Category Archives: Education

Future of Education: Khan Academy

Go to KHAN ACADEMY FOR THE WORLD

It is a lot of fun to learn maths here; and it is absolutely free. 🙂

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New Paradigm for Education is needed

TV Mohandas Pai was a Director at Infosys until recently. He is a Chartered Accountant, but his views as a well-informed outsider to the IIT system, are quite relevant. The article was published in The Economic Times.

IITs may become less relevant
By Mohandas Pai

The IITs have completed 50 years and have helped build India. They were set up for producing high quality technical human capital for India and have met their objectives. But, as is the character with such institutions, they have not changed with the times and are not providing India with what she now needs. They have remained largely teaching institutions , as they were set up, not transforming into research based, innovation driven agents of change for the India that is now emerging.They seem unwilling and unable to change – overburdened by work, driven by a small vision, starved of adequate resources and owned by an apathetic master. They seem to be in a state of perpetual decline though there are some bright spots, but not large enough to meet the needs of time.Very recently, a Union Minister made a statement that IITs are known for their world class students and their world class alumni, of which he presumed himself to be one but not world class faculty. Partly true, but forgetting that he and his ilk are largely responsible for this outcome. The IITs today enjoy substantial academic autonomy but lack adequate administrative and financial autonomy . The IIT boards and the directors are unable to take any financial decision which they deem fit without the approval of the government . Even for an overseas travel of the director or the faculty, permission is needed. They are subject to austerity measures of the government, a perfect situation to emasculate an educational institution.

The demand for an IIT seat is enormous and has spawned a tutorial industry that earns more revenues than the IITs themselves. This has resulted in large number of students spending up to two years of their youth going to cramming schools learning pattern recognition, forgetting the art of thinking and problem solving knowing that their lives are made once they get entry into the hallowed portals. Today about 60% or more of the intake is from the coaching mandis. This has also resulted in many bright young Indians deciding not to undergo the ordeal and go overseas for higher education. 250,000 of them study overseas, over 110,000 in the United States, about 45,000 in the UK spending about $ 6bn on fees and costs annually, depriving this country of much needed resources for education and talent, adding to the wealth of those countries. The IITs too have steadfastly refused to change. They remain small by global comparison . They are between 6,000-9 ,000 students in size, with an annual intake of about 500 PhDs, and about 1,000 undergraduates.

Overall , the 15 IITs graduate 7000 undergraduates, 6000 post graduates and about 1700 PhDs annually . Sadly only about 2% of the undergraduates go on to their masters and PhD in the IIT system. The IITs hold fast to the idea that by squeezing input they can get a quality output, an idea that has been consigned to the dustbin of history. Increasing the scale and size can give them the diversity of talent, the resources, the ability to have more quality faculty and the depth and width needed for an elite educational institution. Even the current increase in size was forced on them because of social initiatives. Contrast this with China. China today has about 1,000 universities, each between 25,000 to 40,000 students, running fully residential courses, turning out over 50,000 PhDs annually . China may, in the next 20 years, it will overtake the United States as the world centre of higher education.The Top Five Chinese universities , in the global top 50 now, have between 25,000-35 ,000 students and about 7000 PhD students each. China has invested for growth through quality institutions while India has lost out and is oblivious to it. Even in comparison to the engineering education system in India the IITs have become insignificant today. 10 years ago the IITs made up about 10% of India’s engineering output of human capital. Today they are less then 2% and declining further. India currently has about 3800 engineering colleges with an annual intake of 1.2 million, a size to rival China. Yes, about 50% of the colleges are of indifferent quality, some rank bad; but they are offering an answer to India’s youth. About 1,000 of them are of reasonable quality , very many have improved over time. No university or college was founded great, they evolved over time, so there is hope for India that these bad colleges will provide the sinews for India’s growth and answer the need of India’s young.In the meantime, the IITs will live in their ivory tower and possibly become less and less relevant to India’s need as neither are they meeting India’s need for more human capital nor producing the kind of PhDs India needs. What needs to be done to change this? The government has all the answers setting up many eminent committees, the latest of which is the Anil Kakodkar Committee of which the author is a member. The solutions are known to all, the government, the policy makers, the academics and the intelligentsia .

Total autonomy to the IITs, driven by a board of governors with a new vision, accountability through public opinion and transparency. Yet there is resistance to change, from government for the fear of losing control, from some part of academia because they become more accountable and lose the shelter of blaming the government for all ills and for inadequate performance and from some opinion makers who believe that the existing feudal system should continue since they have a disproportionate influence on them.

The best solution is to open up the education system and allow competition, the dreaded word in academics, to come forth. India should revise her educational policies and allow the private sector to set up “innovation universities” granting them all that they need. Full autonomy, academic, administrative and financial to chart their own future. Some safeguards are needed, as this is a public good. A large corpus of say Rs 100 crore, an open merit based admission policy, a faculty compensation policy based on minimum UGC scales and an assurance that they will aim to be amongst the top 100 in the world over the next 25 years. To ensure access to the merited we need a national scholarship scheme which will fund students. India needs to trust the genius of her citizens to create institutions that are world class and not look at them through myopic eyes with suspicion.

