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The Importance of Numeracy

Updated: May 1

book cover for counting on fingers by richard whitehead and ronald d davis

Free Excerpt. Chapter 1 of

Counting On Fingers:

Why Some Bright And Creative People Struggle With Numbers And Mathematics,

And How That Can Be Changed

by Richard Whitehead

In 2017, a few weeks before a general election, a prominent UK politician made a mistake. The mistake was made in a live interview; it was mathematical rather than political and, as such, much harder to hide.

Shadow Home Secretary Diane Abbott announced that her party, if elected, would recruit 10,000 new police officers at a cost of £300,000 — the equivalent of a £30 annual salary per police officer.

The interviewer immediately queried the figures: ‘£300,000 for 10,000 police officers? What are you paying them?’

Abbott laughed embarrassedly and corrected her costings to £80 million. This, too, was questioned by the interviewer, who pointed out that this would still amount to a miserly £8000 annual salary per officer recruited.

currency and a calculator

Abbott then went on to explain that the officers would be recruited over a four-year period, ‘recruiting 25,000 extra police officers a year at least’. Later in the interview, the numbers changed again: ‘The figures are that the additional costs in Year One when we anticipate recruiting about 250,000 policemen will be £64.3 million.’

Of course, Abbott was not planning to turn the UK into a penurious police state. Her party was not about to recruit one million UK citizens to serve as police officers on a salary of £257.20 per year each. Subsequently, Abbott explained that she was suffering from Type 2 diabetes and that this, combined with the pressures of a gruelling election campaign, had affected aspects of her lucidity.

Assuming this was indeed the case, her treatment at the hands of some of the media after the mishap was nothing short of cruel. Just like the rest of us, politicians are allowed to be human, to mis-speak, to have a bad day and to fall ill.

Nonetheless, the Abbott incident provides a stark illustration of an important point. If a Cambridge University History graduate and eloquent politician of many decades’ experience can cite figures in a public broadcast for which a maths teacher would give nul points to a twelve-year-old, it all goes to show that intelligence is not a single ‘thing’ that can be measured on a linear IQ scale. Like the sliding controls on a sophisticated audio recording device, our intelligence is a complex interplay between a number of ways in which we take in, categorise, analyse, deduce, and innovate. And what is more, each aspect of our intelligence can have a ‘good day’ or a ‘bad day’, depending on how robustly it is built to withstand issues that impact on our day-to-day well-being.

a woman looking up and behind her is a series of pathways

The idea of multiple intelligences is not new. First proposed by Howard Gardner in 1983[1], multiple intelligence theory maintains that intelligence cannot be measured on a single linear scale but, rather, consists of many distinct components, each of which can be developed to its own particular level within the same individual. Though disputed by some, multiple intelligence theory makes sense to anyone who knows, for instance, a linguist (such as me) who cannot kick a ball or put up shelves, a mathematician who writes awful poems, a numerically challenged artist, a tone-deaf engineer, or a software developer who stands in the corner alone at cocktail parties. Multiple intelligence theory has played an important role in exploding the cruel myth that there are ‘clever’ people and ‘stupid’ people. It has made us much more intelligent about intelligence.

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However, multiple intelligence theory on its own is not much use to a parent or an educator. Telling a maths teacher that their most failing student may actually be very good at dance, embroidery or horse-riding will be neither revelatory nor cathartic. When multiple intelligence theory is reduced to an ‘everyone-is-good-at-something’ statement in scientific packaging, it is just another form of learning disability theory with a comfort blanket attached. ‘There, there — it’s a shame that you can’t count — but don’t worry, neither could Henry Winkler — and it didn’t stop him becoming an actor.’

