7. Traps in thinking about probability

Preamble: As mentioned in the last activity, some commentators on mathematical thinking claim that probability and statistics are more important to teach than calculus. The last activity focused on statistics in the sense of data analysis. Let us shift to thinking probabilistically. One way to engage people is to get them to chew on traps.

Preparation

• Read Gilovich, "The Hot Hand in Basketball"
• Time permitting, preview some of the videos and other items listed under 1 below.

Goals

• Chew on traps in thinking about probability until you can explain them to others

Activity
Although this activity is to be pursued individually, you will be put into breakout rooms. If you want to chat about what you are thinking, ask your breakout partner(s) whether they too want to chat.If they do, don't let that divert you from drafting and posting something for the task under 2.

1. Make notes on the traps in thinking about probability in a selection of the following videos and web articles with a view to explaining them to others—or explaining what questions you still have about the issue (40 minutes)
"Gilovich doubles down on hot hand denial," http://andrewgelman.com/2017/04/02/gilovich-doubles-hot-hand-denial/ (Skip if this is hard to grasp. But note that someone who was confident about a trap was shown to have made a mistake.)
"Nate Silver says conventional wisdom, not data, killed 2016 election forecasts," https://news.harvard.edu/gazette/story/2017/03/nate-silver-says-conventional-wisdom-not-data-killed-2016-election-forecasts/
"The Bayesian Trap," https://www.youtube.com/watch?v=R13BD8qKeTg
"Is most published research wrong," https://www.youtube.com/watch?v=42QuXLucH3Q
"Khan Academy and the Effectiveness of Science Videos," https://www.youtube.com/watch?v=eVtCO84MDj8

2. Revise the notes into a draft of something in the style of "Top 10 Thinking Traps Exposed — How to Foolproof Your Mind," https://litemind.com/thinking-traps-2/
Post on the wordpress site.
Make notes on what others post.
(30 minutes)

3. Plus-delta feedback on activity (5 minutes)

References
Gilovich, T., R. Vallone and A. Tversky (1985). "The Hot Hand in Basketball: On the Misperception on Random Sequences." Cognitive Psychology 17: 295-314.