“Holes” in Understanding

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Reference: Critical Thinking in 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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