Research Paper on Virtual Manipulatives In the Math ClassroomDocument Transcript
Virtual Manipulatives 1Running 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
Virtual Manipulatives 2 The Effects of Using Virtual Manipulatives Versus Physical Manipulatives to Teach Basic Fractions to Elementary StudentsIntroduction Many elementary math teachers use manipulatives to assist children with visualizing andprocessing mathematical concepts. McClung states that “manipulatives assist students inbridging the gap from their own concrete sensory environment to the more abstract levels ofmathematics” (Brown, 2007). Physical manipulatives have been used over the centuries to bringmath to life and still play an important role in education. Research has shown that physicalmanipulatives 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 areproviding other options to use virtual manipulatives in the classroom. Taylor (2001) states that“progression in technology has increased the boundaries of mathematics and emphasized theimportance of the integrations of technology in the mathematics curriculum” (Brown, 2007).Virtual manipulatives are widely available through the World Wide Web, which can be accessedin most classrooms. Current elementary teachers have the opportunity to use physical and/orvirtual manipulatives in their classrooms. The technology resources that allow the use of virtual manipulatives to be integrated intothe math classroom are becoming relatively easier and more accessible. According to Rosen andHoffman, “teachers around the country and the world guide children’s mathematical learningthrough the use of manipulatives – pattern blocks, base blocks, geoboards, Unifix cubes,Cuisenaire rods, coins, clocks, and so on. Manipulatives allow concrete, hands-on explorationand representation of mathematical concepts. In the past few years, online resources for virtualversions of these common manipulatives have become available” (Rosen and Hoffman, 2009).
Virtual Manipulatives 3Furthermore, children are growing up with technology as an integral way of life. It is imperativefor teachers to integrate technology in the classroom to engage students, enhance and promoteactive visual learning. Using virtual manipulatives in the classroom is still largely underresearched. However, from personal experience, students are enthusiastic to learn math using anew and exciting way to visualize learning of mathematical concepts. Virtual manipulatives are aresource that engages students and have the potential to greatly enhance their math achievement.Research ProblemThe Effects of Using Virtual Manipulatives Versus Physical Manipulatives on Achievement toTeach Basic Fractions to Third Grade StudentsResearch 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 TermsManipulatives are defined by Taylor (2002) as “physical objects (e.g., base ten blocks, algebratiles, pattern blocks, etc.) that can be touched, turned, rearranged, and collected” (Brown, 2007).According to Rosen, “manipulatives allow concrete, hands-on exploration and representation ofmathematical concepts” that children can explore (Rosen and Hoffman, 2009).Physical Manipulatives are described by McClung (1998) as “objects that appeal to several ofthe 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
Virtual Manipulatives 4Mendiburo, “what is “concrete” to a child may have more to do with what is meaningful andmanipulable 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 constructingmathematical knowledge” (Moyer, 2005). Moyer (2005) further describes virtual manipulativessaying “virtual manipulatives are essentially replicas of physical manipulatives placed on theWorld Wide Web in the form of computer applets with additional advantageous features”(Brown, 2007) In another study, virtual manipulatives are defined as “computer based renditionsof common mathematics manipulatives and tools” (Suh, 2007).
Virtual Manipulatives 5 Review of the Literature Maria Mendiburo and Ted Hasselbring learned that in 1990, fewer than half of the highschool seniors, who took the NAEP Mathematics Assessment, demonstrated successfulperformance with problems involving fractions, decimals, percents and simple algebra. Only 14percent of eighth graders who took the NAEP Mathematics Assessment also demonstratedsuccessful 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 thissuccessfully. Believing that fractions are the most difficult mathematical concept for elementarystudents to learn, Mendiburo and Hasselbring decided to conduct their own study to “advance thecurrent literature about manipulatives and rational numbers by using a randomized experiment tocompare virtual and physical manipulatives” (Hasselbring, 2011). They also decided to conductthis research to answer the question of “are there differences in students’ knowledge of fractionmagnitude when they are taught basic fraction concepts using virtual manipulatives compared towhen 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 inMiddle Tennessee. There were four fifth grade mathematics classes, with 39 girls and 28 boyswho participated in the study with parent consent. Classes at the school were single-gender. Itshould 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. Accordingto a comprehensive mathematic benchmark assessment recently administered by a privateassessment company before the study took place, 62 percent of students participating in the studytested below grade level.
