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vocabularization

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Hello everyone,

Howard Roark in ‘The Fountainhead’ says, “We inherit the product of the thought of other men. We inherit the wheel. We make the cart. The cart becomes an automobile. The automobile becomes an airplane. But all through the process what we receive from others is the end products of their thinking. The moving force is the creative faculty, which takes this product as material, uses it and originates the next step”

And a question arose in my mind: how do we take the end products or more precisely how are we taught to take the products of the creators?

I have penned my views in this article about how things are being taught to young students.

.........................................................................

Do you know what is ‘malus pumila’?

Of course you do, but the term 'malus pumila' is alien to you. It is the scientific name for apple, a fruit so common to all of us. The point being made is one cant attach any intrinsic value to knowing the term 'malus pumila' as, not knowing it will not diminish your taste for it, nor would it render you incapable of acquiring one.

Let me give another example to reinforce my argument, knowing that there are 12 inches in a foot and 3 feet in a yard have no intrinsic value attached to it because, if you are in a country where the metric system of measurement is prevalent this knowledge is useless.

Of course one may say that the knowledge of the scientific term for apple has no value for a layman but is significant for a student of botany, in the sense that it is elementary and a proficient student is expected know this much. But at this point many make the mistake of putting the cart before the horse, that is, assuming that the one who knows the elementary terminology essentially is proficient in his field.

So to make the knowledge of vocabulary as the basis to gauge ones proficiency is logically incorrect.

Because a person might have done a path breaking research on the medicinal properties of apple and still be stumped when asked, what is ‘malus pumila’?

But what happens when students are in fact asked the same question again and again?

The students stop worrying about everything else. When the students realize that it is the rote memory that is being rewarded you no longer expect them to think (the tendency to do least work-as perceived, to reap the same reward is one of the reasons…….but we’ll come to it later).

Students, to coin a new word, start to vocabularize knowledge.

Vocabulary in this context means: the knowledge that is non-applicable or in more general terms ‘non-amenable to reason or manipulation’. And the term vocabularize refers to the process of assimilating useful knowledge in a way so as to render it non-amenable to reason or manipulation, or in other words accepting truth as uncorrelated list of names.

One of the extreme forms of vocabularization is manifested when students are unable to carry out basic operations in calcuus when applied to elementary engineering problems despite the fact they have learnt the subject (calculus) in great detail.

The Modus operandi of vocabularization essentially consists of knowing the ‘end-product’ and understanding the ‘what’. As opposed to the rational method of knowing and understanding the ‘initial conditions’ and following the dynamics that make the end product possible.

The end product here is any artificial creation of human mind and labor and hence the domain of the discussion is about the way we understand and apply abstract concepts like the calculus and the way we learn (analyse) and later design material objects like an earthen dam or a bridge.

The initial conditions are the requirements or the inspiration (the original rudimentary idea of the creator) that trigger the process that culminates in an end product.

Dynamics here mean the interpretation and application of the laws of the nature using his imagination and creativity by the creator to come up with the end product.

Vocabularization bypasses the law of causality and accepts the end products as thunderbolts out of blue that strike for ‘some reason’ of their own.

This acceptance of an end product presupposes the validity of dynamics and ignores the initial conditions, thus obviating the need to understand the ‘some reason’, hence minimizing work.

From the forgoing discussion it follows that Vocabularization by the students is only a response to the teachers asking the ‘what’ and not the ‘why’. But the objective is only to minimize work (which is not an irrational thing per se)

What gives the students the sanction to vocabularize is the belief that an understanding of the ‘some reason’ is unnecessary.

The root lies in the lack of respect for the individual capacity, the habit of escaping from responsibility and taking refuge in the ability of others.

From this stems the notion that ‘I am’ not capable enough to comprehend a thing that others accept as such.

That’s why the teacher assumes that the person who writes the book is always correct

(He takes refuge in the judgment of the publisher and the thousands others like him.) And tells his students to accept what he has to feed them on his authority. Any question from the students is taken to heart not because it challenges his conviction (he has no conviction of his own) but because it undermines his faith in others.

So the creative faculty of the student gets progressively deteriorated, as the only thing he is taught to do is to repeat mechanically the procedures elaborated by others, and study passively the things made by others.

In other words the student is trained to learn by observation, observing the existing end products as they exist and reproducing them as an when necessary.

Here the pragmatic person would interject: isn’t this the simplest of all methods which even the least intelligent person can use as it involves nothing more than a keen sense of observation.

The answer is NO. The rational method ensures that every possible end product can be explored as this method presupposes only a reasoning mind and the knowledge of the laws of the nature. On the other hand the person habituated to learn by observation can’t conceive of the ramification of even a slightest change in the initial conditions and needs to observe still more end products to find the one that suits the changed initial conditions. An end product, which may not exist in the first place. But a pragmatic person can’t wait for want of ideas, so the expediency of the situation allows for a poor imitation.

