and experience the world around them" (Hicks, 2011, p. 188). The place of computers in the classroom and the functionality of their use can be best described with a "cognitive tool" metaphor that supports cognitive thinking through the use of scaffolded processes of articulation and reflection that are the foundations of knowledge construction (Durmus, 2006). Norman (1993) states that computers support reflective thinking which is defined as the careful, deliberate kind of thinking that helps us not only make sense out of what we have experienced and what we know but also to compose new knowledge by adding new representations, modifying old ones, and comparing the two. One such way to incorporate the use of technology in a mathematics classroom is through the use of virtual manipulatives. Many studies have been conducted to show the advantages and disadvantages of using virtual manipulatives in the instruction of math concepts. Despite any variances in findings, one thing has been made clear, "Technology integration should be meaningful -- it should have a specific purpose with meaningful measurable goals to achieve the desired outcome" (Hicks, 2011, p. 190).
Further Implications of Virtual Manipulatives
As students become more engaged by technology enhanced learning environments, they begin to make fewer connections with basic curriculum instruction through the use of text books and teacher lectures. When it comes to mathematical instruction, making connections to the real world yields the highest gains in student learning (Stigler and Heibert, 2004, p. 12). Virtual manipulatives help students achieve the ability to make these higher level connections to the world around them. "The ability to manipulate the visual representation, or object, on the computer connects the user with the real teaching and learning power of virtual manipulatives, that is, the opportunity to make meaning and see relationships as a result of one's own actions" (Moyer et al, 2002, p. 373). Moyer and Bolyard describe the way knowledge arises as 'from an individual's ability to see relationships and connect the tools used for representation with the ideas they represent. Students' observations of their own actions may allow them to see relationships and construct new knowledge" (Moyer and Bolyard, 2002, p. 20). Bouck and Flannigan state that virtual manipulatives have the potential to facilitate student's understanding of mathematical concepts (2010, p 187). Whether it happens this year or ten years from now it is clear that virtual manipulatives continue to develop and will eventually span beyond a simple mouse click to more dynamic ways of manipulation such as voice commands and infrared signals (Moyer et al, 2002, p. 373).
Responsive and Interactive
The educational systems see the use of virtual manipulatives as referring to "any computer generated image that appears on a monitor and is intended to represent concrete manipulatives" (Moyer et al, 2002, p. 373). This definition is, however, far too broad and not nearly descriptive enough to detail the true nature of a virtual manipulative. There are in fact two types of virtual manipulatives, static and dynamic (Moyer et al, 2002; Moyer and Bolyard, 2001; Moyer et al, 2005). Static representation are merely pictures that are placed on a web based program and offer little to no manipulation capabilities on the users part. Dynamic manipulatives, on the other hand, are much more versatile and can be manipulated in the same way that a concrete manipulative can (Moyer et al, 2002, p. 372). Dynamic virtual manipulatives are the type that will be focused on here since they offer a greater range of flexibility, and have been shown to improve overall students academic gains and engagement (Moyer et al, 2002; Bouck and Flanagan, 2010; Bouck et al, 2013; Suh and Moyer, 2012). Students working with dynamic virtual manipulatives are afforded the opportunity to fully engage and interact with the virtual manipulative just as they would a concrete manipulative. The mere click of a mouse can flip, turn, slide, change size, and change color of the manipulatives, making them fully interactive and responsive to user input (Moyer et al, 2002, p. 373). It is imperative that educators differentiate between static and dynamic virtual manipulatives and focus student experiences to more dynamic, interactive, and responsive virtual manipulatives to ensure the greatest ability to form cognitive relationships between virtual manipulatives, mathematical concepts, and real world applications.
Unique Properties
There are several unique properties to virtual manipulatives that promise to make them great assets to classroom instruction. Despite the fact that virtual manipulatives are still fairly new in the development process, they already "link iconic and symbolic notations, highlight important aspects or features of individual manipulatives, provide links to other resources on the web, and record and store user's movements and other work tasks" (Moyer and Bolyard, 2001, p. 185). Dorward and Heal describe virtual manipulatives as being able to provide just as much engagement as concrete manipulatives. But what makes virtual manipulatives even more unique is the availability and their capability to offer unlimited resources. "They offer teachers and students inside the wired classroom free and unlimited access to interactive manipulative experiences" (Moyer and Bloyard, 2001, p. 185). Not only are teachers able to access virtual manipulatives free of charge, they no longer have to worry about supply. Students can obtain more pieces with the simple click of a mouse. Another unique feature is their ability to be altered by the user. Traditional concrete manipulatives lack in their ability to be altered but virtual manipulatives can change size, shape, and quantity based on the users preferences or need. There is also no clean up required, decreasing teacher stress and anxiety when using manipulatives in the classroom and saving on valuable and limited instructional time since virtual manipulatives do not need to be distributed or cleaned up. The unique characteristics that virtual manipulatives have make them a popular choice for classroom instruction and allow students to focus on learning and not on the actual manipulation of a concrete object.