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Next semester I will teach an elementary statistic course for the first time (which I am actually quite excited about). A brief description can be found here. I am told to expect very little math background from the students. The class size is about 40-50, meeting twice a week , each class lasts about one and half hour. I do have a graduate student helping with grading and recitation.

My first question is about textbook. Please let me know of suitable texts which are:

1) Fun to teach and learn from, especially for students with less background. I would like a book with lot of interesting, engaging, probably more exotic examples ( so less diseases and more, say, gambling! ).

2) Relatively cheap (preferably less than 100 USD). In this economy we don't want to make students pay too much. Most texts I came across seem quite expensive. (Unless if the text is really a treasure, then one can worry less about price.)

The second question is about the best way to teach such a course. My instinct is that a heavy lecture style would not work very well, especially since the class is one and half hour long. Do you know ways (preferably with references, especially visual references) to teach this materials without too much lecturing?

Thanks in advance.

(I did not make this community wiki since I want to reward the best answer, and also I am not sure there will be many equally good answers given how much I wanted. Let me know if you disagree, I am open to change on this issue.)

EDIT: The student body will be quite varied. I am told there will be psychology majors and some engineering students, but the majority would prefer examples to proofs.

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What is the purpose of the course? Is it to teach students in the (social) sciences enough statistics to analyze data and read papers? –  Douglas Zare Mar 10 '10 at 18:24
    
Make sure you use a book that is available in the usual places. Also, you'd be surprised how much a little bit of rigour can clarify things for students. Most statistics courses avoid rigour like the plague, but actually proving the formulas clarifies the motivation for them. Luckily, you're a pure mathematician, so that should be no problem. –  Harry Gindi Mar 10 '10 at 18:32
    
If this is for psychology majors, then I doubt rigor will help them to build an intuition, which is what they really need. –  Douglas Zare Mar 10 '10 at 18:40
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fpqc: What courses have you taught before (to weak or strong students)? I find it useful when thinking about teaching a class to non-math majors to remember what it was like when I learned how to drive: I wanted to learn how to move forward, stop, reverse, park, check the oil (in short, how to use a car) without engineering lectures. Hailong's students are in the same position. Explanations through well-chosen examples will be meaningful, general proofs will not. As Lang would say, these students do not have the proper psychological background to accept general proofs. –  KConrad Mar 10 '10 at 19:01
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Ah, but we need to be careful not to project our own mathematical tastes onto a class we're teaching. I might find a computationally based class to be a bore as a student, but when the tables are turned and I have to teach people who are not very mathematically inclined, I need to make the material attractive to them. I'm not saying the course should be made completely plug-and-chug, but if you only teach the way you like math to be presented to yourself, you will be despised by the class and have a miserable experience. Take pleasure in creating good examples instead of slick proofs. –  KConrad Mar 10 '10 at 20:19

4 Answers 4

up vote 14 down vote accepted

A bit of background: a few years ago, I designed such a course, after noticing that many of our social science majors were ending up taking a precalculus course (spending much time learning trig), which was mostly useless for their later study. I created a case-study approach to probability and statistics for students with weaker mathematics backgrounds (i.e., most of my students have been terrified by math in the past).

I wonder how much time the OP has to prepare -- it took me a long time (and a bit of grant support), as a pure mathematician to not only learn the basic probability, but more importantly to change my mindset from pure to applied mathematics. The formulas in basic probability and statistics are nearly trivial for a professional mathematician. The real work is identifying sources of statistical bias, interpreting results correctly, and accepting the fact that no studies are perfect. In statistical mechanics, you have an absurdly large sample size of molecules behaving in a very well-controlled environment. In practical statistics, you have a smaller, usually "dirtier" sample; as a pure mathematician, it's hard to accept this sometimes.

I'd begin preparing yourself by looking at three books -- the classic "How to Lie with Statistics", the new classic "Freakonomics", and Edward Tufte's "Visual display of quantitative information" (and/or his other books). None of these is directly relevant to your course material, but they will give you many ideas for teaching, for caution in the application of statistics, and for good and bad aspects of visual display of statistical information.

Directly regarding your questions: I'm not familiar with textbooks enough to advise you on this one (I wrote my own notes). But I strongly disagree with your assumption that "less diseases and more gambling" will make your class more engaging. Most people don't care about gambling; this is supposed to be a useful class, not training for a poker team. Real statistical studies are extremely interesting, especially given their life-and-death importance. Your students should be able to answer questions like "what is the probability a person has HIV, if their test result is "reactive"? How does the answer differ for populations in the U.S. vs. Mexico vs. South Africa?". Diseases, discrimination, forensic testing, climate extremes, etc.., are important issues to consider.

You might find gambling more interesting than diseases, but a teacher of math for social science students has a responsibility to approach important questions, and not contrived examples. Take it seriously!

There are many activities that you can enjoy with students. You might play a version of the Monty Hall game, for one. There are many activities with coin-tosses (e.g., illustrating the central limit theorem). You can illustrate sample size effects, by randomly sampling students in the course. You can certainly find cases in the media and recent studies, and use them as jumping-off points for discussion: you can even find funny ones in magazines like Cosmo, or on CNN.com so that the students can practice picking apart statistical arguments and deceptive rhetoric. I often make students find an article in popular media (like NYTimes.com) that refers to a study, then track down the original study, and compare the media summary to the published study to analyze how statistics are used and misused. This can make great classroom discussion.

Finally, it might be personal taste, but I would place a heavy emphasis on probability, especially Bayesian probability. Otherwise, the course can become mechanical and reinforce a common malady: students will think of statistics as the process of collecting data, putting data through a set of software/formulas to compute correlation coefficients, p-values, standard deviations, etc.., interpreting these numbers as facts about nature, and being done. The Bayesian approach, I think, requires more thought in setting up a problem, and yields more applicable results. In particular, there are significant Bayesian criticisms of "null-hypothesis statistical testing" that is the centerpiece of many studies; especially the overreliance on p-values is disturbing to me, and you might want to include criticisms of such things.

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Thanks for your thoughtful answer! I used diseases and gambling mainly as an example that I wanted examples that are more exotic and thought-provoking. May be it sounds worse than I intended. –  Hailong Dao Mar 10 '10 at 19:51
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Oh - another fantastic source that you (and maybe your students) should look at is the article "The Most Dangerous Equation", by Wainer. You can download it at nsm.uh.edu/~dgraur/niv/TheMostDangerousEquation.pdf –  Marty Mar 10 '10 at 19:55

I was amazed at how much was done in the book by Freedman, Pisani, Purves, and Adhikari without using any math beyond what an equation of a line looks like, and that in only one small part of the course.

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I currently teach from this book; I agree with this comment. –  Michael Lugo Feb 10 '11 at 4:52

Have a look at Statistics by David Freedman, Robert Pisani, Roger Purves. There is a paperback edition for about $50.

It is extremely well written, but its suitability will depend on the interests/background of the students.

His (Freedman) more recent books have some interesting examples that you may want to use to supplement the material.

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Regarding Q1: how about Introductory statistics by Sheldon Ross. Disclaimer I did not read or taught from this one, but I taught from his "first course in probability", and looked at several of his more advanced books at some point. He writes well, and his books usually target the audience they claim they do.

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