Part D: Findings and Implications

Formative:  Did the project get implemented as planned?
As noted in the post, Part C:  Implementation, the implementation of the Algebra Balance Scale Virtual Manipulative intervention experienced revisions prior to the onset of implementation as well as early on during implementation.  Some of those revisions coupled with time constraints induced both by the end of the school year and absences of students selected to participate elicited further alterations to the implementation plan.  The chart below highlights the proposed implementation plan juxtaposed with the actual implementation plan.  Play the video to hear the explanation and continue on to hear about evidence of success, or read the explanation about the implementation plan below.

The proposed implementation plan provided time to model the virtual manipulative to students and provided independent time to familiarize themselves with the tool to be used for the intervention.  Additionally, students would both see demonstrations and have opportunity to practice capturing and saving screen shots.  Working with the group of students throughout the course of the year, I selected students to participate who struggled during the Algebra unit having difficulties both writing and solving equations.  Students previously participated in intervention activities during the Algebra unit to help develop a better understanding of equations.  The plan dedicated the second lab day to completing an activity on solving equations.  The plan called for the third meeting to be a reflection and discussion of the activity.  Journal prompts would provide an opportunity for students to individually think through the activity, and then process and discuss observations and thoughts with the group.  The discussion was intended to help focus student thinking, clarify identified misconceptions and questions, and help students articulate the necessary information to create the tutorial on solving equations.  I intended the remaining four meetings to provide groups time to create the tutorial.


Lending consideration to thoughts and questions of peers as well as problem solving a few issues, the actual implementation began with students completing a survey to gauge current understandings of solving equations.  As originally planned, the first day included time to model the Algebra Balance Scales applet and provided students individual exploration time.  Due to inconsistent attendance, field trips, and a lack of available computer labs, the remaining meetings for students occurred in the listed order; however, some students experienced the steps nearly a week apart.  Student's second meeting included using the Algebra Balance Scale to solve equations generated by the applet.  As explained in Part C: Implementation, the create feature in the applet had unforeseen limitations.  Students captured screen images and saved the files for future review and reflection.  After the images were captured, I created presentations for students to view the sequence of images which were used to complete a reflection using another survey created with Google Forms. 


Summative:  Evidence of success in addressing the problem of practice.
The intended indicators of success were the explanations presented by students in the tutorial modeling and explaining how to solve equations.  The altered implementation also impacted the success indicators.  For the aforementioned reasons, students did not produce the tutorial.  The reflection and discussion involved students viewing the images captured working with the Algebra Balance Scales and responding to questions presented using Google Forms.  Here are two examples of the image sequences students used to reflect and explain their thinking. 

Reflecting further on identifying the level of success led to the conclusion success did not depend on the creation of the tutorial.  The actual implementation plan merely changed the presentation of the evidence.  Instead of listening to student explanations of solving equations, to look for evidence of success I needed to consider student reflection responses in light of the educational need which remained the same:

• 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)

 Please watch the following to hear the analysis of two student's reflections and what success can be evidenced from their responses.

How would you approach another project of this type differently given what you've learned here?
Given the opportunity to consider a similar project of this type, the first step after identifying an educational need would be to gather and analyze information regarding student prior knowledge necessary to address the identified educational need.  In the case of the Algebra Balance Scales Virtual Manipulative Intervention, the educational need identified, although relevant, provided insight as to why students struggled with solving equations.  Student responses and explanations demonstrated an insufficient understanding of equations.  Students needed to develop a conceptual understanding of equations, the necessary previous knowledge, before moving on to the standards identified for this project.  Assessing student understanding of prior knowledge essential for approaching the educational need provides opportunities to refine the educational need to better meet students where they are at and perhaps provide insight as to how to approach the subsequent educational need.  


Future approaches to similar projects will allow for more implementation time and considerations for the circumstances which made it difficult to arrange meeting time with students.  Creating a greater implementation window offers not only more time for students to work with the manipulative itself to see if that fosters a deeper understanding and progress toward the educational need, but also more time for students to reflect.  This too would provide time to discuss and question students regarding their reflections and thoughts on the activity to better gauge their level of understanding.  


What are the lessons learned that others might benefit from knowing about?
Although not a novel thought, one lesson reaffirmed during this project is the need as an educator to try the activity before asking students to complete the task.  Although I spent time working with the virtual manipulative applet and its features, I did not try solving the real-world scenarios using the create feature of the Algebra Balance Scales.  Trying the activity would have helped combat the troubleshooting on the fly when I realized with several students at computers that the virtual manipulative could not be used to solve the equations I had created.  


A second lesson, again reconfirmed throughout the project, is to ask for feedback.  Posting the activity and having others respond with questions and thoughts helped shape my final project.  Responses prompted ideas I had not considered and in turn resulted in revised or clarified plans.  


In what ways will you endeavor to do the same project again, and what will you change or not do?
The Algebra Balance Scales Virtual Manipulative provides great opportunity for impacting student understanding of solving equations.  I would consider use in the future to help students develop connections between verbal and visual representations.  In the future, I would again assess students before working with the applet.  In this instance, student responses indicated another educational need:  developing an understanding of equations.  Aspects of the implementation plan such as modeling the manipulative and offering students time to individually experiment with the applet would remain.  Using Google Form to create surveys also provided significant benefits.  Students navigated to the form from a link on my wiki page.  Also, the results were compiled in one place accessible from anywhere with an internet connection.  Additionally, Google Forms provided user-friendly options for viewing and representing the data collected.  Reflecting on the actual implementation plan, I would still have students complete an activity using context based questions for students to solve; however, the questions need modification to work with the manipulative.  Lastly, students would still reflect and discuss their experiences.  One suggestion to incorporate is VoiceThread.  Students could narrate explanations to their screen images captured step by step.  Additionally, this would provide another piece of evidence to consider when determining student understanding that allowed dialogue between myself and the student.  To facilitate discussion among students in the group, students could post responses to prompts and comment to each other using a blog.  This could be the platform used for groups to discuss ideas and concepts prior to creating the tutorial.  Another modification to the project includes a greater timeline.  Working with the manipulative over the course of a marking period or semester provides students more time and opportunities to impact their understanding of solving equations.  The tutorial then serves as a summative assessment to evaluate student understanding and progress.