Sunday Musings

‘He needs to score more marks. He has lost 4-5 marks in language and literature, and in my subject, general science. Though he has got 100% in mathematics, I’m not sure if that is correct, as his math teacher is very lenient…’ That is how the conversation between my six and a half year old son’s class teacher of grade 1 and me, started yesterday. It was the first parent-teacher meeting after his first term tests. ‘And yes,’ she went on, ‘His handwriting has gone to the dogs…’ Sniff, sniff! My son sat next to me. I wondered what was going on in his mind. ‘If he had got ten more marks, I would have ranked him,’ she rued. Thus, in the general remarks section, she had written, ‘Good. Could do better. Try for higher rank.’ We discussed nothing else about his schooling experience.

As this monologue went on, I interrupted: ‘I’m not so much concerned about his marks…I know he is intelligent.’ What bothered me instead was this overt emphasis on scoring marks, almost to the exclusion of everything else. What a stifling way to begin one’s schooling!

Just the other day, as I was helping him with his math homework, I discovered that he had started learning subtraction with borrowing. He had been taught, ‘When the number below is more than the number above you have to borrow one from the neighbor…’ I soon found out that this had been taught without introducing the notion of place value. The teaching of mathematics depends on a sequence in which higher order concepts cannot be taught without first teaching the more basic concepts. This was just one instance where this rule had been violated.

I requested a meeting with the math teacher, an old woman who had probably seen many years of teaching. “We have taught them ‘units and tens’,” she said. For proof’s sake, she asked my son. He nodded in agreement. But her explanation was not satisfactory. What does ‘borrow the one’ mean? Are we really borrowing one? Why should we borrow only one? It was clear that this had not been explained. Likewise, in addition, children are told to ‘carry forward’. Unlike subtraction in which you can subtract only one number at a time, in addition, one can add any number of numbers. You can carry forward more than one: thus, when we add the numbers 9, 19 and 27, 9+9+9 = 27. We then write down 7 and ‘carry forward 2’, i.e. 20, which is actually two tens (or two units of ten). All of this looks like a bag of tricks which children learn quite fast through endless repetition at school and home. What they do not learn is the underlying structure of the numbers, and how this structure comes into play during number operations. For this, a basic idea of place value is necessary. This expands the child’s conception of number and prepares her for greater learning adventures.

I have seen much older children going around chanting this ‘borrow the one’ procedure as they solve subtraction sums. Thus, by limiting ourselves to a teaching of mathematical procedure, we are preventing the child from understanding the deeper structures and patterns of the subject. This is not surprising, since teachers have also come through the same system for years. It has worked because exams also do not test understanding. Even if they cannot understand everything in the first instance, it is our job as teachers and parents to set them up on that path. I have come across many 90%+ children whose understanding of the basics is very suspect.
One of the aims of education, I would believe, is to foster understanding in children. Much to my frustration, I continue to discover this aim being bypassed without much thought, day after day. ‘I must change his school soon,’ I thought. Finding a school which teaches for understanding is going to be difficult…

Giri
18th November 2007
Bangalore