Awhile back, I tried to teach myself Spanish. I got some used primers and some notebooks, and away I went. After a few weeks, I tried to converse with a friend of mine who was fluent. It didn't go well. I would hear the words she spoke and get this nagging feeling of familiarity, but true understanding evaded me. As I went back to the drawing board, I realized that as I studied alone, I tended to do it silently. Instead of processing the words as sound and phonemes, I was processing text and symbols. Subsequently, I could read and write, but not speak or listen.
As I study calculus, I am reminded of this past mistake and am taking pains not to repeat it. I speak the words aloud as I work through a problem, rather than simply processing symbols and manipulating formulas. I get the same answers, but I gain more understanding.
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2 comments:
Tony,
I too speak aloud as I'm solving problems/writing proofs (drove my husband crazy when I was taking anaylsis). I need to share this strategy with my students, so thanks for the reminder.
As an interpreter/translator, I have to agree with the value of reading aloud. I consider myself fluent (I would have to be to do my job properly) and I still find great benefit from reading something I am translating aloud to myself.
There is something about hearing your own voice that allows you to understand your the words more profoundly. More often than not, this reading aloud prompts me to fine tune something I've translated, do further research, or scrap it altogether to start anew. I find it interesting that there is such a similarity with the learning of mathematics.
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