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Article Excerpt
With recent advances in computer technology, it is no surprise that the manipulation of objects in mathematics classrooms now includes the manipulation of objects on the computer screen. These objects, referred to as virtual manipulatives, are essentially replicas of physical manipulatives placed on the World Wide Web in the form of computer applets with additional advantageous features. The purpose of this project was to explore the effects of using several virtual manipulative computer applets for instruction during a fraction unit in a third-grade classroom. The participants in this study were 19 third-grade students. During a two-week unit on fractions, students interacted with several virtual manipulative applets in a computer lab. Data sources in the project included a pre and posttest of students' conceptual knowledge, a pre and posttest of students' procedural computation skills, student interviews, and a student attitudes survey. The results indicated a statistically significant improvement in students' posttest scores on a test of conceptual knowledge, and a significant relationship between students' scores on the posttests of conceptual knowledge and procedural knowledge. Student interviews and attitude surveys indicated that the virtual manipulatives (1) helped students in this class learn more about fractions by providing immediate and specific feedback, (2) were easier and faster to use than paper-and-pencil methods, and (3) enhanced students' enjoyment while learning mathematics.
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"Tools of some kind are unavoidable and essential for doing mathematics" (Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Olivier, & Human, 1997, p. 2). Mathematical tools can build a foundation for children to understand concepts, which can then initialize an abstract understanding (Hiebert et al, 1997). Mathematics educators and cognitive theorists have supported a theory of concept development based on a progression from physical objects (or mathematical tools) to representational forms and abstract thought (Bruner, 1960, 1986; Piaget, 1952). These theories are evident in school classrooms where physical manipulatives have become popular for mathematics instruction, and where teachers are now using computer or virtual manipulatives. Although the availability of computer technology in elementary schools has increased rapidly in recent years, national surveys of teaching practices show that a small percentage of elementary-school teachers use computers to teach concepts during mathematics instruction (Weiss, 2000). The purpose of this project was to explore the use of several virtual manipulative computer applets for instruction during a fraction unit in a third-grade classroom.
What are Virtual Manipulatives?
Virtual manipulatives are essentially replicas of physical manipulatives placed on the World Wide Web in the form of computer applets with additional advantageous features. Moyer, Bolyard, and Spikell (2002) define a virtual manipulative as "an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge." Although the use of physical manipulatives in the teaching and learning of school mathematics has produced positive results with students (Parham, 1983; Raphael & Wahlstrom, 1989; Sowell, 1989; Suydam, 1985, 1986), teachers have often questioned how to translate students' interactions with manipulatives to proficiency with abstract symbols. Researchers and educators have argued that the mere use of manipulatives does not guarantee that students will understand concepts and procedures and be able to connect these concepts to abstract symbols without teachers making these connections explicit (Ball, 1992; Baroody, 1989; Meira, 1998; Moyer, 2001; Thompson & Thompson, 1990). In other words, simply using the manipulatives does not insure learning.
One feature that makes virtual manipulative applets advantageous for mathematics instruction is their capability to connect dynamic visual images with abstract symbols--one limitation of physical manipulatives. Unlike physical manipulatives, electronic tools use graphics, numbers, and words on the computer screen to connect the iconic with the symbolic mode (Kaput, 1992). For example, a base-10 blocks applet may show both the visual representations of the blocks and, at the same time, show the number of hundreds, tens, and ones in a place-value notation. These pedagogical notations provide support that bridges students' manipulations of the virtual blocks with the formal symbolic system, and this connection holds promise for improving student learning.
Recent publications have described how elementary teachers can use virtual manipulatives to teach fraction concepts (Suh, Moyer, & Heo, in press) and how middle school teachers can use virtual pattern blocks, virtual platonic solids, and virtual geoboards to investigate concepts in geometry (Moyer & Bolyard, 2002). These virtual manipulative applets are available on the World Wide Web on web sites such as the National Library of Virtual Manipulatives (http://matti.usu.edu/nlvm) or the National Council of Teachers of Mathematics electronic resources (http://www.nctm.org). Elementary teachers have begun to discover these free resources and to develop lessons for their classrooms using these applets.
Limited Research on Virtual Manipulatives
It is a challenge to find research that specifically describes and documents work in classrooms with virtual manipulatives. One of the reasons for this lack of information may be the specialized knowledge required of teachers who wish to use virtual manipulatives for instruction. To use virtual manipulatives, 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. Research has shown that it is a challenge for teachers to transform mathematical ideas into representations (Ball, 1990; Orton, 1988). Teachers must also be comfortable with technology and be prepared for situations where computers may not be reliable or Internet connections are not working properly. These factors may deter teachers and researchers from designing lessons with virtual manipulatives.
Previous research on related technology sheds some light on the possibilities of virtual manipulatives. Studies on computer-based manipulatives have produced inconclusive results, due to a variety of design and sampling characteristics that may affect student achievement results. A variety of studies in which "computer manipulative programs" were examined for their ability to support student learning in mathematics confirmed positive results in student achievement and attitudes (Char, 1989; Clements & Battista, 1989; Kieran & Hillel, 1990; Thompson, 1992). For example, students' ideas about shapes were more mathematical and precise after using the computer program Logo (Clements & Battista, 1989). Studies where computer manipulatives were used in combination with physical manipulatives also showed positive gains in increasing students' conceptual understanding (Ball, 1988; Terry, 1996). Yet other studies using computer-based attribute blocks (Kim, 1993), pegboards and color cubes (Berlin & White, 1986), geometric shapes (Nute, 1997), and transformation geometry concepts (Pleet, 1990) produced results that indicated no significant improvement in student achievement. Although these results are mixed, the amount of research on high-quality dynamic virtual manipulatives is so limited that a judgment about their potential uses in mathematics instruction is entirely speculative.
Research, descriptive information, and classroom projects involving virtual manipulatives are beginning to appear in print (Cannon, Heal, & Wellman, 2000: Dorward & Heal, 1999; Drickey, 2000; Moyer, Bolyard, & Spikell, 2002; Nute, 1997; Terry, 1996). In a recent study, kindergarten children created a variety of patterns using virtual pattern blocks, concrete pattern blocks and drawings. Researchers compared the...
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