Photo: Rudyanto Wijaya
Photo: Rudyanto Wijaya

The joy of X

My daughter and I have arrived at a pactthat beginning this year, the both of us will undertake a journey to understand everything that lies between zero and infinity

I want you to first take a crack at these questions.

1. The numerical expression 3/8 + (-5)/7 = (-19)/56 shows that

(a) Rational numbers are closed under addition

(b) Rational numbers are not closed under addition

(c) Rational numbers are closed under multiplication

(d) Addition of rational numbers is not commutative

2. Which of the following is an example of distributive property of multiplication over addition for rational numbers?

(a) -1/4 x {2/3 + (-4/7} = [-1/4 x 2/3] + = [-1/4 x (-4/7)]

(b) -1/4 x {2/3 + (-4/7} = [1/4 x 2/3] – (-4/7)

(c) -1/4 x {2/3 + (-4/7} = 2/3 +(-1/4) x -4/7

(d) -1/4 x {2/3 + (-4/7} = {2/3 + (-4/7)} -1/4

3. Between two rational given numbers, we can find

(a) One and only one rational number

(b) Only two rational numbers

(c) Only 10 rational numbers

(d) Infinitely more rational numbers

I’m willing to wager that many of you cannot answer these. This, in spite of the fact that you are well read and can make sense of business news. And if you think you can, may I suggest you head here and try scoring whatever you can at the 152 questions that appear on this link? So, what’s my point?

The other day, the missus got home from a parent-teacher meeting. She dejectedly told me that the feedback from school was that our older daughter, who will now start Class VI, is weak at math. And that something ought to be done about it.

This time around, I told myself I ought to take matters into my hands and figure out what really is the problem. Because, I think of math, particularly in the formative years, as a life skill—much like we learn languages and appreciate the basics of science. So, the both of us went out for a walk. For whatever reason, the poor thing was under the impression she was being taken to a convenient location for a tongue lashing. It took me a while to make her feel comfortable and get her to open up.

Eventually, she told me she loved math as much as she loved her art classes. Then why, I asked her, is she doing badly at math? Because, by her own admission, when looked at from her eyes, math is a language much like English, Hindi and Marathi. She loves languages. But math is put across to her in a manner that is incomprehensible. She feels lost and doesn’t quite know how to deal with it.

When we got back home, I thought I would take a random online math test for Class VIII students. Technically, I’m qualified. I graduated in the biosciences before I shifted streams to finance and economics, which demand I understand numbers. I have reported on businesses for many years now. So, how difficult can it get to answer a question paper set for Class VIII students?

The three questions I started out with are reproduced from a “model question paper" for them. I must confess I was stumped and had no answers to any. So, if I were to take a test that comprised questions like these, I would flunk right away.

To test my hypothesis, I turned to two people who understand the subject. The first is my good friend Achu. He’s the kind of guy who talks in algorithms and works on resolving complex problems on banking platforms across the world. He promptly got back in response to the first question listed there, saying: “This one I could only best guess. I had to Google what ‘closed’ meant. It is a very specific definition. It’s not a difficult concept if you know the definition."

In response to the other questions, he got back saying: “These are great problems. They can be used to explain terms like inverse, etc…like these. I think these should be used to teach concepts and test the understanding of students."

I then turned to my brother, a computational neurobiologist for another perspective. He thought it a great set of questions as well. In fact, he reinforced Achu’s point that the questions are not the problem. It is the language—or rather the lack of context—that is the problem.

He reminded me of our younger days when the both of us went to the same school. I told him I’m perhaps weak in math because our classrooms were filled to the brim and our teachers perhaps had too much on hand to deal with.

To which, his riposte was, “How come as parents we don’t give up on languages? When it comes to something as abstract as explaining an adverb in English or ‘mhatra’ in Hindi, we take time out. Children get it. What’s the problem with math then?" By way of example, he reminded me of our math teacher in Class VII and IX—a firm Tamilian lady by the name of Mrs Prasad. All of the concepts she drilled into us then is still fresh in his head. That it isn’t in my head, he told me, was because I was then infatuated by a pretty young thing.

Both Achu and my brother pointed out that the onus is on us, the parents, to take some time out, be clear in our minds that math is nothing but a language we can gain proficiency in, and then ensure we pass it on to our children.

So, where do we start? Let’s take the first question illustrated above. Intuitively, all of us know it comprises numbers, fractions, additions and negative numbers. How do you put that across cogently to a child still coming to terms with the complexities of languages she was born into and is compelled to learn at school?

What if I were to tell Nayantara to think of herself as somebody facing a complex problem. Say, six of her friends are home and all of them want a plate of chips each. She could run into the kitchen and tell me: “Chips, chips, chips, chips, chips, chips for my friends."

What an awful way to put it!

Instead, what if she were to simply say, “Six plates of chips for my friends, dad."

There, it’s simple, elegant, saves her breath, and me the problem of comprehending.

Then, out of the blue, four more friends drop in. This time around, instead of yelling “Dad, I need more chips, chips, chips, chips", she would say, “Dad, I need 10 plates of chips". What she just discovered is addition. Simple.

Imagine this for a moment now. Just when I get those four plates of chips, five more friends drop in and she screams impatiently, “Dad, I need five more chips." But I have got only three to go around. A few things begin to happen and the numbers begin to take a life of their own.

(a) If I were to take just three plates in there, she would have two pissed-off friends to deal with because they have “zero" chips.

(b) Another way to look at it is that because Nayantara could offer them zero, she is in negative territory. That is, she now owes two plates of chips (or -2). How she makes up to them is her problem.

(c) One way she could wriggle out is divide the three plates into five equal portions (3/5), or fractions, as we call them. When her friends look at these smaller portions, will it piss them off even more?

(d) But as compared to the others who came in earlier and got one full plate each, between these five, Nayantara now has choices to make.

As she grows older, she will have to deal with increasing complexity, all on the back of a language she isn’t used to, but she ought to know.

My limited point here is this: as parents and teachers, we are then morally obliged to teach our children the language that is mathematics that they may grow into adults who can make informed choices.

A good place to start with is The Joy of X by Steven Strogatz, an applied mathematician and acclaimed columnist at The New York Times. By the time you are done with it, none of what is listed above will sound like gobbledygook. And that is why, beginning this year, my older daughter and I are going to set out on a journey from zero to infinity.

Charles Assisi is co-founder of Founding Fuel Publishing.

His Twitter handle is @c_assisi

Comments are welcome at feedback@livemint.com

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