MET:Virtual Math Manipulatives
The influx of interactive whiteboards (IWBs) into many classrooms has afforded the teacher the opportunity to engage students in new ways. The use of virtual manipulatives, whether projected up on the IWB or a students' own computer, can assist students in their learning (Reimer & Moyer 2005; Steen, Brooks & Lyon 2006; Olympiou, Zacharia & Papaevripidou, 2008; Mendiburo & Hasselbring, 2011;) and will be examined in the following entry.
What is a Virtual Manipulative?
The term virtual manipulative is used to indicate “…an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” (Moyer, Bolyard, & Spikell, 2002, p. 373). Interestingly enough, this term is not universally used by educators or developers as some simply refer to virtual manipulatives as interactive web applets. Specific developers have also coined their own names for virtual manipulatives by designing their Web sites around these original names. Examples of this are JOMA’s Mathlets, Washington State University’s Wazzu Widgets, or Explore Learning’s Gizmos (Young, 2006).
Moyer and Bolyard (2001) define two types of representations that educators and developers are calling virtual manipulatives. First, there are “static visual representations of concrete manipulatives, graphs, or worksheets” (p. 184). This type of virtual manipulative is essentially a picture. It cannot be moved, rotated or manipulated but merely exists as a visual picture. The second type are more dynamic in nature and users are able to rotate, clone, flip and slide the representations around on the computer screen using a mouse.
Moyer and Bolyard contend this dynamic visual representation is “truly a ‘virtual manipulative’” (p. 184) and that the term virtual manipulative “should be restricted to describing only those sites that offer this interactive capability” (pg 185). As such, this entry will focus on these dynamic virtual manipulatives as defined and described by Moyer and Bolyard.
Suggestions for Classroom Use
Virtual manipulatives can be utilized in two main ways: teacher-directed or student-directed. In teacher-directed, virtual manipulatives are projected on an IWB. The teacher uses the virtual manipulatives as a teaching tool during instruction portions of the class. All student focus on the same virtual manipulatives with students being called up one at a time to the IWB to interact with the manipulatives.
Student-directed use involves students having access to their own computer and using the virtual manipulatives at their own pace and desire. Students can choose which manipulatives they see as being helpful for a problem they are given. It is very likely that with student-centered use the choice of manipulatives and how they are used will vary from student to student. With the student-centered approach, teachers may have to initially give some direction and instruction on how to navigate around and use the website that hosts the virtual manipulative applets.
Clements and McMillen (1996, as cited in Durmus & Karakirik, 2006) encourage teachers to consider the following recommendations before implementing virtual manipulatives in any classroom:
- the virtual manipulatives that are selected should allow students to show their thinking.
- students should work collaboratively in pairs when utilizing virtual manipulatives.
- when possible, the teacher should use an IWB to allow for extension discussions with the class.
- recognize the need for the introduction of the software and hardware that will be used by the students.
Noteworthy Websites for Virtual Manipulatives
National Library of Virtual Manipulatives
This is one of the more common websites for virtual manipulatives. Created and maintained by Utah State University (through funding by the National Science Foundation), the site is easy to navigate around in as you start by selecting a grade level and content area. You are then given a list of suggested virtual manipulatives to work with that align with that particular grade and content.
In conjunction with the previous site mentioned, Utah State University has created a website where teachers can customize many of the virtual manipulatives available on the NLVM's original website. Registration is required but is free. Once logged on, teachers can customize the manipulatives for their own classroom use. Customizations can be saved and used again via the teacher's account.
McGraw Hill Education
Upon first glance, this website appears to be extremely basic. However, by selecting a grade, a work mat and then the manipulative you desire, it is quite powerful and easy to use, especially for students. The site also offers a basic drawing tool bar which includes options such as a timer, protractor and ruler. A print screen button also allows students to easily print what they have created in order to "show their work".
