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As well as being a proud maths geek I am also a self-confessed comedy nerd, and one of my favourite podcasts is The Comedian’s Comedian with Stuart Goldsmith. In a recent episode he discussed the process of writing comedy with Zoe Coombs Marr, an Australian comic, who intriguingly described her perception of “the audience” as a single entity - not as a collection of individuals, each with an individual sense of humour, but as a gestalt with a distinctive character of its own. Not only this, but she described how even though every audience consists of different people, “the audience” has pretty much the same predictable sense of humour wherever she performs.
This struck me as a perfect example of aggregate distribution in action. Each individual member of the audience is a single data point with specific characteristics; some will like one-liners, some will like complex repeat narrative jokes, and some will like Mrs Brown’s Boys. Put them all together in a room, and all those individual differences contribute to an aggregate sense of humour that is predictable to the professional comic. As with all statistical samples, sometimes an audience will be in one of the tails either side of the distribution, leading to the comedian either walking off to a standing ovation, or dying horribly and facing a long dark night of the soul in a lonely hotel room. Most of the time though, the audience’s sense of humour will be between the quartiles and the gig will be a success. Zoe describes how one important skill for a comic is to move the sense of humour of the audience towards the jokes they want to tell, effectively skewing the distribution in the comic’s favour; or alternatively to read the room and pitch jokes at the audience where their collective sense of humour is.
There has been a resurgence of a particular kind of TV comedy over the last few years and it’s rare that there is not a panel show, live stand-up, or something fronted by a comedian on at least one channel at any given time. I wonder if the familiarity students in our classrooms have with comedians could be used to help them move from thinking locally about individual data values to thinking globally about the aggregate properties of data. This is a concept that research has shown students find very difficult to develop and it requires multiple experiences over a long period.
Perhaps identify a short list of joke types or examples of jokes, and ask each student to rank them numerically in order from most to least funny (a suggestion for this is included below). A distribution of ranks could then be produced for each type of joke, for example a set of bar charts showing the frequency of the scores for the students in the class. Students could be challenged to decide what sort of jokes a comedian should tell if they were putting on a show for the class. By creating an ordinal system for comedic preference, some interesting shapes should emerge; are there ‘Marmite’ joke types that have a peak at either end of the scale, suggesting people either like or dislike them? Are there jokes that everyone ranks around half way, suggesting these will be reliable if unspectacular (“strawberry jam” jokes)? Are there jokes that seem very niche – only one or two students are into them and others are left puzzled? (Unicorn toast, anyone?)
This kind of activity meets the recommendations from research reports such as GAISE, allowing students to attend to the entire statistical cycle from data collection to interpretation in a meaningful (and hopefully engaging) context. Of course, this is not the only scenario that could be mathematised to allow this kind of investigation – different contexts will work better for different groups of students. The key is to identify opportunities to create meaningful explorations of data that demand students think in the aggregate sense in order to help them develop this fundamental concept.
Example of a list of maths jokes for ranking (many thanks to the originators):
a) Narrative jokes
b) Questions and answers
Q: Why did the Viking fail the graph question?
A: He forgot to label his axes.
Q: How many numbers are there between 1 and 10 inclusive?
A: Five, because 1,3 5 , 7 and 9 aren’t even numbers.
Q: What do you say to a mathematical cat who’s stuck in a (geome-)tree?
Q: Why did the chicken cross the Mobius strip?
Q: Why did I divide sin by tan?
A: Just cos.
Q: Why is 6 afraid of 7?
A: Because 7 8 9
Q: How does a ghost solve a quadratic equation?
A: By completing the scare.
c) Other puns
I hired an odd-job person to do 8 jobs for me, but when I got back, she'd only done half of them.
Last night I dreamed that I was weightless… I was like, 0mg
Did you hear about the mathematician who was afraid of negative numbers? She'd stop at nothing to avoid them.
Did you hear about the Improper Fractions shop? It’s open 24/7.
d) What’s the difference? jokes
What’s the difference between a pupil studying exponentials and a lumberjack? Nothing, they both involve moving logs around.
What’s the difference between an angle measurer and the President of the Agriculturists’ Union? Nothing, they’re both pro-tractors.
What’s the difference between 0.9 recurring and 1? Nothing.