A couple of straightforward lessons in statistics I don't get to teach my Y11 students:
- The mean vs the median, as this issue applies to the 2014 New Zealand budget.
For most voters this year, their main concerns will be over job security and wages. At best, these factors seem likely to flatline and may well decline. In his Budget speech, English pointed to the jobs being created by the government, and the rise in the average wage – now at $54,700 and forecast to rise to $62,300 by 2018. The figures are misleading and that’s mainly because – thanks to the extremes at both ends of the income spectrum – the average wage figure conceals as much as it reveals. The median wage would give a truer picture of the income spread but, according to Treasury, that figure isn’t collected. However, judging by the charts in the small blue “Key Facts” Budget handout, 69% of income tax payers in New Zealand are earning less than $50,000 a year. Two thirds of us are earning below $40,000.
From Gordon Campbell's analysis here
I do teach the difference between the mean and the median, but there are so many other things to cover in the curriculum, that I don't have time to spend to linger on this very important and highly relevant application. This sort of lesson could be part of an integrated course of study, which would include economics and demographic statistics.
- The interpretation of this graph, from Thomas Picketty's book Capital in the Twenty First Century:This lesson, or more likely series of lessons, would be taught as part of an integrated history topic, studying the history of capitalism over the course of the twentieth century. The concept of a ruling class would be introduced, and we would consider carefully whether or not we can identify this class with the top 1% of income earners. We would cover the economic and social forces prior to the outbreak of WW1, and what effect the war had on the economy. Then we would study the first major spike in the graph, which corresponds to the 'bubble economy' of the 1920s. This would be followed by the study of the 1929 crash, and the resulting depression. We would consider the question: what social and political forces decreased and held down the income of the top 1% for such a long period of time between the 30s and the 70s? And what happened to society that allowed these top 1% to suddenly increase their share of wealth by such a massive amount after the 1970s? Did they suddenly become much more clever at making money? Where does their money come from anyway?
Instead of teaching lessons such as these, we busy ourselves with studying the fascinating set of data gathered together by the “Census at schools database”. The most crucial question we use our sophisticated statistical techniques examining is this: “I wonder if Y11 boys are taller than Y11 girls?” We use clever computer programmes to select random samples, and we ponder the box plots with excruciating attention to detail. Are the heights normally distributed? Have we thought carefully enough about sampling variability? Is the data reliable, or did some of those naughty students lie about their height?
As a teacher, I have to carefully plan out my lessons to cover a huge amount of technical statistical jargon. Because of time constraints, we have to race through concept after concept, without any time left in between to ponder those concepts or put them into meaningful contexts. I am responsible for delivering the curriculum as it is written, and I must do my best to prepare my students for those highly important events we now call “internal assessments”. In the Bad Old days these were called exams, and they stayed in the same usual reliable place always: the end of the year. Now we are more enlightened, and we effectively put the exam pressure on the students throughout the entire year, with continual internal assessments every few weeks. As a teacher this means having almost no room to move within the curriculum. There is very little space for innovation, creativity or idiosyncracy. We feel the exam pressure too, and also the pain and boredom resulting from meaningless and trivial questions like “I wonder if Y11 boys are taller than Y11 girls?”.
Obviously the examples of lessons which I outlined above reflect my deeply held political beliefs. Not everyone agrees with those beliefs, and anyone who knows anything about statistics knows that for every statistic or graph which tells one story, there is another statistic or graph which tells a very different story. Would I not be guilty of indoctrinating my students into my way of thinking?
My response to this would be to point out the fact that they are already being subtly indoctrinated now anyway. They are being encouraged to view statistics as a dry, technical and boring set of exercises which don't relate to any important issue or question. They are being encouraged to accept without question the validity of the boundary lines between different subjects like history, economics, statistics and geography. They are also encouraged to accept the notion that only Very Clever People can really understand statistics. The crucial fact that very simple ideas, like the difference between the mean and the median, allow us to critically examine the obfuscating and bullshit ridden presentation of things such as the 2014 budget – this crucial fact is crushed beneath the pressure on teachers and students to perform according to a set script. The script requires that Mathematics Must Be Difficult, and only a select few will be smart enough and hardworking enough to earn “Excellence” grades. Most will have to settle for mediocre “Achieved” or B grade “Merits”. The dummies will of course fail to jump through the hoops completely. When they read the newspaper later on in life, I doubt they will pay much attention to a statistical analysis of any budget.
The truth of the matter is I am not much of a statistician in any case. My main focus at uni was on the more abstract aspects of the mathematical universe. A brainy Y12 or Y13 student could easily present to me a solid counter argument, backed with lots of sophisticated statistics, which ran counter to my socialist narrative. I would relish such a challenge, and it would actually inspire me to improve my own statistical literacy. As it is, I am just as bored and alienated as the students I teach, and I only do the barest minimum that I have to in order to fulfill those all important Achievement Objectives those Gods in the MOE have laid down for me to teach.