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- ZeroSum Ruler: Finding Success With Negative Numbers
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## ZeroSum Ruler: Finding Success With Negative Numbers

As an Algebra teacher, I assumed that my students had already mastered a few things: fractions, multiplication, addition and subtraction, solving simple equations. As I have learned, reality hardly follows theory! My ninth graders struggled with solving equations. At first, I thought this was because the equations were relatively new, but as I looked more closely at their work, it wasn’t the equations that were giving them problems, but the addition and subtraction. How could that be?

After a year or so of telling myself that this couldn’t be, it dawned on me that my students were really struggling. They would tell me that “-22 + 5 = -27” and “8 – 12 = 4”. These mistakes came up in the equations we were doing where we needed to add or subtract terms on each side, and my students were making all kinds of simple mistakes.

In the summer of 2007, the first prototype of the ZeroSum rule was created. It was hard – two number lines of paper articulated to zero with an earring – and it was not yet ready for the classroom. Over the years, the manipulative went through many incarnations until it reached its final form and was tested in the classroom with great results.

A few years later, I was moved to teach advanced algebra to 11th graders, who made the same mistakes! My students could solve complex logarithms, but they would make mistakes in the last parts of the problems—the parts involving, you guessed it, the addition and subtraction of whole numbers! The ZeroSum Ruler was then in its final form and ready to be used in the classroom. I gave my eleventh graders a pretest of eight simple addition and subtraction problems. Over the next several weeks, I gave each student a zero-sum rule to use as they solved each of the three sets of nine simple equations. Immediately after the last series, I did a post test and a month later I gave my students the delayed retention test. Both the posttest and the delayed retention were set up exactly like the pretest only with different simple integer problems.

To my surprise, there was not much difference in scores between the posttest and the delayed retention test. However, there was a large difference in scores between these two tests and the pretest. 62%! My students had made 62% fewer mistakes.

As part of my research, I studied the curriculum my students had in elementary and middle school. It seemed they only had 16 days to learn addition and subtraction of whole numbers. No wonder they needed help!

The ZeroSum Rule helped my students. I hope to bring this manipulative to more students so they don’t struggle like my students did. There’s nothing like making a simple mistake to destroy a child’s math confidence. My goal is to prevent that from happening.

Happy calculating!

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