The IMA Blog team welcomes new author, Linda Duke, Director of Education.
When I was very young, I had a special sense about written numbers. It’s hard for me to access that now, through all the years of education devoted to making sure I understood numbers in a standard way. But I still have a feeling about that early relationship, and sometimes I wonder how it might have developed if I hadn’t learned to be ashamed of it and to ignore it.
Here’s what I can recall: I knew the shapes of the numerals as indicators of the distinct characters of each. Though my sense for some of them has slipped out of reach, in the way dreams do, I can still feel the stronger personalities. The numeral five was intimidating in appearance, but in actuality quite sweet. Seven was both stern and judgmental. Eight had complexity and depth – and eight led to a painful collision with my first grade teacher, Miss Logan. She taught us to write eight with one continuous figure-eight line. Soon after, she exhorted us never to write it as one circle on top of the other – an idea that had, frankly, not occurred to me.
Once I heard about this forbidden way of making the image, I badly wanted to try it, to find out why it was seductive and wrong. I hunched over my practice sheet to try what sounded to me like an ingenious alternative. The hurtful rap of a ruler on the back of my head shocked and scared me. I could hardly believe she caught me in the act so quickly and easily. Miss Logan’s efficient suppression of dissent gave me, early-on, the impression that privacy and experimentation had no place in the classroom.
Back to the personalities of numbers: you might think it’s just as well that this idiosyncratic notion of numerals having distinct natures signified by their visual forms was scared out of me. Even in first grade it was beginning to raise some dauntingly complex dimensions of arithmetic. What kind of psychodrama might be the sum of 8+7? If 5 were subtracted from 9, what interpersonal consequences would that equal? Left unmolested, I wonder if I might have been able to craft an alternative way of working with numbers that allowed me to derive answers that approximated my classmates’. I’ll never know. As it is, I developed a serious case of math phobia and went on to do poorly in math classes throughout my schooling – with only the slight exception of geometry, to which I was timidly attracted. It is only in middle age that I’ve come to terms with the fact that I am actually fascinated by mathematics as logic, and by the more philosophical implications of mathematics, rather than the computing tasks. I’ve also noticed that the concept of numbers having “natures’ isn’t entirely far-fetched when one considers mathematics as a system for describing relationships and processes.
My early sense about numbers may be one indication of something it’s taken me years to notice about myself: I believe I am a primarily a non-verbal thinker. Until I reached this hypothesis, I thought everyone thought approximately the same way.
Several years ago, I began asking my colleagues in the art museum education department how they thought – not what they thought, but how. Were they conscious of thinking in words, for example? I started this line of questioning because I realized that I was completely unable to describe or explain my experience of thinking. Of course I could mentally use words. If I needed to craft a statement of some kind and make decisions about the most effective wording, I could certainly rehearse the possibilities in my mind and make a choice. However, that would be a particular situation, very different from my ordinary, day-to-day thought/language processes. Truth be told, I had to admit that in my on-going mental life, words don’t play a part. In ordinary conversation, I do not plan or even know what words will come out of my mouth. I would even go so far as to say that the times I have jotted notes for a talk or to teach a class have led to my most lack-luster presentations. The notes always flummox me. It’s taken me a while to trust myself, but I now feel that I am better off speaking “spontaneously.”
But back to the question about thinking that I posed to my co-workers: Most people seemed taken aback by the question and several mentioned that they had never considered how they thought. Upon reflection, quite a few said that they were conscious of words and sentences going through their minds. Several said they “heard” their thoughts as an on-going voice inside their heads. One person described being vaguely aware of punctuation in his thoughts! Another described dreams in which she read the narrative and conversations in a way that reminded her of the bubbles over the heads of comic book characters.
It was difficult to cover my own surprise at these revelations. Even now, as I type this anecdote into my laptop, I wish I could form the ideas on this screen with my hands. I wish that you could take them in with a probing – or a playful – gaze, rather than following various linear sentences to various open or dead ends. I don’t think with words.
How do you think? Can you describe your experience of thinking? Please let me know. I think others will be interested as well.
Filed under: Education