The NCTM (National Council of Teachers of Mathematics) has created this website of helpful virtual manipulatives. The website offers the typical virtual manipulatives in the Activities section. What is unique to this website is the Lessons area. Here, teachers can search a grade and math content area and appropriate lessons are available for the teacher. All lessons include the use of virtual mnaipulatives, but also come with printable blackline masters and a formal lesson plan for the teachers to follow (if so desired).
This website offers online activities that involve virtual manipulatives. The activities are organized by math content area or grade level. Once an activity is selected, students can work through the activity using the virtual manipulatives that the activity has set out. Students are also asked questions related to the math content area and can respond and check their answers immediately. One drawback is that teachers cannot customize or select "blank" versions of the virtual manipulatives, but instead have to use the activities that are laid out for them.
Benefits of Using Virtual Manipulatives
Potential benefits of using virtual manipulatives in a classroom are:
- students are provided with unlimited quantities of manipulatives to use with a problem (Bouck & Flanagan, 2009)
- interactive features that prompt students to go onto the next step or give feedback (Bouck & Flanagan, 2009; Dumus & Karakirik, 2006)
- the range of manipulatives that can be accessed at a low cost, often free (Bouck & Flanagan, 2009)
- teachers can demonstrate a concept to the whole class or students can work individually or with partners at computers (Bouck & Flanagan, 2009)
- students can work at their own pace, whether at school or at home (Bouck and Flanagan, 2009; Dumus & Karakirik, 2006; Moyer & Bolyard, 2001)
- promotes positive attitudes towards mathematics in students (Dumus & Karakirik, 2006)
- the manipulatives can be modified and altered to meet specific needs (Moyer & Bolyard, 2001)
- students in upper grades view virtual manipulatives as more sophisticated than physical manipulatives and as such are more likely to use them (Moyer & Bolyard, 2001)
- can simultaneously provide multiple representations of one concept (Young, 2006)
Pitfalls of Using Virtual Manipulatives
Despite the many benefits of virtual manipulatives, there are also some pitfalls that educators should be aware of:
- any type of manipulative (virtual or physical) is only beneficial if teachers know how to integrate them into their classroom (Bouck & Flanagan, 2009)
- students require time and access to virtual manipulatives to develop comfort, knowledge and appropriate skills (Rosen & Hoffman, 2009)
- students are not actually able to touch them (Hunt, Nash & Nipper, 2009)
- some models of physical manipulatives are not yet available virtually (Hunt, Nash & Nipper, 2009)
- it can force students to think abstractly which is a struggle for some (Hunt, Nash & Nipper, 2009)
- some students have been observed to be disengaged with virtual manipulatives (hit the "Hint" or "Reset" buttons without really solving a problem) (Speer, 2010)
- despite a teacher's best instruction and direction, some students will still struggle to understand how to use virtual manipulatives (Speer, 2010)
Current Research on the Effectiveness of Virtual Manipulatives
Steen, Brooks and Lyon (2006) examined the impact of virtual manipulatives on first grade students’ achievement in a geometry unit. By using experimental research, the authors randomly assigned 31 first grade students to either a control or treatment group. Both groups studied identical objectives but the treatment group received instruction and practice utilizing virtual manipulatives. The treatment group made significant gains during the study. Steen et al. concluded that the use of virtual manipulatives is extremely beneficial for student achievement.
Reimer and Moyer (2005) completed a similar study. They chose to examine how using virtual manipulatives with third graders learning about fractions affected achievement. Nineteen grade 3 students were initially instructed using physical manipulatives. They were given an initial test on their conceptual and procedural knowledge of fractions. Following this, the grade 3 students were taught the same objectives but this time the teacher used virtual manipulatives to assist in the teaching. Students were then re-tested using the same tests. Results of the study show that 10 of the 19 students increased their conceptual knowledge and 7 of the 19 increased their procedural knowledge. The authors indicate that high scores on the initial conceptual and procedural knowledge test led to only about half the students improving.
