# ZeroSum Ruler (home)

## Blogging on math education and other related things

### Income and Debt with ZeroSum RulerJuly 10, 2011

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One of the ZeroSum ruler’s main purposes is to calculate debt/income problems.   In the problem “I owe you \$12 and pay you back just \$7. How much do I still owe you?” how do you come to your answer?   Do you count backwards from \$12 to \$7?   Or do you count forwards from \$7 to \$12?   No really, how much do I owe you?   How did you figure this out?    The ZeroSum ruler allows the student to count forwards instead of backwards just like we do in real life!    So why do we make our kids count backwards in school?

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### Have an idea? Write an Ezine Article!April 12, 2011

It’s exciting to be published!  Now, Ezine makes this process even easier.  Ezine literally takes articles written on anything.  Below is an article about the ZeroSum ruler… you can click on the text for the full article and to get to Ezine’s website to write your own article!

### Was math discovered or invented?March 14, 2011

On this Pi Day in 2011, I find myself wondering if math was discovered or invented.   The Pythagoreans believed that math was discovered and that whole numbers ruled the universe.  They also did not believe in irrational numbers, of which we now know there are an infinite amount.  So then was math invented?  I’m not sure….

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### My Old Schoolhouse review debut!January 27, 2011

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.

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.

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.

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.

-

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.

-

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.

-

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.

-

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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### Solving equations with the ZeroSum RulerDecember 18, 2010

The ZeroSum Ruler came from a need to teach my algebra students how to balance equations such as “solve for x in: 22x + 17 = 3x + 5″, where the student has to either subtract 3x – 22x or 5 – 17 to get to the answer. My students were having a lot of difficulty with this, answering that “3x – 22x = -25x”, and so on. As it turned out, this was the BIGGEST mistake my students were making in algebra, which boils down to simple integer subtraction!

(Click the picture over there <— to go to the ruler’s video)

The ZeroSum Ruler has proven to increase understanding of integer addition and subtraction (click here to read the RESULTS of my thesis study) by 62%! One other method of teaching this idea is the “red chip/black chip” model where an amount of red (negative) chips cancel out a same amount of black chips. Sure this method works, but the chips get cumbersome. The ZeroSum Ruler works the same way as the chips except without the chips. No more buying multiple sets of checkers to perform integer addition and subtraction!

Another method that is in widespread use to teach problems such as “-22 + 17″ is the rigid number line. With this example, a student would be directed to find -25 and count 17 spaces to the right. A real-world example of “-25 + 17″ might be “Jim borrowed \$25 from you and has paid you back just \$17. How much does he still owe you?” In this problem, which is exactly “-25 + 17″, it is easier- and intuitive- to count up from positive 17 to 25. But how would that work on a number line? It doesn’t! But, the ZeroSum Ruler is foldable, allowing its positive numbers to align with their negative counterparts and therefore allowing students to solve integer addition and subtraction intuitively.

The ZeroSum Ruler eBook contains a ZeroSum Ruler cut-out to put together, simple instructions on how to construct and use the tool, and practice problems.  You can purchase a ZeroSum Ruler eBook through CurrClick or through SmashWords

HaPpY Calculating!

### When does -22 + 5 = -27?December 6, 2010

My graduate thesis is a study of the long-term effects the ZeroSum ruler has on eleventh grade student understanding of negative integers.  By eleventh grade, students should easily be able to answer “-22 + 5 =”, but on a diagnostic test given to 57 students, 40.35% of the students answered this problem incorrectly.  Why does this matter?  It matters because it shows that students did not learn the relationship between negative and positive numbers in elementary or middle school.  By the time they get to me in eleventh grade and need to be fluent in equation manipulation, answering “-22 + 5 = -27″ is a real problem.

My thesis was set up the following way:

1: Diagnostic test: eight simple sums and differences of integers  (ie: ’22 + 5=”) without a ZeroSum ruler or calculator

2: Introduction to the ZeroSum ruler with examples

3: Three activities, spaced out over 2 weeks,  using the ZeroSum ruler

4: A post test within days of the last activity (no ZeroSum ruler or calculator)

5: A delayed retention test one month after the last activity (no ZeroSum ruler or calculator)

Because the attendance rates of students in Boston Public Schools is not the best, especially by the 11th and 12th grades,  a subgroup of 31 students was identified who took the diagnostic test, participated in at least 2 of the 3 activities with the ZeroSum ruler, took the post test, and took the delayed retention test.  The data shows a 62% decrease in student error from the diagnostic test to the delayed retention test because of the ZeroSum Ruler!  These results indicate that the ZeroSum ruler works to improve student comprehension long-term even without the ruler.

Pretty exciting stuff.

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