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## ZeroSum Ruler: Finding Success With Negative Numbers

As an algebra teacher, I assumed my students had already mastered certain things: fractions, multiplication, addition and subtraction, solving simple equations. As I learned, reality barely follows theory! My ninth graders struggled to solve equations. At first I thought it was because the equations were relatively new, but looking at their work more closely it wasn’t the equations that they had trouble with, it was the addition and subtraction. How is it possible ?

After about a year of telling myself that it just couldn’t be, I gave in to the fact that my students were really struggling. They told me that “-22 + 5 = -27” and “8 – 12 = 4”. These errors appeared in the equations we were making where terms had to be added or subtracted from either side, and my students made all sorts of simple errors.

In the summer of 2007, the first prototype of the ZeroSum rule was created. It was rough – two paper number lines hinged to zero with an earring – and by no means was classroom-ready yet. Over the years, the manipulator went through many incarnations until his final form was achieved and tested in the classroom with excellent results.

A few years later, I had to teach advanced algebra to 11th graders, who were making the same mistakes! My students could solve complex logarithms but would make mistakes on the latter parts of the problems – the parts involving, you guessed it, the addition and subtraction of whole numbers! At that time, the ZeroSum rule was in its final form and ready for use in the classroom. I gave my eleventh graders a pre-test of eight simple addition and subtraction problems. Over the next few weeks, I gave each student a ZeroSum Ruler to use when solving each of three sets of nine simple equations. Immediately after the last set I did a post-test, and a month later I gave my students their delayed retention test. The posttest and delayed retention tests were set up exactly like the pretest, but with different simple integer problems.

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

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

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

Good calculation!

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