Let ’em Discover It…
Almost every day I have moments where I think about how I teach now versus how I would have taught it several years ago. I definitely had one of those moments today.
I spent 20 minutes after school helping a learner understand that calculating the mean requires that we divide by how many numbers are in the set (his misconception was that we always divide by 2). It would have been soooo easy to simply tell this learner what to do – but I’m confident that it would have done little to help dispel the misconception and create a lasting understanding. So I took my time, tried several examples, and helped the learner see a pattern. In the end, I received one of teaching’s greatest gifts: the “Ohhhhhhhh, now I get it!” (Kudos to this learner, by the way, for persisting and not yelling at me to just give the answer). I have much more confidence that this learner has a deeper understanding and has overcome the misconception because, in a sense, he discovered it for himself.
On a related note, last year we spent a week working on measures of dispersion in an effort to become more adept at interpreting and using data. In the end, however, I felt like the learners still had no clue about the purpose of things like standard deviation. This year I wanted it to be different. I wanted them to understand why measures of dispersion are important and useful. I wanted them to discover this themselves. So I gave them sets of data that had the same mean, median, and mode, but had very different spreads. Then I asked them to “invent” a measure of spread – they even got to name it – so that we could better interpret the data.
We spent two days on this and they developed some interesting methods. Many of them were very similar to interquartile range, and a few were similar to standard deviation. We tuned and tested their measures with various data sets, and as an extension some groups were tasked with “breaking” their measure by finding a data set for which it did not work properly. It was a bit messy, but fun (for me, at least).
Tomorrow we begin a couple of days of studying established measures of dispersion. While they may not become experts, I have no doubt that they will better understand their purpose and use…because they have already discovered it for themselves.