Confidence Intervals all at once in AP Stats
I tried something very new in AP Stats this year. Okay, it may not be all that new, but it was new for me. Last year when teaching confidence intervals, I taught it as it shows in the book, first 1 prop z, then 2 prop z, then inference testing, then 1 sample t, then 2 sample t.
I ended up with a class that saw confidence intervals as 4 separate things, and never once (except for those few exceptional learners) connected the dots to see that all 4 intervals, 5 actually, because you can have 1 prop z and 1 sample z, were all the same, exact idea separated only by what kind of data you have.
This year, while working with a colleague in another state (thank you @druinok and your blog) I learned that while the curriculum to AP Stats is pretty set, the creativity to teach it better comes from me. So, I changed it up. Last year, my problem was that the learners did not see the intervals as the same thing.
This year, I decided to teach all 4 intervals at the same time. Slight exaggeration. I taught the 1 prop z interval, and the conditions for it, and how to interpret, and how to do them. Then, I offhandedly mentioned, “and you know, there are other types of intervals we will get to as well.” In the restaurant business, that is called planting the seed. English teachers call it foreshadowing. I call it darn good stuff.
The reaction from the learners was immediate. “What are they?” “Are they different?” “How are they different?” were some of the immediate questions. So I went into them. Next I covered the 1 sample t interval. Here are the conditions, here is where you use them, etc.
They were hooked. The class, as a whole immediately saw that the intervals really weren’t all that different. Next, I made a worksheet with 12 problems. Several from each type, but purposefully NOT 3 of each type. Actually, 3 of the 1 prop/sample z, 2 of the 2 prop z, 5 of the 1 sample t, and 2 of the 2 sample t. The learners cut out the 12 problems, and had to sort them. There were a couple of purposefully tricky examples, like:
Suppose the average height of randomly sampled 100 male students at University of Reno is 67.45 inches with a standard deviation of 2.93 inches. Find a 95% confidence interval estimating the height.
The class put this in the “t interval” category at first, and that categorization would probably not be wrong on an AP test. It fits better in the “z” category though. Why? This was tricky because it doesn’t say we actually DID take a sample of 100. It says “Suppose ….” Yup, this is Mr. Waddell being a jerk and trying to trick the learners. But they got that. It was the only question worded that way on purpose.
At the end of class, the learners had 4 stacks of problems. I worked 1 problem all the way out using PANIC (Parameter of interest, Assumptions check, Name the interval do the math, Interval in correct notation, Conclusion in context). They had to pick 1 from each stack and do the problem.
They left class in good spirits with some very complex problems. They left feeling like they understood something important. I walked away chalking the last 3 days up as a success. Now it is just up to them to recall it.
