In my last post I mentioned I'd be posting excerpts from my Precalc students' midterm exams (and a few assorted comic strips offering explanations of complex multiplication). Here's the first installment.
Tonya's always challenging me with what I believe is the best question a student can ask in a math class, a question which can be paraphrased succinctly by the words "who cares?" She's always on the lookout for relevance and applicability. "That's cool," she'll say, slightly sardonically, and then add, "but how can that be used?" I love it. Every math class should have three or four Tonyas.
Tonya's response to my midterm question asking students to indicate the most meaningful thing they've learned so far this semester was a near-perfect defense of writing-to-learn. It was a delight to read! I asked her for permission to quote her response in full, and she gave me the go-ahead.
Before letting Tonya take it home, I should note that several other students indicated the same realization (of the power of writing as a tool for discovery and for gaining understanding) as the most meaningful outcome of the course so far.
As much as I hate to admit it I think the most beneficial thing that I have learned or rather have incorporated into my learning process during this class has been providing sort of narrative explanations for the mathematical concepts in our homework assignments. This practice really brings light to the idea that the best way to learn something is to teach it. Although laborious, time consuming, and even a bit tedious it has proven beneficial to my comprehension.
I think it may be in some way related to uniting the two sides of the brain or the two main avenues in which human beings tend to process information. It seems that people so often separate quantitative reasoning and verbal reasoning as almost dichotomic and even hierarchical in nature. The fact of the matter is however that both approaches to logic are inherent to one another. Both numbers and words are at their most fundamental level simply expressions humans use to describe the world. Thus I have found great significance in the practice of incorporating those two expressions.
In my mind (as is obvious from my questions in class) mathematics bares very little significance independent of some broader meaning or application. Being forced to go through problems step by step and constantly attend to the looming “why?” in explaining the process that leads to the solution has been instrumental in illuminating that broader meaning. Being able to explain why something was done at a certain step in the problem forces you to draw on the most rudimentary understanding of the process and ultimately universalizes the relevance of that action. I believe that this is the underlying principle behind all creative thought. It is the ability to rearrange, expound, and theorize about the world with our little tool kit of axioms if you will.
As I move forward in my professional/academic life I think it will serve me to have been denied the temptation to skip steps or overlook details in order to more readily achieve whatever end it is that I am vying for whether it be the solution to a hw problem or a policy report. It has been an exercise in demonstrating that anything whole is made up of nothing less than the sum of its parts (maybe more but definitely not less).
I love my job.