The fractal drawing period went well enough. I suggested to the students that they instruction sheets increased in difficulty (when in the same order as in the previous post). I expected most to go for the Sol LeWitt drawing. In fact, that was kind of a wash! I had really hoped to have a nice full sized Wall Drawing 797 poster made by the kids. Most went straight for the dragon fractal. I can’t really blame them, since it looks so cool, but my instructions were unclear enough to make it difficult for most. The biggest issue was that most students didn’t pick up that each “elbow line” needed to be drawn so that it connected opposite corners of the squares on a piece of graph paper. Their dragon drawings ended up looking flat and floppy, and after only a couple iterations there wasn’t a whole lot left to work with.
Most of the kids were not thrilled to be doing any mindfulness activity. Many asked if I could ask the administration to never have a mindfulness advisory day again. There were, however, a few who quietly and attentively worked on drawing the curves, and a couple did quietly exclaim that the dragon curve was pretty cool.
I’ll keep things in perspective. My goal wasn’t to make them experts on drawing these figures, but to at least expose them so that they can recognize the ideas if they happen to come across them later. I’d also hope that a seed of interest has been planted in at lease one student, so that they’d be motivated to read a bit more about these things on their own.
The ratio of interested kids to uninterested kids reminded me of something called the Pareto Principle. This rule of thumb asserts that, in a situation like this, I could expect 80% of the effort or participation to come from 20% of the students.
This is a really lousy model for the drawing activity, not only because effort isn’t a well-quantified value. Number of drawings, time spent with pencil to paper, some arbitrary standard for quality all could play into the measure of effort. In addition, the “4:1 for 1:4” Pareto rule is a goofy way of putting it; the statement that “20% do 80% of the work” can make one think that there are some students who are doing 4 or 5 times the work of another. In fact, it would mean that the hard-working students would be doing 16 times more than one from the larger population. This seems a bit high for a typical high school class.
The Pareto rule might work a bit better in the business example, “20% of your customers will give you 80% of the sales,” but any decent business would hopefully make predictions based on their particular situation and history. Perhaps most hover around this distribution — it doesn’t seem too wild of an idea that a few die hard regulars are the ones keeping any given bar afloat.
The real benefit of this rule of thumb is to give that sense of perspective. It would have been unrealistic for my goal to have the room be lit with energy, all of the kids scrambling around in excitement because they were given some drawing instructions. To expect 1/5 of the students to be truly interested might sound pessimistic, but in retrospect it’s a good place to start when making expectations. It might also be a good place to start in a brand-new business.
The rule is an instance of a Pareto distribution, which is a generalization that would be able to tell you exactly how much each student is producing (rather than big groups), as well as describe groups of students who are producing work at different ratios than 4:1. The benefits of being able to describe your system (be it schoolchildren, sales, volunteer participation, whatever) with a Pareto distribution would not only lie in how accurate the shape is, but also in knowing exactly the parameters that fine-tune that shape.
The Pareto concept has other ways of showing itself. Zipf’s Law says that you order the words in the English language by how often they’re used, the Nth word in the list will be 1/N as popular as the 1st. So, you see a very small number of words showing up a very large percentage of the time in writing. Like the Pareto principle, this is a generalization, and different people, regions, and documents will have variations on word popularity. These variations allows for statistical stylometry, as well as making sure every book in the library isn’t identical.
The Internet %1 Rule (or 1-9-90 Rule) is one that suggests that only about 1% of users on a website actively create content for that site. This doesn’t mean 1% of people who read BBC.com are writing news articles, but it might mean that 1% of a news site’s readers are leaving comments. I’ve heard this referred to often in the realm of podcasts, where show hosts can expect about 1% of users to email in, or participate in a contest, etc.
Again, it’s key to note the error bars we’re willing to accept. If 2% rather than 1% of listeners responded to a call for podcast questions, the creators might not notice the difference. Using the Pareto principle as a very rough rule of thumb, as a suggestion for what to expect, is the way to make it work for you effectively.