ZeroSum Ruler: Finding Success With Negative Numbers

As an Algebra teacher, I assumed that my students had already mastered some things: fractions, multiplication, addition and subtraction, simple equation solving. As I learned, reality hardly follows theory! My ninth grade students struggled with equation solving. At first, I thought this was because equations were relatively new, but as I looked at their work more closely, it wasn't the equations that were giving them trouble, it was the addition and subtraction. How could this be? After a year or so of telling myself that this just couldn't be, I gave into the fact that my students really were struggling. They would tell 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 types of simple errors. By the summer of 2007, the first prototype of the ZeroSum ruler was created. It was rough - two paper number lines hinged at zero with an earring - and was in no way yet ready for the classroom. Over the years, the manipulative went through many incarnations until its final form was reached and tested in the classroom to 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 would make errors on the last parts of the problems - the parts involving, you guessed it, addition and subtraction of integers! By then, the ZeroSum ruler was in its final form and ready to be used in the classroom. I gave my eleventh graders a pre-test of eight simple addition and subtraction problems. Over the course of the next few weeks, I gave each student a ZeroSum ruler to use while solving each of three sets of nine simple equations. Immediately after the last set, I gave a post-test, and one month later I gave my students their delayed-retention test. Both the post and delayed-retention tests were set up exactly like the pre-test only with different simple integer problems. To my surprise, there was not much difference in the 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% less errors. As part of my research, I looked into the curriculum that my students had in elementary and middle school. It seemed they only ever had 16 days to learn integer addition and subtraction. No wonder they needed help! The ZeroSum ruler helped my students. I hope to bring this manipulative to more students so that they do not struggle like my students did. There's nothing like making a simple error to knock a kid's math confidence. It's my goal to stop this from happening. Happy Calculating!