# ZeroSum Ruler (home)

## Blogging on math education and other related things

### New (free) ZeroSum ruler – for teaching addition with negative numbersSeptember 30, 2012

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.

-

### Discover something new! The ZeroSum Ruler FREE eBookDecember 21, 2010

-

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!)

-

### Subtraction as “as compared to”December 10, 2010

I learned the best thing today at an interview, which I know sounds a bit weird.  Usually at interviews it’s all about what I’ve done and where I see myself in 5 years and whatnot.  This interview was far different, and better, and awesome.  Today at my interview, I learned something really great about… subtraction.

Let’s take a problem like “7 - 2“.  We can read the subtraction sign as “as compared to“.  When we find 7 and we find 2 on a number line, comparably they are 5 apart.  And indeed, 7 - 2 = 5.

But does it work for subtracting negatives?  let’s check…

“7 - -2″.  Seven as compared to negative 2.    7 and -2 are 9 apart, and in fact    7 -  -2   =   7 + 2 =   9!

This is a SUPER model that, as my boyfriend just said, opens a whole new world.  Who knew at 33 I’d still be learning subtraction!

Awesome!

### 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.

-

### ZeroSum Ruler eBook!December 5, 2010

An eBook, complete with a ZeroSum Ruler cut-out, may be coming soon to CurrClick.com!

In the meantime, you can download a ZeroSum Ruler eBook and cut-out for \$4.00 through the ”Buy Now” button below, hosted by PayLoadz.com and PayPal…

### How the ZeroSum ruler worksOctober 24, 2010

Filed under: Boston hip hop,videos,ZeroSum Ruler — ZeroSum Ruler @ 12:04 pm
Tags: , , ,

Thank you for visiting my site.  I hope you find it informative and that you will see the usefulness of the ZeroSum Ruler.  I am currently testing the ruler’s effectiveness for my graduate thesis, and so far the results have been positive.   Student quiz scores went up!  In a month or so, I plan to give a delayed retention quiz that will test if student knowledge of the relationship between positive and negative integers stuck long-term.  Hopefully it did, but they will always have their rulers if they still need help.  I made one for every student to give out at the end of my study.

Please email me with any questions!  In the meantime, below is the unedited video on how the ZeroSum Ruler works.  If you like shorter videos, the green one over there in the margin is the one for you ——————————————————->

-

That’s Beck in the background. I hope he doesn’t mind!

### Negative Numbers. OH NO!October 6, 2010

In our BPS high school, there’s a big focus on the “broken window theory”, made famous recently in The Tipping Point.  One broken window we’ve identified in the school as far as discipline goes is hats and ipods.  So, there’s been a big push to get rid of them.

I’d like to mention to you a “broken window” that has somehow gotten lost in the mess of school closings, going charter, union fighting, pension plans, longer days, MCAS scores.  As a high school math teacher, the biggest broken window I face – in fact, it’s a gaping hole not even bothered to be temporarily covered with plastic- is… negative numbers.

What do I mean by negative numbers?  I’ve done my research as they’re the topic of my Harvard thesis.  Students using the TERC Investigations curriculum in Boston elementary schools do not do problems like “-22 + 5″.  One TERC representative told me they “leave that topic to middle school”.  So, I looked at the middle school Connected mathematics Project 2 (CMP2) curriculum, and negative integer problems, like “-22 + 7″ are taught for 20 days total in the 7th grade.  20 days.  From then on, students are assumed to know how positives and negatives interact and to be able to evaluate “-22 + 5″.

Then students get to me, their 11th grade Algebra 2 teacher, and they can’t solve for y in “y + 22x = 5x – 7″ because they don’t know what “5 – 22″ is.  The kids think -22 + 5 = -27.  Why?  Maybe the rules of multiplication get mixed in.  I don’t know.  Or maybe it’s because these problems were taught to them for a total of 20 days four years earlier and were never touched n again except in the context of other problems.  Understanding why and how kids think is beyond the scope of my thesis and my means for data collection.  What I can tell you is that because my students don’t know what “5 – 22″ is, they can’t solve y + 22x = 5x – 7 for y.  Because they can’t solve the equation for y, they can’t graph the equation.  I assume you know where I’m going with this.

Please, as someone on the front lines of math education in Boston, I’m telling you that the biggest difficulty our students have in math is adding and subtracting positive and negative integers.  It seems ridiculous and that there are bigger fish to fry, some of which I have listed, but if you want more competency in math, please, heighten the focus on negative numbers.  It will lead to better test scores, more understanding, but most of all, to students who feel good about themselves when they’re not still making silly 7th grade mistakes in high school.