This document summarizes an action research project that investigated the effects of using virtual manipulatives to teach fractions to 2nd grade English Language Learners. The researcher administered pre- and post-tests to students who used virtual manipulatives for 20 minutes per day over 3 weeks. Student engagement and enjoyment were also observed qualitatively. The literature review discusses prior research supporting the use of both concrete and virtual manipulatives for math instruction, particularly for ELL students. The methodology describes the sample, data collection through tests and surveys, and analysis plan to evaluate the impact of virtual manipulatives on student achievement and engagement with fractions.

1. Action Research Project on
Using Virtual Manipulatives Lends to 2nd
Grade Student Engagement
Terri P. Smith
Fresno State University

2. Abstract
I wanted to demonstrate that allowing 2nd grade English
Language Learners (ELLs) to participate on the
computer with web based virtual manipulatives would
assist these students to stay engaged in learning fractions.
Fractions are difficult for many second grade students to
learn and this difficulty gets more complex for students
also struggling to acquire English language skills. My
experience with 2nd grade students in general is they are
very willing to be allowed to work on the computer. I
was hoping to combine their willingness with the need to
learn fractions and prove that exposure to virtual
manipulatives would assist 2nd grade ELLs to be engaged
in learning fractions and to demonstrate an increase in
test achievement results.
Over a three week period, I conducted this action research
project by allowing the students to have exposure to computer /
web based virtual manipulatives in the area of fractions for 20
minutes each day or 15 consecutive school days. Quantitatively, I
utilized an identical Pre-test and Post-test. Qualitatively, I
monitored the study participants engagement and enjoyment. I
also conducted an Attitude Survey and transcribed Student
Interviews which allowed insight to the study participants’
feelings regarding learning fractions with the computer / web
based virtual manipulatives.
Analysis of the results demonstrated the students test scores
improved and the study participants were very willing and eager
to stay engaged in participating with the computer / web based
virtual manipulatives.

3. Literature Review
Introduction
Educators often use visual, kinesthetic, and auditory applications by means of concrete and virtual manipulatives to
assist students in accessing the content of mathematics which can be especially helpful for English Language Learners
(ELLs). As ELLs speak a language other than English in their homes, they have difficulty with understanding words
spoken in English. Utilizing concrete and virtual manipulatives can assist these students in developing clear mental
images. Children need many experiences with physical materials and visual images in order for mathematical learning
to occur (Suh, 2005). When students are able to see, touch, take apart, and sort physical objects, they develop mental
images that are clearer than only utilizing words and accompanying worksheets. Developmental theorists like Piaget
and Bruner have stated cognitive benefits are obtained when young children explore mathematical concepts with
concrete manipulatives. (Bruner, 1964; Piaget, 1962).

4. Literature Review (con’t.)
Introduction (con’t.)
Teachers use manipulatives as a tool in mathematics education in order to promote progression from concrete to
abstract understanding for children. Examples of concrete manipulatives are students’ fingers, base-ten blocks, paper
and plastic money, clocks, cubes, 3-dimensional shapes, etc. An additional theoretical perspective indicates that
children (age 7 and younger) should benefit from exploring mathematical concepts with manipulatives (Montessori,
1964). Utilizing concrete manipulatives is considered an effective strategy in teaching mathematics as manipulatives
assist students in visualizing the concept and leave less room for misunderstandings because they can visually see the
mathematical concept and participate in it (Shaw, 2002). A great deal of research has proven that when mathematical
learning for children is firmly grounded in experiences with manipulatives, they will be more likely to make
connections between real world activities and the abstract world of mathematics. In many classrooms today using
virtual manipulatives is being added to the list of effective teaching strategies.

5. Literature Review (con’t.)
Introduction (con’t.)
Technology continues to progress and students are utilizing various types of smart pads, phones, tablets, etc.
Educators provide this technology or have instituted a policy to bring your own device. Many students, including
ELLs come to elementary classrooms with an increasing amount of knowledge gained outside of the classroom
regarding usage of computer programs of a variety of types. As technology improves and virtual manipulatives are
becoming more accessible to educators, utilizing virtual manipulatives as a teaching strategy for young students,
including ELLs, is proving to be an additional effective strategy; allowing improved cognitive development for
students in the area of mathematics.

