What They Say About Math and What We can Learn From It
By Dr. Eugene Maier |
The following text is the content of Dr. Maier's April 14th, 2000 presentation at the 78th annual meeting of the National Council of Teachers in Mathematics in Chicago, IL..
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Quotations about school math experiences, from biographies and autobiographies of the famous and not-so-famous; the picture they paint of societal perceptions of mathematics, motivations for studying math, and classroom practices.
A number of years ago, I read "Dreams, Memories and Reflections," the autobiography of Carl Jung. It contains a long chapter on his school years and within that chapter, a number of pages are devoted to his school mathematics experiences. I found them fascinating. They resonated with much of what I had observed and come to believe about school math. Here are a few passages:
I felt a downright fear of the mathematics class. The teacher pretended that algebra was a perfectly normal affair, to be taken for granted, whereas I didn't even know what numbers really were. They were not flowers, not animals, not fossils; they were nothing that could be imagined, mere quantities that resulted from counting. To my confusion these quantities were now represented by letters, which signified sounds, so that it became possible to hear them, so to speak. Oddly enough, my classmates could handle these things and found them self-evident. No one could tell me what numbers were and I was unable to even formulate the question. To my horror I found that no on understood my difficulty. ... All my life it remained a puzzle to me why it was I never managed to get my bearings in mathematics when there was no doubt whatever that I could calculate properly.Equations I could comprehend only by inserting specific numerical values in place of the letters and verifying the meaning of the operation by actual calculation. As we went on in mathematics I was able to get along, more or less, by copying out algebraic formulas whose meaning I did not understand, and by memorizing where a particular combination of letters had stood on the blackboard. I could no longer make headway by substituting numbers, for from time to time the teacher would say, "Here we put the expression so-and-so," and then he would scribble a few letters on the blackboard. I had no idea where he got them and why he did it--the only reason I could see was that it enabled him to bring the procedure to what he felt was a satisfactory conclusion. I was so intimidated by my incomprehension that I did not dare to ask any questions. Mathematics classes became sheer terror and torture for me. Other subjects I found easy; and as, thanks to my good visual memory, I contrived for a long time to swindle my way through mathematics. I usually had good marks. 1
Jung's experiences were a clear indication to me that math anxiety is no respecter of intelligence, and I have found recounting Jung's experience to a math-anxious person helps them understand that just because they have been terrorized by a math class doesn't mean they're stupid. Also Jung's experiences are a graphic illustration of how divorced school math can be from one's natural knowledge of number and number operations. Finally, Jung's story gave me a way of describing what I find to be a common phenomenon : swindling one's way through math, that is, getting good marks and not having the slightest notion of what's going on.
Shortly after reading Jung's biography, I was describing his math experiences to an acquaintance who mentioned that they just en