Virtual Manipulatives 6 Due to the school’s preference that classes stay intact and single-gender, the researchersrandomly assigned half of the students within each of the four classes to a virtual manipulativecondition and the other half of the students in the four classrooms to a physical manipulativecondition. The students were grouped according to gender and treatment condition, creating a2x2 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, theresearcher administered a pre-assessment to all participating students to determine priorknowledge of fifth grade fraction content. The paper-and-pencil assessment was created by theresearcher using software provided by a private assessment company that contracted with theschool to measure and improve student achievement and to predict students’ performance onstate exams. The pre-test was made up of 20 multiple-choice questions about fractions. All of thequestions were validated by fifth grade assessment items. Students did not use manipulativeswhen completing the pre-assessment. The results of the pre-assessment showed that moststudents had at least some prior knowledge of fractions, while most of those same students fellshort of demonstrating mastery of the fifth grade fraction concepts that would likely be on stateassessments. The researcher taught all classes using a script to control for possible teacher effects andpedagogical differences between treatment conditions. The research was conducted for a total of10 days. Students who were assigned to the physical manipulative condition were taught basicfraction concepts using a popular commercial curriculum and fraction manipulatives that thestudents made out of colored strips of paper. In comparison, the students assigned to the virtualmanipulative condition were taught basic fraction concepts using Macbook laptops. The laptops
Virtual Manipulatives 7were loaded with a software program designed specifically for the study that was basically avirtual 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 virtualmanipulatives group scored marginally higher than students assigned to the physicalmanipulative condition. However, when controlling for students’ scores on the pre-assessment,the main effect of the manipulative treatment condition was not statistically significant. Genderdid have an effect, but there was no interaction effect between manipulative treatment andcondition gender. On day 10 a post assessment was given that showed the virtual manipulative groupanswered an average of 1.78 more questions correctly than students in the physical manipulativegroup. The contrast was statistically significant. However, the difference between boys and girlswas not statistically significant and the interaction between gender and manipulative treatmentwas also not significant. This study concluded that physical and virtual manipulative sharepositive effects on student learning and there are no negative learning gains associated with usingthe virtual manipulatives. With the rapid rise of technology in classrooms, Patricia Moyer conducted a study toexplore the use of several virtual manipulative computer applets for instruction during a fractionunit in a third grade classroom. The researcher also stated that there is limited research on virtualmanipulatives, mainly due to researchers’ lack of both technology and mathematics mastery. Theresearch 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, NonequivalentControl Group Design research was conducted on 19 third grade students. This was an intact
Virtual Manipulatives 8class of 25 students, of which only 19 were included since the others were absent and fourchildren with Autism attended mathematics classes in a self-contained classroom. The schoolwhere the research took place is half an hour away from Washington DC Metro area and had adiverse student population, including 10 Caucasian, 2 Hispanic, 1 African-American, 3 Asianand 3 Middle-Eastern students. The teacher of the class had previously taught the fraction concept and tested thestudents. The teacher taught the same fraction concepts again to control for the effect of thevirtual manipulatives. The teacher desired to know if there would be changes in students’ testscores, favorably or unfavorably, attributed to the virtual manipulatives. Students were given apre and posttest before and after the two weeks experiment to measure students’ conceptualknowledge and students’ procedural computation knowledge. The teacher created four tests, apre and posttest to determine students’ understanding of the procedural knowledge and a pre andposttest to determine the conceptual knowledge. Week one of the experiments involved the teacher instructing students using virtualmanipulatives by having her laptop displayed through the classroom TV. The teacher taught aunit on base-10 blocks, and also taught students how to use the virtual applets on the computersin the computer lab. She purposely did not teach the fraction unit during the first week so that thestudents could become familiar with the virtual applets. In the second week, the teacher taughtthe unit on fractions in the computer lab. The students worked in the computer lab during mathtime, which was 1 hour, for four days using the virtual manipulatives. On day one, students usedthe “Fractions – Parts of a Whole” virtual manipulative applet under the Numbers andOperations 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