6. Literature Review (con’t.)
Concrete Manipulatives
Concrete manipulatives are tangible objects that students can touch, move around, put together and take apart to
model or demonstrate learning of concepts. Concrete manipulatives include, but are not limited to, base-ten blocks
(that can be manipulated to reveal concepts regarding place value), paper money bills or plastic coins (to allow
understanding the value of money), clocks (that can be moved and changed to allow access to the concept of time),
cubes (which allow students to count and make patterns), 3-dimensional shapes of cones, prisms, etc., (for better
understanding of shape and volume). These manipulatives are often colorful adding visual and tactile appeal to
young learners. Math manipulative-based instructional techniques are approaches that include opportunities for
students to physically interact with objects to learn target information (Carbonneau & Marley, 2012). As these objects
can be touched and seen, their utilization allows ELLs access to mathematics content during the developing phases of
their English language acquisition.

7. Literature Review (con’t.)
Virtual Manipulatives
Virtual manipulatives are computer based visual representations of cubes, shapes, patterns, etc. Much like concrete
manipulatives, they can be colorful as well which adds to their appeal. They can be manipulated with a keyboard, a
mouse, or by touch, and because they are interactive and web based, they are, “Web-based visual representation of a
dynamic object that presents opportunities for constructing mathematical knowledge” (Moyer, Bolyard, & Spikell,
2002, p. 373). An advantage for the teacher is that there are no materials to take out, organize, control, or clean up.
An advantage for the learner is the associated sounds and instant feedback that can be provided as the student
progressively moves through the computer based lesson. An additional advantage for the teacher and the learner are
reports that can be generated by many computer programs to demonstrate progress. As well, young students,
including ELLs, are generally willing to participate with computer programs

8. Literature Review (con’t.)
English Language Learners
English Language Learners (ELLs) are a focus for most California school districts. The designation ELL is assigned
to any students who primarily speak a language other than English in their homes. Some of these students were born
in other countries and some were born in the United States. The State of California reports 22.3% ELL students,
Riverside County reports 20.7% ELLs, Desert Sands Unified reports 22.7% ELLs, and John F. Kennedy Elementary
reports 65% ELL students with 71.27% poverty. “Research shows that children in families with a primary language
other than English experience disparities in health status, quality of health care services, and access to care, compared
to children with English as a primary household language. Academically, children with limited English proficiency
tend to have lower test scores than their native English-speaking peers. English Learners face the challenge of
mastering content presented in the school curriculum at the same time they learn a new language.”
(http://kidsdata.org/topic/51/english-language-learners)

9. Literature Review (con’t.)
English Language Learners (con’t.)
These circumstances create exceptional challenges for later educational attainment and socioeconomic success. It is
incumbent upon educators to develop strategies to assist these students in English language acquisition along with
access to the content of the standards appropriate for their grade level. CELDT testing is provided as a lens into
students’ English language acquisition. Educators utilize teaching methods and strategies to assist ELLs to have
access to curriculum by using sentence frames, choral reading, partner work, Realia, extra think time, and other
methods including manipulatives to allow access to content and improve their CELDT scores. Manipulatives help to
visualize the mathematical concepts which can be very helpful for English Learners in accessing the content (Shaw,
2002).

