Introduction
I went into this action research study with great enthusiasm that I was implementing technology into my mathematics instruction. As I implemented my action research, I investigated what would happen if I changed my teaching practice of place value and added virtual
manipulatives (Baroody, 1990; NCTM,1989; Reys, et al., 1997; Sharma, 1993). My research question was:
How will the use of virtual manipulatives, in addition to physical manipulatives, influence the mathematical understanding of my students and inform my practice of teaching place value in my second grade class?
In this chapter I review the results of my study. I also discuss implications, limitations, and recommendations for further research.
Results
After conducting this action research study, I found that virtual manipulatives, in addition to physical manipulatives, influenced student acquisition of place value concepts. Studies and research indicate teachers must change their methods of instruction to help students reach a more profound understanding of mathematics (Baroody, 1990; NCTM,1989; Reys, et al., 1997;
Sharma, 1993). I found that when I added virtual manipulatives to my practice of teaching place value (Barta, 2002; Clements & Sarama, 2002; Moyer-Packenham, et al., 2008), mathematical language increased. Students showed a more in depth knowledge of thinking strategies and showed how they can represent numbers in more than just one way. This was revealed through student journals as students increased their mathematical language and applied terms such as
regroup to their writing after using the virtual manipulatives. Along with another study, I also found thatpracticing with the visual computer images might have enhanced students' abilities to explain and represent their thinking using pictorial models (Reimer & Moyer, 2005). Their drawings more closely resembled the models and actions they were viewing on the computer than they did using the physical manipulatives. Adding virtual manipulatives to my practice of place value also increased students’ ability to represent more conceptual understanding of composing and decomposing numbers as evidenced by the variety of ways in which they were representing a number in a variety of ways. The enhancements that the virtual base-ten blocks offered allowed students to “see” regrouping and interact with it in a way that is more inline with mental actions we want students to learn (Clements & Sharma, 2002). The virtual manipulatives helped students build on their physical experiences, tying them tightly to symbolic
representations, also evidenced in their journals and increase in posttest scores. (Clements & Sharma, 2002). In comparison to other studies, I also found that the use of base-ten blocks helped students learn place value concepts that move from concrete to abstract and assisted students in acquiring grouping and trading rules and determining the value of the number being represented as evidenced in their language, drawings, and posttest scores (Baroody 1990; Fuson, 1997). This was accomplished as they moved and touched the blocks and saw the results of their actions. The use of expanded notation cards connected the base-ten blocks to representations of their numerical values. Having students draw quick pictures furthered their understanding through another form of representation. Having students use a journal helped them formulate understanding through the use of mathematic language. Finally, the actions of the virtual base- ten blocks closely mirrored the actions of composing and decomposing numbers that we want
students to do mentally. “Virtual manipulatives, used in combination with concrete
manipulatives and other real world exploration, and in ways that encourage discussion and critical thinking, can make a unique and significant contribution to young children’s mathematics education” (Rosen, D., Hoffman, J., 2009, p.32).
Furthermore, I learned through Moyer-Packenham, et al., (2003) that one of the most important differences between virtual manipulatives and the physical manipulative is the
computer’s ability to provide the student instant feedback as the student works. This was true in my study and because of this instant feedback the virtual base-ten blocks were self correcting which allowed me more time to work with individual students in their areas of need. I felt my students were more on task and engaged and that I could spend quality time helping each student acquire place value concepts at their individual level of learning because of this feature. This feedback was instrumental in my struggling student’s growth. I observed how his understanding of values and grouping increased as we worked together. When he worked independently, the computer continued to motivate him when his thinking was correct and when it was not, allowed him the opportunity to manipulate the blocks in a manner that let him see how to arrive at the desired results. I believe this student made notable gains during this study although they did not reveal themselves through his posttest.