India’s future is too important to be left to the benevolence of an apathetic, insensitive government which has destroyed academic excellence over the years, driven her young out and even today shows callous indifference. See the state of our universities today, so many have fallen from the high standards they had, see the state of the Presidency Colleges, it is indeed sad! Most policy makers and leaders have solved their personal issues by sending their children out to get a good education, so they are not impacted by the poor quality of higher education in India. It is the middle class and the poor who suffer, because they love their country more and see their future here; maybe they too want to take flight but do not have the resources to. As the saying goes “Yankee go home, but take me with you.” But will competition work? Yes, it will indeed.

The engineering colleges have opened up, very large numbers set up by political influence and plain bribery but they have served another purpose. Today there is a flight to quality. The bad colleges are dying since students have a choice, they are voting with their feet. The good ones are expanding and seeing greater demand. The market mechanism has worked, not by design but by serendipity. So there is hope. Look at various other sectors today. Bharti has made BSNL redundant and has given us a choice, Jet has overtaken Air India and given us a choice, the power system in Mumbai is still the best, and in education the Indian School of Business has turned our IIMs inside out. The IIMs actually want reform, expansion and are concerned about their future .

Competition and an open liberal environment for higher education will work . India’s best higher education institution, the Indian Institute of Science , was started by a private citizen many years ago and is still the best we have. India’s needs in higher education are too large to be met by the government , they need the genius of India’s citizens to meet them.

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Looking at Knowledge

knowledge paradigm

Please see Course on Subject Clearing

From Wikipedia: Knowledge is a collection of facts, information, and/or skills acquired through experience or education or (more generally) the theoretical or practical understanding of a subject. It can be implicit (as with practical skill or expertise) or explicit (as with the theoretical understanding of a subject); and it can be more or less formal or systematic.”

Knowledge is acquired through personal experience, but much of it consists of the use of observations made by others. We absorb this knowledge when we listen to our parents, go to school, go to the church, work on a job, read books and use Internet.

Full benefits may be obtained from observations made by others only when we can grasp the facts as clearly as the original observer grasped it through direct experience. As knowledge travels via different routes, and passes through various hands, it may acquire opinions and distortions. A person, looking at the knowledge coming from others, may not know of the distortion present. It is important to detect such distortion and the underlying filters. This is especially true when one is looking at the fundamentals of a subject.

Knowledge is imparted primarily via written and spoken “words” (NOTE: “Word” is used here to include all symbols). Therefore, the first step in looking at knowledge is to recognize the meaning of words that are being used.

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Words and their meanings

We have dictionaries available to help us find the meaning of words. When doing so, keep in mind that words have evolved over time and they have acquired different shades of meanings.

(1) Start with the root meaning of the word.

A good place to start would be to grasp the common denominator of the various meanings attributed to a word. The derivation of a word may help you understand how the various meanings have evolved. Look up the derivation of the word first. Follow the derivation back to its roots to find the “root meaning.”  For example, when you follow the derivation of the word study, you may come up with the root meaning “eagerness.” This may be the common denominator of the various meanings of the word study as “eagerness to know.”

Dictionaries usually provide useful derivations of words. You may use dictionaries on Internet, such as, link http://dictionary.reference.com. To really get the history of a word, you may have to go to a reference, such as, “Dictionary of Word Origins” by John Ayato. Check out the derivation and history of the word arithmetic.

(2) Look up and visualize the various definitions of the word.

Next, look up the definitions provided for that word. As you look at each meaning, relate it to your experience and visualize it in your mind. If the word is exuberant then look at the times when you felt exuberant, or perceived somebody else being exuberant. It is much easier to visualize when the word refers to something concrete. You can find the actual thing to look at, or you may find a model or, at least, a picture of that thing. For example, for the word archipelago, you may easily find models or pictures in an encyclopedia or on the Internet.

If the definition refers to something abstract, then you can still find examples that illustrate that idea or concept. For example, the word ineffable is very abstract; but you can find enough examples to define it for yourself. Look up as many examples as necessary, and follow it up with your own examples. You may even work out how ineffable is that way, or not that way until it starts to make sense. Use your experience and visualization.

(3) If there are words in definitions that you don’t understand then look them up too. 

It is possible to get into long word chains when looking up the words in definitions, but this needs to be done. Keep in mind that words are only approximations. What is important is getting a clear visualization of what is meant. So, get enough understanding of the word to be able to visualize the context. Keep on visualizing that word in different contexts until suddenly the meaning becomes clear.  A skillful use of visualization may help you keep the word chains short.

Keep a record of the words as you look them up. Cross out a word as soon as its meaning is understood. Sometimes a word may come up again that you had looked up earlier. But this time it may be used differently. It is okay to look up the same word as many times as necessary. Each time you look up a word you may pick up a new dimension of its meaning.

(4) Select the definition that clarifies the context the most.

