07 August, 2007

Fractions

I remember in school when I was first introduced to fractions. I and a few other students in my class sat at a semicircular table facing our instructor and a blackboard. The first fraction we met was 1/2. Together we explored the nature of this creature and how the bottom part, called the "denominator," told us how many parts there were to the whole, and that the top part, called the "numerator," told us how many parts we had. 1/2 meant that a pie (we all liked pie) had been cut into 2 pieces, and we had one of them. This was illustrated on the blackboard, much to our wonderment. The instructor than drew a pie on the board and sliced it into four pieces. She then asked us how many pieces we would need to have the same amount of pie as 1/2. One student said one piece, since we had one piece in the first example. I silently scoffed at her specious reasoning. Another said two, which was praised as the correct answer. Then came the difficult question: how would we express this new pie as a fraction? After some deep thought, 2/4 was spoken in a hesitant voice. Correct! exclaimed the instructor, who then wrote it on the board by the four slice pie. We spent some more time exploring how 1/2 and 2/4 were "equal" fractions, how they described the same quantity, but with different numbers. We also learned that a good way of identifying equal fractions was to "reduce" them by dividing the top and the bottom by the same number, which we all agreed was a very useful fact to know. If we divided the top and bottom of 2/4 by 2, we would get 1/2. Our instructor then encouraged us to employ this new found skill by thinking of other fractions that were equal to 1/2. Several examples were given and tested, some were right and others wrong. 4/8, 8/16, 16/32, were among the correct answers. Up to this point I had refrained from responding, wishing to give my classmates the opportunity to expand their own minds, as I had already grasped the principles being taught with my lightning intellect, but now I felt the need to remind everyone, including the instructor, of just how superior my mind was. I raised my hand and, when called upon, smugly offered 3/6, a set of numbers that had yet to be explored by any of my class mates. The instructor duly wrote it on the board and then quickly put it to the test. "Who can tell me what 3 divided by 2 is?" she asked. It was readily apparent that this was an impossible calculation. "I'm sorry," she said to me, "but 3/6 can't equal 1/2 because 3 can't be divided by 2." Needless to say, I was crushed. I knew I was right. It was impossible for me to be wrong. I would have pressed the issue, but as a small child I had not the skills necessary to debate the facts. The rest of the lesson is a fog, as I spent it in shock trying to see how 3/6 did not equal 1/2, but failed in every attempt.

Looking back, I think this is moment I began to lose my belief in the infallibility of adult knowledge, and to lose my respect for my school teachers.

3 comments:

Janet said...

Interesting memory, Adam! Although I feel I need to follow it with the question, why do you now choose to be a teacher in public schools as your career now? Ironic, isn't it?

Your poor teachers....hehe...

Mom

Geilshaif said...

It's not really ironic, if you think about it. I just want to do a better job than my teachers ever did. :)

Janet said...

You will be a good teacher because when you are faced with a child who's way of thinking does not "fit in the box", you will be able to completely relate! :-)

Mom