Using T-Charts to Solve Equations?

A couple of years ago, when I first began to work as a paraprofessional in the middle school math classrooms, I was introduced to this new ways to solve equations. To use this method students were told to draw a line straight down from the equal sign and then draw a line underneath the equation. Students then designated one side of the chart for variables and the other for numbers. Then students moved the different terms around to get them on the correct side of the chart. The had a little saying that if it crosses the line you change the sign. Here is an example of how this works:

With this example I chose to make the left side numbers and the right side x values. If the term drops straight down it remains the same and if it needs to cross the line you change the sign. After that you add up the terms on each side and you have your answer. With this example we only needed to use adding and subtracting, but if you also needed to use multiplication and division you would just do that at the end after you take care of the adding and subtracting. Here is an example of one that will use dividing at the end.

So with this one you can see that it starts off the same way and when you get to the end you need to divide both sides by 3 to find the final answer.

I like the overall idea of this method, but I feel the way it is being taught is not useful for the students and ends up being a problem when they get to the high school. The main problem that I have with how it is being taught, is that students are not getting an explanation of what is really happening when they are moving terms across the line. I think that it would be beneficial for students to understand that they are undoing the problem to find the answer. In oder to undo something you need to go backwards or do the opposite. I like expelling to students that both sides of the equation need to remain balanced, so what ever you do to one side you need to do to the other. I think that also helps students understand that even though we are moving things around, the equation is remaining the same. I think that if the students have a solid understanding of keeping both sides of the equation balanced and how to undo the different operations, then the t-chart can be used to help students organize their work.

As I was looking for some examples of how other teachers were using t-charts, I actually did not find anything like what  was used where I teach, but I did find a different use for them that I liked a lot better. This version was called a do/undo chart and on one side of the paper there were t-charts set-up that had "DO" on the left side and "UNDO" on the right side. The problems are presented as a mystery that needs to be solved, that the variable is the mystery. The first step is to look at what has been done to the variable, using the order of operations, and write it down in the "DO" column. The next step is to look at what they wrote in the "DO" column and use that information to fill in the "UNDO" column. They will need to know what the opposite operations are of those in the "DO" column. Now that they have there "UNDO" operations they go to the other side of the paper and solve the equation using the "UNDO" steps. So if the students had the equation 3x-6=3, they would dart by listing the operations in the "DO" column. They would use the order of operations and begin by writing x3 and then -6. Now in the "UNDO" column they would write +6 and they would go to the equation and add 6 to both sides of the equation. Then they would write /3 in the "UNDO" column and the divide both sides of the equation by 3. They would now have the solution of x=3. Here is a link to the worksheet and directions. http://www.teacherspayteachers.com/Product/Solving-Two-Step-Equations-with-a-DoUndo-chart-97427

I really like this idea a lot better then the t-charts from above. I feel like the students will have a better understanding  of how to solve an equation with this method. The second method is also just how it is introduced and after students are comfortable with the process they do not need to use the chart anymore. The students that are learning the first method do not receive the necessary understanding that is needed to solve an equation and when the get to high school they have no idea what to do. The teachers have to start all over teaching them how to solve simple two step equations.