Sunday, April 14, 2013

Ubiquitous Teaching

In the couple of months since my last post, I have been trying to incorporate small dabs of problem solving throughout my interactions with Suhana. These small doses are designed to be non-intrusive, yet, taken together, I believe they encourage thinking.

Suhana and I have created a cast of characters that appear in bed-time stories and in problems. The stars of our stories are two six-year old siblings, Ram and Chetty; Alpha, Bravo, Charlie, Delta, Echo, and Juliet (respectively, an alligator, a bee, a cat, a dog, an elephant, and a pheasant-tailed jacana); Sher Khan, Bhaloo, and Holly the Hippo. Consistently using the same characters has allowed a rich narrative to develop, including typical things these folks do. For instance, Ram and Chetty are farmers and they have to travel to sell the Bhindi they grow, and their travels and day-to-day problems form a natural backdrop for setting up arithmetical problems.

In a recent bed-time story, for example, Ram wanted to grow Bhindi as a birthday gift for that all important day, May 13, Suhana’s birthday. It happens that Bhindi takes two months to grow. So when should he plant it? This very tiny puzzle can be presented with zero intimidation. My actual words were: “Ram knew that Bhindi takes two months to grow. So he thought ‘When should I plant?’”, followed by a pause. In this case, Suhana counted backward and said “March”. If she had not said that, or ignored the pause, the story can still smoothly proceed to how Ram found the answer. Similarly, Ram knew that Bhindi should be planted two days before it rains, and the weather prediction is for rain on Sunday. So what day did he plant?

Every night, the bed-time story lasts about fifteen minutes and invariably involves some computation. Recently, Chetty had five toys but Ram only three. So Chetty gave some to Ram so that they had the same number. How many did she give him? I like this problem because the answer is not one of 5 - 3, 5 + 3, 5 * 3, or 5 / 3. Suhana came up with the right answer. Had she not (if she said “2”, for instance), the story could have smoothly continued with “yes, you know, that is what Chetty thought and so she gave Ram two toys and then counted both their toys. Do you know what she found?”. No right answer can be made to work even when there is  a right answer.

One final example from this morning to justify the “ubiquitous” in the title. I was working and Suhana kept pestering me. On a whim, I opened an excel stylesheet, her first exposure, and let her play around. My computer does not have a mouse, and she used the arrow keys to move the active cell around. We randomly typed stuff in various cells, and at one point she decreed that everything on the right was her territory (pointing to column F onward), and the left portion was mine, and that we should only change things in our area. When it was my turn, in cell C3, I typed “= G3”. Naturally, when she modified G3, her words appeared in C3 as well, and we had a mock fight. I then explained what I had done. Not much of my explanation was likely to stick, but the entire exercise made her more aware than before of the two-dimensional coordinate system, and we played a game of naming a cell (say, “F8”) and navigating there using arrow keys.

I then set up a stylesheet corresponding to the story “Ram had five toys, Chetty had three. Chetty asked her mother for more. Her mother said that she would get Ram the same toys she got Chetty. In the stylesheet, there was a column for Ram (with a sum at the bottom) and one for Chetty (with a sum), and the sums were 5 and 3 at the start. The stylesheet was set up so that any number added to Chetty’s column was copied to Ram’s column and no matter what Suhana tried, the sums of the two columns stayed two apart.

What did Suhana learn from this? Probably nothing that can be pin-pointed. However, even the realization (even the very wispy almost non-existant realization) of a coordinate system and the very vague realization of the possibility of using such tools to set up games or to solve problems, even if she has no clue how, are very very slightly useful, I think.  The other possibility of course is that I am just deluding myself.

In any case, all our stories share the common characteristic of being quite silly and yet just plausible in the right sort of imagined world given the right background story. We have plenty of fun along the way, so even if I am deluding myself regarding the edification I provide, not all is lost.