By Dr. Eugene Maier
One of the tenets of The Math Learning Center is that every human being has an innate mathematical spirit that harbors a natural sense of number and space—an affinity for things numerical and geometrical. The possession of this spirit is as normal as having two eyes, walking upright, experiencing emotions. It is part of what it means to be human.
The evidence of this mathematical spirit abounds. Toddlers are fascinated by numbers and shapes. As they learn to talk, number names are sprinkled throughout their vocabulary. They are quick to imitate the counting process, perhaps a bit nonsensically from the point of view of adults who don't consider eleventy-six a number. But gradually the child sorts out the correct sequence of counting numbers, learns how they are connected to the number of objects in a set, and how they combine to form other numbers. Although the vocabulary may not be there, the child distinguishes between properties of various geometrical shapes, realizing that balls roll and blocks don't and that you can't fit round pegs into square holes. And, all too soon perhaps, the child has the lay of their surroundings firmly in mind, devising strategies to reach all sorts of nooks and crannies in an ever widening range of space explorations.
This everyday evidence of the toddler's natural mathematical inclinations are confirmed by the results of experiments by researchers studying mathematics cognition. Neuropsychologist Stanislas Dehaene (see the article, Num·ber Sense/Numb·er Sense) is convinced that all human beings, within their first year of life, have a well-developed intuition about numbers.
Like all infant life, the nascent inner mathematician is fragile and requires nurturing. Left to its own devises it can starve; given the wrong care, it can be strangled to unconsciousness. Many adults profess they are terrible at mathematics and have no aptitude for the subject, when in reality the mathematician within them was never allowed to flourish. Rather than having no mathematical nature, the truth more likely is someone, in the interest of providing it with their version of a proper mathematical diet, choked it to death.
Of course, that wasn't the intention. This strangling of a mathematical nature can happen in subtle, unnoticed ways. I'm sure I've contributed to a number of gasps for breath by my students, and scarcely noticed when it happened. Perhaps such instances are clearer to the eye of the classroom observer. I remember visiting a first grade class. The teacher displayed a calm and caring attitude towards her young charges. The day's arithmetic lesson dealt with writing numerals. The teacher had placed several dots on the board, like so:
and asked if anyone could take a piece of chalk and fill in between the dots to obtain the numeral 5. Several hands shot up and the teacher called on a child who eagerly went to the board and drew the numeral in one continuous motion, starting at the dot in the upper right hand corner. The teacher, in her kindly voice, said no, that wasn't right, could anyone do it correctly. Whereupon another child, went to the board, started in the upper left, drew the lower part of the numeral first and, in a second stroke, drew the top line of the numeral. The teacher said yes, that was right, and cemented her verdict with a little verse about putting the cap of the 5 on last.
My, I thought, this may be how it all starts. How the seed is being sown for those oft repeated phrases, "I'm not good at math,"; "I quit taking math as soon as I could,"; "Math never made sense to me." Imagine being a first-grader during arithmetic period. You have just done something that made perfectly good sense and you're told you're wrong. The task must be done this other way. What does one conclude? That math is an arcane subject, governed by mysterious rules, revealed by the teacher, which are to be observed under all circumstances. To be successful, I must abandon my way of doing things and adopt the teacher's, even though my way works just fine and makes more sense to me. I better quit listening to my inner voice.
Fortunately, the mathematical spirit is resilient and can be resuscitated, even after years of dormancy. The evidence for that also abounds. If one can manage to entice adults into math workshops where their inner mathematician is honored and heeded no matter how feeble and constrained its voice, renaissances occur. A teacher discovers her belief, formed as a consequence of her own schooling, that she was "not only a failure in mathematics, but incapable of learning it" discovers that she can, indeed, make sense of mathematics. A struggling sixth grade math teacher, who thought of herself as a "math dummy" and "didn't care diddly squat about math" finds an unexpected enthusiasm for math and is professionally recognized for her math teaching.
While it is exciting to see these revivals of mathematical spirits, one has to believe that it were better that the stifling of one's inner mathematician never occurred. Certainly one doesn't wish that for one's students. There is no magic elixir I know of that we can feed our students to keep their inner mathematician healthy. But rather than constraining it and attempting to conform it to our image, we can listen to its voice, allow it room to exercise and explore, and provide it with a menu of mathematical activities that promotes its growth and broadens its understanding.