Virtual Manipulatives:

1. Virtual Manipulatives: Are they better than their concrete counterparts? John Meyer Governors State University University Park, IL

2. Do manipulatives automatically work? Manipulative use does not automatically mean better learning Are they helpful? �Yes, but there are no guarantees. Rote use is not effective Teachers must work with students to connect manipulation with understanding the notation which describes the actions They are not a magic bullet. While they certainly help, they are only as good as the activities, questioning, and explanations you use. Use alone is not effective because there needs to be a connection drawn between the activities with the materials and the symbols. Otherwise, students will view them as totally separate activities.They are not a magic bullet. While they certainly help, they are only as good as the activities, questioning, and explanations you use. Use alone is not effective because there needs to be a connection drawn between the activities with the materials and the symbols. Otherwise, students will view them as totally separate activities.

3. Are virtual manipulatives concrete? �concrete� cannot be only equated with physical manipulatives �Computers might supply representations that are just as personally meaningful to students as real objects; that is, they might help develop integrated-concrete knowledge. These representations may also be more manageable, �clean�, flexible, and extensible� (Clements & McMillen, 1996). It really depends on the individual students as to the effectiveness of virtual manipulatives. With so many students being visual learners these days, it makes sense that virtual manipulatives would be well accepted and understood. However, we still need to insure that students are taught visual literacy skills to maximize their learning. We cannot assume that the mathematics understanding will be drawn from virtual manipulatives by virtue of their use alone.It really depends on the individual students as to the effectiveness of virtual manipulatives. With so many students being visual learners these days, it makes sense that virtual manipulatives would be well accepted and understood. However, we still need to insure that students are taught visual literacy skills to maximize their learning. We cannot assume that the mathematics understanding will be drawn from virtual manipulatives by virtue of their use alone.

4. Why use virtual manipulatives? They�re �free� If used in a lab, everyone can have their own manipulatives Multiple materials are available for each student Can individualize for each student With online access, virtual manipulatives are available without cost to the users. In a computer lab, everyone has their own materials. You can select appropriate materials and activities for each student based on individual needs. In addition, students can use as many manipulatives as desired or needed. With online access, virtual manipulatives are available without cost to the users. In a computer lab, everyone has their own materials. You can select appropriate materials and activities for each student based on individual needs. In addition, students can use as many manipulatives as desired or needed.

5. Why use VM? (cont�d.) Students� � � work can be saved and worked on again and again (Clements, 1999, p. 5)� Work can be saved and printed out Shapes are easier to make with software manipulatives�they snap to outlines and stay where they are put. Students control their interaction with the mathematics Many of the NLVM activities are marked with the term SAVE which means that �they can be configured as desired and called up for lesson-plans, demonstrations, exercises, or assessment hand-outs.� (NLVM)Many of the NLVM activities are marked with the term SAVE which means that �they can be configured as desired and called up for lesson-plans, demonstrations, exercises, or assessment hand-outs.� (NLVM)

6. Why use VM? (cont�d.) Actions possible with software model the processes we want students to internalize Students can change the size of some manipulatives and not others. This is not possible with physical manipulatives. Some tools allow shapes to be �glued� together. Software has allowed us to do things that we can�t do with physical manipulatives. We can use computer graphics to demonstrate what we want students to internalize. Learners can resize some or all manipulatives for exploration, experimentation, or better understanding. Students can even attach figures together, such as in Space Blocks.Software has allowed us to do things that we can�t do with physical manipulatives. We can use computer graphics to demonstrate what we want students to internalize. Learners can resize some or all manipulatives for exploration, experimentation, or better understanding. Students can even attach figures together, such as in Space Blocks.

7. Why use VM? (cont�d.) Students make decisions, then see what happens as a result of those choices Built-in tools such as flips and turns In Base Blocks, students can break base 10 rods into 10 singles for regrouping. When blocks are changed, the numbers are automatically changed to reflect the change in the manipulatives. In Triominoes, students can execute slides, flips, and turns. Base Blocks and Base Blocks Decimals assist the learner to trade units for tens rods, rods for hundreds flats, or flats for thousands cubes in addition and to break the blocks up in subtraction as regrouping takes place. In Triominoes, students can execute slides, flips, and turns. Base Blocks and Base Blocks Decimals assist the learner to trade units for tens rods, rods for hundreds flats, or flats for thousands cubes in addition and to break the blocks up in subtraction as regrouping takes place.

8. Why use VM? (cont�d.) In LOGO, students connect ideas about characteristics of geometric shapes, because they must create directions for the turtle which reflect angle turns and side lengths. LOGO ideas are covered in the Turtle Geometry applet.LOGO ideas are covered in the Turtle Geometry applet.

9. Why use VM? (cont�d.) Students using physical manipulatives didn�t always connect activities with what they wrote on paper. They viewed them as separate activities. Computer groups linked the base 10 block activities to the symbols. More �grown-up��acceptable to middle and high school students It seems that it is easier for groups using virtual manipulatives to make the connections between the grphic representations and the associated notation.It seems that it is easier for groups using virtual manipulatives to make the connections between the grphic representations and the associated notation.

