I was showing Daivik images of Ravana, the demon emperor from the epic Ramayana. Ravana, with his ten heads, was bound to elicit Daivik's curiosity. I was wondering what he might ask. The most obvious question was why does he have ten heads ? Instead, he asked something far more interesting. "What does he do with ten heads?". This question took me off the tangent and I ended up wondering how exactly does Ravana control and co-ordinate all the thoughts that arise and criss-cross across all of his heads. One head is already sometimes a little too much for me...
Daivik was waiting for an answer. Without thinking much about it, I asked, "So, if he has ten heads, how many noses does he have". "Ten", replied Daivik promptly. "And how many eyes?", I asked.
Daivik thought for a moment and hesitantly ventured, "ten?". I asked him to explain it, he could not. Then I told, "Okay, he has ten heads and two eyes in each head. So how many eyes does he have in total?". Instinctively Daivik pulled his fingers out to count. But then, how exactly does one count things when it is not clear what needed to be counted. Fingers frozen mid-air, he asked, "What do you count?". "This is called multiplication", I said and tried to explain the concept to him. However, I stopped soon enough as it was getting a little complicated. Addition, subtraction and the concept of zero were easy. How do you explain multiplication in a fun way ? (and, later on, division, division by zero...)
At school, we were forced to commit the multiplication charts to memory first. (from 1x1 all the way upto 20x20!). Perhaps the assumption behind it was that once you have the facts ingrained, understanding and appreciation of it will follow, or can be thought later. Maybe that is true. But, while forcing that commitment was easy, teaching that appreciation was not. Since people largely tend to do what is easy, the said appreciation never quite followed. For me personally, the intricate beauty of Mathematics (and Physics) remain sadly buried behind those scary formulas. I wonder now if it should be the other way around. First teach the appreciation, facts can follow.
As I was mulling over this, Daivik offered me a way out. "Is it the same as ten plus ten", he asked.
That's right, yes, of course, exactly, that is what it is.
Daivik was waiting for an answer. Without thinking much about it, I asked, "So, if he has ten heads, how many noses does he have". "Ten", replied Daivik promptly. "And how many eyes?", I asked.
Daivik thought for a moment and hesitantly ventured, "ten?". I asked him to explain it, he could not. Then I told, "Okay, he has ten heads and two eyes in each head. So how many eyes does he have in total?". Instinctively Daivik pulled his fingers out to count. But then, how exactly does one count things when it is not clear what needed to be counted. Fingers frozen mid-air, he asked, "What do you count?". "This is called multiplication", I said and tried to explain the concept to him. However, I stopped soon enough as it was getting a little complicated. Addition, subtraction and the concept of zero were easy. How do you explain multiplication in a fun way ? (and, later on, division, division by zero...)
At school, we were forced to commit the multiplication charts to memory first. (from 1x1 all the way upto 20x20!). Perhaps the assumption behind it was that once you have the facts ingrained, understanding and appreciation of it will follow, or can be thought later. Maybe that is true. But, while forcing that commitment was easy, teaching that appreciation was not. Since people largely tend to do what is easy, the said appreciation never quite followed. For me personally, the intricate beauty of Mathematics (and Physics) remain sadly buried behind those scary formulas. I wonder now if it should be the other way around. First teach the appreciation, facts can follow.
As I was mulling over this, Daivik offered me a way out. "Is it the same as ten plus ten", he asked.
That's right, yes, of course, exactly, that is what it is.
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