[Introduction to Series: Dr. Anjum Altaf, former Dean of the School of Humanities and Social Sciences at LUMS, is writing a page-by-page review of the model textbooks (Pre-I to Grade 5) accompanying the recently implemented Single National Curriculum. These detailed reviews intended to involve parents in the education of their children will appear as a series in Sindh Courier. Parents would benefit by having a copy of the primer under discussion in front of them while reading the review.]
SNC Model Textbooks: Pre-I Mathematics Primer
By Dr. Anjum Altaf
I have concluded the page-by-page review of the Pre-I Mathematics Primer introduced as part of the Single National Curriculum and implemented from the current school year. It is woefully inadequate and someone would have to try really hard to make anything worse. It is an unforgivable cruelty to have children subjected to it although some would surely survive it.
In order to clear my head, I revisited a village school yesterday to talk to the teachers and double-check my conclusions. The principal had compared textbooks for the same classes, produced, respectively, by Oxford University Press and the SNC and was categorical in stating the former were much better — they were conceptually clear while the SNC’s were all muddled up (gad-mad was the word she used).
The class teachers brought up another issue that is central to communication — that of language. They said the students were ‘bewildered’ when teachers tried to read out lessons in English. Almost immediately, the communication would switch to Punjabi or Urdu. (Recall the references to coriander and mint and olives in explaining the color green in the math primer.) This reconfirmed what I had observed in earlier visits where I had also seen locally produced Urdu translations of the textbooks being used by students.
I would really like the Textbook Board to present a coherent justification for having in English a Pre-I Mathematics primer that is to be taught in very varied locations including remote villages. This justification would need to be validated against the views of all the instructors who have to teach it. Is it intended to leap-frog the students of remote villages on to the mythical level playing field where they would compete on an equal basis with children attending the leading private schools in metropolitan cities? And, even if this delusion can be accepted as plausible, can this leapfrogging be accomplished by the terrible murder of the English language that occurs in the primer and having it taught by teachers who have an imperfect command over it?
In her latest book (Reforming School Education in Pakistan and the Language Dilemma, 2021), Zubeida Mustafa has a quote from Rabindranath Tagore that provides a very vivid analogy cutting through the theoretical obfuscations and making the matter very easy to understand:
“Learning should, as far as possible, follow the process of eating. When the taste begins from the first bite, the stomach is awakened to its function before it is loaded, so that its digestive juices get full play. Nothing like this happens when the Bengali boy is taught in English, however. The first bite bids fair to wrench loose both rows of teeth — like an earthquake in the mouth! And by the time he discovers that the morsel is not the genus stone, but a digestible bonbon, half its allotted span is over. While one is choking and spluttering over the spelling and grammar, the inside remains starved, and when at length the taste comes through, the appetite has vanished. If the whole mind is not functioning from the beginning its full powers remain undeveloped to the end.”
This undeveloped mind is not just the fate of marginalized children but that of all those taught in languages they don’t understand. Zubeida Mustafa’s book includes a first-person story (‘Qurratul Ayn’s Educational Journey’) that should be compulsory reading for everyone having anything to do with early childhood education. After saying that English was a major obstacle to both her success and her self-image, Qurratul Ayn mentions her peer group that had the “advantage” of an English-medium education and was proud of its linguistic skills. Looking back, she notes perceptively that “Little did I know that their English was not really all that great” because it was short on understanding.
Every community has its own unique way of teaching languages (and numbers, which are just the alphabet of another language) that resonates with its culture. I recall one from Urdu that has stayed embedded in my mind ever since I first came across it:
paanch choohey ghar se nikle, karney chaley shikaar
aik chooha reh gaya peechey, baqi reh gaye chaar
chaar choohey josh me aa kar, lage bajaane been
aik choohey ko aa gayee khaansi, baqi reh gaye teen
teen choohey dar kar boley, ghar ko bhaag chalo
aik chohhey ne baat na maani, baqi reh gaye do
do choohey phir mil kar baithe, dono hii they nek
aik choohey ko khaa gayee billii, baqi reh gaya aik
aik chooha jo baqi reh gaya, kar lii usne shaadi
beevi us ko milii laraka, yun hoee barbaadi
Note the following about this introduction to numbers: First, when children enter school, they already know numbers and the basics of counting. So, they need not begin mechanically from one and move mindlessly to 50 on the backs of disconnected poems. One can really start anywhere if there is an interesting story attached to it. This particular introduction begins with five, which is a number familiar to all children.
Second, there is no unfamiliar word in the verse — go through it line by line. Even the final two lines do not contain concepts that children are unfamiliar with — they have all been to a ‘shaadi’, they have often come across ‘laraka’ individuals and ‘barbaadi’ is a commonly employed term for disaster.
