Part A: Description of Need or Opportunity

I.  Educational Need or Opportunity
Solving algebraic equations represents the focus of the educational need to be addressed with this project.  Algebra represents a significant number of grade level content expectations for the sixth grade students I work with.  Specifically, this project targets the following algebra standards:

• Understand that adding or subtracting the same number to both sides of an equation creates a new equation that has the same solution (A.FO.06.12)
• Understand that multiplying or dividing both sides of an equation by the same non-zero number creates a new equation that has the same solution (A.FO.06.13)

Reflecting on my students performance through the unit on algebra and solving equations, revisiting the content and representing the ideas in a way different than students experienced in their respective math classroom would benefit student understanding and skill development.  I intend to use this project as an intervention to address student misconceptions related to solving equations as well as promote a deeper understanding of algebraic equations.


II. Proposed Technological Solution to Educational Need
I intend to use the Algebra Balance Scales applet from The National Library of Virtual  Manipulatives to address the educational issue articulated above.  The balance scales applet will be used to investigate solving equations of the first degree with whole number coefficients.  The applet provides students with a visual representation of the equation; students model the given equation on the scale by placing blocks representing the variable (x) and the number of unit blocks on each side.  Student users receive visual and verbal feedback from the applet.  If students attempt to continue to solve before the equation is modeled correctly, a message appears noting that the scales are not yet equal.  Visually, the scales shift left and right as blocks are added to both sides until equal also indicating to students the need to adjust the blocks on the scales.  After correctly modeling the equation, students proceed  to solving the equation.  Students must decide which operation to perform and the amount to add, subtract, multiply, or divide in order to keep the scales balanced.  Again, verbal feedback prompts student thinking lending consideration to how equations can be manipulated.  The Algebra Balance Scales applet offers students a link between visual and symbolic representations.  As students manipulate the blocks on the scale below, the display box above manipulates the equation.  Students have the opportunity to see the connection between what happens on the scale and what happens to the equation.  The applet is free to use and requires only an internet connection to access.  Additional technology to be used includes audacity and windows movie maker for students to produce a tutorial describing how to solve equations.  This use of technology encourages students to process and reflect on the activity and additionally create a new resource collaboratively with a group demonstrating new understandings about solving equations. 


III.  Logistics
The Algebra Balance Scales applet will be used during one hour sessions in the computer lab by two student groups on my caseload.  The eight students identified for the intervention will be provided time to work independently with the applet after brief instruction of how to manipulate the applet.  The technology will be used to reteach solving equations by providing and connecting multiple representations.  Screenshots will be captured as students work through solving equations keeping the scales balanced for use in the final student created tutorial.  The students on my caseload are sixth graders identified as at-risk at a public middle school in Kentwood, MI.  Students will document responses on an assignment sheet and will also complete journal reflections related to the use of the applet.


IV.  Relevant Research and Resources
Research suggests the use of virtual manipulatives increases student understanding of mathematical ideas and  concepts.  I tagged resources "Wicked" on my delicious page relevant to the educational need identified.  Initial findings helped clarify what constituted a virtual manipulative.  Moyer, Bolyard, and Spikell (2002) articulated that virtual manipulatives are, "an interactive, web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge" (p. 373).  The Algebra Balance Scales applet does fit this definition in representation as well as opportunity for students to construct and model mathematical concepts.


A study by Suh and Moyer entitled Developing Students' Representational Fluency Using Virtual and Physical Algebra Balances used the Algebra Balance Scales applet to compare student understanding of solving linear equations based on instruction using either physical or virtual manipulatives.  The authors state, "The use of multiple representations and the flexibility to translate among those representational forms facilitates students' learning and has the potential to deepen their understanding" (p. 155).  This study showed manipulatives enhanced students understanding and concluded, "Different representations, including those increasingly available through technology, can facilitate the teaching of these fundamental ideas." (p. 172).  In this case, research supports the use of the Algebra Balance Scales applet to help increase student understanding of solving equations.  This article also provides suggestions for implementing the technology effectively as the students evidenced increased understanding when following the implementation method described in the study.


