Friday, April 13, 2012

Review, Remember, Retest, Relate

            So I did an interesting thing in my class yesterday. I gave a geometry test in which the front page was the exact same as a test that I had given back in November. I must say, I was both surprised and disappointed with the results. What surprised me were the results and the stratification that was exhibited.
            For the most part students who performed very well on the first round of the test performed equally as well. These are students with a strong understanding of mathematical concepts and most of the have assuredly been doing math longer and more often than their counterparts. These students generally do well and could have probably handled the majority of this page with only the equations I presented even before I taught the unit.
            It was the students that struggled to pull their work up to an acceptable level by the end of the unit that still struggled significantly. Many of these students had worked hard, very hard, to gain an understanding of the work four months ago. However, for many of them, it simply didn’t sustain. These students had managed to handle the Monday-Friday problem, but really hadn’t advanced significantly in their learning five months later.
            I’m beginning to wonder if fully summative testing is the only way to see what knowledge sticks. I had one student who astutely asked me why he couldn’t remember how to find the area of the shapes in question. I answered by asking him what they best gun in Call of Duty: Modern Warfare 3 (MW3) was.
He quickly piped up with “The MP7, but everyone thinks you’re lame if you use it.”
“What does it look like?” I asked.
He then described the gun in great detail as well as the social ramifications of using it.
“You remember what you use.” I said as I walked off to answer another question.
The chorus of “Ahhhh” that my comment drew from the table was illuminating. Every student at that table played MW3, understood the reference, and knew the gun. None of them reliably remembered how to get the area of a parallelogram.
I remember using the peg board in 2nd grade to solve square roots. While I don’t remember the exact process, I remember enjoying it and if I had all the same materials I could probably recreate it. I kept asking for more and more difficult square roots to figure out. I enjoyed it. I remember researching the Loch Ness Monster for my 6th grade project and writing the report on it. It was fun, engaging, and even as I read it now, well written.
I also remember how to get the area and circumference of a circle, how order of operations works, and how to divide and multiply fractions. But even after working as an IT recruiter for five years I can’t reliably spell consultent consultant or recieve receive. You remember what you use. Or something like that.
I think that the groundwork for some kids has already been built that when you discover length times height equals area it fits in and they move on. There are some that can’t even remember what area refers to. Education is doing great things for the first group, but I can’t help feeling that no number of repetitions will ever get it to click with some other students until some different framework has been established. How to we reach back to build that framework for the kids that need it, and where did it even come from with those that have it?


  1. It is a very abstract concept for a child to grasp, that at some point down the line, they would will need this knowledge. I am not sure I have ever needed to know how to find the area of a circle, except in a math class. 2(pi)^2 would be my guess.
    You know what you use.
    If there is a way to show the kids that it is useful information to them, or make it socially useful, then maybe they'll care. I think games could be a great way to do this.

  2. Pi x radius ^2 = Area
    2 x radius x Pi = Circumference