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- 1. Virtual vs. TraditionalManipulatives: The impact of virtual manipulatives on sixth grade students’ geometry learning and attitudes Virtual Manipulatives Action Research Proposal Jillian Bronkema
- 2. Research Questions • What impact do virtual manipulatives have on sixth grade students’ knowledge of surface area & volume compared with traditional manipulatives? • What are students' attitudes about using virtual manipulatives?
- 3. Manipulatives • Manipulatives help students convert abstract ideas into concrete models – Examples: Algebra Tiles, Geoboards, Pattern Blocks, Counters, Tangrams • Cons of physical manipulatives – High Cost – Not adequate amount for class – Management Issues • Storage • Passing out • Getting all pieces back – Difficult to send home for practice
- 4. Virtual Manipulatives • Also called online computer manipulatives • “an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” • Examples
- 5. Literature Review • First Grade - Geometry – Steen, Brooks & Lyons, 2006 • Third Grade - Fractions – Remier & Moyer, 2005 • Third Grade - Algebra concepts – Suh & Moyer, 2005 • Fifth Grade - Fractions – Suh, Moyer & Heo, 2005 • Sixth Grade - Integer Operations – Boyar & Moyer, 2006 • Middle School - Spatial Reasoning – Drickey (2000)
- 6. Literature Review • Advantages – Increased quality & quantity of practice – Allows for differentiated Instruction – Flexibility to address many objectives – Great cost (usually free!) – Appeals to visual learners – Dynamic nature
- 7. Literature Review • Impact on Student Attitudes – Engages students – Appeal to upper elem. & middle school students – Third graders & fraction example
- 8. Timeline • Before research begins… – University Approval of Human Research Form – Increase students familiarity with computers & internet • Geometry Unit (mid 2nd semester) – Pre-test – Pre-survey – Activities with traditional & virtual manipulatives • Surface Area & Volume • Follow Up – Post-test – Post-survey
- 9. Study Population • Four sections of 6th grade math students (n≈80) – ≈ 97% Caucasian – English Speaking – Mean Age: 12 years – ≈ 40 boys and ≈ 40 girls • Control Group – 1 morning & 1 afternoon class – Learns concepts with traditional physical manipulatives – Takes paper/pencil unit test • Experimental Group – 1 morning & 1 afternoon class – Learns concepts using virtual manipulatives – Takes paper/pencil unit test
- 10. Data Collection • Pre-test Scores – Knowledge of area & volume • Post-test Scores • Collect Descriptive Statistics – Gender, Socioeconomic status… • Video Tape & Observation Notes – Students using physical & virtual manipulatives • Survey of Attitudes – Pre and Post Test
- 11. Limitations • Sample size – Large enough for statistically significant results? • Population – Lack of diversity • Setting – Rural – Low income
- 12. Confounding Variables • Difference of environments • Computer Issues – Questionable reliability – Student familiarity • Teacher Issues – Technology bias – Time of day • Student Issues – Time of day
- 13. Study Results • Audience – Teachers – Manipulative developers • Release Results – Web • Blog – Video clips • Questions?
- 14. Finding Virtual Manipulatives • Activities Search. Retrieved July 10, 2007, from Illuminations Web site: http://illuminations.nctm.org/ActivitySearch.aspx • Gizmos. Retrieved July 10, 2007, from ExploreLearning: http://www.explorelearning.com/ • Math Manipulatives. Retrieved July 10, 2007, from Computer Technology for Math Excellence: http://www.ct4me.net/math_manipulatives.htm • MetaMedia Mathematics Program. Retrieved July 10, 2007, from George Mason University: http://www.galaxy.gmu.edu/~drsuper/ • National library of virtual manipulatives. Retrieved July 9, 2007, from national library of virtual manipulatives Web site: http://nlvm.usu.edu/en/nav/vlibrary.html • Shodor Interactives. Retrieved July 9, 2007, from Shodor Web site: http://www.shodor.org/interactivate/
- 15. Resources • Drickey, N.A. (2000). A comparison of virtual and physical manipulatives in teaching visualization and spatial reasoning to middle school mathematics students. (Doctoral dissertation, Utah State University, 2000). Dissertation Abstracts International, 62(02), 499A. (UMI No. 3004011) • Hodges, Tim (2003). Web-based manipulatives. Teaching Children Mathematics. 9, 461. • Lindroth, Linda (2005).How to...find online math manipulatives. Teaching PreK-8. 35, 24,26. • Marzano, Robert J., Gaddy, B. B., & Dean, C. (2000). What works in classroom instruction. Aurora, CO: Mid-continent Research for Education and Learning.
