# Too clever by graph

- Cambridge Mathematics
- Mathematical Salad
- Too clever by graph

## Too clever by graph

Recently, the MP for Braintree James Cleverly posted the image below on social media with the comment ‘*Why “more time” doesn’t actually help “get a deal”*’. Of course, as is often the way of these things Twitter responded with quick humour and the graph became a meme. Twitter users invented increasingly ridiculous axis labels for the curve – due in no small part to the perfectly reasonable idea that the empirical foundations of the original graph were questionable.

Image source: https://twitter.com/JamesCleverly/status/1181158343571918849

As a mathematics teacher it’s tempting, and perhaps valuable as a classroom activity, to begin to pull apart this graph from a mathematical perspective. If we treat this as an attempt to produce a legitimate model, it’s easy to find fault or ask questions which will almost certainly have unsatisfactory answers. What data was this based on, if any? If not, is this a type of ‘theoretical graph’ and what place might they occupy in statistical thinking? Why not a linear model? Just what is infinite decisiveness and how can I get some?

But then again, perhaps this is missing the point. A graph is not just a representation of empirical data or of some defined function; it is at its heart a tool for communication and in this case, regardless of how you may view the graph mathematically, it neatly and succinctly communicates a very specific message. The message here: the more time available, the less focused people are on making a decision. It’s accessible and visually arresting. It also adds a visual hook to a tweet – thus making the viewer much more likely to engage with the ideas in it.

This makes me reflect on the need to take care in educational settings not to create the impression that technical correctness is the *only* criteria on which to judge the effective use of a mathematical technique. The example here shows how powerful a ‘looser’ use of a mathematical idea can be – and this power, as we know, can be used for good or evil. Even for the less mathematically confident, for whom the graph may be largely meaningless, the effect of ‘mathwashing’ (the idea that giving something a mathematical flavour automatically adds credibility and/or neutrality) lends more credence to the idea described in the text. For many, the fact that there is a graph – any graph – may act as a signal that the words can be trusted…because maths.

So what is the message here? Should we redouble our efforts and attempt to teach all students to reject any representation that is not slavishly following the schema laid out in our assessment specifications? I would argue that a more productive approach is to ensure that alongside technical skills we encourage students to consider how the rules can be broken and subverted, just like we encourage students to do when working in the arts: in short, to practise mathematical jazz.

The goal of statistical education is not to train students to produce charts that a computer can do better, faster, and neater, but to furnish them with the skills to engage critically with the substance of the message and the context behind statements clothed in the trappings of mathematical credibility. Not only that, but also to bring humour, design flair and lateral thinking to the table as only humans can. Only then will we be able to claim that we are supporting the creation of a statistically literate – and a statistically *creative* – society, providing learners with the tools to recognise and engage deeply with the opinions of others, even when couched in ‘mathematical’ terms.

**Join the conversation:** You can tweet us @CambridgeMaths or comment below.