Monthly Archives: April 2011

Filling the “Blanks”

April 14, 2011 – 7:45 PM

Reference: Subject: Education

[This is the third essay on Study from 1996.]

“Blanks” in understanding cannot be filled properly unless one starts out very simply and then proceeds on an easy gradient of increasing complexity.  For example, when tutoring on addition, one should start out with single-digit numbers before working with double-digit numbers and carry overs.

In a Math Club meeting, a second grader was having difficulty writing large numbers in spite of repeated attempts by the parent to assist her.  A troubleshooting session went something like this:

TUTOR:           “Is it ok if I ask you to write some numbers for me?”

STUDENT:      “Yes.”

TUTOR:           “Alright.  Can you write six thousand, seven hundred

____________ eighty-three?”

STUDENT:      “Umm…”

TUTOR:          “That’s ok.  See if you can write seven hundred eighty-

____________ three?”

(The student thinks for a moment and writes “700 83”.  The tutor noticed that she could write eighty-three correctly.)

TUTOR:           “Ok.  Can you write eighty-three for me?”

(The student smiles and writes “83”.)

TUTOR:           “Excellent.  Can you write one hundred?”

(The student writes “100” correctly.)

TUTOR:           “Very good.  Now, can you write one hundred one?”

(The student writes “101” correctly.  The tutor then asked the student to write “one hundred nine” and “one hundred ten”.  The student wrote them correctly.)

TUTOR:           “Excellent.  Can you write one hundred eighty-three?”

(The student pauses then writes “183” correctly.)

TUTOR:           “That is correct.  Now write seven hundred eighty-three

____________ for me?”

(The student feeling more confident writes “783”.)

The troubleshooting session was ended at this point.  The parent then continued in this manner with the student writing larger numbers successfully.

This demonstration illustrates the necessity that a student’s understanding must be established at each step on a gradient for learning to occur.  This can be done only by letting the student assimilate the data by himself or herself.  The tutor must not think for the student.

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By vinaire | Posted in Education | Comments (0)

The Earlier “Blanks”

April 13, 2011 – 8:36 PM

Reference: Subject: Education

[Here is another essay on Study from 1996.]

A “blank” is created in the mind by a “concept not fully understood.”  Such blanks prevent later concepts from being understood and, thus, multiply themselves rapidly.  In trouble-shooting, if a student is unable to grasp a concept, it is certain that there is an earlier concept not fully understood.  The following case demonstrates the effect of earlier “blanks.”

Once, a mother came to the Math Club with her daughter who was in fifth grade.  The daughter was having great difficulty in math.  According to her mother, she did not want to memorize the multiplication tables, and that was the problem.  The troubleshooting went something like this:

TUTOR:          “Is there something in math you don’t feel quite

____________ comfortable with?”

STUDENT:      “Yes… multiplication.”

TUTOR:          “Alright.  What does the word MULTIPLY mean?”

STUDENT:      “Umm…” 

(The tutor explained the process of multiplication as “repeated addition.”)

TUTOR:          “I am going to check you out on the multiplication of

____________ two single-digit numbers.  What is three times two?”

STUDENT:      “Six.”

TUTOR:          “What is four times three?”

STUDENT:      “Twelve.”

TUTOR:          “What is six times six?”

STUDENT:      “Oh, that’s a big number.”

(The student could multiply with very small numbers, but got nervous when larger numbers were asked.)

TUTOR:          “Six times six would be adding six to itself six times.  Can

____________ you do this addition and tell me the sum?”

STUDENT:      (Pause)  “Oh! I don’t like adding either.”

(The tutor then demonstrated the process of addition as “counting together.”)