Virtual Manipulatives 9Fractions” and “Comparing Fractions” applets under Number and Operations. At the end ofweek two, students were given posttests on conceptual knowledge and procedural computationknowledge. Results showed that students scored significantly higher on the conceptual knowledgeposttest compared to the pretest using virtual manipulatives. On average, the class scored 60percent on the pretest and scored 69 percent on the posttest. However, the results indicated thatthe virtual manipulatives helped 53 percent of the students improve their conceptualunderstanding of fractions; while 21 percent of students showed no change and 26 percentactually had scores decrease. The procedural knowledge assessment indicated no significant difference between thepretest 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 sohigh, the experiment was limited. It is important to note that even though the pretest scores werevery high, that 74 percent of the students had scores that stayed consistent or increased on theposttest. This study had a small sample size and with more subjects, the outcomes could befurther generalized. Overall, the majority of the students showed improvement on their posttestusing the virtual manipulative applets. Sonya Brown wanted to know whether or not students who used virtual manipulativeswould out-perform students who used concrete manipulatives on the researcher and teachergenerated posttest. She conducted this study to investigate the impact of using computersimulated, virtual, manipulatives and hands-on, concrete or physical, manipulatives onelementary students’ learning skills and concepts in equivalent fractions. To research thisquestion, the researcher used a quantitative method, Quasi-Experimental Pretest-posttest,
Virtual Manipulatives 10Nonequivalent Control Group Design research, administered a pretest to both a control andexperimental groups, and administered a posttest. The subjects were 49 sixth graders from two mathematic classes in one of Detroit’spublic schools. Students were already assigned to classes, were intact and hopefully the variationin students’ gender, ethnic background and socioeconomic status reflected the composite to thegreater population in that geographic area. Group A received mathematics instruction withvirtual manipulatives and Group B received mathematics instruction with concretemanipulatives. Group A is the experimental group and Group B is the control group. Theindependent variables were the mathematics instruction with the use of virtual manipulatives andthe mathematics instruction with the use of concrete manipulatives. The dependent variableswere 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 andprocedural knowledge of equivalent fractions. The instruments were designed by the researcherand the content of the instruments was based on the curriculum standards outline by the NationalCouncil of Teachers in Mathematics. The researcher used a two-sample, paired-data, t-test with a0.05 confidence level to analyze the data. The pre and posttest gain score showed that theconcrete manipulative group increased mathematic achievement higher than the virtualmanipulative group. One explanation for this is that the concrete manipulative group’s pretestscores were generally higher than the virtual manipulative group. Another possible reason is thatthe instruction with the use of concrete manipulatives was more effective than that of usingvirtual manipulatives.
Virtual Manipulatives 11 Some concerns for this research study is that the students may not have been exposed totheir respective manipulative for enough time. A single day is not enough time to conductadequate research. Plus, the researcher admits that she was a pre-service teacher with noexperience teaching with physical or virtual manipulatives.Need for the Study Based on the conflicting outcomes stated in the three research studies above, there is aneed for more research on the topic of virtual vs. physical manipulatives. There is a lack ofresearch on the effects of using virtual manipulatives in elementary mathematic classrooms, andthose studies that were conducted conflict with findings. The last study brings some validity andreliability 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 sothat educators can have research at their fingertips before trying something new in theirmathematics classrooms; virtual manipulatives.
Virtual Manipulatives 12 MethodologyResearch Design The study will be conducted to determine whether virtual or physical manipulativesimpact math achievement scores of third grade students the most. This quantitative study will beconducted as quasi-experimental research because it will use two different intact third grademathematic classes. One group will be the control group, meaning they will learn basic fractionsusing traditional physical manipulatives. The other group will be the experimental group becausethey will learn basic fractions using virtual manipulatives. Each class will have 20 students, butdifferent teachers. Both teachers will teach the same math unit on basic fractions, using theirrespective manipulatives. Both groups will take a pretest and posttest to measure priorknowledge and knowledge gained over the study. The quasi-experimental design is diagramedbelow: G1 O1 X O2 GS1 G2 O3 - O4 GS2G1 and G2 represent the two math classes that are participating in the study. G1 is theexperimental group because they will be exposed to the virtual manipulative treatment, which isrepresented with X. G2 is the control group because they will not be exposed to the experimentalvariable, but only the normal tradition teaching style using physical manipulatives. The – is usedto represent that G2 will not have an experimental variable. The mean scores for the pretestinstrument will be represented by O1 and O3. The mean scores for the post test measurementwill be represented by O2 and O4. The gain score, found by subtracting the pretest from theposttest, will be calculated and shown in GS1 and GS2, which represents the gain score.
