Friday, March 9, 2012

Musings of a Kindergarten Mathemommician

At the start of N's Kindergarten, my zeal for working with his class and teachers was unstoppable. What a wonderful concept, getting parents involved in the class, so different from how it was in the time and place that I attended elementary school! On account of being some of the only people that turned up at the first volunteer interest meeting, I unwittingly became a room parent. Good thing I did, too. For soon enough I found that doing organization and logistics was about the only thing that I could fit into our both-parents-employed-full-time lives. All volunteer opportunities in the classroom or the media center or on field trips happen smack dab in the most inconvenient parts of the workday. So with a wistful sigh, I watched volunteer slots being eagerly filled by dedicated and committed parents from N's classroom. But as the school year progressed, the enthusiasm for volunteering seemed to be on a wane. Until it so happened that this month there were two Unit Center slots that no one could volunteer for. I could barely contain my excitement when I noticed that the lunch hour at my work, when many of my co-workers pile into cars and head over to an hour of socializing at their lunch destination for the day, straddled those 30 minute time slots. If I packed a portable lunch and ate it while driving to/from N's school (less than 10 minutes each way), I could easily do the volunteering and still be back at work before all my lunch-going co-workers. Life has an amazing way of making things just fall into place, doesn't it? Now I would be able to meet all of the friends N talks about at home, watch N in action in his class and be a part, however little, of his classroom learning.

I got to work with the same five kids (that N was not one of) on both days, helping with their Unit Center math exercises. And it was a truly fulfilling experience. How much scope and challenge can Kindergarten math really have, you ask. Quite a bit, I tell you.

On the second day, one of the activities was a Number Race. A brief explanation of what that means: each kid is given a sheet of paper printed with rows of empty squares to fill in with numbers. The first column is already printed with the number meant to occupy that row. Kid rolls a die, counts the number on the face and then writes it down in the correct row. Kid repeats this and the numbers race along filling their rows till a row is full and the number for that row is declared a winner.

The instruction card for my Unit Center said that the kids had practiced this before with one die and counting/writing the numbers 1-6; today they were going to count bigger numbers, so there were two dice for each kid and the number they count should be the sum of the numbers that show up on the two faces. I looked at the sheets of paper and noted with dismay that the numbers printed were 7-12 instead of 2-12. Would I be able to get back to work on time? While Mrs. L kept talking to the kids about what people and animals do in winter, I debated in my mind if I should ask if there were rules for what the kids should do when they roll a number from 2 through 6. I decided not to. After all, if anyone had thought of a cleverer thing to do than ignore the number and roll again, they would have put it down on the instruction card. Without guaranteed progress on each roll, this game could stretch on well beyond the time I had (or the time they had allotted to the Unit Center). And there were 5 kids all of who would have to be finished before I could leave. So I added a new rule of my own: If the number rolled was less than 7, then the die with the smaller number on its face would be flipped over to its opposite face. This would ensure that the resulting new numbers add up to at least 7. (I did a quick check of the assumption behind my rule - that the dice were not rigged and were marked correctly with opposite faces adding to 7.) So every roll of the dice causes the game to progress and the number of steps before the game terminates would have a strict upper bound instead of some probabilistic distribution.

Anyway, so the winter lesson ended and the kids came to my table and two of them that remembered me from last time enthusiastically pulled up their chairs next to me. I was happy to know that I was making Kindergarten a more positive experience for them than mine had ever been. We started doing the first exercise, and then we came to the Number Race. Explaining the new rules, including the one I had added, went over easy enough. The kids were actually getting excited about the race and three of them were lamenting about how 12 was not even getting started. Indeed, looking across at how the 5 sheets of paper were getting filled with the roll of 5 pairs of dice, I saw my chance to introduce a bit of permutations and probability theory to my bright-eyed students. Even though several of them got their 7's laterally inverted, they had no trouble understanding my explanation of why 12 was having so much trouble getting started. If it were up to me, I'd give these bright budding mathematicians extra credit. But then, life has a way of giving out extra credit to those who truly deserve it. Eventually. Whether or not we notice it.


smiller

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