Below is a new version of the ZeroSum ruler. This one needs no hardware to construct, just scissors and glue. You can download, print and use this proven tool right now by clicking on the picture, which will bring you to the PDF file that contains 2 ZeroSum rulers.
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I was lucky to get into Oliver Knill’s class Teaching Math With a Historical Perspective, one of the choices within the Harvard Extension School’s ALM in Mathematics for Teaching program. It changed the way I think and the way I teach. He explained complex topics, such as code breaking and non-verbal proofs, with such ease. He was inspiring and made me look at math in a way I had never before – from a historical perspective! His site is worth checking out, especially if you can not get into his class! (Click on the red circle to go to Oliver’s site)
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During a 4th grade substituting assignment, the teacher left a set of word problems for the kids to do. A bunch of these word problems involved division, and the students were directed to use their counting blocks. As I walked around the room, I saw kids doing just about everything a kid will do with giant leggo-type blocks. There were guns, there were swords, there were towers. Some kids were using the blocks to work the word problems, but many of the students who wanted to use them for good were having trouble. My role morphed from teaching math to teaching the kids how to use the counting blocks. One word problem called for dividing 125 by a variety of numbers. There is a large margin of error while counting 125 of anything, and with a string of problems that all rely on a 100% accurate count, it felt to me that the kids’ time could have been better spent. When do manipulatives cross the line from helpful to hurtful?
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A great article titled Teacher Learning and Mathematical Manipulatives: A Collective Case Study About Teacher Use in Elementary and Middle School Mathematics Lessons by Laurel Puchner, Ann Taylor, Barbara O’Donnell and Kathleen Fick, outlines one of the many problems that can arise while using manipulatives in math. This article is a worthwhile read, especially for those teachers wondering why manipulatives don’t seem to work as well as advertised.
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contact blog author Shana Donohue: shanadonohue@gmail.com
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After many many years of jumping through many many hoops, I am finally graduating with my MA in Mathematics for Teaching in May. My thesis, Negative Number Misconceptions in High School: An Intervention Using the ZeroSum Ruler is right now at the printers being printed and bound. I don’t know about you, but that instantaneous feeling of relief after taking a final exam or passing in a final paper stopped hitting me sometime in college. So now, I’m just feeling a bit burnt out. OK, completely burnt out. But I’m sure it will hit me soon since it kind of needs to; I need to now get in a post-Bach program to get my Initial teaching license. I like to do things backwards.
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So here it is for download! For all to read! Or maybe to just glance. In my study, the ZeroSum ruler proved effective in reducing eleventh grade error on integer addition and subtraction problems (especially with negative integers). If I wasn’t so burnt out, I’d want to test it with younger kids. Imagine how our world would be if my eleventh graders actually mastered integers when they learned them in, and only in, 7th grade. But that’s in my thesis.]
The ZeroSum ruler improved my student’s understanding
of integers
by 62%
in a very short 2 weeks.
Surpassed even my high expectations!
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HaPpY Calculating!
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The ZeroSum Ruler was recently reviewed by The Old Schoolhouse Magazine! You can read their full review – and get a glimpse at my old address where I fought a slumlord to the death of my career and almost me – at: The ZeroSum Ruler’s Old Schoolhouse Review!
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“Math is a subject that students can sometimes fake their way through. They might not understand how a problem works, but given the formula, they can follow rules and get things to come out all right in the end. Faking can only get them so far, though. Eventually, they will either forget the formula or not be able to recognize it when arranged in an unfamiliar manner. What a math teacher wants to see is the light bulb moment–when a student doesn’t just use a formula but understands why it works.
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Working with negative numbers is an abstract concept that many students have a hard time visualizing. How does one visualize what isn’t there? According to the website, the ZeroSum Ruler naturally brings this abstract “knowing” into concrete “showing”! This simple little device helps students see not only the negative numbers but also their relationship with other numbers.
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For instance, a student might not see how subtracting 10 from 5 is actually the same as saying 5 + -10. Visualizing the process with the ZeroSum Ruler helps students see that when they are figuring out a real-life scenario, such as how much someone owes them, they are really counting forward in positive numbers.
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The ruler itself is of laminated cardstock and is hinged at zero so that it can be folded, making the positive numbers line up with the negative numbers. This allows students to count forward the number they are subtracting or adding.
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The true gem of the ZeroSum Ruler is the creator herself. Shana is passionate about math and making it reachable for students. Her website contains math videos and commentaries that help students see that math is fun, interesting, and relevant. She breaks things down in an easy-to-understand method, and she is also happy to help with math questions from students and teachers.
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The ZeroSum Ruler is a great asset for students struggling with the concept of negative numbers. And its creator is a great help to parents struggling to teach those students.
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Math is a subject that students can sometimes fake their way through. They might not understand how a problem works, but given the formula, they can follow rules and get things to come out all right in the end. Faking can only get them so far, though. Eventually, they will either forget the formula or not be able to recognize it when arranged in an unfamiliar manner. What a math teacher wants to see is the light bulb moment–when a student doesn’t just use a formula but understands why it works.
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Working with negative numbers is an abstract concept that many students have a hard time visualizing. How does one visualize what isn’t there? According to the website, the ZeroSum Ruler naturally brings this abstract “knowing” into concrete “showing”! This simple little device helps students see not only the negative numbers but also their relationship with other numbers.
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For instance, a student might not see how subtracting 10 from 5 is actually the same as saying 5 + -10. Visualizing the process with the ZeroSum Ruler helps students see that when they are figuring out a real-life scenario, such as how much someone owes them, they are really counting forward in positive numbers.
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The ruler itself is of laminated cardstock and is hinged at zero so that it can be folded, making the positive numbers line up with the negative numbers. This allows students to count forward the number they are subtracting or adding.
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The true gem of the ZeroSum Ruler is the creator herself. Shana is passionate about math and making it reachable for students. Her website contains math videos and commentaries that help students see that math is fun, interesting, and relevant. She breaks things down in an easy-to-understand method, and she is also happy to help with math questions from students and teachers.
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The ZeroSum Ruler is a great asset for students struggling with the concept of negative numbers. And its creator is a great help to parents struggling to teach those students.”
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Thank you, Old Schoolhouse Magazine! 
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You can purchase a ZeroSum Ruler eBook here: The ZeroSum Ruler on CurrClick or on my blog over there —>
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I am excited to bring to you this free version of the ZeroSum Ruler’s eBook! In this book, you will find pictures and explanations of how the ZeroSum Ruler is different yet more intuitive in its way of teaching integer addition and subtraction. if you like what you read, there is a version of the eBook on CurrClick that includes a ZeroSum Ruler, practice problems, and some more fin pictures. Enjoy! (click the picture below to be directed to your free download!)
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If you need convincing to download this eBook for free (??), you should go to the GRADUATE THESIS tab (up there) to read how the ZeroSum Ruler decreased student error by 62%!
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The ZeroSum Ruler is on CurrClick! In the FREE informational eBook, you can learn all about the ZeroSum Ruler, how it works, and what makes it a different and more INTUITIVE way to learn. 