TUTOR:          “Adding is counting numbers together. Are you comfortable

____________ with counting?”

STUDENT:      “Yes, I can count.  One, two, three…,”

TUTOR:          (Stops her at the count of twenty)  “Very good.  Now count

____________ for me starting from eight hundred ninety.”

STUDENT:      (Taken aback) “Oh! That is a big number… (thinking) eight ____________ hundred ninety-one, eight hundred ninety-two… (and so on) ____________ eight hundred ninety-nine (long pause) two hundred, two ____________ hundred one…” 

The student did not know what number followed eight hundred ninety-nine.  By this time it was evident that the student was shaky in her understanding of the numbering system itself.  She was not aware of the repeating pattern of hundreds in counting.  The troubleshooting was ended at this point.  The mother was given a program to establish an understanding of the numbering system first before working with her daughter on multiplication.

Evidently, the understanding of MULTIPLICATION depends on an understanding of ADDITION, which in turn depends on an understanding of COUNTING and the NUMBERING SYSTEM.  If a person has simply memorized the sequence of first few hundred numbers, and has no understanding of the patterns of tens, hundreds, thousands, etc., he or she will have difficulty not only in counting with large numbers, but also with addition and multiplication.  This principle of earlier “blanks” applies not just to mathematics but to any subject one is having difficulty with.

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By vinaire | Posted in Education | Comments (0)

“Holes” in Understanding

April 12, 2011 – 6:51 PM

Reference: Subject: Education

[I wrote this essay back in 1996 when I was running a Math Club. This student went on to study later at Harvard, Cambridge, USA.]

If there is a virus, which can infect and incapacitate the thinking of a person, it is a “hole” created in the mind by a “concept not fully understood.”  Such holes prevent later concepts from being understood and, thus, multiply themselves rapidly.  Sometimes they are well camouflaged and hard to detect until they have multiplied to a great extent.  Their effects show up in the declining curiosity and interest of a child long before his or her grades start to slip.  Due to pressures at school and at home, a child still tries to keep the grades up by memorizing his materials.  The remedy to this situation is to “fill in the holes.”

Once, a parent came to me very much worried about his son.  According to him, his son was slow in study across the board and could not remember what he studied.  He was in seventh grade, but he could do math only up to fourth grade level.  The parents were so worried that they were considering taking their son to a psychiatrist.  Upon checking it was found that this student had been moved around to different schools as the parents tried to settle down in their business.  Upon consultation, a program was worked out to tutor the child at least four hours a week during the first month.  The parents agreed to defer any psychiatric treatment until the gaps in their son’s understanding were located and filled.

The first few sessions were quite interesting.  The student was compliant and easy to work with.  A short list was made of areas in math that he was confused about.  These areas were then addressed one by one.  The basic approach was to check the key concepts in each area to find what was misunderstood and then to clarify it.  Each confusion was traced back to the most fundamental concept which was not understood.  Once the basic concepts were explained, later concepts could be fully clarified.  An interesting discovery was that this student, who could not remember, had no difficulty retaining the basic concepts once they were fully comprehended.  A foundation in math was being built up slowly by locating and filling the “holes” one by one.

During these sessions, “holes” were found not only in math but also in Grammar, Science, and other subjects.  These were clarified as and when they came up.  However, the main focus was kept on math.  At times the student needed help on his current homework, and it was addressed by giving him working knowledge of the advanced concepts.  But as soon as he was through with his homework, the underlying concepts were addressed.  Things were discovered which he should have known, but he was never taught.  Soon the student’s interest and confidence started to improve.  He understood the importance of not going past a word or a concept until it was fully understood.  In addition, he was encouraged to become more curious.  He now had questions about things, such as, INFINITY, SPACE, ATOMIC BOMBS, and even UFO’s.

In a period of three months, a definite improvement was visible in the student’s grades.  Tutoring continued with much less intensity for another two months.  Summer arrived, and there were no more sessions.  Six months later when I happened to run across the parent, I found him quite satisfied with his son’s performance in school.  The boy was getting A’s in math and doing quite well in other subjects too.  He never went for any treatment.

The parent, however, was more impressed with something else.  The son was now spending more time reading the text books on his own.  He used a dictionary to clarify the meaning of words as he studied.  He now followed a discipline because he understood what “holes” could do to his thinking.  This student was not about to let the “holes” have their way again.

