Talking maths with GPs
Communicating maths ideas to patients brings plenty of challenges
31 July 2025
Yesterday I spent a fascinating morning talking maths with a group of GPs. All professions require some level of numeracy, but doctors face particular challenges, as they need to communicate mathematical ideas to patients who might have limited education and often bring emotional and cultural baggage with them.
The 'Talking maths' workshop for GPs, held in a private wood in deepest Kent. Note the Monty Hall buckets.
The conversation was wide ranging, but we focused on three topics and here are some of the highlights.
MEASUREMENT
As an ice-breaker, I asked the group to estimate my height. It was an exercise that probably comes as second nature to any doctor. However I wasn’t directly interested in their answers. I wanted to know what UNITS they had used. It turned out that of the seven GPs, five thought in feet and inches. The other two, one of whom grew up in continental Europe, thought in centimetres. The group were surprised to hear that their bias towards feet and inches reflects the population as a whole. In fact even the majority of UK teenagers think of other people’s heights in feet and inches, despite our education system having been entirely metric for over 50 years. Yet those same teenagers think of almost all other measurements - such as room dimensions - in metres. British measurement is an eccentric mishmash, and the choice of units is often down to someone's personal history. You might think in, say, feet and kilograms, but your neighbour could be a metres and pounds person. For doctors and patients, maths doesn't get more basic than communicating a measurement, and yet even this can be a barrier. It’s still common for a new mum to be told that her baby is, say, 3.4 kilograms, to which she responds: “what's that is in pounds?”. If you tell a patient they’ve lost 2kg in weight, can you be confident they know how much that is?
ISH-NESS
Arithmetic and estimation are a routine part of a GP's job. 'How long will these pills last before they’ll need a new prescription?', 'how long is it going to take us to get through this patient list?', and so on. My GP group were typical of the population at large in that most of them never do written calculations. They either work things out in their head, or they use a spreadsheet or calculator. And often they don’t need precise answers, they need to know a rough ballpark answer. I showed them my ‘Zequals’ technique (see this Guardian article ) and we talked about the value of the word ‘Ish’. However, not all patients appreciate an ‘ish’. Some like to hear precise numbers because it conveys a sense of confidence and control. “5.3% of patients get this side effect” can sound more convincing than “about 5% of patients”. This means that doctors sometimes face a conundrum. On the one hand, numbers quoted to several significant figures can sound persuasive. On the other, they can give a misleading sense of precision and certainty. I brought up one of my favourite cautionary tales about the spurious precision in Imperial College's January 2020 report after the first outbreak of Covid in China (see https://robeastaway.com/blog/covid-spread). Imperial had estimated that about 1700 people currently had Covid, and that was the figure quoted in the media. What nobody mentioned was the confidence intervals, which had said there was a 95% chance the actual figure was between 400 and 5,000. And as it turns out, the real figure was outside even those wide goalposts. Statistics can be dangerously misleading, even when they come from authoritative sources.
COMMUNICATING RISK
The topic that got the GPs most animated was risk. Probability is a difficult and counter-intuitive topic for most adults – even mathematicians – and helping patients to make wise choices that involve an element of risk can be extremely difficult. To highlight how slippery probability can be, I did one of my favourite demos, the Monty Hall game. I challenged them to locate a toy bird that was hidden under one of three buckets, A, B and C. I told the group that I’d let them pick a bucket, I’d then turn over a different bucket that I knew didn’t have the bird under it, then I’d give them the option of swapping. My volunteer chose bucket A. I then turned over bucket B which was empty.
“Would you like to stick or swap?”
“I don’t see any point in swapping, it’s 50:50 now, so I’ll stick”.
Alas for my volunteer, the bird was under bucket C. None of the GPs were familiar with this game, and like most newcomers, they were baffled that the odds of the bird being under C had been 2/3 rather than 1/2. The point of this exercise was to reveal just how counter-intuitive even an apparently simple situation like this can be. Doctors have to deal with, and must communicate, far more complex conditional probability. It's no wonder many patients struggle to make good decisions on treatment. One of the real life case studies we discussed involved deciding whether a patient should have a lumbar puncture to test for a suspected mini stroke. The patient had displayed some stroke symptoms and the chance of this test revealing a stroke was quite high, but the patient then had a CT scan, which was clear. The chance of the lumbar puncture revealing anything new was now tiny – and given the discomfort etc, not worth doing. The probability had changed based on new information. More topical was the area of measles vaccination. A patient's reaction to the offer of a vaccination might be: “My parents had measles as kids and it never did them any harm”. Presenting patients with the data is often not enough in the face of personal anecdotes like this.
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