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- 1. Virtual Manipulatives 1 Running Head: VIRTUAL MANIPULATIVES The Effects of Using Virtual Manipulatives Versus Physical Manipulatives on Achievement to Teach Basic Fractions to Third Grade Students Susan Scheurer East Stroudsburg University ELED 570: Introduction to Research Dr. Wilson July 11, 2011
- 2. Virtual Manipulatives 2 The Effects of Using Virtual Manipulatives Versus Physical Manipulatives to Teach Basic Fractions to Elementary Students Introduction Many elementary math teachers use manipulatives to assist children with visualizing and processing mathematical concepts. McClung states that “manipulatives assist students in bridging the gap from their own concrete sensory environment to the more abstract levels of mathematics” (Brown, 2007). Physical manipulatives have been used over the centuries to bring math to life and still play an important role in education. Research has shown that physical manipulatives enhance the learning experience and are met with positive achievement results. However, with the rapid growth of technology in the past thirty years, technology devices are providing other options to use virtual manipulatives in the classroom. Taylor (2001) states that “progression in technology has increased the boundaries of mathematics and emphasized the importance of the integrations of technology in the mathematics curriculum” (Brown, 2007). Virtual manipulatives are widely available through the World Wide Web, which can be accessed in most classrooms. Current elementary teachers have the opportunity to use physical and/or virtual manipulatives in their classrooms. The technology resources that allow the use of virtual manipulatives to be integrated into the math classroom are becoming relatively easier and more accessible. According to Rosen and Hoffman, “teachers around the country and the world guide children’s mathematical learning through the use of manipulatives – pattern blocks, base blocks, geoboards, Unifix cubes, Cuisenaire rods, coins, clocks, and so on. Manipulatives allow concrete, hands-on exploration and representation of mathematical concepts. In the past few years, online resources for virtual versions of these common manipulatives have become available” (Rosen and Hoffman, 2009).
- 3. Virtual Manipulatives 3 Furthermore, children are growing up with technology as an integral way of life. It is imperative for teachers to integrate technology in the classroom to engage students, enhance and promote active visual learning. Using virtual manipulatives in the classroom is still largely under researched. However, from personal experience, students are enthusiastic to learn math using a new and exciting way to visualize learning of mathematical concepts. Virtual manipulatives are a resource that engages students and have the potential to greatly enhance their math achievement. Research Problem The Effects of Using Virtual Manipulatives Versus Physical Manipulatives on Achievement to Teach Basic Fractions to Third Grade Students Research Questions 1. What are the gain scores on an instrument measuring achievement of students taught basic fractions using virtual manipulatives? 2. What are the gain scores on an instrument measuring achievement of students taught basic fractions using physical manipulatives? 3. How do the scores compare? Definition of Terms Manipulatives are defined by Taylor (2002) as “physical objects (e.g., base ten blocks, algebra tiles, pattern blocks, etc.) that can be touched, turned, rearranged, and collected” (Brown, 2007). According to Rosen, “manipulatives allow concrete, hands-on exploration and representation of mathematical concepts” that children can explore (Rosen and Hoffman, 2009). Physical Manipulatives are described by McClung (1998) as “objects that appeal to several of the senses. They are objects that students are able to see, touch, handle, and move” (Brown, 2007). Physical manipulatives are also called concrete manipulatives and according to
- 4. Virtual Manipulatives 4 Mendiburo, “what is “concrete” to a child may have more to do with what is meaningful and manipulable than with physical characteristics” (Mendiburo, 2006). Virtual Manipulatives are defined by Moyer, Bolyard and Spikell as “an interactive, Web- based visual representation of a dynamic object that present opportunities for constructing mathematical knowledge” (Moyer, 2005). Moyer (2005) further describes virtual manipulatives saying “virtual manipulatives are essentially replicas of physical manipulatives placed on the World Wide Web in the form of computer applets with additional advantageous features” (Brown, 2007) In another study, virtual manipulatives are defined as “computer based renditions of common mathematics manipulatives and tools” (Suh, 2007).
