David Franklin Quotes

Recognising competing purposes Although few would have much trouble identifying ‘maximising learning’ as the purpose of the class, there may be several competing purposes in play, all of which are invisible. For students, maximising enjoyment, minimising effort, maximising test scores, maximising learning about something else, and making friends are all likely to be found across the classroom. For the teacher, we can add to that list maximising evaluation scores, which may be closer linked to student satisfaction than to student learning.

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.

But everyone who guessed in this way went low, rather than high. It suggests that there is some form of systemic bias in play.

In Dan’s case, the interest in policymaking is so central to the students’ presence at Harvard that it would be foolish to run a statistics course that did not acknowledge it. He goes as far as to build this into the purpose of the course: as we heard earlier, his purpose is “not just to maximise learning about statistics, but also to maximise learning of the skills that will be useful to have out there in the world.

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.

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.

For these ‘future leaders’ in the classroom, it is more important to understand the psychology of certainty. Often, we believe what we want to believe. Dan starts with an example of the 2016 Presidential Election in the United States. He asks the question: “Relative to what you expected to happen, how surprised were you when you learned that Trump had won the election?

The inclusive atmosphere of the class was the key driver of allowing the class to be eager to learn. The focus really shifted away from grades and points, and towards understanding concepts and learning.” The key link is between inclusivity and the shift of focus away from test scores. When students are given the responsibility to support each other, their own score falls down the list of priorities.

I remember he said something like ‘this should be completely obvious to you’, and to me that was crushing… we had a conversation after the mid-term exam, in which the class had averaged 20 out of 90. It was 25 years ago, and I still remember what he said: ‘Frustration is necessary for learning. This idea that you can enjoy learning is a very American idea’.” Dan pauses, the memory of that conversation etched on his face. “I felt so offended by that claim. My professor felt that to learn, you had to push yourself. One of my dreams was to go back to Venezuela[7] and start a university, and I vowed that I would write in the walls of the university that frustration was not necessary for learning.

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.

Exams also give us a concrete example of Dan’s attempts to promote understanding over memorization. He encourages students to bring with them a ‘cheat sheet’, which can include anything they want. He does not want students being tested on whether they can remember the formula for the standard error of a distribution, and does not believe that it will be helpful for them to do so. Allowing cheat sheets means that students can bring more than just formulas with them: if they were struggling with a topic, they could bring all sorts of pre-cooked explanations to help them with the exam questions. In turn, this acts as an extra incentive to Dan to set questions that rely on a deeper understanding.

It turns out that you only need 23 people for it to be more likely to find a shared birthday than not.

I’d like anyone who was born on March 22nd to stand up.” Two students stand up. They link eyes from across the room, and smile. The room laughs. “Now, anyone born on June 14th.” Another two stand up. The room laughs again. “Now, anyone born on August 2nd.” Two more: the class is laughing at each pair, and re-examining their original takes on how low the probability was likely to be. They are learning through experience about human fallibility with estimating probabilities, and at the same time learning something about their classmates. “How about December 21st?” This time, three students stand up. This gets a big laugh for two reasons: firstly, it is unexpected, and secondly, it helps to ram home the idea that in a class that size (there are about 3,000 pairs in a class of 80), there are likely to be “coincidences” everywhere.

What is the probability that at least two people in a group of 20 people will have the same birthday?

The great economist John Maynard Keynes is supposed to have said “when the facts change, I change my mind. What do you do, sir?