I am studying for the GRE. This is proving very difficult, as I haven't worked with math for years and even when I was working with it, I wasn't very good at it. As I've worked in earnest over the last few days, I have noticed several things about myself, which are making me revert back to my mindsets of high school and college. I'm struggling with checking my work and being careful with positive and negative signs, for instance. I'm also struggling with the use of algebra in any cases in which the question differs at all from the manner in which it was taught. I am able to do exactly what was laid out in the text, but then when I'm asked to find a different number, or I'm given a different value to start with, I'm unable to translate the problem and then can't figure out the answer. Sometimes, I mindlessly "do" the problem, plugging in the numbers and then realizing that my work is not geared toward the posed question. This is a symptom of "exercise" versus "activity;" a matter of memorization versus understanding; of plugging versus thinking.
I can't help but think that this is what is happening to our students via standardized testing. In standardized testing, our students can memorize a process, whether in writing or mathematics and they can plug the information into the formula or pattern they have created, but they struggle with using the information practically. I will try to use these symptoms of my own work to inform my teaching of writing and of thinking. I thought it would be helpful to point this out.
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