As I refine my teaching to meet the Next Generation Sunshine State Standards for Mathematics, I am pleased that I took on the challenge of integrating technology into my mathematics instruction to further student understanding of place value. Using virtual
manipulatives benefited me as a teacher in many ways. Keeping young children motivated to use hands-on materials the correct way for an entire lesson can frustrate even the most veteran
teachers. It is difficult for many young children to understand “their space” at a table with others causing manipulatives to get mixed up, fall, or be used by other students. This created confusion and frustration with the students and stopped the momentum of the lessons. Having to sort out which blocks were being used for the lessons was time consuming (Clements, 1999). Having a central bag for each table helped, but storage was an issue as well in my small classroom. With virtual manipulatives, I did not have any of these issues. In fact, virtual manipulatives provided the students with unlimited access to base-ten blocks. I only had to make sure I had internet access. Most importantly, it allowed me more time to work with individual students in their areas of need and increased positive attitudes about mathematics in my students.
Implications
Since data showed that using virtual manipulatives in addition to physical manipulatives helped students make gains in the acquisition of place value concepts, perhaps more teachers should consider adding virtual manipulatives to their mathematics instruction.
NCTM (2006) stated in their expectations for grades Pre-K through 2nd grade that students should:
Use multiple models to develop initial understandings of place value and the base-ten number system.
Develop a sense of whole number and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
Connect number words and numerals to the quantities they represent, using various physical models and representations (p.14).
It is imperative to present place value in ways that students have the opportunity to develop mathematical competence (NCTM, 2000). Using base-ten virtual manipulatives accomplished this for my students. Using physical and virtual manipulatives together supports NCTM’s view of providing opportunity for students to make connections by relating various representations of concepts or procedures to one another (NCTM, 2000). This study gives valuable insight to teachers who will be considering adding virtual manipulatives to their mathematical instruction in the coming years.
Limitations
The results found in this study cannot be generalized to all other classroom populations. One factor to consider is the population of my study. The population of students involved in this study was not large enough to make conclusive assumptions. My students generally come from homes that support their students’ learning. These children may have an advantage over other students who do not have the same level of parental support. All of my students had access to a home computer. Another factor to consider is the time frame in which this study took place. I had to abide by my school’s scope and sequence of the textbook and was required to move on to other skills. If I had been able to devote more classroom instruction time specifically to virtual manipulatives, I believe the students would have benefited more. Research says that place value concepts emerge over time (Fuson, et al., 1997)
Recommendations
Educators need to have access to research based information on how best to teach students. This study was informing and leads to additional questions such as: Is it just as
beneficial for the students to have them use only virtual manipulatives? Would introducing virtual manipulatives at the beginning of the study along with physical manipulatives produce the same results in mathematical language usage? What would the results be if the order of this study were reversed (virtual first, then physical manipulatives)?
If I were to do this study again, I would want to look into researching how composing and decomposing numbers using virtual manipulatives helps students acquire a deeper
understanding of addition and subtraction with regrouping. Research suggests that students should learn multi digit addition and subtraction alongside place value concepts suggesting that this provides a context for motivating and supporting the development of base-ten number concepts (Baroody, 1990; Fuson, 1990; 1997).
I would also change some of my data collection techniques. Specifically, I would use video to capture the students’ rich discussions. I found that even though students’ written language in their journals was providing more insight into their thinking, it was not the same as their oral conversations and comments.
Summary
As I look for ways to improve my teaching practice and meet the needs of all my students for the 21st century, incorporating technology into my mathematics practice was a natural fit. I wanted to know how the use of virtual manipulatives when used with physical manipulatives would influence my students’ acquisition of place value concepts. I wanted to see how adding this computer applet might better meet the needs of all learners while also meeting the needs of today’s technological classroom. Through this study, I found that both physical and virtual
had features that engaged students in a way that increased their mathematical language, increased students’ ability to represent more conceptual understanding of composing and decomposing numbers, and express enthusiasm towards mathematics.
This action research helped me reflect on my practice of teaching place value by focusing on my instruction based on the research of others, and my students had positive attitudes and achievement outcomes. Most importantly, it is important that all students have opportunities to use technology in appropriate ways so that they have access to interesting and important mathematical ideas.