10. Teaching with computers ��adults play a significant role in successful computer use. Children are more attentive, more interested, and less frustrated when an adult is present (Binder & Ledger, 1985). Thus, teachers may wish to make the computer one of many choices, placed where they can supervise and assist children (Clements, 2002, p. 171). As always, you are always needed for supervision and individual assistance.As always, you are always needed for supervision and individual assistance.

11. Teaching with computers (cont�d.) ��teachers whose children benefit significantly from using computers are always active. They closely guide children�s learning of basic tasks, then encouraging, questioning, prompting, and demonstrating. Such scaffolding leads children to reflect on their own thinking behaviors and brings higher-order thinking processes to the fore (Clements, 2002, p. 172). Read quote��..�again, you are essential in the learning of your students.Read quote��..�again, you are essential in the learning of your students.

12. Sample Websites

13. Let�s take a look at some of the activities I mentioned in the last few slides.Let�s take a look at some of the activities I mentioned in the last few slides.

14. This is the Illuminations section of the NCTM website. You can search for activities, lessons, or standards based on words or phrases of your choosing.This is the Illuminations section of the NCTM website. You can search for activities, lessons, or standards based on words or phrases of your choosing.

15. The NEIR-TEC site is arranged by algebra readiness skills. Tool links come from NCTM, NLVM, and other resources.The NEIR-TEC site is arranged by algebra readiness skills. Tool links come from NCTM, NLVM, and other resources.

16. The OTEC site from the University of Oregon extends the information on virtual manipulatives and provides ways of integrating technology into mathematics.The OTEC site from the University of Oregon extends the information on virtual manipulatives and provides ways of integrating technology into mathematics.

17. Concrete manipulative advantages over VM Concrete vs. pictorial More �natural� to manipulate If used in groups, can foster discourse Don�t require computers or Internet access. Don�t �go down� as Internet may. So how about the benefits of concrete (physical) manipulatives over virtual ones? Is there such a thing as �more concrete?� Doug Clements doesn�t seem to think so. Concrete materials like blocks are natural things to manipulate. Rather than one-child-to-one-computer, we can group students to discuss their understandings and solutions to problems posed. Besides, we don�t have to have a lab full of computers with internet access�and concrete manipulatives don�t �go down.�So how about the benefits of concrete (physical) manipulatives over virtual ones? Is there such a thing as �more concrete?� Doug Clements doesn�t seem to think so. Concrete materials like blocks are natural things to manipulate. Rather than one-child-to-one-computer, we can group students to discuss their understandings and solutions to problems posed. Besides, we don�t have to have a lab full of computers with internet access�and concrete manipulatives don�t �go down.�

18. So which one is better? �Studies show that a combination of physical and virtual manipulatives is more effective than either alone. Activities in which children first move their bodies, for instance, walking around a shape on the floor, and then use commands to direct an onscreen turtle to make the same motions, improve mathematical understanding and problem-solving skills (Clements & Samara, 1997, 1998).� Quote Clements & Samara. So where can you find Internet resources? Here are some URLs which you are welcome to write for. I�ll put up my email address at the end.Quote Clements & Samara. So where can you find Internet resources? Here are some URLs which you are welcome to write for. I�ll put up my email address at the end.

19. Resources National Library of Virtual Manipulatives for Interactive Mathematics � Utah State Univ. (http://nlvm.usu.edu) NLVM CD (www.mattimath.com) Interactive math lessons (http://enlvm.usu.edu) http://nlvm.usu.edu/en/nav/vlibrary. html

20. Resources (cont�d.) www.standards.nctm.org/documents/eexamples/index.htm http://mason.gmu.edu/~mmankus/talks/nctm2000/nctmch00.htm http://arcytech.org/java www.ies.co.jp/math/java/geo/index.html

21. Resources (cont�d.) www.illuminations.nctm.org/Activities.aspx http://otec.uoregon.edu/virtual_manipulatives.htm www.math.fsu.edu/Virtual/index.php?f=4 www.ct4me.net/math_manipulatives.htm www.emints.org/ethemes/resources/S00000592.shtml

22. References Clements, D.H. (1999). Concrete manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60. http//www.triangle.co.uk/ciec/ www.pbs.org/readytolearn/resources/2005_summer_institute/Clements_Computers_Math.pdf The greatest amount of research has been done by Doug Clements at the State University of New York at Buffalo and his colleagues.The greatest amount of research has been done by Doug Clements at the State University of New York at Buffalo and his colleagues.

23. References (cont�d.) Clements, D.H. and McMillen, S. (1996). Rethinking concrete manipulatives. Teaching Children Mathematics, 2(5), 270-279.

24. Want a copy? E-mail me at: DrMath@aol.com Put NCTM in the subject line I will e-mail you the URL where the presentation will be posted Thanks for coming! Thanks for coming! I�d be very interested in hearing about your experiences using virtual manipulatives with your students. Please feel free to e-mail me with your experiences and observations. Thanks again for coming!Thanks for coming! I�d be very interested in hearing about your experiences using virtual manipulatives with your students. Please feel free to e-mail me with your experiences and observations. Thanks again for coming!