Another study by Mendiburo and Hasselbring (2011) researched fifth grade students and how virtual manipulative use compared to physical manipulative use. Students learned about basic fraction concepts in the study and were placed into a treatment group. The treatment groups saw two groups that used virtual manipulatives and two groups that used physical. A 20 question multiple choice test was given prior to the research, on day 5 of the experiment, and then a final time on day 10. Based on the mean scores of all four treatment groups, the researchers concluded that the students who used the virtual manipulatives scored higher on the post test than those who used physical manipulatives. Mendiburo and Hasselbring also concluded that students who used virtual manipulatives were more efficient at solving the questions in terms of time to complete.
Zacharia, Olympiou, and Papaevripidou (2008) conducted an interesting study on how virtual manipulatives can be used in a Science classroom. Students were learning about the concept of heat and temperature and were placed into either a control or experimental group. The control group only used physical manipulatives to conduct their experiments while the treatment group used both physical and virtual manipulatives. Conceptual understanding tests were administered before, during and after the study's treatments. The researchers found that the combination of physical and virtual manipulatives was effective in enhancing the students' conceptual knowledge.
These four research articles are only a sampling of the current research regarding the positive impact that virtual manipulative use can have in a classroom.
- Bouck, E. C., & Flanagan, S. M. (2010). Virtual manipulatives: what they are and how teachers can use them. Intervention in School and Clinic, 45(3), 186-191. doi: 10.1177/1053451209349530
- Durmus, S. & Karakirik, E. (2006). Virtual manipulatives in mathematics education: a theoretical framework. The Turkish Online Journal of Educational Technology, 5(1). Retrieved from http://www.tojet.net/articles/5112.pdf
- Hunt, A. W., Nach, L. E., & Nipper, K. L. (2009). Virtual vs Hands-On Manipulatives in Teacher Education: Is One Type More Effective Than the Other [PowerPoint slides]? Retrieved from http://cims.clayton.edu/ahunt/AMTE%20presentation%202-5-2009.ppt
- Mendiburo, M., & Hasselbring, T. (2011). Technology's impact on fraction learning: an experiment comparison of virtual and physical manipulatives, SREE Spring 2011 Conference. Washington D. C. Retreived from http://www.sree.org/conferences/2011/program/downloads/abstracts/148.pdf
- Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2001). Virtual manipulatives in the K-12 classroom. Retrieved from ERIC database. (ED468203)
- Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics. 8(6). 372-377.
- Reimer, K. & Moyer, P.S. (2005). Third-graders learn about fractions using virtual manipulatives: A classroom study. Journal of Computers in Mathematics and Science Teaching, 24(1), 5-25. Retrieved from http://www.editlib.org.ezproxy.library.ubc.ca/p/18889
- Rossen, D., & Hoffman, J. (2009). Integrating concrete and virtual manipulatives in early childhood mathematics. Young Children. 64(3), 26-29, 31-33. Retrieved from http://www.naeyc.org/yc/pastissues/2009/may
- Speer, W. (2010). Virtual Manipulatives: Potential Instructional Hazards and Possible Design-based Solutions. Retrieved from http://web.gnowledge.org/episteme3/pro_pdfs/26-speer.pdf
- Steen, K., Brooks, D. & Lyon, T. (2006). The impact of virtual manipulatives on first grade geometry instruction and learning. Journal of Computers in Mathematics and Science Teaching, 25(4), 373-391. Retrieved from http://www.editlib.org.ezproxy.library.ubc.ca/p/19812
- Young, D. Y. Virtual Manipulatives in Mathematical Education. Retrieved from http://plaza.ufl.edu/youngdj/talks/vms_paper.doc
- Zacharia, Z. C., Olympiou, G. & Papaevripidou, M. Effects of experimenting with physical and virtual manipulatives on students' conceptual understanding in heat and temperature. Journal of Research in Science Teaching. 45(9), 1021-1035. doi: 10.1002/tea.20260