So to view the problem from another perspective the difference in the two methods lie in the amount of knowledge and the degree of understanding and creativity required.

So the pragmatic is incorrect on the count that to learn by observation is the simplest and the most practical way of learning. So are the students who vocabularize in order to minimize work when in fact they are choosing the most cumbersome way.

The system of learning by observation is faith masquerading as reason. It is a refuge of the second-handers and such a system of learning only produces second handers whose very existence primarily depends on others and unaided are incapable of doing anything.

Whereas a reasoning mind, from a rational approach is capable to create new ideas and build things ab-initio.

And it is to these reasoning minds who in most cases started form the scratch that the mankind owes the progress from the cave to the skyscrapers.

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I would agree in general, but I disagree with some minor points.

Its not always possible to teach someone 'why' the end process works. It is a lot easier to teach a highschool student how to do rudimentary calculus than it is to explain to them why this calculus works, since the latter normally requires several semesters of college level Analysis courses. Likewise, its easier to give highschool children the end products in chemistry than to expect them to learn the quantum physics which they are based on. Sometimes the explanations are a _lot_ more complicated than the final answers, to the degree where teaching them to the average high school student is both time consuming and perhaps futile (You could also argue that it is largely pointless. Almost nobody 'needs' to know why calculus works in great detail, unless they plan on a career as a mathematician. You could be a highly successful engineer without having once went near a textbook offering a rigorous treatment of limits).

Ideally we would try to find a happy medium - students dont have to know the justification of a process/answer in excrutiating detail, but at the same time choosing to simply present them with a few forumulae accompanied by a blithe 'hear you go, memorize this' certainly isn't condusive to encouraging rational thought. It would be best to find middle ground, where the details are outlined in an oversimplified way, so that the students can sort of understand where the answers are coming from, without getting bogged down in too much detail. I remember something similar happening in my high school physics class - we started off being told to think of atoms as being solid spheres (the Dalton model) while also being informed that this wasnt strictly true and was hideously oversimplified. As we progressed our models got more refined, but we were constantly being told that the information we were being given was tailored to 'our level', rather than being at the cutting edge of modern physics. I think this kind of approach works because it allows the students some degree of conceptual understanding of the material, without causing confusion by exposing them to advanced material which they simply do not yet have the intellectual tools to cope with (indeed physics was one of the very few highschool classes in which I actually felt I was being treated as a being with some degree of intellect, rather than as a tape recorder expected to learn a host of data for which I had no perceived use.)

Having said that, I would definitely also say that the students who are genuinelly interested in learning about things more advanced than those taught in standard class should be both helped and encouraged. Those who are intellectually curious and/or talented should certainly be exposed to more advanced material, which is something that unfortunately I don't think happens enough in the current education sysetm.

By the way, I think that "Whole Math" tries to move away from rote memorization, and attempts to engage children creatively instead. I know little about it myself, but it has been criticized fairly heavily on capmag for being 'irrational' or something. Possibly a case of "right idea, terrible implementation", but I dont know enough about it to say.

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By the way, I think that "Whole Math" tries to move away from rote memorization, and attempts to engage children creatively instead. I know little about it myself, but it has been criticized fairly heavily on capmag for being 'irrational' or something. Possibly a case of "right idea, terrible implementation", but I dont know enough about it to say.

It's as invalid an approach as "ethnomathematics." It's a product of so-called "Progressive" education, which also gave us the "whole word" method of reading--which has been thoroughly discredited by innumerable intelligent and reputable people, Objectivist and non-Objectivist alike. Far from "engaging children," the methods of Progressive education fail miserably at teaching children anything (with the result that they end up bored and hating school), and in fact stunt their cognitive development by keeping them on the perceptual level.

Tell me, where in math, of all subjects, is there room for "creativity"? Math (in the context of the grade school level, anyway) is largely composed of mechanical algorithms, and no points should be given for a "creative" approach if an incorrect answer is given (which is what the "whole math" gang advocates).

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Tell me, where in math, of all subjects, is there room for "creativity"?  Math (in the context of the grade school level, anyway) is largely composed of mechanical algorithms, and no points should be given for a "creative" approach if an incorrect answer is given (which is what the "whole math" gang advocates).

Where do you think the algorithms come from? Telling someone to memorise a bunch of algorithms that other people have discovered does not generally help to impart the creative skills necessary to invent algorithms for yourself. I think it would be better for a child to think in a 'mathematical' way and come up with the wrong answer than it would be for them to know the right answer because they learned it out of a book.

Obviously if youre an engineer there's generally little need for you to be able to invent 'new maths', but if you want to be a mathematician or theoretical scientist, these things become important.

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Where do you think the algorithms come from? Telling someone to memorise a bunch of algorithms that other people have discovered does not generally help to impart the creative skills necessary to invent algorithms for yourself.

