|devpsy.org > k h grobman >|
I can not recall a time when I was not fascinated by figuring things out, any things. Why was the sky blue? What made me like some foods that others did not like? For most of my childhood I wondered why I could not escape gravity, like the birds. I would endlessly swing on swing-sets, going higher and higher, feeling myself lift up from the seat just a bit, only to be snatched back by gravity at the final second. Clearly my strategy for understanding gravity did not work, but what strategy would? Into high-school I would always look for new ways to think and solve problems. I stumbled upon a book in the library, "Conceptual Blockbusting: A Guide to Better Ideas" by James Adams and read it voraciously. Most books I could find about problem-solving were written by engineers or physicists. These books and some wonderful classes led me to major in Physics as an undergraduate.
Learning Physics was fascinating and it left me with a love of science. Among other things, I figured out how I mis-conceptualized gravity and why swinging would never help me to escape it. After completing the physics classes my university offered for undergraduates, I began taking graduate-level classes. I also had the opportunity to be involved in a of study sub-atomic particles at the Stanford Linear Accelerator Center. As I became more deeply involved in Physics, I found myself more perplexed. Though I could typically get the right answers for problems, the mathematics and our scientific methods seemed almost magical and barely within my grasp.
Following graduation I became a teacher for a non-profit organization, Project SEED whose mission was to teach mathematics to children living in inner-city housing projects. There were so many new experiences for me here; perhaps I learned more from these children than they did from me. But there were also things I learned that were repeated lessons through my life. For example, to introduce a sixth grade fraction lesson I asked a class to guess my favorite number as I said, "higher" or "lower." They determined it was between zero and one; then students accused me of tricking them because there are no numbers between zero and one! Just like I could solve physics problems without necessarily understanding them; these students could solve fraction problems without understanding them.
After this experience, I went to graduate school at Carnegie Mellon University to study Logic, the philosophical origins of mathematics and science. Having satisfied my need to understand science, I decided to return to science. But Physics was not where my deepest questions lied. Instead I wanted to focus on the puzzle that kept appearing throughout my life. How is it that people solve problems? How do we conceptually understand things? And how does the relationship between conceptual understanding and problem-solving change as people grow?
I was fortunate to find a Developmental Psychologist to mentor me for my Masters thesis in Logic. Together we decided to examine one possible link between problem-solving and conceptual understanding. She had previously found that young children misunderstand the equal sign. They would say "find an answer", as though it was an "operation." Conceptualizing the equal sign as a "relational" symbol, "the same as", would be more mathematically accurate. I remembered my middle school students believed the same thing and thought this might be why learning algebra was difficult for them. In my Masters thesis study, I found that: (1) those children who understood the equal sign as a relation were better able to learn from a lesson in algebra, (2) having an algebra lesson helped students form a more relational understanding of the equal sign, and (3) having an algebra lesson that was more conceptually focused on the equal sign helped students transfer strategies to novel algebra problems more than a procedural lesson. As a graduate student of Developmental Psychology at The Pennsylvania State University, I became more focused on basic questions about the origins of problem solving and the origins of ideas such as "means" and "ends."
|devpsy.org > k h grobman >|
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