Virtual Manipulatives 13Subject Selection Subjects for this research study will be 40 third grade students at a public middle schoolin 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 evenlydistributed among the groups and ability levels should be mixed. Students will be randomlyassigned to their classes by school administration and each class will have 20 students. Bothclasses meet in the morning at the same time during their block period 3, which is right aftertheir special for the day.Procedures Each class will have a different teacher instruct, since they are intact classes and alreadyassigned to their respective teacher. Both classes will be exposed to the same math conceptsduring 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 taughtwill differ since the experimental group will be using a projector, smart board and students maybe at the computer lab. The teacher for the experimental group will give homework from theworkbook because not all students have access to the internet or have computers. Plus, without aschool provided math homework site, it would be hard for the teacher to access and assess thehomework online. The control group will stay in the classroom and use the overhead andphysical manipulatives. The control group will also have homework from the workbook. Thestudy 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 theperiod to take the test. The pretest will add internal validity to the study because the ability andknowledge level of basic fractions can be determined for each class. This will help indetermining which group actually had the largest gain score. After the students have taken the
Virtual Manipulatives 14pretest, they will be introduced to the manipulatives in a fun way that excites children to startlearning basic fractions for the coming days. Formal instruction will not take place as studentsare usually drained after taking a test. Days 2 though 9 will be spent with the students receiving direct instruction from theirrespective teacher, using their respective manipulative and same lesson. A typical day consists ofone lesson. In group one, the teacher models, and guides and then allows the students to workindependently to complete a task, using the virtual manipulatives throughout each stage. In grouptwo, the teacher models, guides and then allows the students to work independently to completea task, using the physical manipulatives throughout each stage. The teachers will have 8 days tocomplete six lessons in the unit. Teachers cannot go on to other lessons past the stopping point ifthey finish early and must teach the six lessons in the 8 days allotted. Due to having two differentteachers, teaching styles will vary, but content and homework will be the same. On day 10, theposttest will be given to students and they will have all period to complete the posttest. Nomanipulatives, 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 fractionproblem, but do ask different questions. They each contain 20 questions, with a correct orincorrect answer being possible. Students will write their answer under the fraction image andthe scores will be averaged to find the mean scores for the pretest and posttest. Scores will thembe 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. Thisinstrument has moderate validity because the tests are extremely similar and do test basicfraction knowledge of third graders in a way that is appropriate for the intended age level. The
Virtual Manipulatives 15measurement instrument is kid friendly, while having the fraction content and criteria for thecontent 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 gainscore can be calculated. Gain scores will be calculated by subtracting the mean pretest scorefrom the mean posttest score. Results will be shown in the table below:Mean Gain Scores on Survey Instrument Experimental Group Control Group (G2 (G1 Virtual with Physical Manipulatives) Manipulatives)Mean Score Pretest O1 O3Mean Score Pretest O2 O4Gain Score GS1 GS2The mean gain scores for each group will be compared in order to interpret the outcome of thestudy and to verify and experimental effect to due to the independent variable, the virtualmanipulatives. A copy of the measurement instrument follows on the next two pages.
Virtual Manipulatives 16 SignificanceAnticipated OutcomesThe proposed study asks three research questions. The first question is “What are the gain scoreson an instrument measuring achievement of students taught basic fractions using virtualmanipulatives?” I predict that the students in the virtual manipulative group will demonstratepositive gain scores because manipulatives enhance student comprehension and conceptualizingin math. The second question asked is “What are the gain scores on an instrument measuringachievement of students taught basic fractions using physical manipulatives?” I predict thatstudents the control group will demonstrate positive gain scores of significance, since instructionand manipulatives will enhance learning, therefore the students should do better on the posttestthan the pretest. The third question asked is “How do the scores compare?” I expect both groups to havepositive gain scores because both use manipulatives as a teaching tool. However, I predict thatthe manipulated group with the virtual manipulatives will score slightly higher than the controlgroup since students are active learners when technology is used.Relevance This study is relevant to educators because if both groups demonstrate positive meanscores, 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 basicfractions 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
Virtual Manipulatives 17reach more children and stimulate children’s minds to become better mathematicians.
Virtual Manipulatives 18 REFERENCE PAGEBrown, 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). technologys 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.