- September 18th, 2008
- Filed under Education
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.
September 27th, 2008 at 3:14 pm
I must agree, I have always associated characteristics and personalities with written numbers, and later to letters of the alphabet. I remember when first seeing the Hindi alphabet, thinking such letters were filled with ancient power and wisdom, the curvacious Arabic script seemed fluid and easy going, and the points of Hebrew letters seemed alive and all powerful with flame. I alwys have thought, however, that all individuals do indeed create such associations, and thankfully having never been reproached for such experimentation, encourage it within my own third grade students. It is amazing the stimulating writing a student can generate when directed to explain the interaction when for example, “R first met E”!
September 27th, 2008 at 5:59 pm
Chuck, how great that you encourage your students to explore ways of considering the marks on paper that comprise alphabetic and numeric systems! I do think that the human mind constantly “calculates” the meanings of sensory experiences. Images on paper are just the start! What is the “sum” of red, sunset sky plus a rising coolness from the earth plus the smell of smoke in the air? In my view, the “sum” or outcome of those kinds of experiences can be an aesthetic meaning, not a logical deduction – a whole-person way of knowing, rather than a systemized one. I say “can be” because I think our culture teaches us not to give value to (or even note) such meanings because they are not logical. Perhaps this is one reason our culture has had so much trouble sustaining several kinds of holistic systems: health and environmental spring to mind.
Thanks so much for sharing your perspective as a teacher!
Linda
October 7th, 2008 at 2:13 pm
For as long as I can remember, I have thought in terms of music. I have a sound track in my head running almost continually, with either the last song I have heard, or some accompaniment running beneath a group of images. It started to make more sense to me when my mother described how she put me to bed as a little kid….my crib was across the room from the piano. We would play a couple of tunes on the keyboard, then she would lay me down. The fresh songs were still running through my mind as I started to get more and more sleepy. And as I slept the music fragments became the background of my dreams.
Now, many years later, a musician, I can read music and practice simpler pieces in my mind without my fingers ever hitting the keys. Some music comes to comfort me when I have troubles. Music has formed a bond with my thinking to such a degree that I memorize lyrics to ballads with an ease that surpasses my ability to memorize straight poetry unaccompanied by music. Once I learn a piece, it doesn’t leave. And I have been able to play the piano by ear since the age of two, and to put a name with a sound (a skill called perfect pitch) since my earliest days. Much like your fascination with numbers, I was a child who had a favorite note, and would seek it out to hear it much as you assigned personalities to numbers.
October 12th, 2008 at 12:52 pm
Your reflections are truly fascinating to me, Elaine. I do not have any formal education in music, but my informal musical experiences may be the factor that allows me to empathize very much with you description. My father was a tenor and had a fairly serious avocation as a soloist at weddings, funerals and in musical programs performed at churches all over the Chicago area. I grew up to the background sound of his bedroom practices; he sang along to a tape-recorded accompaniment for hours each night and on weekends. That sonic backdrop to my childhood, perhaps more than the performances I attended, left a strange affinity for music in my brain! Unhappily, without the education to sort it out, I am usually tongue-tied when called upon to discuss music.
How interesting that you felt attracted to a particular note! It almost seems as though it served as a kind of home-base for you, musically. I’d be very interested to know if that attraction has continued to play a role in your adult life as a musician.