Third, without ever making it the explicit focus of a separate unexciting lesson (pp. 137-139), the verse slips in the concept of subtraction — taking one away at every step and indicating the remainder. This verse was composed by Sufi Ghulam Mustafa Tabassum, a great poet sensitive to the psyche and needs of children. It is no wonder it has remained evergreen over the decades. Culturally rooted introductions like these are extremely compelling resources that we have perversely thrown away in a foolish attempt to level the global playing field that only ends up crippling our children. Compare it with the ridiculous verse in the SNC primer accompanying the number 4 (“Day and night they worked hard / Success of Pakistan is their yard”). Who will remember this after even a few days except those who want to hold up Pakistan’s primer as an example of how not to educate children?
There is an even bigger loss to the use of English to teach maths in Pre-I that goes unremarked but has very significant social impacts — the severance of intergenerational continuity and the wastage of another huge resource, that of parental knowledge. Even illiterate parents know how to count and do various numerical computations. They can easily help their children at least through the primary grades. But if language comes in the way, this resource is negated. One parent mentioned that her child asked her for help to figure out the LCM of a set of numbers. She found she knew it well enough but didn’t know the terms in English and so had to engage a tutor. It came back to me that the foundational concept of ‘ikaai, dihaii, sainkra’ (related to the zero that means “nothing at all”) had been taught to me by my mother and my thinking is still oriented around it because it sank its roots deep into the cognitive soil.
I wish the intergenerational loss stopped there but its damage is even more pernicious. Children begin to think of their parents as ignorant (jaahil) because the latter don’t know English and very soon this perception spreads to all of society that is non-English speaking. It is as if Lord Macualay, who said that “A single shelf of a good European library was worth the whole native literature of India and Arabia” had never left. I can only presume that the thinking underlying the SNC is that in a few generations everyone will know English well enough to heal this social divide and that Pakistan, in the spirit of Rupert Brooke, will be transformed into a “corner of a foreign field that is forever England.” (Readers would also enjoy the story ‘Dr. Walter’ in Bilal Minto’s entertaining collection Model Town in which the 11-year old narrator is dazzled by his neighbor, Mrs. Walter, because she would wave her hand in the manner of a foreign lady in an old English film and say, “Hello, boys.”)
I had ended the last installment of this review with a mention of the dearth of internationally acclaimed Pakistan mathematicians and promised a story. I will just reference it here and leave it for the interested reader to pursue. It is the story of how one nurtures talent in mathematics or in any field for that matter. It is the story of two globally recognized Indian mathematicians, M.S. Narasimhan and C.S. Sheshadri, both born in small villages in Tamil Nad, whose ‘Narasimhan-Seshadri theorem’ is still the subject of international conferences 60 years after it was enunciated. (The legendary. S.R. Ramanujam, one of their role models, was also born in Tamil Nad.)
The story of C.S. Sheshadri should be read for its underlying pedagogical and institutional message and the vision and implementation required to achieve excellence; the details of mathematical theory can be ignored since very few, asides from mathematicians, are likely have the domain knowledge to grasp them.
By contrast, read about what might be called a similar attempt in Pakistan and its fate. It is well documented by Dr. Pervez Hoodbhoy (here and here) and narrates how one of the few reputed mathematicians in Pakistan was driven away. The rot starts from the top and it is no surprise to see it filtering down to the SNC pre-I Mathematics Primer. Dare one ask, who made it, who edited it, who vetted it, who signed off on it, and who touted it as being amongst the best in the world?
This concludes the page-by-page review of the SNC Pre-I Mathematics Primer. Readers will note that I have a problem with it but one that cannot be resolved by the advice on Problem Solving on page 6 of the primer: “If you have a problem: Take a nap, pray, count till ten, play with toys, talk about happy things, take exercise, or read a book.” The only advice that might be relevant would be “Tell an elder about the problem you are facing.” But, I have done so already to an elder (in terms of authority) and been told that I belong to a tiny elite (ashraafiya) that is enslaved by the West and opposed to Islam and that I need to read the primer page-by-page to appreciate its greatness.
Instead of allowing the evaluation to be distracted in this fashion (‘Mirror, Mirror on the Wall, Who is the Most Islamic of Us All’ — as if being Islamic absolves sub-standard work), I propose a fairer test: Send this Pre-I Primer to the last ten winners of the Fields Medal and ask them if they would have liked to start their journey in mathematics with this introduction to the subject. And, let us agree beforehand to abide by the verdict.
Personal Note: I was fortunate to be with Dr. Narasimhan for two hours in his apartment in Bangalore. He was consumed by the illness that took him away this past May but even then his presence was larger than life. One had the feeling of being in a powerful magnetic field, strong and simultaneously very calm. It was the presence of one who had attained mastery in a field and yet conveyed the sense that there was still much to learn.