10. Literature Review (con’t.)
National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics (NCTM) is a public voice of mathematics education, providing vision,
leadership, and professional development to support teachers in ensuring mathematics learning. The NCTM looks for
improved methods of teaching and learning. The mission of the NCTM is to support teachers “to ensure equitable
mathematics learning of the highest quality for all students through vision, leadership, professional development and
research” (Board of Directors, 2009, para. 2). The NCTM recommends students have access to manipulatives for developing
mathematical understanding and encourages teachers to utilize manipulatives through the use of technology and hands-on
strategies to exceed the goals of curriculum standards. The NCTM’s Principles and Standards for School Mathematics emphasize
the role of representation in mathematics stating that students should “…create and use representations to organize, record,
and communicate mathematical ideas; select, apply, and translate among mathematical representation to solve problems; and
use representations to model and interpret physical social and mathematical phenomena” (NCTM 2000, p. 67). Students
learn in a variety of ways and need opportunities to use these diverse strategies to help them better understand mathematical
concepts. Supportive theorists also suggest that instructional strategies that use manipulatives are often suggested as effective
approaches to improve student mathematics achievement (Gürbüz, 2010; Sherman & Bisanz, 2009).

11. Literature Review (con’t.)
Common Core State Standards
Most of the states in the U.S. are transitioning to the adoption of Common Core State Standards (CCSS). Standards
define what students should know and understand in mathematics. The NCTM (2010) process standards focus on
problem solving, reasoning and proof, communication, representation, and connections (CCSS, 2010, p. 6).
“Learning opportunities will continue to vary across schools and school systems, and educators should make every
effort to meet the needs of individual students based on their current understanding” (CCSS, 2010, pg. 5). The CCSS
Standards for Mathematics states that “proficient students are sufficiently familiar with tools appropriate for their
grade or course to make sound decisions about when each one of these tools might be helpful, recognizing both the
insight to be gained and their limitations” (CCSS 2010, p. 7). With the advent of CCSS, many students will be taking
assessments on computers therefore, providing access to computers for all students will be highly important (CCSS,
2010). Although these assessments will have their own unique methods and process, utilizing programs with virtual
manipulatives will familiarize students with the basic usage of computers.

12. Literature Review (con’t.)
Controversy Regarding Usefulness
A recent study of multiple elementary grade levels indicates instructional strategies that use manipulatives may be
effective because of physical enactment , however, the end results of the study were that instruction that used
manipulatives produced a greater effect when students were measured on retention and smaller effects when higher
level outcomes with problem solving, transfer, and justification. (Carbonneau, Marley & Selig, 2013).
Some studies have been performed that have found negative results after manipulatives are used in mathematics
instruction. McClung (1998) compared a group of students using manipulatives to a group not using them and
found scores were higher for the students that did not use manipulatives. The opposing views regarding manipulative
use in mathematics instruction have various reasons to question or oppose the usage stating that manipulatives may
lead to students having fun at the expense of learning. As well, manipulatives may make learning more difficult as
they require dual representation. (McNeil & Jarvin, 2007) However, this study adds to the confusion that needs to be
further researched as it also states that using both traditional and hands-on teaching methods, a teacher helps students
draw on their practical, real-world knowledge and the teacher can reach a larger range of students.

13. Literature Review (con’t.)
Research
Students’ attitudes toward mathematics can be improved with manipulative usage, and this will help students to retain
information which will increase test scores (Sowell, 1989). Steen, Brooks, and Lyon (2006) performed a study of first
grade students regarding the effects of virtual manipulative use versus traditional mathematical instruction. The
students were divided into two groups to learn fractions. One group was taught using traditional methods and the
other group utilized virtual manipulatives. The levels of achievement were measured which demonstrated the virtual
manipulative group progressed considerably better and it was concluded that the students were motivated to work
with the virtual manipulatives and stay engaged in the learning process for longer periods of time. An additional
study performed by Suh (2005) researched two third grade classrooms for units on fractions and algebra using
physical and virtual manipulatives. For the unit on fractions, the first group utilized fraction circles while the second
group utilized a virtual fraction web-based program. For the unit on algebra, the first group utilized a virtual balance
scale while the second group utilized a physical manipulative to engage in balancing linear equations

14. Literature Review (con’t.)
Research (con’t.)
The students utilizing virtual manipulatives were found to outperform the students utilizing the physical
manipulatives. In addition, Suh (2005) reported the step-by-step procedures of the virtual manipulative environment
to be more effective in providing immediate feedback. Reimer and Moyer report an action research study for two
weeks utilizing virtual manipulatives in a third grade classroom learning about fractions. The data were collected from
pretests, post tests, student interviews, and attitude surveys. The results demonstrated improvement in conceptual
and procedural knowledge for these students. In addition, the attitude surveys demonstrated the students appreciated
the immediate feedback and the speed over using paper and pencil methods as well as increased enjoyment of
utilizing virtual manipulatives while learning fractions (Reimer and Moyer 2005)

