Mathematicians love mathematics. They love the elegance and the purity and the abstract nature of it all. Consequently they think there is something not quite nice about the practical real life messiness of statistics. Now this is fine, so long as they keep their prejudices away from their students! I recently met a high school maths teacher who was completely vocal about her dislike for statistics. Fortunately she doesn’t teach the final year statistics course, but she can’t avoid the sections of statistics all through the curriculum at lower levels. It hurt me to hear statistics so disliked.
Elementary school-teachers who dislike mathematics harm the good attitude formation in their pupils. They don’t like maths, and they feel uneasy doing it, and that rubs off. High school teachers are often frustrated by the attitudes with which students arrive at high school. There are moves in New Zealand to address this, through the Numeracy Project, which helps to develop skills in our Primary teachers.
What bothers me is similar. Many, if not most, of our high school teachers are pure mathematicians. Some of them allow their dislike for statistics to colour the students’ experience. Or if they don’t actively dislike statistics, they may still feel ill-at-ease, as they did not get enough background knowledge in their training. They may know the mechanisms, but have no experience of statistical analysis. I know this to be true, as I was once one of them. It is difficult to go from an exact subject like mathematics, where you find x and know when you have found it, to an art/science like statistics, where x changes depending on the context.
However I am now a born-again statistics applier. I hesitate to call myself a statistician, as I don’t use R, and I’m not exactly sure what a moment is. But I know how to do statistics in the real world. I know what you should and shouldn’t do with different data, and I know how important context is. I know that you seldom get a simple random sample, and sometimes your sample is so far from random that you blush, but soldier on anyway. I’m skeptical about Factor Analysis. And I keep learning. Every time I do a real statistical analysis I gain insights into the nature of the discipline. And I love it. Statistics is a detective game. The numbers tell a story, and it is up to us to help them reveal their secrets without so much coercion that they tell us lies to make us go away.
My wish is that pure mathematicians in high schools would accept that statistics is not mathematics and never will be. It is a mathematical science, and needs to be taught differently from mathematics.
George W. Cobb and David S. Moore wrote a paper, “Mathematics, Statistics, and Teaching”, which gives answers to questions such as “how does statistical thinking differ from mathematical thinking? and “What is the role of mathematics in statistics?”. They emphasize that beginning statistics should be taught as statistics. A beginning statistics course should use real data and automated production of graphs and analysis.
This is antithetical to a pure mathematician. “Remove the maths and the graphing – or get the computer to do it, and where is the maths?”, they cry! “Exactly!”, reply the statistics teachers.
I hope there are maths (or math) teachers reading this. You can do it – you just need to accept that statistics is NOT mathematics, and learn to see the rigour and excitement in it. Embrace the messiness! Throw off the shackles of finding the one correct answer! Statistics, well-taught, will be more use to most of your students than calculus.