- 16. Resources • Moyer, Patricia S., Bolyard, Johnna J., & Spikell, Mark A. (Feb 2002) What are virtual manipulatives?. In Teaching Children Mathematics, 8, p372(6). Retrieved July 11, 2007, from InfoTrac OneFile via Thomson Gale: http://find.galegroup.com.proxy1.cl.msu.edu:2047/itx/infomark • Moyer, Patricia S., Bolyard, Johanna J. (2006). The impact of virtual manipulatives on student achievement in integer addition and subtraction. Technology. 2, 879,880.
- 17. Resources • Moyer, Patricia S., Bolyard, Johanna J., Spikell, Mark A. (2001). Virtual manipulatives in the K-12 classroom. In Proceedings of the International Conference on new Ideas in Mathematics Education. Palm Cove, Queensland, Australia, August 19-24, 2001. • Suh, Jennifer, Moyer, Patricia S. (2007). Developing students' representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching. 26, 155-173. • Steen, Kent, Brooks, David, Lyon, Tammy (2006). The impact of virtual manipulatives on first grade geometry instruction and learning. Journal of Computers in Mathematics and Science Teaching. 25, 373-391. • Reimer, Kelly, Moyer, Patricia S. (2005). Third- graders learn about fractions using virtual manipulatives: A classroom study. Journal of Computers in Mathematics and Science Technology. 24, 5-25.
- 18. Resources-No Access • Moyer, P. Exploring representation in the middle grades: Investigations in geometry with virtual manipulatives The Australian mathematics teacher… 58, 19 - 25. • Moyer-Packenham, Patricia (2005). Investigations - using virtual manipulatives to investigate patterns and generate rules in algebra. Teaching children mathematics. 11, 437.
Editor's Notes
- #3 Through my research I will be looking at these two questions: What impact do virtual manipulatives have on sixth grade students’ knowledge of surface area & volume compared with traditional manipulatives? What are students' attitudes about using virtual manipulatives?
- #4 Manipulatives in general help students convert abstract ideas into concrete models (Lindroth, 2005) An article by Moyer, Bolyard, and Spikell (2002) lists some of the Cons of physical manipulatives: high cost, having an adequate number for a whole class, management issues such as storage, getting them out & getting all pieces back and it is also not feasible to send manipulatvies home for student practice (Moyer, Bolyard, and Spikell, 2002).
- #5 Virtual manipulatives are similar to the physical traditional manipulatives in that they allow students to think about abstract ideas using models. A major difference, of course, is that virtual manipulatives are used on computes can be accessed via the Web or from other math software. One definition of a Virtual Manipulative, that was used in almost every study that I found, comes from researchers at George Mason University. They describe a virtual manipulatives as "an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” ( Moyer, Bolyard, Spikell, 2002). The word DYNAMIC in this definition narrows the category to only include only those manipulatives that let users take an active role in creating representations in order to explore concepts. One site recommended in the same article from GMU recommends the National Library of Virtual Manipulatives where the manipulatives are organized by the standards of the National Council of Teachers of Mathematics (NCTM). {go to site}
- #6 Much of the research I found about virtual manipulatives has come from George Mason University particularly from Patricia Moyer. She has done her own research and has collaborated with several other professors and graduate students on their own action research projects. In one of her articles she states that virtual manipulatives “offer a new, enhanced approach for teaching and learning…yet very little is known or written about them.” (Moyer, Bolyard, Spikell, 2001). An article by Reimer & Moyer (2005) states that 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.” This is only a partial list of the studies I found on virtual manipulatives in the classroom and there were also 2 more studies listing Moyer as an author that I was not able to access.