Further support for using the Algebra Balance Scales applet comes from Suh's dissertation (2005) entitled, Third Graders' Mathematics Achievement and Representation Preference Using Virtual and Physical Manipulatives for Adding Fractions and balancing equations, summarized from (Dorward, 2002):

"The creators of the National Library of Virtual Manipulatives designed the virtual manipulatives in hopes that it would add to some of the benefits of using physical manipulatives in the classroom and eliminate some of the drawbacks such as:  classroom management, structuring activities with manipulatives, connecting manipulative use with symbolism, and lack of resources and professional development."

The Algebra Balance Scales applet, contained in the National Library of Virtual Manipulatives, was created to address some of the concerns with using physical manipulatives in the classroom.  The applet was designed with the intent of fostering connections among representations for students encouraging a conceptual understanding of solving equations and promoting transfer of ideas to be applied in a variety of scenarios.


An identified resource, Computer Technology for Math Excellence, cited research answering the two questions below which offered perspective related to virtual manipulatives as a solution to the defined educational need:

• What is a virtual manipulative
• What role can virtual manipulatives play in the classroom?

The site noted, "Virtual manipulatives provide that additional tool for helping students at all levels of ability "to develop their relational thinking and to generalize mathematical ideas"" (Moyer-Packenham, Salkind, & Bolyard, 2008, pg. 204).  With specific regard to the Algebra Balance Scales, this statement suggests the applet will assist in developing student understanding of solving equations.  


Further research exposed a theory called Dual Coding.  According to the Dual Coding Wiki, this theory states that verbal and visual representations are processed and stored differently.  The Algebra Balance Scales applet provides both verbal and visual representations for students while engaging with the mathematical content.  Quoting Suh and Moyer (2007) who referenced (Rieber 1994):

"...it is easier to recall information from the visual processing codes than the verbal codes because visual information is accessed using synchronous processing rather than sequential processing," (p. 158). 

Again, this lends support to using the virtual manipulative Algebra Balance Scales to help students learn how to solve equations since it provides visual representations and additionally connects the different representations present.


The findings described above and the list of resources linked above were found initially using Google Scholar.  The search began with keywords such as:  solving equations with virtual manipulatives, using technology to teach solving equations, and examples of teaching math with technology.  After the preliminary searches, a few articles seemed worth investigating further.  Dissertations and research studies provided a wealth of literature and research reviews.  I used the reviews attached to the studies in order to find additional resources specific to the defined educational need.  To locate online versions of articles and documents, I often copied the citation and entered that in the search engine.  Locating articles used within studies and dissertations proved difficult at times to find a viewable copy.  Often times the articles were available for purchase of either the specific article or a membership to a database housing the articles.  In these instances, I resorted to using the synthesized information as found in the research review.  In the future, I would utilize similar strategies.  I would additionally add the search engines and subscriptions available through Michigan State University's library.




V.  Implementation Plan 
Students participating in this intervention to readdress solving equations will participate in two computer lab opportunities prior to the end of the school year.  During those times, students will work with the Algebra Balance Scales applet in order to increase and solidify their understanding of solving equations.  Additional meeting time will be used for students to reflect on and discuss the completed tasks using the virtual manipulative.  Also, students will respond to journal prompts regarding their experiences working with the applet.  Time permitting, students will compile screenshots of working with the manipulative, reflections from journal entries, and thoughts from discussion to create a tutorial to share with both math classes.  The tutorial will include an explanation of how to solve equations including links between the representations.  The tutorial may be created after the course depending on availability of lab time and permission from my students' teachers.  Additionally, the tutorial will be shared with the different math classes after the completion of the course.  


VI.  Indicators of Success
Successful learning of solving equations with the Algebra Balance Scales applet will be evidenced ultimately by the created tutorial.  The tutorial will present accurate methods for solving algebraic equations as well as mathematically correct explanations of the steps.  Additionally, students will correctly connect and link the different representations modeled by the applet.  Student discussion of their experiences in small groups prior to creating the tutorial will also be an indicator of success as well as offering another opportunity to clarify and discuss any remaining misconceptions.  The discussion group also serves to help students articulate the learning which took place while using the applet.