- 5. Virtual Manipulatives 5 Review of the Literature Maria Mendiburo and Ted Hasselbring learned that in 1990, fewer than half of the high school seniors, who took the NAEP Mathematics Assessment, demonstrated successful performance with problems involving fractions, decimals, percents and simple algebra. Only 14 percent of eighth graders who took the NAEP Mathematics Assessment also demonstrated successful performance with problems involving fractions, percents and simple algebra. In 2000, eighth graders were given a test where they had to order three fractions from least to greatest. The fractions were less than 1 and in reduced form. Only 41 percent of eighth graders did this successfully. Believing that fractions are the most difficult mathematical concept for elementary students to learn, Mendiburo and Hasselbring decided to conduct their own study to “advance the current literature about manipulatives and rational numbers by using a randomized experiment to compare virtual and physical manipulatives” (Hasselbring, 2011). They also decided to conduct this research to answer the question of “are there differences in students’ knowledge of fraction magnitude when they are taught basic fraction concepts using virtual manipulatives compared to when they are taught basic fraction concepts using physical manipulatives?” (Hasselbring, 2011). The subjects of this study were 67 fifth grade students at a charter middle school in Middle Tennessee. There were four fifth grade mathematics classes, with 39 girls and 28 boys who participated in the study with parent consent. Classes at the school were single-gender. It should be noted that approximately 98.9 percent of the students in the school were African- American and that 88 percent of students qualified for free and reduced priced lunch. According to a comprehensive mathematic benchmark assessment recently administered by a private assessment company before the study took place, 62 percent of students participating in the study tested below grade level.
- 6. Virtual Manipulatives 6 Due to the school’s preference that classes stay intact and single-gender, the researchers randomly assigned half of the students within each of the four classes to a virtual manipulative condition and the other half of the students in the four classrooms to a physical manipulative condition. The students were grouped according to gender and treatment condition, creating a 2x2 Experimental Factorial design. The quantitative factorial design can be better explained as 2 (treatment: physical vs. virtual) x 2 (gender: girls vs. boys). Before the study started, the researcher administered a pre-assessment to all participating students to determine prior knowledge of fifth grade fraction content. The paper-and-pencil assessment was created by the researcher using software provided by a private assessment company that contracted with the school to measure and improve student achievement and to predict students’ performance on state exams. The pre-test was made up of 20 multiple-choice questions about fractions. All of the questions were validated by fifth grade assessment items. Students did not use manipulatives when completing the pre-assessment. The results of the pre-assessment showed that most students had at least some prior knowledge of fractions, while most of those same students fell short of demonstrating mastery of the fifth grade fraction concepts that would likely be on state assessments. The researcher taught all classes using a script to control for possible teacher effects and pedagogical differences between treatment conditions. The research was conducted for a total of 10 days. Students who were assigned to the physical manipulative condition were taught basic fraction concepts using a popular commercial curriculum and fraction manipulatives that the students made out of colored strips of paper. In comparison, the students assigned to the virtual manipulative condition were taught basic fraction concepts using Macbook laptops. The laptops
- 7. Virtual Manipulatives 7 were loaded with a software program designed specifically for the study that was basically a virtual copy of the commercial curriculum and included a set of virtual fraction manipulatives. An assessment was given to all students on day 5, where the students in the virtual manipulatives group scored marginally higher than students assigned to the physical manipulative condition. However, when controlling for students’ scores on the pre-assessment, the main effect of the manipulative treatment condition was not statistically significant. Gender did have an effect, but there was no interaction effect between manipulative treatment and condition gender. On day 10 a post assessment was given that showed the virtual manipulative group answered an average of 1.78 more questions correctly than students in the physical manipulative group. The contrast was statistically significant. However, the difference between boys and girls was not statistically significant and the interaction between gender and manipulative treatment was also not significant. This study concluded that physical and virtual manipulative share positive effects on student learning and there are no negative learning gains associated with using the virtual manipulatives. With the rapid rise of technology in classrooms, Patricia Moyer conducted a study to explore the use of several virtual manipulative computer applets for instruction during a fraction unit in a third grade classroom. The researcher also stated that there is limited research on virtual manipulatives, mainly due to researchers’ lack of both technology and mathematics mastery. The research question posed was what impact do virtual fraction manipulatives have on students’ conceptual and procedural understanding of fractions? To answer the above question, Quasi-Experimental Pretest-posttest, Nonequivalent Control Group Design research was conducted on 19 third grade students. This was an intact