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By vinaire | Posted in Education | Comments (0)

Approach to Looking #2

April 12, 2011 – 6:33 AM

October 2, 2013: This essay has been superseded by:

KHTK EXERCISE #3: Unwanted conditions

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When no incident, confusion, shift or shock comes up in Approach to Looking #1 then approach as follows:

(1)   Look at the area absorbing most of your attention, and locate

(a)   Persons attached or connected to it

(b)   Places or locations attached or connected to it

(c)   Incidents or events attached or connected to it

(d)   Times or moments attached or connected to it

(e)   Situations or circumstances attached or connected to it

(f)    Anything else that comes to mind in connection with it

(2)   If at any time you spot when the condition, which is absorbing most of your attention, started then make a note of the fact.

(3)   If the attention goes back again and again to the moment when that condition started then apply Approach to Looking #1 to that area.

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By vinaire | Posted in Self-Improvement | Comments (0)

An Analysis of Cause

April 10, 2011 – 10:18 AM
Cause

The following statement seems to summarize very efficiently what is believed in most western religions and philosophies.

“Before the beginning was a Cause and the entire purpose of the Cause was the creation of effect.”

Judaism emphasizes God as the ultimate creator. Christianity makes God a personal being. Islam seems to de-emphasize that identity of a personal being by declaring God to be formless. However, God is still retained as the cause of all existence.

Spinoza starts his philosophical system with the premise of “uncaused Cause.”  Aristotle starts his philosophical system with the premise of “unmoved Mover.” The system of philosophy that follows from either premise is pretty rational. But the underlying premise is at best arbitrary.

Regardless of how rational a system of philosophy might appear, the logical consistency of that system is set by its starting postulate.

Let’s examine the premise of “Cause.” It is taken for granted by the western religions. Cause is supposed to be there before the beginning of a manifestation. The question then arises, “Can Cause be there all by itself before its effect manifests itself?”

If the answer is “yes” then Cause will be a manifestation on its own right. The question then becomes, “What is the cause of the Cause?” This logic inevitably leads to an endless chain of causes, and the beginning keeps getting pushed back earlier and earlier.

If the answer is “no” then the “Cause” must occur simultaneously with effect. “Cause-effect” would then be part of the same manifestation as the beginning. The idea “before the beginning” would then be a projection that is created after the fact of beginning.

Cause is a projection backward that is created after the fact of beginning.

This is consistent with the idea that time itself would start at the beginning, and there would be no such thing as “before the beginning.” Cause would, therefore, be a consideration created at the beginning. As there is no “before the beginning,” Beyond the beginning would be unknowable. See Knowable and Unknowable.

The premise “uncaused cause” seems to be an attempt to fix the unwieldy conclusion of the endless chain of causes when Cause is assumed to exist all by itself.  “Uncaused cause” is just another arbitrary consideration. No wonder it appears to be self-contradictory.

“Uncaused cause” is a consideration that is self-contradictory.

CAUSE is part of the creation, and has no meaning prior to the creation as assumed in the statement at the beginning of this essay. Neither “Cause,” nor “Uncaused cause” is an independent premise. It is part of the system of philosophy it generates.

The system of western religion and philosophy is made up of interdependent considerations. They are not linear but they form more like a circle. We may visualize this system as a sphere of consideration, which is ballooning out from a premise at its center. The premise is forever contained within this sphere; and it cannot lead to anything beyond that sphere.

What is beyond the sphere of considerations may only be speculated. But a speculation being a consideration would remain within that sphere.

The assumption that the consideration of “Cause” can extend beyond the “system of considerations” seems to be the basic inconsistency.

“Cause” may appear to be consistent but only within a system of consideration and not beyond. What is beyond is unknowable and it cannot be symbolized as Cause.

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Glossary

Starting Postulate
No matter how rational a system of philosophy might appear, if the starting postulate is inconsistent, the whole philosophical system would ultimately become unsustainable. The starting postulates, such as, “uncaused cause,” and “unmoved mover” are inconsistent in themselves. Therefore, the philosophical systems based on such postulates have become unsustainable in spite of all the effort to make them appear rational.

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By vinaire | Posted in KHTK | Comments (45)