It ain’t what you don’t know that counts. It’s what you know that ain’t so – Will Rogers
The year was 1986. I was in the fourth standard. My maths teacher Mrs. Leila Abraham (popularly known as Mrs Cherian because her husband’s name was Cherian Abraham) had just asked us to get an Amul or a Cadbury chocolate for the next day’s class. She wanted to teach fractions through a bar of chocolate.
The idea was exciting enough to motivate a few students to blackmail their parents to get what she had asked for. Over the next few days she taught fractions to the class by breaking the bar into half, three fourths, one fourths and so on. Even the dullest students picked up the concept very quickly.
As my interest in the subject grew, the quality of teachers who taught me went rapidly downhill. The ordeal ended when I graduated with a BSc in Mathematics from St Xavier’s College, Ranchi.
The quality of teaching was so bad that before the last class in the third year started I wrote this on the blackboard: Mentally (M) Agitated (A) Teachers (T) Harassing (H) Students (S). An English professor in the college who was also the best quiz master going around in Ranchi had come up with this expansion for M.A.T.H.S.
Professor Pankaj Chattoraj who taught us co-ordinate geometry among other things, was supposed to take the last class. He was the best of the six professors who taught us. So the joke wasn’t really on him. He took it in a good spirit made a few more jokes, taught what he had to and left.
I have no numbers or research to back this but I feel that Maths ends up being taught by the worst teachers. The impact of bad teaching of Mathematics is clearly seen when people have to apply Maths.
Let me share a few examples which I have come across over the last few years.
Justice Markandey Katju in a recent column in The Hindu titled Professor, teach thyself wrote: “When I was a judge of Allahabad High Court I had a case relating to a service matter of a mathematics lecturer in a university in Uttar Pradesh. Since the teacher was present in court I asked him how much one divided by zero is equal to. He replied, “Infinity.” I told him that his answer was incorrect, and it was evident that he was not even fit to be a teacher in an intermediate college. I wondered how had he become a university lecturer (In mathematics it is impermissible to divide by zero. Hence anything divided by zero is known as an indeterminate number, not infinity).”
Rather ironically the teacher Katju castigated was right. Any non zero number divided by zero is infinity. But when zero is divided you get what is known as an indeterminate. The following example should explain things a little better:
A2 = A2
A2- A2= A2- A2
[A(A-A)/(A-A)] = (A+A)
In the fourth step of the equation we are dividing (A-A) by (A-A) and that allows us to come to the fifth step i.e. A=A+A and which finally leads to 1=2.
Now it need not be said that one cannot be equal to two. When we divide zero by zero we can prove anything. Hence dividing 0 by 0 (which is what A-A is) is not allowed in Mathematics.
So I guess Justice Katju’s Maths teachers did not teach him the right thing here. Justice Katju’s being wrong did not harm anyone and was more confined to the realms of what we can call an esoteric argument. But there are occasions when a lack of basic understanding of maths can lead to totally wrong interpretations.
Recently ABP news (formerly Star News) ran a report with a headline “Mahangai ghati kya aapko pata chala kya?”.This was in response to the consumer price inflation falling to 9.86% in July against 9.93% in June. The report went onto show that how the prices of vegetables and a lot of other goods had gone up. So it then questioned that how was the government claiming that prices are down?
This again shows the lack of basic understanding of Maths. When inflation comes down no government can claim that prices are coming down. What they can only claim is that the rate of increase in prices is coming down. Let me explain this through an example.
If the price a product increases from Rs 10 to Rs 12, we say inflation is 20% ((Rs 2/Rs 10) x 100%). Let us say the next month the cost of the product goes up to Rs 13. What is the month on month inflation now? The inflation is 8.33% ((Re 1/ Rs 12) x 100%). Now the inflation has fallen from 20% to around 8.33%. Does that mean that price has fallen? No it hasn’t. What has fallen is the rate of increase in price, not the price.
This is something very basic which a lot of people don’t seem to understand. On more than one occasion in the past I have been asked by fairly senior colleagues in the media “But why aren’t prices falling, if inflation is falling?”.
Another common mistake that people make is that they add or subtract percentages. Take the case of what Jerry Rao (an alumnus of IIM Ahmedabad, founder of the IT company Mphasis Corporation, and the former head of consumer banking of Citibank in India) wrote in a column in the Indian Express on October 6,2008.
“If stock market wealth drops by 50 per cent in six months, we get concerned. We conveniently forget that it went up by 200 per cent over the previous two years. At the end of 30 months we are still 150 per cent ahead.” (Read the full article here)
At the end of 30 months we are not 150% ahead but 50% ahead. Let us say an individual invests Rs 100. A 200% gain on this would mean that Rs 100 invested initially has grown to Rs 300 ( Rs 100 + 200% of Rs 100). A 50% fall would mean Rs 300 has fallen to Rs 150 (Rs 300 – 50% of Rs 300). This in turn means that we are 50% (((Rs 150 – Rs 100)/Rs 100) x 100%) ahead and not 150% ahead, as was written.
So what this means in simple English is that a 50% loss can wipe off a 100% gain. Let us say an investor buys a stock at Rs 50. The stock does well and runs up to a price of Rs 100. What was the gain? The gain was Rs 50 (Rs 100- Rs 50). What was the gain in percentage terms? 100%. ((Rs 50/Rs 50) x 100%).
After achieving its peak, the stock started to fall and is back at Rs 50. What is the loss from the peak? Of course Rs 50 (Rs 100- Rs 50). But what is the loss in percentage terms? 50% ((Rs 50/Rs 100) x 100%).
The point I was trying to make was that a 50% loss can wipe off a 100% gain. Or to flip it around, a 100% gain would be needed to wipe off a 50% loss.
But the example that clearly takes the cake was when a former colleague remarked that sales of a company that she was tracking had fallen by 110%. Anyone who understands percentages wouldn’t make a remark like that. Anything cannot fall more than 100% (Unless we are talking about things like temperature which can become negative. Then the concept of percentage becomes meaningless). Let me elaborate. Let us say a product sells 700 units in a month. In the next month no units are sold. What does this mean? It means sales are down by 700 units or 100%.
On the flip side when it comes to gains, they can be unlimited. A product sells one unit in a month and in the next month it sells 71 units or 70 units more than the previous month. Or a gain of 7000%.
Now, theoretically, there is no upper limit to the number of units that the product can sell. And so there is no upper limit to the gains can that can be expressed in percentages.
These are a few examples of lack of basic understanding of Maths that came to my mind on this teachers’ day. The bigger question is why is there such lack of basic mathematics? My theory on this is that it all boils down to the way teachers teach mathematics in schools. The entire emphasis is on solving a problem, rather than trying to explain to students why we are trying to solve a problem, and then getting into the nitty gritty. In colleges, it gets even worse.
So it’s time we stopped respecting our Maths teachers and re-title them as Mentally Agitated Teachers Harassing Students.
(The article originally appeared on www.firstpost.com on September 5,2012, with a different headline. http://www.firstpost.com/living/what-your-maths-teacher-didnt-teach-you-at-school-444727.html)
(Vivek Kaul is a writer and can be reached at [email protected] After eleven years in school and eight years in college, from all that he was taught the only thing he partly remembers is some elementary mathematics)