March 30, 2011
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My thesis is available for download here or through the “flash_widgit” in the sidebar –>
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My printed and bound thesis was ready for pick-up today at Wells Bindery in Waltham, Massachusetts, a tiny little place you would never suspect was a business, nevermind one of Harvard’s choice binders. It’s hard to belive that I somehow and finally made all the dots connect and will graduate in May. I started Optimistically in 2006 with one class taught by my eventual thesis advisor Srdjan Divac, the best professor I’ve ever had. I ended jobless, emotional, fried and a few pounds lighter (extreme stress is good weight loss). For most of the time, I was able to teach in the day and plan lessons, go to class and complete homework and projects at night, but by my fifth year of this, I needed to admit to myself that I could no longer do it all. Now that I’m done with graduate school, I am looking forward to a new start with new kids in September 2011.
So what does a math thesis look like? I didn’t know when I started, but as I continued to teach and see one error over and over again – negative numbers – the focus of my research became clear. My teaching began to center around the simple things that trip up even high school Advanced Algebra students and the ZeroSum ruler came soon after. The prototype was made from two strips of paper held together with a stud earring! It’s cleaned up a bit since.
As I slowly progressed through Harvard’s Mathematics for Teaching masters program, my teaching became better and better, which led to me finding more and more student errors. Hands down without a doubt, the error my students made most often was on problems like “-22 + 5″ – a relatively easy problem as compared to logarithms and quadratics. My students’ work would tell me that “-22 + 5 = -27″. In an equation such as:
x – 5 = -22
where a 5 needs to be added to both sides of the equation to find the value of x, my students would add – 22 + 5 and get -27. This happened so much that I made it the focus of my thesis!
My students took a pre-test where they solved eight simple addition and subtraction problems (ie: -15 + 7 =). My students then completed three activities with the ZeroSum ruler over the course of a few weeks. Lastly, I gave them a post-test directly after the last of the three activities, and a delayed-retention test one month later.
When all was said and done and all the data was in, my students made 62% less errors on the delayed-retention test than they had on the pre-test. Pretty great stuff.
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