15. Literature Review (con’t.)
Conclusion
The studies mentioned above reflect a positive research base to promote the use of concrete as well as
virtual manipulatives in elementary classrooms. Research suggests that ELL students are assisted in
their acquisition of academic content in all areas including mathematics when pictures, diagrams, charts,
and manipulatives are utilized. These technological advances toward virtual manipulatives would seem
to be a benefit to all students including ELLs. This researcher would like to perform an action research
study that would add to the body of knowledge with respect to virtual manipulatives and specifically
attempting to prove the thesis that utilizing virtual manipulatives assists 2nd grade ELLs to stay engaged
in mathematics.

16. Methodology
Research Question
This action research focuses on the question,
“Does utilizing virtual manipulatives assist 2nd
grade ELLs to stay engaged in mathematics?”
This study tested the achievement of students
after participating with various on-line virtual
manipulative applications. As well, this study
evaluated the interest and enjoyment of the
students during a 4 week period of
participation.
Research Design
The focus of this action research was to test the hypothesis that the
use of virtual manipulatives lends to increased engagement of second
grade ELLs in mathematics, specifically in the area of fractions.
• Quantitatively, a Pre/Post-test (Appendix 3) was utilized which
was previously designed and utilized by Moyer-Packenham, Ulmer
& Anderson (2012).
• Qualitatively, to evaluate engagement with respect to enjoyment
and willingness to participate, a phenomenological study
demonstrating human consciousness and self-awareness was
performed by utilizing a Student Attitude Survey and Interview
Questions to determine each student’s thoughts and gain insight
into their feelings regarding the use of virtual manipulatives.

17. Methodology (con’t.)
Sampling Strategy
The students for this action research were selected from a second grade
classroom. The class consisted of 32 students of which 14 were males
and 18 were females. One female student has an Individualized
Education Plan (IEP) which did not exclude her from participating. The
demographics of the class included 88% Hispanic and 12% Caucasian
children. The socio-economics of this school reports 71.27% poverty
and 87% receive free and reduced lunch. Data was analyzed and reported
on study participants who included those students who signed the
Student Assent Form (Appendix 1) in combination with those students
whose parents signed the Parent Permission (Parental Consent)
(Appendix 2).

18. Methodology (con’t.)
Data Collection
Study participants were administered the Pre-test (Appendix 3). Next, over a 3 week period for 20 minutes a day, study
participants were exposed to and participated with virtual manipulatives available through the National Library of Virtual
Manipulatives http://nlvm.usu.edu/, and a Pearson commercial site, Success Maker. These activities closely mirror the
second grade common core standards in the area of fractions. The researcher gave support to the students to insure
access and availability. The researcher monitored student behavior and participation. The students were only taught
fractions through exposure to these two websites for this 3 week period. Then, study participants were administered the
Post-test (Appendix 3). After the Post-test, study participants were administered an anonymous Student Attitude Survey
(Appendix 4) based on a Likert scale in which the study participants recorded their positive, negative or neutral feelings
about utilizing the computer and the virtual manipulatives to learn fractions. They recorded their opinions by coloring in
a smiley face for “I liked it,” a frowny face for “I did not like it,” or a straight face for “I am neutral.” Last, study
participants answered informal Interview Questions (Appendix 5) about their thoughts regarding learning fractions using
the computer and virtual manipulatives. The questions were given by the researcher and their responses were recorded
and transcribed.

