National Knowledge Commission on Math Education: Macaulay II?

Why did science management fail so badly in post-independence India?  Are we repeating the same mistakes? Why do we mindlessly imitate the West in science and math? Why do we regard Western formal math as superior  without ever having carried out a comparative evaluation? Are our science and math “experts” even capable of carrying out such a  comparative evaluation? Do they avoid public debate and prefer to operate behind closed doors just to hide their lack of capability? From what sources do they get (or hope to get) their wealth?

Here are some answers—background propositions and documents—on which  my objections to the National Knowledge Commision recommendations are based.

Background propositions (argued in detail elsewhere)

 

1. Science management in post-independence India. Was science mismanaged in post-independence India? Perhaps not. The managers lived luxuriously—just look at Bhabha’s TIFR or BARC, or Narlikar’s IUCAA. They could readily explain why the vast investments in science in post-independence India led to little improvement in quality of life for others; or why the performance of individual scientists too was worse after independence. National Knowledge Commission (NKC) did not study this, hence it is repeating past mistakes. (Pushpa Bhargava did write a book on post-independence science; it started as an essay for my proposed book on this issue, but didn’t provide a causal analysis, and he is no longer with NKC.)

Briefly, Nehru wanted science to work for industry, so he gifted key science departments to the scions of industrial families: atomic energy to Bhabha, space to Sarabhai, and CSIR to Birlas. He thought the research output, freely available to these managers, would be an invisible state subsidy to help rebuild India as a modern capitalist society. (E.g. Tatas wanted to diversify into the energy sector, but lacked the capacity to invest in developing knowhow in atomic energy.) By focusing on elite institutions, Nehru’s strategy permanently damaged Indian universities, giving us only cliques of “experts” from elite institutions, who still rule, though they mismanaged science, worse than sports, in India.

 

2. Information poverty. Capitalism necessarily leads to information poverty (in addition to economic poverty) or scientific illiteracy even among the educated.

 

3. Expert raj. Information poverty allows “expert raj”, where designated experts decide on behalf of the entire society. There are no explicit criteria for selecting experts, and huge sums are involved, so ulterior motives often prevail while choosing “experts”. The scientifically illiterate cannot directly judge the expert’s knowledgeability; they go by indirect social criteria which may merely reflect the existing power structure. (E.g., Raja Ramanna was our top expert in atomic energy, since he was close to Bhabha. But in response to my question, he said “any matrix has a diagonal, even a rectangular matrix has diagonal elements”! He illustrated this by drawing a rectangle and its diagonal on the board! So he did not know even school mathematics.) Hence, the process fails to deliver, even when not motivated.

 

4. Need for debate. Public debate is the only safeguard against “expert raj” in a scientifically illiterate society—not mere durbars, but actual engagement with dissenting expert opinion. This debate has not happened with NKC. For example, I have publicly criticised our system of math education; my criticism is backed by a major book, critically examining the history and philosophy of mathematics, and proposing a new one, as well as suggesting a new approach to math education. The current system only helps build the soft power of the West like Macaulay; see, e.g., my article on racist history. (Note that changing this history also impacts the current philosophy of math, and the content of math teaching, as I have demonstrated for the case of trigonometry in my letter to Mr Pitroda.) The “experts” of NKC or NCERT etc have no clear public response to this criticism. What is the point of putting recommendations on the website if they cannot be defended publicly? Debate-avoidance in expert raj is suspect, since there is no other reliable way to validate the “expert’s” credentials.

 

5. Knowledge is socially constructed. Current formal mathematics is overlaid with a Western metaphysics and religious beliefs. So, the old way of teaching perpetuates Western hegemony.

 

The very word “mathematics” derives from “mathesiz” meaning “learning”, and the famous Platonic dictum “all learning is recollection” relates learning to a notion of the soul. Another way to expose these underlying religious beliefs is to challenge them from another religious perspective. Current formal mathematics collapses if it is interrogated from a Buddhist perspective. Since Buddhist and Jain logics are different, the theorems of mathematics would also change, So why continue to do formal math? Should policy again concern the welfare of the “experts” (who come from a formal math background) and not that of the people?

 

In a secular society, one ought to go by practical value: mimesis of the West is not a virtue in itself. Hence, I have called some NKC recommendations as “Macaulay part II”.

 

6. Comparative evaluation of alternatives. As an analogy, the traditional Indian calendar offers practical value by identifying the rainy season, which identification is critical to an economy based on rain-fed agriculture. Replacing this by a less precise calendar led to the false droughts of 2004-05 one of which turned into a flood! Why unscientifically mimic the West, to our detriment, to cater to the vanity of long-dead Roman emperors (Julius, Augustus) by having months of unequal days? Is it not a bit like wearing a woolen suit in the Indian summer?

 

Likewise, let us have a proper comparative evaluation of different types of mathematics, not mere “expert” opinion from an expert who has only trained in one tradition, and has not studied those alternatives, and whose social legitimacy derives primarily from linkages with the West, and not from any practical contribution to the welfare of Indian people.

 

Can the NKC even explain why school children should use a compass box and not a string? Why not teach “calculus without limits” the way I have suggested—by which any secondary school child, after ten lectures, is enabled to solve in 30 seconds any problem in a college calculus text of today? (Or for that matter, solve most common differential equation of Newtonian physics.)