- 8. Virtual Manipulatives 8 class of 25 students, of which only 19 were included since the others were absent and four children with Autism attended mathematics classes in a self-contained classroom. The school where the research took place is half an hour away from Washington DC Metro area and had a diverse student population, including 10 Caucasian, 2 Hispanic, 1 African-American, 3 Asian and 3 Middle-Eastern students. The teacher of the class had previously taught the fraction concept and tested the students. The teacher taught the same fraction concepts again to control for the effect of the virtual manipulatives. The teacher desired to know if there would be changes in students’ test scores, favorably or unfavorably, attributed to the virtual manipulatives. Students were given a pre and posttest before and after the two weeks experiment to measure students’ conceptual knowledge and students’ procedural computation knowledge. The teacher created four tests, a pre and posttest to determine students’ understanding of the procedural knowledge and a pre and posttest to determine the conceptual knowledge. Week one of the experiments involved the teacher instructing students using virtual manipulatives by having her laptop displayed through the classroom TV. The teacher taught a unit on base-10 blocks, and also taught students how to use the virtual applets on the computers in the computer lab. She purposely did not teach the fraction unit during the first week so that the students could become familiar with the virtual applets. In the second week, the teacher taught the unit on fractions in the computer lab. The students worked in the computer lab during math time, which was 1 hour, for four days using the virtual manipulatives. On day one, students used the “Fractions – Parts of a Whole” virtual manipulative applet under the Numbers and Operations strand. On day two, students explored parts of a group using the “Pattern Blocks” applet under the Algebra strand. On days three and four, students used the “Equivalent
- 9. Virtual Manipulatives 9 Fractions” and “Comparing Fractions” applets under Number and Operations. At the end of week two, students were given posttests on conceptual knowledge and procedural computation knowledge. Results showed that students scored significantly higher on the conceptual knowledge posttest compared to the pretest using virtual manipulatives. On average, the class scored 60 percent on the pretest and scored 69 percent on the posttest. However, the results indicated that the virtual manipulatives helped 53 percent of the students improve their conceptual understanding of fractions; while 21 percent of students showed no change and 26 percent actually had scores decrease. The procedural knowledge assessment indicated no significant difference between the pretest and posttest, presumably because on average, the class scored 90 percent on the pretest. The class on average scored 96 percent on the posttest, but because the pretest scores were so high, the experiment was limited. It is important to note that even though the pretest scores were very high, that 74 percent of the students had scores that stayed consistent or increased on the posttest. This study had a small sample size and with more subjects, the outcomes could be further generalized. Overall, the majority of the students showed improvement on their posttest using the virtual manipulative applets. Sonya Brown wanted to know whether or not students who used virtual manipulatives would out-perform students who used concrete manipulatives on the researcher and teacher generated posttest. She conducted this study to investigate the impact of using computer simulated, virtual, manipulatives and hands-on, concrete or physical, manipulatives on elementary students’ learning skills and concepts in equivalent fractions. To research this question, the researcher used a quantitative method, Quasi-Experimental Pretest-posttest,
- 10. Virtual Manipulatives 10 Nonequivalent Control Group Design research, administered a pretest to both a control and experimental groups, and administered a posttest. The subjects were 49 sixth graders from two mathematic classes in one of Detroit’s public schools. Students were already assigned to classes, were intact and hopefully the variation in students’ gender, ethnic background and socioeconomic status reflected the composite to the greater population in that geographic area. Group A received mathematics instruction with virtual manipulatives and Group B received mathematics instruction with concrete manipulatives. Group A is the experimental group and Group B is the control group. The independent variables were the mathematics instruction with the use of virtual manipulatives and the mathematics instruction with the use of concrete manipulatives. The dependent variables were the students’ conceptual knowledge and procedural knowledge as it related to fractions. The groups each received only 1 day of instruction with their respective manipulative. The pre and posttest instruments were identical and tested students’ conceptual and procedural knowledge of equivalent fractions. The instruments were designed by the researcher and the content of the instruments was based on the curriculum standards outline by the National Council of Teachers in Mathematics. The researcher used a two-sample, paired-data, t-test with a 0.05 confidence level to analyze the data. The pre and posttest gain score showed that the concrete manipulative group increased mathematic achievement higher than the virtual manipulative group. One explanation for this is that the concrete manipulative group’s pretest scores were generally higher than the virtual manipulative group. Another possible reason is that the instruction with the use of concrete manipulatives was more effective than that of using virtual manipulatives.
