What would you teach?

I’d love some insights for the statistics content of a non-AP senior math course.

BACKGROUND: I’ve been asked to step into a combination terminal course for seniors covering an introduction to statistics in the fall semester and an introduction to calculus in the spring.  The course has no prerequisite and most of its students have seen precious little high school statistics or probability beyond model regressions to bivariate data in 10th grade.  The class is populated almost entirely by students who are very smart, but who’ve never experienced an honors math course.  A large portion have been frustrated and unmotivated by their previous math courses; for some, this is the last math course they ever take.

The very broad purpose is to introduce students to both branches to learn the fundamentals of what each does.  The department’s pitch for the course when it was created last year acknowledged that we could not know whether our students would be required to take calculus or statistics once they got to college, so this was the “best” way we could prepare students for college mathematics.  It meets 4 days/week for 55 minutes/session.

REFINED QUESTION:   Imagine you were to teach statistics for exactly one semester with no external limitations beyond what has already been described.  What would you make the key focal points for your class?  Why?

2 responses to “What would you teach?

  1. Here’s a very quickly thought out suggestion—but why not strive to make sure that all the datasets and examples are things pulled from current events and daily life. Have students take samples of data themselves from all sorts of data sources (their classmates, their campus, the internet) and use those instead of the boring samples you find in the textbook. And likewise pull examples from the news, rather than the examples in the text. I think this would go a long way to helping students see the power and relevance of statistics.

  2. Chris, I agree with John, but I’d go a step further. So much of statistics is used to support an argument: is the region more or less conservative, does Product A have significant side effects, are test scores rising? I’d have students use real world data to test real world claims. After a year of teaching regular statistics, I found hypothesis testing the most useful set of skills, and the most illuminating; when getting information from every member of a population is impractical, the next best thing is to get it from a representative, random sample (a determination in itself fraught with pitfalls) and use analysis from the sample to make a claim about the population, with some degree of confidence. There are quite a few tools here, but you wouldn’t have to use all of them in a single semester, and you really have to pay attention to the wording. You could have students test a claim, say, about the average of something. The math is straightforward, but the TI does the heavy lifting. You should be able to use Wolfram Alpha for calculations as well.

    I’d also have students create and give a sound survey. Doing on something relevant would be swell, but the simple skills of drafting just the right questions, with little room for misinterpretation or leading words, and of determining just who makes a representative, random sample are TOUGH, and worth everyone’s time.

    Hypothesis testing and survey work will help students become more critical consumers of media, which is a primary reason to take a stats course, in my humble opinion. They could also be especially pertinent in an election year.

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