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?