Now – those who got it right. On the count of three, I’d like you to sit down if you’d seen the question before. 1, 2, 3!” Everyone who was standing sits down. This gets a huge laugh. The students who got the answer wrong suddenly feel much better about their mistake: in a Harvard class, not a single person got it right unless they had seen it before.

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Dan’s goal, taken from his mentor Richard Zeckhauser, is to get students to think probabilistically about the world. This means engaging with the challenge of understanding and accepting what 29% means in the context of a Trump victory, and fighting the brain’s natural inclination to see things in binary terms.

He asks the 80 students to respond based on their ‘gut feeling’. Again, students are given five options, ranging from ‘less than 1%’ to ‘above 40%’. About half of them believe the true answer is less than 5%, of which plenty go for the ‘less than 1%’ option. Only 1 in 6 get it right, picking the highest option: it turns out that the true figure is 41%. He invites those people – 13 in total – to stand up.

In advance of the class, he asked students to fill in a quick survey in which he asked them to describe their own experiences with one of these three uses of statistics. He tells the students that he has read their answers, as well as their student profiles, and asks for volunteers to talk about what they wrote. Several hands go up, and he picks Juliana, a student from Brazil, interested in education. She starts to talk about a program she helped to run in Brazil which assessed whether improvements in teacher training had a causal effect on test scores. As she is talking, her words appear on the big screen, in big quotation marks, along with her photo. The class laughs, and as she looks up she realises she has become a celebrity.

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After pausing, the student continues: “There’s also an element of believing something because you want it to happen.” This betrays a second bias in which we believe what we want to be true. This is a form of confirmation bias, which exacerbates the distorting effect of availability bias. We seek out information that confirms our existing beliefs or desires, and ignore information that refutes them.

The brain has conflicting goals: to provide you with information, and to reduce your anxiety about the worrying outcome. If you wanted Clinton to win in 2016, your brain achieved both goals by accepting the 30% figure but telling you it would not happen.

Maximising enjoyment All students want to enjoy their classes. This simple truth means that teachers who can make learning fun will, other things equal, be more successful. If the only way students can enjoy themselves is to ignore the class and play on their phones, then student enjoyment is a headwind that slows the boat’s progress. By making learning fun, teachers can adjust the sails to take advantage of the wind and speed the boat up. The progress it makes may not be directly towards our destination, but we can use the sails nonetheless to pick up speed and get closer to it than we would otherwise have done.

It sounds like a lot of you are not too surprised if this 30% chance materialises,” Dan replies. “You take precautions against it. The rain, if it comes, doesn’t shock you, and you have your umbrella. So why was everyone so shocked about Trump?

But few of us really stop to ask ourselves what new information might change our minds, especially on questions of politics and identity. We fall into the trap of confirmation bias, in which rather than updating our prior beliefs, we mould new information into a form that will confirm them.

Dan’s use of two-stage exams kills two birds with one stone. Firstly, he maximises learning by ensuring that the exam itself is a learning experience. Second, in doing so, he makes clear that the grade is less important than the learning. Two-stage exams have not yet ‘taken off’ around the world, and grades remain the key outcome of most exams for most students. Dan, though, has taken advantage of his position in a graduate university environment to push the idea forward.

Dan asks the class whether any of them has ever checked the weather on their phone to see if it’s likely to rain while they’re outside. Everyone has. “What do you do if you see there’s a 30% chance of rain?” “Take an umbrella”, several students all say at once.