- #7 Overall, the conclusions drawn from the studies were similar. It was found that virtual manipulatives have many advantages over traditional physical manipulatives. One of the most important benefits of virtual manipulatives is the affordance of the dynamic nature. The dynamic nature allowed students to test hypothesis in a safe environment with trial and error. The dynamic nature also makes it easier for children to make the connections between the images and abstract mathematical symbols. Much of the research has focused on whether the use of virtual manipulatives leads to learning. I want to take a little different focus with my first research question and look for a difference in the amount of learning gains of students who use traditional manipulatives versus those that use virtual manipulatives. In a summary of over 100 research studies, Dr. Robert Marzano (1998) found that one instructional technique that demonstrated a consistent positive impact on student achievement was the use of graphic or nonlinguistic representations to explore and practice new knowledge. Traditional AND virtual manipulatives have graphic characteristics but I want to see if there is a difference in learning about area and volume. This topics is also different than the other studies because the objectives involve learning about 3-Dimensional figures. I think it will be interesting to see if learning about 3-D figures in a 2-D environment such as with a computer screen will impact student understanding.
- #8 The second questions I am researching has to do with students’ feelings & attitudes about using virtual manipulatives for learning geometry concepts. In the article “Virtual Manipulatives in Mathematics Education: A Theoretical Framework,” it is suggested that the flexible nature of virtual manipulative will engage students (Durmns & Karakrik, 2006). A study by Drickey published in 2000 also found that teachers involved in studies using virtual manipulatives report that students appear to be more engaged, on task, and motivated than when using physical manipulatives (Drickey, 2000). It will be important to look at my results to see if they are similar when students use virtual manipulatives to learn about three-Dimensional figures. The article “Virtual Manipulatives in the K-12 Classroom” suggests that older students might associate physical manipulatives with elementary school and like the sophistication of exploring math with computers (Moyer & Spikell, 2001). The research with third graders and fractions had some interesting results regarding students attitudes about using virtual manipulatives. The study found that students enjoyed using virtual manipulatives more than they liked the traditional classroom methods. But, the study did find that the students did not think that the virtual manipulatives helped them to answer the questions on the post-test (Reimer & Moyer, 2005).
- #9 Before research begins… University Approval of Human Research Form Increase students familiarity with computers & internet Geometry Unit (mid 2 nd semester) Pre-test Pre-survey Activities with traditional & virtual manipulatives Surface Area & Volume Follow Up Post-test Post-survey Geometry Unit & follow-up should take approximately 5-7 class periods to complete all activities, tests, and surveys.
- #10 Since I don’t yet have my class lists, I have approximated the numbers. Control group will work in the classroom and experimental group will work in the computer lab for activities requiring the internet connection.
- #11 I will collect data through several different instruments in order to come to conclusions about my research questions. I will collect descriptive statistics that I will account for differences such as gender, socioeconomic status, and academic ability in control & experiment groups by using standard statistical methods (SPSS or free method).
- #12 There are limitations to my study. Factors that influence the generalizability of my research include the sample size. I will be studying approximately 80 students which might not be a large enough number to generate statistically significant results. My population will also be predominately Caucasian students that are twelve years old. Also, my school is located in a rural, low income area. This is quite a contrast to many other school setting which could limit the generalizability of my study.
- #13 Confounding Variables are extraneous variable which for some reason has been left uncontrolled. In my research there are a few issues that are very difficult to control. For instance: Difference of environments —classroom vs computer lab. Virtual manipulatives requires the use of computers and the internet which must be accessed in the computer labs. Computer Issues– Our internet, some of the equipment in the computer labs, and our network are sometimes unreliable. Also, the students at our school have quite a range of experience with computers. These problems combined could affect the productivity of class time and students’ attitudes towards virtual manipulatives. Teaching : Another issue that could affect the objectivity is my bias towards technology based solutions. My affinity for technology could potentially influence my results. Also, I know that my teaching changes from hour to hour. It might take a class period to work out the kinks in a lesson or I might have more energy in the morning than the afternoon Students : Attention differences throughout day, before or after lunch, coming from a particularly exciting or boring class… All of these things can make a difference in the research results.
- #14 This study would be important for other math teachers and for virtual manipulative developers. At first I thought the best way to get my study results out there would be to write a paper…because that’s what researchers do. Then, I thought about how I could best share the video and manipulative demos and I think that some web based medium would be more effective. A blog could be interesting because other educators could ask questions, comment on my work, or offer suggestions. What questions can I answer or any suggestions? Show list of virtual manipulatives…
- #15 There are many really great sites that offer free virtual manipulatives and this a partial list of some of the best. Some like explorelearning’s Gizmos require a free for full use. I will be using a combination of virtual manipulatives from several sites including Illuminations & Shodor.