While some of my students will go on to take a statistics class either in high school or college, my main goal is for them to have a basic understanding of statistics and it's "ishy-ness." We are constantly bombarded with statistics (politics, sports, health) and it can very easily be used to sway public opinion with innuendo and implications. As an educator, I want to teach my students to love mathematics, but I also work on preparing my students for real life. Having some knowledge of statistics can be very powerful.
Our first day was learning some basics of statistics. I posed a question that I found at Sarah Carter's blog mathequalslove regarding the hiring practices of airline pilots and whether or not a discrimination case could be made. The scenario describes an airline with 25 junior pilots, 15 male and 10 female. The airline is going to promote 8 of these pilots and all are equally qualified. To make it fair, all names are put into a lottery and the promotions go to the 8 people randomly selected. When the results of the lottery are announced, 5 women and 3 men receive promotions. Some of the men claim that the lottery was not carried out fairly and want to file a discrimination charge.
The question I posed to the kids was whether the men have a case? I have not asked a question all year that got such strong, vehement responses! It was beautiful to witness! No one really said anything that was unexpected
The male:female ratios should be the same so they have a case.
But it's not impossible to get the results they did so they don't have a case.
Yeah, but how likely was that to happen? It must have been rigged!
We should find the probability of this particular result. (This was followed by lots of murmuring about how to do just that. Since combinatorics are no longer a part of our curriculum, they had absolutely no idea how to do this.)
Then I dropped the bomb - we're not going to answer the question yet. The plan is to learn about stats and re-visit the discrimination claim at the end of our unit. I wanted my kiddos to start statistics by understanding that it is not about finding a specific value, which is their belief about anything with math, but more about interpretation. This was a great intro.
The next task for students was to write their reactions to two different studies and the subsequent news articles written about them - no conversation, just gut reactions. The first study was funded by a tobacco company claiming that they made "healthier" cigarettes. The reactions were thoughtful regarding the statistics themselves, as well as the danger of smoking cigarettes.
22% less tar and 34% less nicotine means there is still tar and nicotine in the cigarettes. You shouldn't put any of that crap into your system!
I don't think people should use statistics to make something bad look good.
The second study was regarding the IQ scores of first-born males vs. second-born males. It was a well-presented study, giving a margin of error with a 95% confidence interval (which we haven't discussed at all). My favorite comment:
It's only a 95% confidence level, so they really shouldn't be making such a strong statement.
We went on to discuss different types of studies, their advantages and disadvantages, as well as what types of questions should be asked when evaluating a study. There was a lot of really good discussion and debate. Then, they broke out into groups to discuss the class' reactions to the smoking and IQ studies. The conversations were rich and insightful. Even the students who are generally not the "talkers" in class were speaking up and mostly because of the issue being presented, not the mathematics behind it.
The goal for day 1 was to get students thinking about claims that have roots in science or psychology or the law and whether the information presented to them was meaningful or actionable. The next goal is to demonstrate how statistics can support (or collapse) their arguments.