 

If alternatives are not studied, or publicly debated, the NKC recommendations are likely to be bad.

 

6. Past record. To return to the question of practical value: the formal math promoted by TIFR math school has offered no practical value in the last 50 years (or ever since Bhabha brought in K. Chandrasekharan to sideline D. D. Kosambi, and he openly promoted south Indian Brahmin’s). To the contrary, the pervasive influence of this school has destroyed the possibility of practical value: when at C-DAC, I badly needed mathematicians for various practical tasks, I could find none in the country, despite offering very high wages, since the ability of mathematicians to contribute to practical tasks has been damaged by the sort of mathematics they were taught. Today, so many children find math difficult, and are repelled by it, just because it has got mixed with obscure concerns of theology which cannot be taught to children. Why continue with this rotten system just for the benefit of a few “experts” who have been peddling their influence? The TIFR math school has received enormous resources under the persistent false pretence that its work was contributing to atomic energy. This illustrates their ethics. It has built up a powerful clique across all key Indian universities and national institutions where “experts” from TIFR have had a tremendous say in appointments. The NKC math expert, irrespective of her personal qualities, is part of this powerful clique and represents its interests.

 

Summary of criticism on math education

 

Against this background, my criticism relating to math education may be summarized as follows. I welcome the NKC focus on math education. However, (1) formal math offers no practical value to us, and the TIFR math school has demonstrably produced none for the past 50 years. By teaching the wrong sort of math, they have actively destroyed any possibility of doing practically-oriented math in this country. (2) They could peddle their influence through “expert raj” in a scientifically illiterate society, holding out mimesis of the West as the prime value, and the NKC math expert is a formal mathematician from this school, which has unethically received large funds in the name of atomic energy to which it has not contributed. (3) The NKC recommendations have been arrived at without studying past mistakes, and hence repeat those mistakes. (4) No comparative evaluation of alternatives (such as rope vs compass box, or calculus without limits, or sunyavada as opposed to formalism) was carried out. Therefore the recommendations are not informed by the latest thinking which could make math easy. This is contrary to both constructivist and socially constructivist theories of education. (5) There was no public debate or engagement with criticism (which is needed to validate the very choice of experts). Public meetings without serious debate are reduced to the mere ritual of interacting with lay stakeholders. Why does the NKC advertise its recommendations through its website if there is no intent to engage in wider debate? (6) Hence, the NKC recommendations are like Macaulay II, they will only reinforce the soft power of the West.

 

 

Partial list of relevant supporting documents (authored by C. K. Raju)

 

Book

 

Lecture notes and education theory

 

Expository articles

  1. Teaching racist history”, Indian Journal of Secularism, 11(4) (2008) pp. 25-28. http://ckraju.net/papers/Teaching-racist-history.pdf.

  2. Itihas ke vichalan”, Jansatta 23(?) Jan 2008. http://ckraju.net/papers/Jansatta-Euclid.jpg.

  3. Logic”, Springer Encyclopedia of NonWestern Science, Technology, and Medicine, 2008. Draft available at http://ckraju.net/IndianCalculus/Nonwestern_logic.pdf.

  4. Towards Equity in Math Education 1: Good Bye Euclid”, paper presented at 31st Indian Social Science Congress, Mumbai, Dec 2007, session on Math Education. Available online at: http://ckraju.net/papers/MathEducation1Euclid.pdf. (To appear in Proc.)

  5. Towards Equity in Math Education II: The Indian Rope Trick”, paper presented at the 31st Indian Social Science Congress, Mumbai, Dec 2007, session on Math Education. Available online at http://ckraju.net/papers/MathEducation2RopeTrick.pdf. (To appear in Proc.)

  6. “Time Measurement in Classical Indian Tradition and the Present-Day Representation of Time as a Continuum”, in Proc. 2nd International Pendulum Conference, ed. M. R. Matthews, UNSW, Sydney, 2005, pp. 225-248.

  7. “Time: What is it That it Can be Measured?”, Science and Education, 15(6) (2006) pp. 537–551.

  8. Alternatives to Eurocentric Education”. Meet on BRIC & EU, IIC, Delhi. (Report in Hindustan, 6 Nov 2008, http://ckraju.net/press/hindustan.jpg.)

Expert-level articles

  1. The Religious Roots of Mathematics”, Theory, Culture & Society 23(1–2) Jan-March 2006, Spl. Issue on Problematizing Global Knowledge, ed. Mike Featherstone et al., pp. 95–97.

  2. Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhasa”, Philosophy East and West, 51(3) 2001, pp. 325-62. Draft at http://ckraju.net/IndianCalculus/Hawaii.pdf.

  3. The Mathematical Epistemology of Sunya”, in: The Concept of Sunya, ed. A. K. Bag and S. R. Sarma, IGNCA, INSA and Aryan Books International, New Delhi, 2002, pp. 168–181.

  4. Zeroism and Calculus without Limits”, invited talk at the 4th Dialogue on Buddhism and Science, Nalanda, Oct 2008. http://ckraju.net/papers/Zeroism-and-calculus-without-limits.pdf.

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