View My Stats

Monday, August 31, 2009

Mathography V

Another in a series from my university math class.

In my life, childhood memories meld with stories told and retold by my family. Fact and fiction blend together to create the story of my math life. Following are some slices of historical fiction from my memories.

I am six or seven. My father is drilling my older brother with multiplication flashcards at the kitchen table. While my brother is clearly frustrated, unhappy, and slow to recall his facts. I quickly and happily call out the answers from over his shoulder. As an adult I would add “demoralized” to how he must have been feeling. As an adult I also know my brother has a learning disability. As an adult I recognize the differences between how my brother and I learn but the commonality between us that we are each intelligent problem solvers, with different perspectives, strengths, and strategies. P.S. He outscored me on the math SATs.

More slices:

It is my first year at a new school. I am in fourth grade. A parent takes a small group of GATE students into a separate room for challenging math lessons. There are beans on the table and we are learning about powers. One girl just doesn’t get it. She keeps multiplying the base times the exponent. At the time I think she’s not that smart. As an adult I don’t recall if or how we used the beans to better understand the concept. It seems to me we learned a rule and vocabulary for “quick” or “fancy” multiplying. The beans were incidental.

At the end of fifth grade I have a distinct memory of thinking to myself, “I don’t think we learned anything in math this year.” Sixth and seventh grade math didn’t make the memoirs. No memories at all. In Eighth grade my dad attempted to support my learning in several ways. He challenged my teacher because he felt the instruction was not organized. And when I didn’t know how to solve a problem my dad showed me a formal algebra strategy for solving the problem. I had no idea what he was doing and our relationship hurt because of this communication chasm. Amidst my discomfort now with two adult males in my math life, I scored in the top three of my class on a high school math competition.

External praise continued to be a part of my math life. Therefore, as long as I understood what to do and did it correctly, I felt externally satisfied. I had no clue as to what connections we left unexplored and I had no intrinsic desire to seek them out. So as I continued on the Algebra I to Calculus path, my father’s repetitive question in response to my pleas for quick math help, “Do you understand why that works?” only irritated me and widened the chasm. I heard the question as an opportunity for him to explain something to me in his words which I expected not to understand and decided not to care about. Besides, I had no time for understanding.

The irony here is that I now work with teachers and students to embed that same question my dad asked me into everyday teaching and learning. I work to build a learning community where teachers and learners alike ask such as questions as, “Will that always work? How do you know? What’s going on in this problem? Is there another way to solve it?” This is no accident. The artistry of helping seventh grade students to understand integer operations first opened my eyes to the creative world hidden behind the wall of rules and procedures. Ample professional development and learning beside my colleagues continues to challenge my perceptions of understanding mathematics. Though I describe my math life as having fallen into math instruction from a path of environmental education and social justice, I truly believe I landed solidly with a sound purpose. My math life is about the social justice of providing quality, equitable, applicable math education for all students, not just a select few