This book will try to be more interesting than that. Rather than treating mathematical difficulties as a life sentence, it will demonstrate that even the most severe forms of dyscalculia can be addressed using the individual’s existing cognitive and intellectual assets. Rather than telling bright but struggling mathematicians to ‘buy a pocket calculator and go and find something you’re good at’, it is supremely important to consider how mathematical learning can be repackaged to play to these individuals’ natural and often considerable strengths.

a woman with a shopping cart using a calculator

Why supremely important? Because a pocket calculator does not replace mathematical intuition. In the supermarket, in the clothes shop, ordering pizzas for an office party, timing a journey, working out what monthly data package to get for our phone, deciding whether to pay upfront or in monthly instalments for our car insurance, we find ourselves taking snap decisions based on more or less sensible estimations. If we are starting or running a business, these scenarios can be multiplied many times over, in both frequency and import. Poor numeracy, if not addressed, can be a lifelong curse. While business insolvency, personal bankruptcy, rent arrears, unpunctuality, spoilt meals and missed deadlines can have a variety of causes, problems with counting, measuring, timing and mathematical logic will certainly not help. Like it or not, that is why the media pressed Abbott so relentlessly on her misspoken figures. When politicians get elected to power, they take control of billions of pounds of our taxes. The idea that they may not be able to count freaks us, frankly, out.

a button for purchasing a copy of the book counting on fingers

In February 2022, 12-year-old Rory and his mother were very worried. Rory had just received the results of his Mathematics Common Entrance Trial Examination: 22%. To receive a place at the senior school that he dearly wanted to attend, he would need to more than double his marks in the space of three months.

In March, Rory was assessed by an educational psychologist. His Number Operations were found to be at 2nd percentile. For readers unfamiliar with percentiles, a 2nd percentile score indicates that 98% of people of your age perform better than you do.

image of davis method using clay to master numeracy

In April, Rory came to me for a 48-hour intensive Davis Maths Mastery Programme. This quietly revolutionary intervention enables bright, creative, but numerically challenged individuals to become mathematically confident and competent, step-by-step, in specially tailored ways that play to their natural strengths. As Rory worked through the programme, he became rapidly numerate. He found not just that he was able to perform mental and written arithmetic much more accurately and fluently, but that the revision coaching he was receiving from his maths teacher was now making much more sense to him.

In May 2022, Rory took the Common Entrance Examination and passed Mathematics with 65%. He was accepted by the school that he wanted to attend.

Rory’s story is markedly similar to Clara’s. In 2006, aged 30, Clara wanted to study nursing at a local college of further education. Because of the importance of accurately measuring doses, comparing treatment risks, interpreting screen test results, and so on, healthcare workers need to be numerate. When I met Clara, she was devastated for two reasons. Firstly, she had failed the Access to Nursing Mathematics test, obtaining 19%. Secondly, by way of investigating the failure, her college had arranged an educational psychologist assessment to ascertain whether she might be dyslexic. As none of her assessment scores had been particularly high, the assessor had concluded that dyslexia was not indicated, just limited overall intelligence. I recall Clara repeating to me again and again, ‘She basically said I’m not dyslexic, I’m just stupid.’

Except she wasn’t. Six weeks and a Davis Maths Mastery Programme later, Clara retook the Access to Nursing Mathematics Test and passed with over 60%. When her college tutor contacted the assessor to enquire how a person of limited intelligence could improve her mathematical ability by more than 40% in six weeks, the assessor revised the report and allowed Clara to be dyslexic after all.

Whether we call it dyscalculia, ‘maths dyslexia‘ or ‘not good with figures’, a mathematics and numeracy deficit is not a life sentence. Rather, it is the product of mis-steps in the nature, speed and/or sequencing of a person’s mathematical learning in the early years of their schooling.

Before a child can successfully be taught maths, they need to be thinking mathematically.

Children develop mathematical thinking at differing speeds from one another, and some need outside assistance in developing it. If you try to teach symbol-based mathematical operations to a child who hasn't yet developed mathematical thinking, you will get rote-learnt answers at best, and confusion and ‘hit-and-miss’ answers at worst. In all cases, there will be an impact on self-esteem and a conclusion that ‘maths is not for me’. A conclusion, in my experience, that is entirely and tragically wrong.

image of a ladder and a chalkboard with lots of maths equations

Copyright ©2023 by Richard Whitehead, and Ronald D. Davis and Alice E. Davis as Trustees of the Ronald D. Davis and Alice E. Davis Living Trust dated June 8, 2017. All rights reserved. No portion of this book may be copied, retransmitted, reposted, duplicated, or otherwise used without the express written approval of the authors, except by reviewers who may quote brief excerpts in connection with a review.

[1] (Gardner, H., 2011. Frames of Mind: The Theory of Multiple Intelligences. 3rd edition ed. New York: Basic Books.)

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