Today I attended the winter meeting for one of my favorite organizations: PASTA, the Philadelphia Area Statistics Teachers Association. This group meets a few times a year to discuss best practices in statistics education, and includes a number of AP teachers, many of whom are AP exam readers. As always, lots of interesting ideas today:
Joel Evans, from my home school, spoke on his first attempts to “flip” his AP Statistics class. Based on feedback from his students, Joel realized that Powerpoints often dominate his classroom culture. By flipping, Joel hoped to have students review material before class, then use class time to practice and discuss. Follow Joel’s flipping story in the slides below.
It is always a pleasure to have Daren Starnes at our meetings. Daren, one of the co-authors of the ubiquitous The Practice of Statistics textbooks, joins our group often to discuss his ideas for teaching statistics. Today, Daren shared a presentation, “50 Shades of Independence”.
Daren asked us to think about all of the places where we encounter “independence” in AP Statistics:
- probability of independent events
- independent trials
- independent random variables
- independent observations
- independent samples
- independent categorical variables (chi-squared)
Man, that’s a lot of independence!
Which items from the list above deal with summarizing data? Which are needed for inference? How are they related? How do we help our students understand the varied, and often misunderstood, meanings of independence.
Daren has a knack for leading conversations which invite participants to express and discuss their math beliefs. 
Many of the arguments concerning independence, according to Daren, are “overblown”, in that teaching them in a cursory manner often causes us to lose focus on the big picture. That’s not to say that we should discard them, but that, when teaching inference, we should have students focus on items which would cause a hypothesis test to be “dead wrong” if we didn’t mention them, i.e. randomness, justifying normality conditions.
Ruth Carver continued the presentations with some new tech twists on a lesson used by many stats teachers: analyzing sampling distributions by looking at the age of pennies. A population graph of the ages of 1000 pennies hangs proudly in Ruth’s classroom.
After agreeing that the population is clearly skewed right, we move to the main event – drawing random samples from the population and analyzing the data we get from repeated samples of the same size. Ruth has developed a lesson for the TI Nspire which generates the samples, and challenges students to think about the behavior of the sampling distributions, now considering the effects of sample size. Ruth’s presentation allows students to experience and express the differences between:
- Standard deviation of a population
- Sample standard deviation
- Standard deviation of a sampling distribution
Great job Ruth! Looking forward to more PASTA with my stats friends!
The main differences with a Pincohle deck are that there are only 48 cards, and each card (like the 9 of diamonds) appears twice in the deck. This problem introduce the idea of permutations with duplicate items. In this case, we start with 48!, but then must divide out the double-count which occur with the repeat items. We divide by two for each instance of a repeat item, and the number of permutations is given by:
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