- 11. Virtual Manipulatives 11 Some concerns for this research study is that the students may not have been exposed to their respective manipulative for enough time. A single day is not enough time to conduct adequate research. Plus, the researcher admits that she was a pre-service teacher with no experience teaching with physical or virtual manipulatives. Need for the Study Based on the conflicting outcomes stated in the three research studies above, there is a need for more research on the topic of virtual vs. physical manipulatives. There is a lack of research on the effects of using virtual manipulatives in elementary mathematic classrooms, and those studies that were conducted conflict with findings. The last study brings some validity and reliability concerns since the study was only conducted for one day and by an inexperienced pre- service teacher. Inconsistent research findings compel me to add to the existing knowledge so that educators can have research at their fingertips before trying something new in their mathematics classrooms; virtual manipulatives.
- 12. Virtual Manipulatives 12 Methodology Research Design The study will be conducted to determine whether virtual or physical manipulatives impact math achievement scores of third grade students the most. This quantitative study will be conducted as quasi-experimental research because it will use two different intact third grade mathematic classes. One group will be the control group, meaning they will learn basic fractions using traditional physical manipulatives. The other group will be the experimental group because they will learn basic fractions using virtual manipulatives. Each class will have 20 students, but different teachers. Both teachers will teach the same math unit on basic fractions, using their respective manipulatives. Both groups will take a pretest and posttest to measure prior knowledge and knowledge gained over the study. The quasi-experimental design is diagramed below: G1 O1 X O2 GS1 G2 O3 - O4 GS2 G1 and G2 represent the two math classes that are participating in the study. G1 is the experimental group because they will be exposed to the virtual manipulative treatment, which is represented with X. G2 is the control group because they will not be exposed to the experimental variable, but only the normal tradition teaching style using physical manipulatives. The – is used to represent that G2 will not have an experimental variable. The mean scores for the pretest instrument will be represented by O1 and O3. The mean scores for the post test measurement will be represented by O2 and O4. The gain score, found by subtracting the pretest from the posttest, will be calculated and shown in GS1 and GS2, which represents the gain score.
- 13. Virtual Manipulatives 13 Subject Selection Subjects for this research study will be 40 third grade students at a public middle school in Monroe County. Students will have a mixed socioeconomic profile and a variety of African- America, Asian, Hispanic and a majority of Caucasian participants. Gender will be evenly distributed among the groups and ability levels should be mixed. Students will be randomly assigned to their classes by school administration and each class will have 20 students. Both classes meet in the morning at the same time during their block period 3, which is right after their special for the day. Procedures Each class will have a different teacher instruct, since they are intact classes and already assigned to their respective teacher. Both classes will be exposed to the same math concepts during the 10 day study, since both classes use the same curriculum in the form of teacher guide, student textbook and homework book. However, the way in which the math concept is taught will differ since the experimental group will be using a projector, smart board and students may be at the computer lab. The teacher for the experimental group will give homework from the workbook because not all students have access to the internet or have computers. Plus, without a school provided math homework site, it would be hard for the teacher to access and assess the homework online. The control group will stay in the classroom and use the overhead and physical manipulatives. The control group will also have homework from the workbook. The study will be conducted during the third quarter in the 2011/2012 year. All students will take the same pretest on day 1 of the study. Students will have all of the period to take the test. The pretest will add internal validity to the study because the ability and knowledge level of basic fractions can be determined for each class. This will help in determining which group actually had the largest gain score. After the students have taken the