19. Results
Quantitative Data Analysis
The results of the student’s scores
from the Pre-test and Post-test were
calculated. Analysis of the Pre-test
and Post-test scores revealed an
increase in the test scores on the Post-test
for all study participants
Student Pre-test / Post-test Scores
Pre-test Post-test

20. Results (con’t.)
Qualitative Data Analysis
An Attitude Survey was conducted with all study participants. To ensure the students understood the questions they would be answering, the Student Attitude Survey was read
aloud by the researcher with the document visible utilizing a document camera. The students read the Attitude Survey chorally. The students then read the survey with their
shoulder partner. Any questions were answered until all students understood the questions. Clear instructions were also provided to define the symbols to represent coloring the
smiley face this means “Yes, I like it,” coloring the frowny face means “No, I did not like it” and coloring the straight face means “I am not sure.” Clear instructions were also
provided so the students understood they were free to make their own choice. Students were sent to various places around the room and testing shields were utilized to insure
confidentiality. The results revealed the majority of the study participants enjoyed utilizing virtual manipulatives, found them easy to use, and would like to use them again to
learn fractions.
Yes No Not sure
1
Do you like using the computer to do
mathematics? 16 1
2 Were virtual manipulatives easy to use? 16 1
3
Would you prefer to use virtual manipulatives
on the computer to do mathematics? 15 2
4
Would you like to use virtual manipulatives
again? 14 3
5
Did virtual manipulatives help you understand
fractions? 15 2
Smiley
Frowny
Straight

21. Results (con’t.)
Interview Questions
Interviews were conducted by the researcher with each study
participant. Each study participant was given enough time to answer
questions and encouraged to say, “I do not understand” if they needed
to have more explanation of the question. I felt this was an important
part of the interviewing process as all of these students are ELLs. In
addition, I did not hurry the interviewing process. I made
arrangements to interview each student in a relaxed setting reducing any
distractions and allowing each student to ask questions with the least
amount of embarrassment from peers as a result of needing to ask for
clarification. I found recurring statements in the interview process
which included the following:
“I like using the computer to do math.”
“I like clicking the mouse.”
“I like the colors.”
“I like the fast answers.”
“I like the happy characters when I get the answer right.”
“I am happy that I can change my wrong answers.”
After conducting the interviews it is evident that the study participants
enjoyed working on the computer, getting quick answers, getting
instant praise from computerized characters, and learning easily
utilizing virtual manipulatives on the computer. Although it was not
included in the interview questions, additional helpful information was
gained by asking the last interview question, “Do you want to use the
computer at home to do math?” Unfortunately 14 out of 17 study
participants do not have a computer at home. This is reasonable
considering the low poverty level of the families at this school site.

22. Results (con’t.)
Researcher Monitoring
The study participants were observed to be willing to quickly log
on to either Success Maker or NLVM. The researcher did not
observe any complaining. The only question the study
participants had during the 3 weeks was, “Which site can we log
into today?” The study participants were observed to be actively
engaged in manipulating the fractions on the computer and
chatting with each other about things like: what they were doing,
the various shapes they were creating, the various colors they
found, and how many parts of a whole they were able to create.
The study participants were visibly enjoying participating with the
virtual manipulatives provided on these computer / web based
sites. However, this researcher was hoping for greater gains in
test scores than were achieved solely from exposure to virtual
manipulatives on the computer in the area of fractions.
Maintenance of Confidentiality
During the Pre-test / Post-test sessions, study
participants were separated around the classroom and
required to utilize a testing shield so that each student’s
work reflected their own answers. The tests were
collected and numbers assigned and utilized for data
recording rather than names. In like manner, the study
participants were administered the Attitude Survey. As
well, the researcher interviewed each study participant
separated from the other students to allow privacy in
answering the Interview Questions. All tests and study
documents were locked in a file cabinet and no
documents were seen by anyone other than the
researcher to maintain confidentiality of all documents.

23. Results (con’t.)
Limitations
The number of study participants was low as a result of some parents not giving consent and
some students taking the option of not giving their assent. Only 17 students participated and
therefore these results are too small to be generalized to all second grade ELL students. There
was no prior instruction regarding fractions. For these 3 weeks, the only instruction regarding
fractions was the exposure the study participants had with the virtual manipulatives during their
individual computer time. The difference between the actual concepts learned during the virtual
manipulative exposure and the actual test questions could have skewed the results as it could not
be determined each student was taught the exact concepts tested. It is also possible that the
students chose to answer the survey and interview questions in a manner influenced by their
feelings toward the researcher / their teacher who was asking the interview questions.

