Here is a short account of how my children started to do divisions
and how it led to an unexpected learning outcome.
We had found that basic numeracy was easy for our children
to acquire, so much so that we hardly remember how it came about. We never
really sat down to do math with them. As she went about her daily chores, Hema
had always liked to involve the children, and little by little, in the course
of talking about things, both the kids acquired a sound number sense along with
a good handle on how to add and subtract.
Before we homeschooled, Abhinav went to two
different "liberal" schools in California for 3 years, where at the
end, he was expected to do some simple addition and subtraction of mostly one
or two digit numbers. Abhi was already numerically competent, so none of this
interested him. Unsurprisingly, as the other parents and the teacher told us,
Abhinav was rather bored in the class and was often creating trouble. However
he continued to be fascinated with math and we let him explore his interest on
the Khan Academy website.
One day, while playing with an addition/subtraction math
practice program on the website, Abhinav, 7 at that time, got curious about a
math symbol he hadn't seen before. So he asked me. I said "This is
division" and then remembered my own childhood difficulties about learning
this, so I added, "This is too advanced for you." He wanted me to
tell him anyway, and as I was forced to respond, my sense of responsibility
yielded a simple way to present this idea. I said, "6 divided by 2 means
we find out how many 2's are in 6." He chewed on this unblinkingly for a
couple of seconds and then said, "But you told me this was hard!" He
went back online and spent the next hour or so absorbed in playing with the
division practice program.
Sometime later, my daughter, Aparna, then 5, wanted to know
this division thingy too. By this time I was more willing to question my own
assumptions about what was hard, so I gave her the same simple explanation that
I had given her brother earlier. And it worked this time as well. She was so
thrilled with this new learning that over the next several weeks she would ask either my
wife or me for division problems and then proceed to tackle them with relish.
Soon, I was beginning to get bored with this routine and had to think up something new to keep my
own interest from flagging. I started making certain formulaic stories that featured a seriously math-challenged dad and his two children, a girl and her little
brother (an example will follow). The stories always climaxed with a division
challenge that stumped the hapless dad, and then the two kids would easily do
the division and present the solution to the astonished dad. In the telling of
the story, I would stop it just before the problem was solved. Then I allowed
Aparna to have a go at it first, and I remember clearly how her face would be
agog, waiting for this moment. She would scrunch up her face in total concentration and then furiously start calculating. And finally when she had the answer, be very tickled by how the
dad in the story can find this so difficult. We must have played this game for
months and Aparna never got tired of it.
While she had been interested in many things, Aparna had
never wanted to write. This situation changed suddenly last year when she
picked up a little notebook and wrote a story about the math-challenged dad.
The story is reproduced below with Aparna's permission. (Please note that the
story has been reproduced exactly, alternate spellings and all.)
So ultimately, what had started as a math activity, ended up
becoming an exploration of the writing process.
- Dev
How many autos? (A story by Aparna Jain)
One [day] the father went to a big big parck. With his
family. On the way thay had to take 3 buses 2 autos. Instead of sitting he
started to count the autos. After they were ther they let the kids go to the
playgrond and ther was a session you can make somthing and go sell it so they
went ther. The kid's friends had com so the kids played. whith ther friends.
This session was about organic food. When it was lunch time ther was organic
food so they ate whith everyone. When they went back home the kids asked ther
dad what did you count anything today.
Oh! When we wher going ther in the bus I counted the autos
weels, 96. How many autos? Now readers
figure out the answer.
Note to non-Indian readers: The "auto" referred to here is a three-wheeled taxi
common in India.
