Dick De Veaux gave a talk for us a few years ago, getting to some general points about statistics teaching by starting with the question, Why are there no six year old novelists? Statistics, like literature, benefits from some life experience. Dick writes,
We haven’t evolved to be statisticians. Our students who think statistics is an unnatural subject are right. This isn’t how humans think naturally. But it is how humans think rationally. And it is how scientists think. This is the way we must think if we are to make progress in understanding how the world works and, for that matter, how we ourselves work.
Here’s the talk. I recommend it to everyone who teaches statistics.
Good presentation; I wish I could have heard his talk.
I wonder if there's another difficulty in statistics. In other math, you're usually dealing with numbers. When you occasionally deal with vectors or time series, you know it: vector names are typically printed in bold or have an arrow over them, and time series names are typically followed by (t), as in y(t). Or you're in a linear algebra class and know practically everything is a vector or matrix.
In statistics, there sometimes seems to be a confounding of scalars (the mean of X) and distributions: is p(x) the probability that x takes on a particular value, as discussed in the preceding paragraph of somebody's text, or is p(x) the probability density function for x? Is p(x)*p(y|x) a product of two numbers or of two distributions (and, if the latter, is that really an integration)? While care is often taken in probability to distinguish random variables from instances of a particular random variable (e.g., X vs. x), the other seemed at least as confusing to me.
Certainly with experience comes the ability to tell the two apart, but I think that's one of the few examples where the notation doesn't seem to make the difference clear.
Or did I miss something along the way?
Among subdisciplines of mathematics, some tend to have younger people doing them than others. Combinatorics, for example, tends to skew young (or so I've heard; my own perspective is too limited to tell), because there isn't a huge theoretical basis for it and so one can learn it relatively quickly. (In my opinion, the best combinatorial problems are the ones I can explain to my grandmother. Well, I used to think this; my grandmother's kind of senile now, so I use my aunt instead.) In a field like algebraic geometry where there's a lot more background to be absorbed, the average practitioner is supposedly older. I don't think anybody's done a serious study of this, though; it's all anecdotal at this point.
"and it is how scientists think."
I like the subtle humor in that statement.
The upper-case, lower-case notation for random variables is, in my opinion, old-fashioned and sloppy. In Bayesian Data Analysis, we do it all with lower-case letters.
That shows you the age of my probability book (Dubes)!
> "and it is how scientists think."
> I like the subtle humor in that statement.
right most don't but all "should"
I believe the first step is to "reveal" that even the most brilliant scientists "mislearn" from their observations by just "reasoning" about them. The clinical researcher Dave Sackett used to try to bring this home by presenting randomized study results backwards – if the control group did worse he would say they did better and encourage the audience to explain why you didn't need a study to know that (or least explain why the result made sense). Then he would be honest and time how long it took for explainations of the actual result to be given – usually almost immediately.
CS Pierce roughly put it this way
Math – no risk of being wrong (unless you are careless and others can point that out to you)
Reasoning about how things are (hypothesis) – always wrong (aka all models are wrong)
Statistical methods – usually not wrong (and less wrong with increased efforts)
The third is indeed "weird" but necessary – if we (a community) are to make progress in understanding how the world works
My name is Regina and I am a math teacher and actually I am writing books that help me to share my teachings: Science + MATH + ART + HISTORY
It is a way to demystify those subjects
I would like to present to you the series of books entitled, "Caius Zip – The Time Traveller,"
The main idea behind the "CAIUS ZIP – The Time Traveller" series is to show the history made by great men and how mathematics and other subjects were important in their decisions. Caius Zip is a young man that participates in these discoveries and in the great battles. In each adventure, he acquires maturity and learns that to get out of trouble he must use his most important ability that he unknowingly uses very well: the power of deduction
The first book, " Einstein, Picasso, Agatha and Chaplin:, How to explain the theory of relativity, cubism, travelling in time and unmask a murderer " has been published
Caius Zip, the young time traveller, arrives at Paris in 1905. The turn of the 20th century is a period that sizzles with ideas and realizations and the Universe is about to be contemplated as it never was before.
In this fiction, Einstein was resting in Paris before his innovating Theory of Relativity enlightened him. At that same time, Picasso was just starting on his idea of breaking with conventional perspective.
Both characters seek the same concept: space-time relation. The encounter between art and science is finally possible by means of a limitless imagination.
There are the descriptions of interesting places of the belle époque in Paris and the memorable dialogue between Caius, Einstein, Picasso, Agatha, André Salmon, the poet and Getrude Stein, the sponsor of the novice Picasso, at the Spanish painter's atelier on how art, literature, science, travelling in time and mystery are intertwined.
Caius penetrates the birth of the theory of relativity and cubism and also manages to solve a murder mystery with the help of his two teenage friends, Agatha Christie, with her investigative mind and Charlie Chaplin, who provides a touch of magic to this surprising work of fiction.
After all and as Einstein once said: "The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed".
Please,see a passage from the book in: http://www.caiuszip.com/relativiting.htm
Along those lines, Francis Galton worked out the basics of regression analysis in his 50s and 60s. His paper that launched the "wisdom of crowds" concept appeared in Nature when he was 85.
I think the mathematics vs. statistics age difference is like the difference between lyric poets (young) and social novelists (mature).
On the other hand, Thomas Hardy was a social novelist first and lyric poet when he was older.