Shad’s Blog for Week # 4
AVERAGE VS. PEAK CONCENTRATION (Part II)
Here is another scenario: imagine sipping coffee and having a conversation around a 3-legged coffee table with one leg short. Any weight placed on the table makes it wobble and spill coffee. Assuming there is no remedy for it, we would compensate for the design flaw by modifying our behavior e.g. we would have to watch it! before leaning an elbow, or anything else for that matter, on the table. Even worse, we would be on anxious alert for inattentiveness in others. If such flawed coffee-tables were universally endured because they cannot be cured then coffee-drinking would be elevated to a skill requiring partcular attention to “Spillage Avoidance”.
When the slightest spillage of attention can cause a major spillage of coffee, we’re looking at a pretty wobbly environment for conducting intelligent conversation. A small area of our brain would attend directly to the problem of exchanging ideas and opinions while large parts of it manage the stress and anxiety inherent in such a situation. Once again skilled coffee-drinkers would be in the minority and this would be quite acceptable since smart and minority go together on everything.
Limitations in design influence social cultures and create sub-cultures all their own. Within them certain home-truths mushroom spontaneously and naturally, and are accepted as being organic to such an environment. So, good drivers would naturally be highly paid because they are smarter and fewer and perform a task essential to civilization. There would naturally be fewer cars and more buses. Bus-fares would be naturally quite high. There would naturally be supplementary, private driving schools teaching sub-skills essential to qualify for entrance into prestigious driving schools. It would be natural to expect fewer people wanting to be drivers, so naturally there would be state-sponsored non-profit programs lauding the financial advantages, the social benefits of choosing driving as a profession, etc. Good drivers who also excel in the science of coffee-drinking, would belong to a class all their own…… naturally. So would those considered inept at both.
Traditional Math(s) learning has influenced our culture in similar ways. For a number of historic reasons, success in Math(s) is naturally associated with a clutch of secondary and tertiary skills and abilities like high attention levels, extreme alertness and exceptional memory. We are expected to possess them, develop them and hone them in order to be “good” at Math(s). The counter-pedagogical design in Math(s) teaching-and-learning materials remain unscrutable, un-discussable, even inconceivable as the dominant reason for mass under-achievement. It is easier to see and hear the frustrated attempts of learners struggling to grasp this understandably “complex” subject. The solution to this problem is seen not in a radical and much-needed transformation of the design and delivery of Math(s) but in another area altogether: e.g. teacher-training and student attitudes. Thus, (a) teachers should be trained to apply creative and imaginative approaches when teaching Math(s), and (b) students should deploy more intellectual energy learning it. Typical demands of (b) are:
(1) a high concentration and intelligence for figuring out implicit connections in Math(s). The connections rarely display explicit logic.
(2) a curiosity that collapses into trial-and-error thinking to grasp simple concepts masquerading as complex.
(3) extremely good recall of rules and algorithms that are often vaguely understood.
(4) a rote-learning memory for mathematical facts to compensate for an unreliable grasp of mathematical concepts and operations.
(5) a blinkered focus on learning the Mathematical language (formal terminologies and definitions) first and foremost on the assumption that learning such a language will facilitate the understanding of Math(s) concepts. Usually, it is the other way around: if done right, a well understood Math(s) concept seamlessly assimilates the Math(s) language corresponding to it. We know that language learning in babies is preceded by pre-linguistic concept formation of the immediate environment. As many concepts become familiar via incidental learning, they are smoothly integrated into a child’s linguistic comprehension.
High concentration. Curiosity. Good recall. Mathematical language. One could argue: They all sound good. What’s wrong with developing these?? They are wonderful abilities to develop and use! No doubt. But why should they be learned at the expense of making Mathematics easier to learn? Why should they be fostered primarily to compensate for limitations in the design of Math(s) education materials?
If a movie-camera cannot be rotated, raised, rolled or turned in any direction, then one would have to be pretty inventive in order to make good movies. Even worse, if film was very expensive to use, then mistakes in filming would have to be reduced to a minimum to avoid expensive retakes. The camera’s limitations, along with the budget’s, would ignite the proverbial Necessity that is the Mother of all Inventions. Therefore, movie sets would have to be designed carefully, very methodically. Each shot would have to be pre-conceived, possibly even pencil-sketched from various perspectives. The immobile cameras would need to be placed in precise positions to capture the intended effect. To prevent retakes, actors would need to practice their lines and roles almost to perfection, with no room for mistakes and retakes. The point being made here is that mental abilities galvanized to circumvent limitations, do impel the creative and the perfectionist in us. Ultimately, such movie-sets during earlier years produced giants in the movie-world like Eisenstein, Kurosawa, Fellini and Ray. But those limitations also spurred innovations and improvements. Our creative and imaginative abilities harnessed to today’s digitized movie camera in special-effects techie environments reach higher, more complex levels. They render possible what was once unthinkable. Which is why more people produce more excellent movies today compared to the few memorable ones from earlier decades.
Let’s face it: cars without serious design limitations are simply easier to drive. They enable the driver’s swift mastery of all the operational features e.g. steering, gears, brakes, accelerator pedals, lights, indicators, wipers etc. And mastery lends automaticity to our physical act of driving. The resulting “auto-pilot” mode liberates a wide spectrum of attention for attending to traffic signals and road signs, motorists, pedestrians, road-turns, one-way signals, numbered blocks (when seeking an address), etc. Freedom from the mechanics of driving also helps us relax and attend to more complex mental tasks such as thinking about work-related problems, reflecting upon domestic issues, engaging in a lively conversation with a companion, or toying with abstract ideas. In short, driving a well-designed car, or drinking coffee on a level table, should not demand an excessively high (or peak) level of alertness or attentiveness. As learners attain mastery in the basic skills needed to drive (and drink coffee??), large portions of the brain get disengaged to attend to the more superior function of problem-solving and thinking purposefully and creatively.
The CLSO-MATH Program demands average, not peak concentration. CLSO exercise templates are designed to guide learning in a series of smooth incremental steps. The visual templates arouse curiosity and dispel anxiety because they lure the mind into learning and understanding what once seemed so baffling. Even anxious students feel relieved and become curious to exhibit what they finally understand. Once mastery is achieved in (a) understanding Mathematical concepts (b) reasoning numerically and quantitatively, the learner’s mind is liberated to perform higher level problem-solving tasks requiring peak-level concentration. Summoning such concentration for higher-level thinking (opposed to exhausting it in low-level tasks) makes better economic use of the students’ intellectual energies.
More next week!
Shad
Copyright © Shad Moarif, April 2007, Vancouver, Canada. All rights reserved. No part of “Shad’s Blog” may be reproduced or copied in any form, electronic or otherwise, without the author’s permission.