ZeroSum rule: find success with negative numbers

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

After a year or so of telling myself that this 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 mistakes came up in the equations we were doing, where terms needed to be added or subtracted from each side, and my students were making all kinds of simple mistakes.

In the summer of 2007, the first prototype of the ZeroSum screed was created. It was crude, two hinged paper number lines at zero with a pendant, and by no means ready for the classroom. Over the years, the manipulator went through many incarnations until his final form was reached and tested in the classroom with excellent results.

A few years later, I was prompted to teach Advanced Algebra to 11th graders, who made the same mistakes! My students could solve complex logarithms but would make mistakes in the last parts of the problems: the parts that involve, you guessed it, the addition and subtraction of whole numbers! By then, the ZeroSum ruler was in its final form and ready for use in the classroom. I gave my 11th graders a pretest of eight simple addition and subtraction problems. Over the course of the next several weeks, I gave each student a ZeroSum rule to use as they solved each of the three sets of nine simple equations. Immediately after the last series, I gave a posttest and a month later I gave my students their deferred retention test. Both the posttest and lazy hold 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 post test and the deferred retention test. However, there was a large difference in score between these two tests and the pretest. 62%! My students had made 62% fewer mistakes.

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

The ZeroSum rule helped my students. I hope to bring this manipulator to more students so they don’t fight like my students did. There is nothing like making a simple mistake to hit a child’s math confidence. My goal is to prevent this from happening.

Happy calculation!