- 14. Virtual Manipulatives 14 pretest, they will be introduced to the manipulatives in a fun way that excites children to start learning basic fractions for the coming days. Formal instruction will not take place as students are usually drained after taking a test. Days 2 though 9 will be spent with the students receiving direct instruction from their respective teacher, using their respective manipulative and same lesson. A typical day consists of one lesson. In group one, the teacher models, and guides and then allows the students to work independently to complete a task, using the virtual manipulatives throughout each stage. In group two, the teacher models, guides and then allows the students to work independently to complete a task, using the physical manipulatives throughout each stage. The teachers will have 8 days to complete six lessons in the unit. Teachers cannot go on to other lessons past the stopping point if they finish early and must teach the six lessons in the 8 days allotted. Due to having two different teachers, teaching styles will vary, but content and homework will be the same. On day 10, the posttest will be given to students and they will have all period to complete the posttest. No manipulatives, either physical or virtual, may be used by the students as they take the test. Measurement Instrument The pretest and posttest, called Fraction Fun, look similar with the same kind of fraction problem, but do ask different questions. They each contain 20 questions, with a correct or incorrect answer being possible. Students will write their answer under the fraction image and the scores will be averaged to find the mean scores for the pretest and posttest. Scores will them be compared and analyzed to find the gain score, for each group. Since the Fraction Fun pretest and posttest was generated using an online worksheet tool, the measurement instrument has not been tested for reliability and has no internal reliability. This instrument has moderate validity because the tests are extremely similar and do test basic fraction knowledge of third graders in a way that is appropriate for the intended age level. The
- 15. Virtual Manipulatives 15 measurement instrument is kid friendly, while having the fraction content and criteria for the content with 20 questions of the same fraction concept. Data Analysis Both pretest and posttest means will be calculated for both groups so that the mean gain score can be calculated. Gain scores will be calculated by subtracting the mean pretest score from the mean posttest score. Results will be shown in the table below: Mean Gain Scores on Survey Instrument Experimental Group (G1 Virtual Manipulatives) Control Group (G2 with Physical Manipulatives) Mean Score Pretest O1 O3 Mean Score Pretest O2 O4 Gain Score GS1 GS2 The mean gain scores for each group will be compared in order to interpret the outcome of the study and to verify and experimental effect to due to the independent variable, the virtual manipulatives. A copy of the measurement instrument follows on the next two pages.
- 16. Virtual Manipulatives 16 Significance Anticipated Outcomes The proposed study asks three research questions. The first question is “What are the gain scores on an instrument measuring achievement of students taught basic fractions using virtual manipulatives?” I predict that the students in the virtual manipulative group will demonstrate positive gain scores because manipulatives enhance student comprehension and conceptualizing in math. The second question asked is “What are the gain scores on an instrument measuring achievement of students taught basic fractions using physical manipulatives?” I predict that students the control group will demonstrate positive gain scores of significance, since instruction and manipulatives will enhance learning, therefore the students should do better on the posttest than the pretest. The third question asked is “How do the scores compare?” I expect both groups to have positive gain scores because both use manipulatives as a teaching tool. However, I predict that the manipulated group with the virtual manipulatives will score slightly higher than the control group since students are active learners when technology is used. Relevance This study is relevant to educators because if both groups demonstrate positive mean scores, it could show that there is a positive effect of using virtual and physical manipulatives in a classroom. Educators would then be provided with research that supports teaching basic fractions and math in general, with manipulatives. Most educators would not simply teach using only virtual manipulatives, but may be inspired to use both types of manipulatives in their classroom when available. The use of both kinds of manipulatives, virtual and physical, can
- 17. Virtual Manipulatives 17 reach more children and stimulate children’s minds to become better mathematicians.
- 18. Virtual Manipulatives 18 REFERENCE PAGE Brown, S. E. (2007). Counting blocks or keyboards? a comparative analysis of concrete versus virtual manipulatives in elementary school mathematics concepts. Online submission, Retrieved from EBSCOhost. Mendiburo, M., Hasselbring, T., & Society for research on educational effectiveness, (2011). technology's impact on fraction learning: an experimental comparison of virtual and physical manipulatives. Society for Research on Educational Effectiveness, Retrieved from EBSCOhost. 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 EBSCOhost. Rosen, D., & Hoffman, J. (2009). Integrating concrete and virtual manipulatives in early childhood mathematics. Young Children, 64(3), 26-33. Retrieved from EBSCOhost. Smarkola, C. (2007). Technology acceptance predictors among student teachers and experienced classroom teachers. Journal of Educational Computing Research, 37(1), 65- 82. Retrieved from EBSCOhost. Soft Schools (2005). Fraction fun picture worksheets for third grade. Retrieved July 20, 2011, from http://www.softschools.com/math/fractions/picture_fraction_worksheets/ Suh, J., & Moyer, P. S. (2007). Developing students' representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155-173. Retrieved from EBSCOhost.

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