Which is why I specified the context of grade school. Kids have to learn the basics before they can start theorizing.

I think it would be better for a child to think in a 'mathematical' way and come up with the wrong answer than it would be for them to know the right answer because they learned it out of a book.
Why don't you do some research on this "whole math" method and then tell me whether it's what you have in mind.

Obviously if youre an engineer there's generally little need for you to be able to invent 'new maths', but if you want to be a mathematician or theoretical scientist, these things become important.

Then that's something that they would do in college--not kindergarten.

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I would agree in general, but I disagree with some minor points.

Its not always possible to teach someone 'why' the end process works. It is a lot easier to teach a highschool student how to do rudimentary calculus than it is to explain to them why this calculus works, since the latter normally requires several semesters of college level Analysis courses. Likewise, its easier to give highschool children the end products in chemistry than to expect them to learn the quantum physics which they are based on. Sometimes the explanations are a _lot_ more complicated than the final answers, to the degree where teaching them to the average high school student is both time consuming and perhaps futile (You could also argue that it is largely pointless. Almost nobody 'needs' to know why calculus works in great detail, unless they plan on a career as a mathematician. You could be a highly successful engineer without having once went near a textbook offering a rigorous treatment of limits).

Ideally we would try to find a happy medium - students dont have to know the justification of a process/answer in excrutiating detail, but at the same time choosing to simply present them with a few forumulae accompanied by a blithe 'hear you go, memorize this' certainly isn't condusive to encouraging rational thought. It would be best to find middle ground, where the details are outlined in an oversimplified way, so that the students can sort of understand where the answers are coming from, without getting bogged down in too much detail. I remember something similar happening in my high school physics class - we started off being told to think of atoms as being solid spheres (the Dalton model) while also being informed that this wasnt strictly true and was hideously oversimplified. As we progressed our models got more refined, but we were constantly being told that the information we were being given was tailored to 'our level', rather than being at the cutting edge of modern physics. I think this kind of approach works because it allows the students some degree of conceptual understanding of the material, without causing confusion by exposing them to advanced material which they simply do not yet have the intellectual tools to cope with (indeed physics was one of the very few highschool classes in which I actually felt I was being treated as a being with some degree of intellect, rather than as a tape recorder expected to learn a host of data for which I had no perceived use.).

i am flabbergasted........you have only paraphrased me.....so what are the 'some minor points' on which you disagree.........

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Do you know what is ‘malus pumila’?
malus pomum--bad apple, apple is pomum.
knowing that there are 12 inches in a foot and 3 feet in a yard have no intrinsic value attached to it because, if you are in a country where the metric system of measurement is prevalent this knowledge is useless.
Unless you have a ruler with you.
So to make the knowledge of vocabulary as the basis to gauge ones proficiency is logically incorrect...But what happens when students are in fact asked the same question again and again?  The students stop worrying about everything else. When the students realize that it is the rote memory that is being rewarded you no longer expect them to think
I think you've picked a poor example for what you are trying to say, by complaining about the necessity of naming it. Identifying something by a label like apple is not limiting. From there you can go on to identify different apples, etc. If however the teach denied the existence of different varieties or called the different varieties pear, grape, etc., I could cognitive damage being done.
The Modus operandi of vocabularization essentially consists of knowing the ‘end-product’ and understanding the ‘what’. As opposed to the rational method of knowing and understanding the ‘initial conditions’ and following the dynamics that make the end product possible.

The end product here is any artificial creation of human mind and labor and hence the domain of the discussion is about the way we understand and apply abstract concepts like the calculus and the way we learn (analyse) and later design material objects like an earthen dam or a bridge.

Here your point makes more sense in the realm of creativity and production. Again naming an apple is a bad analogy.

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Vocabularization bypasses the law of causality and accepts the end products as thunderbolts out of blue that strike for ‘some reason’ of their own.
I may be dense, but again identifying something has nothing to do with causality. Just because I know what a bridge is, does not prevent me from building it, but I feel no guilt in not learning how to build it. I don't want to.
From the forgoing discussion it follows that Vocabularization by the students is only a response to the teachers asking the ‘what’ and not the ‘why’. But the objective is only to minimize work (which is not an irrational thing per se)

What gives the students the sanction to vocabularize is the belief that an understanding of the ‘some reason’ is unnecessary.

I believe this happens more in the arts and in liturature than it does in science. I know many people who can name an author's works but have no clue as to what they contain.
The system of learning by observation is faith masquerading as reason. It is a refuge of the second-handers and such a system of learning only produces second handers whose very existence primarily depends on others and unaided are incapable of doing anything.
Mass education is aimed at the mediocre. Schooling does not equate with enlightenment. I think most of us agree.
ab-initio.
ab orsus? ab infinitio?

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