Hey mathematics – leave the stats alone!
Statistics Textbooks suck out all the fun.
10 April 2012Stop faking it! Data should be real.
23 April 2012
Mathematicians love the elegance of mathematics
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.
Statistics lives in the real world
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.
18 Comments
Hi
I totally agree. As a science teacher recently asked to teach Maths, I find that our learners don’t like my favored approach of “generate some numbers, do the analysis / graphing in a computer and spend more time thinking about what it means” – they want to spend more time on the algorithms used as opposed to understanding what the heck is going on. In this context statistics / science are very close and I wish we could blur the boundaries even more.
Try this one – ask your teachers, colleagues or students what the Mean of a data set is. If your lucky, you might get a definition – add up the data and divide by the number of items in the data set — great you say, but what does that number actually represent. Few if any will be able to tell you. We seem to have removed the meaning in Maths and transformed it as a subject where mastering algorithms is more important than understanding what the numbers actually mean.
That’s why I also love stats.
Cheers
Glen
About the mean: balance point. (Variance: moment of inertia)
Hi Glen
Thanks for the comment. The compartmentalisation of knowledge can be a problem in the way we teach and organise schools. Interesting that the learners were also disturbed that stats isn’t maths. They too are used to exactness and “getting it right” and find the requirement to really think hard difficult.
Your example on the mean is so true. But then, the mean is a surprisingly difficult concept. (See my post of 12 January 2012.)
I agree to you completely.I always feel confused what is mathematics in statistics.As being math teacher i agree to you.I will share with my friends. I recently arranged summer camp to teach children with online lessons http://www.youtube.com/user/GuruBix as you know teachers and students get academic holidays every summer.Children wont show up interest in education during holidays. so i arrange online lessons to create interest in them.
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I agree. Stats needs to be taught first as a methodology/thinking process that helps to answer questions using data. Real statisticians/users of stats spend their time trying to find ways to answer questions using data and have to learn to cope with unexplained and unexplainable variation, and have to visualise the information using graphs and models. THIS is what we need to teach students when we teach them stats.
There is a place for probability distribution theory but it can be done in a different course/section and pitched as the theory that the stats is based on. Not to say that distribution theory is not interesting — I think it’s super cool actually — but it doesn’t belong in the same home as the methodologies of how to answer questions using data.
To make sure you know where I am coming from here — I actually am a pure mathematician and I love things with internal logical structure and no immediate application to anything. But I also love how statistics can be used to help answer questions and support the scientific method.
Hullo there,
I reached this page while searching the net for motivation behind pearsons correlation coefficient formula. It is very easy to remember that it is cov(x,y)/(sdx, sdy), but very tricky to understand the exact insight behind the formula. I have studied statistics for two years in the collage (3 years degree course with a math major, I have taken 5 statistics courses in 2 years), and still not able to understand or to feel comfortable with even the basic statistical concepts.
I think the reason is that most of the textbooks that I have seen emphasis too much on what to calculate and how to calculate rather than on why to calculate it in that particular way. Instead of presenting statistics as a set of well thought out strategies and theories for handling vast quantities of data, they present statistics as a collection of tricks and formulas without any motivation or reason.
I passionately hated statistics (and I shared that passion with ALL of my math minded friends) till I got an assignment related to analyzing some business processes. After coming up with some really outlandish mathematical models, discovered that statistics was the simplest and most workable way of quantifying my observations. Two years of statistical education and browsing stat textbooks from time to time just out of plain curiosity could not prepare me to appreciate the essentially statistical (as opposed to analytical, in a mathematical sense) character of data I was working with.
This link to the paper you cite still works – well worth reading for any of you who have not done so. http://www.stat.ucla.edu/~rakhee/attachments/moorecobb.pdf
Hi – I agree. I really love the way George Cobb writes – very easy to read and even entertaining, with a well thought out message.
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hello and thank you so much for this information and i want to tell you that i love mathematics so i also want to know about history of mathematics can you please tell me the best book for history of mathematics thank you so much