In a message of 04 Dec 2003 20:50:52 PST, "Josh English" writes:

I'm a lurker on this list. I joined because I was on track to become a high school level mathematics teacher and I use Python frequently. I am currently a graduate student and I'm working on a final project for the term. I am creating a rough draft of a curriculum that would teach Statistics and Python in the same class. I'm basing this off of two assum ptions: 1) Students in a statistics class do not need the practice of repetitive operations. 2) The most effective way to learn something is to teach it, and programming is functionally equivalent to teaching a subject.

I think that these assumptions are good enough to start with, but I'd like to hear some other opinions about them. Is programming in any language the functional equivalent to teaching a procedural method?

Thanks for any advice, Josh English english@spiritone.com

Your assumptions are not universally true -- though they certainly are in many cases. So you need to check to make sure that they hold true for your case. I have a few questions. First, what country are you in? Second, what is the age of the intended students? Third, how sophisticated is the statistics you wish to teach? I am going to outline here under what conditions I think that what you intend to do may be a mistake, and cause problems for you. This isn't to be taken as a rejection of your plan -- I think that it sounds like a lot of fun, and will be an excellent way to teach the correct bunch of students, which I hope you have. Because in that case, it will be great. Assumption one sets you clearly on the path of _education_ rather than _training_. (Training is pretty much all about repetitive action.) When _educating_ works, you need students who are able to memorize new chunks of abstract knowledge, and then know exactly where to store and apply it in the knowledge structures which they have in their own brains. This will only happen if your students already have a nice collection of mathematical knowledge, and enough mathematical intuition to know how and where to add new stuff. If they don't, then either a) they won't be able to memorize the abstract knowledge, 'It's all words, and it doesn't really mean anything' or, for the good memorisers -- they will know the definitions word perfect and still not have a clue what it means. For this reason, when I am busy teaching elementary school children the difference between a mean, a median, and a mode I make them draw some stick figures and then measure legs and arms and torsos and the lot. This is because 'means' and 'medians' are not about _words_ and not about _numbers_, but about _measuring_, _counting_ and _populations_. The students I get understand counting, but not measuring yet, and have drastic problems understanding populations. If you don't train them how to measure, you end up with a class of parrots who can manipulate the numbers to get the correct answer when you ask them 'calculate the mean of this series of numbers' but who cannot figure out if their allowance is in line with what is usual for their peers, (if there is only one person in the class that gets more allowance than they do, it is still _unfair_, because _she gets more_), or even whether something is 'more common' or not -- if you hand them a series of 30 numbers from one to ten with '4' repeated 8 times in a row and '9' occuring 10 times, but never in a row, about half the class will insist that '8' is more common than '9' _even after you count them_. It is only after you hand people the actual numbers on tiny pieces of paper (or cutout of paper) and actually make piles of 8s and 9s that they can see which is 'more common'. (And even then you will get some holdouts, who think that '8' is more common, because however you slice your series, you can never get a subset which has more 9s in it than the other numbers, and there are lots of ways to slice it where you get more 8s than the other numbers.) I assume that your students will be older than this. Indeed, I assume that they either a) already know how to program, or b) the statistics that you wish to teach them are the sort that you can do in a trivial amount of Python code -- the sort of thing that you can just type into a Python interpreter. If you don't have this sort of match, then what you will end up doing is teaching your students how to program. Now a course 'teaching programming using basic statistical methods' might be a lot of fun -- though my experience is that 'teaching programming using problems that involve words works better' but if the stated aim of the course is to teach statistics, you may get in trouble with your department. You also need to check to see if they are supposed to be learning mathematical fundamentals, or whether symbolic manipulation will be enough. Something to be concerned about is how this course is supposed to fit into the general pattern of their mathematical education. Some places use statistics courses in order to teach students how to make graphs with pen and pencil. The actual statistical knowledge imparted is relatively minor. What is important is to get the ability to visualise data. And to learn that, you have to draw it. Learning how to read graphs is not enough, and learning how to write a computer program that draws graphs is also not enough. You actually have to make a bunch of drawings, again and again and again before, given a series, or an equation, you can actually have a geometrical sense of what is going on. (And some people never get it, no matter what you do. It is quite frustrating.) Check and make sure that this is not what really is supposed to be taught in that class before you replace the pen and pencil with Python, because in that case your assumption 1 is shot, and you are supposed to be training them. The next thing to check is whether the intellectual effort required to make the program is spent on learning the formulas you would like the students to learn (assuming this is what you are up to). It is quite easy to get a mismatch. For instance, a smart student might build a really nice program for making very pretty bar charts, working and polishing on this for days, weeks, months. The actual statistical equations that are used to graph are almost an afterthought -- you crack open your text book, and convert the formula into python in a straightforward mechanical way, and that takes you all of 20 minutes. You can now do a whole family of equations, at roughly 20 minutes an equation. Ooops. That student isn't learning statistics, as in the formulae, he or she is learning how to quickly rewrite formulas in Python. (Which is what I do all the time, and is the reason why I always have to look them up. I never actually _know_ them.) This is a really useful and valuable skill, but probably not what you are trying to teach. This problem can work in the other direction as well. For instance, you will have to give them a nice lecture on 'What is Floating Point, When can you use it, and when must you never use it.' I'd dearly love that lesson taught to high school students, world wide. But it is tough going, and my gut feeling is that it will not be easy to teach this one until your students have an extremely good sense of what experimental error is. If they don't have that background, then they may confuse floating point error with experimental error which is a particularly nasty misconception to uproot later. Also, when building a computer program to do some sort of problem in numerical analysis, you may find that the bulk of the program is spent doing corner cases and handling particularly nasty sorts of data. Writing this code -- at least the way I do it -- is a matter of writing a bunch of unit tests and building the code so that it handles all the perverse cases. But first, your students may be too naive to see the perverse cases -- this is where they are being first exposed to them, after all, and second, in a basic statistics class, you may want the students to focus on how things go when your data is well-behaved, and doesn't provide any problem for the programmer. So there the goals of test-driven design and learning the statistical methods may work at cross-purposes. But, provided these problems do not raise their ugly heads, it looks like a lot of fun, and could be the sort of class where you actually get a taste of 'what life has to offer' rather than 'what school has to offer'. Sounds good to me. We're having an Education Track at EuroPython June 7-9 2004 in Göteborg, Sweden. (And if you are not in Europe, travelling to Europe is probably cheaper than you think.) Come give a talk and let us know how things are going. That goes for the rest of you, as well. The education track chairman is Steve Alexander <steve@z3u.com>, but we are discussing such things on the EuroPython mailing list now -- http://mail.python.org/mailman/listinfo/europython Laura Creighton