Shad’s blog for the week
I just started reading Tobias Dantzig’s “Number: The language of Science” and realized I could quote him selectively, to support my protest, which put simply, runs like this:
Something is seriously wrong with Math education.
You know it. I know it.
I could be a parent, teacher, an employer or an adult who missed out on higher education because I was under-achieving in Math(s). When it came to Math(s), I “wouldn’t get it“. My grades suggested it. My teachers projected it. And society punishes me for it by denying me opportunities for self advancement. By the end I am hopelessly reconciled to an embarrassing truth: “I’m not smart enough. That’s all there’s to it. For Math(s) you need to be smart. ….and I’m not. ”
This is not an autobiographical “I”. It is a positional “I”, an abstract middle seat that keeps this blog pinned down to a center.You can sit on this seat and get a better view of my protestations as a Math teacher.
So, to continue.
I could also be among those who perform brilliantly in any of the non-Math(s) areas I am lured into, like: business, marketing, sports, the performing arts, journalism, creative writing, the behavioural sciences, education, and complex historical studies. Despite my poor Math scores I am able to express, articulate, analyse and synthesise facts, information and knowledge with varying degrees of insight, knowledge and precision. I can display a perceptive understanding of forces sweeping across societies and affecting lives in strange, often predictable, ways.
One would conclude that it takes some thinking to do that. Or brains, whatever. So, even though I cannot analyse complex graphical data or solve quadratic equations I can still be among the many who possess the brains to be successful and content. But I grew up ostracized as “not smart enough to do Math”. It’s a stagnant truth that curdles into a sour abbreviation: “Not smart enough”. Period. A toxic recipe for adolescents caught in the throes of identifying themselves via feelings of self-esteem.
Assuming that you are at least a few centuries old (mentally, as a historical abbreviation of humankind personified and all that sort of thing), you might recall that centuries ago (before the advent of Arabic numerals (0,1,2,3,……), multiplication and division was an extremely convoluted process. Do you remember multiplying and dividing using Roman numerals LXXXVCX and CXVII. Or Greek numerals. Which was superior, I would wonder, sometimes, while wrestling with a post-division headache.
Tobias Dantzig, in his book “Number: The language of Science” replies as follows:
“A far more important question is: how well is the system adapted to arithmetical operations, and what ease does it lend to calculations? In this respect there is hardly any choice between the two methods.: neither was capable of creating an arithmetic which could be used by a man of average intelligence...
…from the beginning of history, until the advent of our modern positional numeration (or the place-value system of writing numerals), so little progress was made in the art of reckoning. Not that there were no attempts to devise rules for operating on these numerals. How difficult these rules were, can be gleaned from the great awe in which all reckoning was held in these days. A man skilled in the art was regarded as endowed with almost supernatural powers… And to a certain extent this awe persists to this day. The average man identifies mathematical ability with quickness in figures.”
So going back to those times, you and I, and folks like us, possessing average intelligence, would be turfed out as people lacking the mental competence to multiply and divide (Add and subtract? Perhaps, yeah, okay, we could do that, maybe).
Would I protest? Would you? Would we?
Well, take the ancient English Tally-Stick bearing notches cut into it of various sizes: the small ones representing Pounds Sterling, the larger ones 10 pounds, the largest 100 pounds etc. Tobias reports that “the English tally persisted for many centuries after the introduction of modern numeration made its use ridiculously obsolete”. A very sarcastic Charles Dickens , in an address on Administrative Reform in the English Parliament, complained about the continuing “savage mode of keeping accounts on notched sticks…. much as Robinson Crusoe kept his calendar on the desert island”. He reminded his audience that: “in the reign of George III an enquiry was made by some revolutionary spirit whether pens, ink and paper, slates and pencils being in existence, this obsolete adherence to an obsolete custom ought to be continued, and whether a change ought not to be effected. All the red tape in the country grew redder at the bare mention of this bold and original conception and it took until 1826 to get these sticks abolished”. (Tobias Dantzig)
I did protest. I know I did because my brain is programmed that way. Yours too, perhaps. You may have been the “revolutionary spirit” that Dickens was referring to. But despite our passionately strident protests, the reforms came long after you and I were dead. Which is too bad, because when we protest and all we see is the red tape “getting redder”, many of us give up and loose the courage to make defiant statements like: “You need exceptionally gifted minds to multiply and divide numerals??!! If that’s so, then we need to find better ways to multiply and divide so that ordinary folks like us can help ourselves to the benefits of knowing how to do it simply, accurately and swiftly“.
And if you were a true visionary, you would gaze into the crystal ball and tell them what you see: “There will come a day when 7-8 year olds possessing average intelligence, even less, will be able to multiply and divide with greater speed, accuracy and confidence than you old farts!”
The entire history of Mathematics education proves over and over again that we reformist spirits were always right. There is always a better way. Today, yes, right now as we speak, Mathematics is being taught in schools throughout the world, using approaches and strategies, methods and materials that have been made very complex and convoluted by well-meaning people who simply don’t know any better. The resulting system victimises one set of people with average intelligence while glorifying another. Victims from the first lot have their normal intelligence denigrated. It is made to appear low and unworthy of learning Mathematics.
Why?
Because throughout the ages, inquiring minds “fail” to blindly accept the manipulation of inconsistent rules as the foundation for learning Mathematics. So the sooner we dispense with the popular myth about Math and its dubious association with the “brainy” for success, the sooner we can cross over to the other side.
“The greatly increased facility with which the average man today manipulates numbers”, writes Tobias Dantzig, “has been often taken as proof of the growth of the human intellect. The truth of the matter is that the difficulties then experienced were inherent in the numeration in use, a numeration not susceptible to simple clear-cut rules. The discovery of the modern positional numeration did away with these obstacles and made arithmetic accessible even to the dullest mind”.
Likewise, the difficulties being experienced by today’s under-achieving Math learners has much to do with difficulties….(”limitations” might be a better word)……. inherent in the obsoleteness of the curriculum design, the redundancies in the teaching materials and the complete absence of intelligent and coherent educational design. Today’s failures in Math(s) learning should no more be allowed to invite the traditional knee-jerk response: “Insufficiency of the Average Intelligence of the Masses”.
It’s why we came up with CLSO-MATH. It’s a programmed response that goes beyond protest …even though my protesting will never cease.
More next week!
Shad