Please feel free to watch the above video or read the implementation updates below.
Surprises
After reviewing feedback and responses to previous blog posts, I revised the implementation plan for using the Algebra Balance Scales Virtual Manipulative. Initially, the plan consisted of modeling the features of the applet to demonstrate for students how to create the equations using the blocks and scale. Students would then model equations to real life situations and use the manipulative to solve, discuss the activity to make connections among representations, and create a tutorial demonstrating how to solve equations. The following questions helped prompt further thinking about the plan and resulted in some revisions to the implementation plan:
"Are you planning on modeling the website before students work on it alone and then create a tutorial?"
"I wonder how you will collect data before and after the technology intervention to see if it worked?"
Although working with the selected students previously during the unit on equations and noting their struggles, I created a survey for students to complete using Google Forms before working with the manipulative to address the second question. The first day students submitted the survey and explored with the Algebra Balance Scale individually to familiarize themselves with the applet. Thus the surprises began…
Student responses demonstrated incorrect, non-mathematical understandings of equations. Some responses require further questioning to determine the student’s level of understanding. This suggests another educational need for students pertaining to developing an understanding of equations, perhaps one to be tackled prior to the selected need linked to specific standards related to solving equations. Most students correctly identified a couple of the listed equations, yet did not categorize others as equations prompting the question of if students know what equations are and moreover how the Algebra Balance Scales manipulative could be used to support and develop student definitions of equations. I anticipated incorrect responses to questions about first steps to solve equations as that misunderstanding was the educational issue to be addressed by using the Algebra Balance Scales. The pie charts display a variety of answers concerning steps to solve equations. No student selected the anticipated answer in two out of three of the questions.
Unexpected Bumps...
In order to work with any of the students on my caseload, I must schedule them out of another class limited to either an elective class, lunch time which in this case doesn’t offer enough time, or during Channel 1 news and reading time in the morning. Difficulties arose finding time in a computer lab for students to work. The second lab opportunity included internet connection difficulties. For the remaining implementation as well as future use of the intervention, an alternative needs to be thought through so the time is not wasted and students can still make progress toward understanding how to solve equations in the midst of internet complications.
A second Google Form was created with real-world scenarios for students to model and solve using the manipulative with the intent of students completing the task the second day in the lab. When I initially experimented with the applet’s “create” feature, I input values to create equations and worked through to solve in order to confirm the applet worked similarly to when users solved equations generated by the manipulative itself. For the brief moments the internet cooperated, I quickly realized a new limitation of the “create” feature. The applet limited the numerical entries to one digit. The scenarios created for students could not be entered in the applet, thus the scenarios will need to be revised in order to use the Algebra Balance Scales to model and solve the equation. Instead, students worked on solving problems generated by the applet as opposed to the activity.
Delights
During the implementation of the intervention, one thing that went well was students taking screenshots while working with the manipulative. I demonstrated for students how to use the “print screen” feature and paste the image in paint. The images can then be saved for future use. Students did an excellent job remembering to both take and save the images. As I monitored student progress, I wanted to help students see the connections between representations. I determined, given the circumstances, the images students captured would be put together in a presentation for them to review. This combines the discussion and reflection sections from the initial plan. In addition to students discussing noticings and wonderings, questions related to the changing representations would be strategically asked of students.
In some instances, students received feedback from the applet offering hints and suggestions to try something different to solve. This provided opportunity to dialogue with students to hear more of their thought process and ask questions prompting students to think. For future implementations, I’d like to think through a way to record those conversations also.
One Student's Experience
Despite internet complications leaving most student work saved to the network and inaccessible outside of school, I had been able to upload one student’s images to Flickr. The following represents one example of solving a problem using the Algebra Balance Scales and the images students have opportunity to review and discuss.
Here the student correctly modeled the equation by placing the blocks on the scale. Visually, the student made both sides of the scale equivalent since the scale is balanced. Although possible to balance the scale by modeling a different equation, the applet does not allow students to proceed without correctly constructing the given equation.
The student attempted to solve the equation by subtracting seven from both sides. The prompting below the scale in red indicated adding seven was incorrect.
Next, the student took away an “x” from the right side of the equation since there was at least one on both sides to subtract.
After that, although not captured as an image, the student took away the unit block on both sides. Lastly, each side was divided by three to create three equal groups of unit blocks and determine the value of each “x” block.
That’s all for the current update, check back for more!