A dictionary may provide several definitions for a word. Check out how each definition fits into the context through visualization. Even if the right definition is not there, the visualization will help you work it out. Once you have a clear idea of the meaning that fits in that context, use that word in several sentences. This is so that you feel comfortable with using the word when writing or speaking.

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Subject and understanding

Sorting out the meaning of words, as above, removes the initial hurdle in understanding a subject. But the distortion due to unknown filters (viewpoints) may still be present. The following steps may help detect unknown curves present in a subject.

(1) List the key words of the subject.

Scan through the material to be studied and list all the key words. These are the words that carry the key concepts. For example, in the subject of mathematics, some of the key words are: mathematics, arithmetic, algebra, geometry, number, addition, subtraction, multiplication, division, equation, unknown, variable, space, and direction, distance, position, etc. This list may grow as you get deeper into the subject. Words may also be added as the definition of a word may refer to additional words in that subject that may carry key concepts.

(2) Arrange the key words in the sequence in which the concepts have evolved.

Start by arranging the words in the sequence that they appear in the material being studied. As you gain familiarity with their meanings, keep rearranging the key words in the sequence they seem to have evolved. Move the words embodying more fundamental concepts toward the top. Move the words embodying derived concepts toward the bottom. You may attach brief clues to the words as to what they mean.

(3) Use the list as the “context” in which to understand the key words.

Go up and down the sequence of the key words. Clarify and align the meanings further as necessary. Notice any gaps or inconsistencies and try to resolve them. Include them in your list if they cannot be resolved.

(4) Study the subject in detail to resolve gaps and inconsistencies.

The purpose of study is not to memorize any information, but to resolve gaps and inconsistencies in understanding. What you already understand should be of no further concern. Make sure you understand the materials as you proceed. The moment some material start to become confusing, stop and locate the source of confusion. Clear the confusion; or, at least, note it down in your list, before proceeding further.

Note that there are likely to be many contributors to a subject. For example, you may look at religion as a subject contributed to by many different cultures. You may find different contributors referring to similar concepts by different key words. Add such keywords to your List. If more than one key word seems to embody the same concept, then note down the similarities and differences among the meaning of those key words.

(5) Clarify the fundamentals of the subject as a priority.

Your Key Words List may branch out and grow into an inverted “Key Words Tree” as you move lower and lower down the list. The gaps and inconsistencies at the lower part of tree may depend on those at the top. It is, therefore, worthwhile to start addressing the gaps and inconsistencies closer to the top as a priority. This is where the fundamentals of a subject would reside.

Study the fundamentals from various sources. You may create a Key Word List or Tree just for these fundamentals. It is the most important part of any subject. You may create experiments where you find obvious gaps in the fundamental knowledge. Fill these gaps with research and make the whole subject as much complete and consistent as possible.

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Gaps and Inconsistencies

It is believed by many that, “God created the universe” and that “God is good.” An inconsistency comes about when one observes that there is evil in this world. Rationalization then enters into the picture in the form of Satan who is created by God, but who has a mind of his own. One then wonders if it is bad to have a mind of one’s own. Any consistency then just falls apart.

Again, if God created the universe then God must have created space too. Then, God would have no location in space in the beginning. Similarly, God will have no form or identity either.

These are some obvious examples of inconsistencies that indicate that there are gaps in knowledge that are rationalized by a large number of people. A gap in knowledge would be obvious if one simply looks and does not rationalize. It is rationalization of such gaps that generates inconsistencies in knowledge.

The whole concept of looking with mindfulness goes against rationalization. It makes the gaps stand out quite uncomfortably clear. However, mindfulness is necessary if any progress is to be made in the field of knowledge.

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The Ultimate Filter

Rationalization comes from attachment to one’s ideas or considerations. One wants one’s considerations to be right. But, more important than any one consideration being right, is the consistency among all considerations.

The more basic is a consideration the stronger seems to be the desire for it to be right. Thus, the strongest attachment seems to be to the idea of self. Even when the body is known to be mortal, one still wants to believe that one is immortal as soul or spirit. This is believed almost universally. In all religions, self is believed to be everlasting.

There is nothing wrong with having such ideas and considerations. It is the attachment to these considerations which creates a filter. It attaches unnecessary importance to those considerations and prevents one from researching and filling the gaps in knowledge.

The attachment to self seems to be the ultimate filter that distorts knowledge.

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Summary

Any subject must be looked at mindfully starting with its concepts expressed as key words. The key words should be listed starting with those that express the fundamental concepts followed by those, which are derived from earlier concepts.

As the study of the subject progresses and better understanding comes about, the list of key words may be continually rearranged to achieve a sort of consistency of ideas. This may reveal inconsistencies and gaps in understanding. This then motivates research deeper into the subject.

The consistencies of the fundamental concepts in a subject are far more important as that affects all the derived concepts. Thus, any worthwhile research shall naturally gravitate toward the study of the fundamentals of any subject and the consistency therein.

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Filling the “Blanks”

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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The Earlier “Blanks”

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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