24. Results (con’t.)
Conclusion
Results of this study concluded exposure to computer / web based virtual manipulatives can assist 2nd grade ELLs to be
engaged in learning mathematics specifically in the area of fractions. During the close read of the Student Assent form, the
study participants defined student engagement as: “learn, pay attention, be on task, and finish the job.” From the
perspective of this definition and as observed through informal monitoring performed by the researcher, each of these 17
students was able to be engaged with the virtual manipulatives. The study participants were observed to be eager to
participate and happy while participating with the virtual manipulatives on these sites.
As can be seen by the qualitative data analysis, the study participants wanted to participate on the computer and enjoyed
learning mathematics, specifically fractions utilizing virtual manipulatives on the computer.
As can be seen by the quantitative data collection, all study participants’ test scores increased after exposure to computer /
web based virtual manipulatives. Therefore, is can be concluded that utilizing the computer as one teaching strategy for 2nd
grade ELLs is effective in raising achievement scores. However, this researcher would have liked to see greater gains in
achievement scores than were demonstrated. Therefore, while this strategy is somewhat effective, combining this strategy
with other teaching strategies may provide students with more understanding of the concept of fractions.

25. Results (con’t.)
Conclusion (con’t.)
Therefore, while this strategy is somewhat effective, combining this strategy with other teaching strategies may provide students with more
understanding of the concept of fractions.
Utilizing the computer can be an effective strategy for engaging 2nd grade ELLs in learning about fractions. The CCSS math standards for 2nd
grade students including reasoning with shapes and their attributes (CCSS 2013). Utilizing the computer / web based virtual manipulatives is a
good strategy to assist teaching 2nd grade students these standards. In a low income area such as this school / district, it is increasingly important
for educators to allow exposure for students to computers as many of these students do not have access to computers at home. CCSS standards
require students 3rd grade and above to take portions of standardized tests on the computer. Therefore giving 2nd grade students exposure to
utilizing the computer would be beneficial as a means toward assisting 2nd grade ELL students in acquiring more ease and comfort with computer
usage to better prepare them for the future testing they will participate in.
These study participants demonstrated an interest in utilizing the computer and were able to perform better on the Post-test than they performed
on the Pre-test. The researcher would have liked to see higher gains on the Post-test scores and therefore, this researcher believes utilizing
computer / web based virtual manipulatives would be an additional strategy to be combined with other teaching strategies including concrete
manipulatives, direct teaching, and model drawing to assist 2nd grade ELL students in accessing the mathematical concept of fractions with
emphasis toward higher gains in academic achievement.

26. References
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Mathematics. Retrieved from: http://www.nctm.org/about/content.aspx?id=172
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Carbonneau, K. J., Marley, S. and Selig, J. P. (2013). Journal of Educational Psychology,
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27. References (con’t.)
Common Core State Standards, California. Adopted by the California State Board of Education, August 2010 and
Modified January 2013.
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28. References (con’t.)
Mertler, C. (2009). Action research: teachers as researchers in the classroom. California: Sage
Publications, Inc.
Montessori, M. (1964). The Montessori Method. New York, NY: Schocken.
Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6),
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ESSN: 1541-4914.

29. References (con’t.)
Moyer-Packenham, P.S., Ulmer, L.A., & Anderson, Katie L. (2012). Examining pictorial models and virtual
manipulatives for third-grade fraction instruction. Journal of Interactive Online Learning, Vol. 11, Number 3, Winter 2012,
ESSN: 1541-4914.
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30. References (con’t.)
Sowell, E. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics
Education, 20(5), 498-505.
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.
Suh, Jennifer, M. (2005). Third graders' mathematics achievement and representation preference using virtual and
physical manipulatives for adding fractions and balancing equations. George Mason University, Fairfax, VA.