Politicised Arithmetic

Updated: Feb 24

Louisa Hadari is a Sixth Form student at King David High School in Manchester and an alumna of the John Locke Institute.



Recently I was looking over a GCSE maths exam with my brother and working through one of the word problems with him. Two sisters, Grace and Jasmine, share pocket money per week in the ratio of their ages. The younger girl is five and the older is seven. The girls are given thirty-six pounds between them.


Whilst working it out I found myself distracted by the numbers: thirty-six pounds of pocket money per week? It struck me that I know several households for whom such a generous allowance for two children would be not only unfeasible but beyond their frame of reference. Let’s do a little extra maths: the national child benefit per week is £21.05 for the eldest child and £13.95 for a second child. The benefit is capped at two children, but a significant proportion of those low-income families have three or more children so the benefit has to go further between them.

Some more context: that £36 pocket money would just cover a weekly Metro bus ticket in West Yorkshire, although the child benefit wouldn’t. The cost of a commute (to school, say) that includes bus and rail would be considerably more. One mother I asked about this said that the government child benefit paid two-thirds of their family’s monthly mortgage. Another, with a full-time job, said it covered their weekly food.


My point here does not concern the arguments for or against child benefit; it concerns the psychological and sociological significance of maths exam questions that carry a set of assumptions about the social and economic context of those working out the problems. Grace and Jasmine’s pocket money, according to the paper, exceeds the maximum amount the government provides to ensure a child has food, shelter and the money to get to school.


An important thing to remember is that maths word problems are supposed to be somewhat plausible: any student preparing for a maths GCSE will be told ‘just check your answer makes sense.’ If you’re calculating the area of a garden and you end up with five million square metres you may have gone wrong somewhere. This means that the answers to the question and the numbers given must be, in the examiner’s mind at least, reasonable.


"The signals that any exam, assessment or interview send to our subconscious brain are often pivotal in the outcome of the exam."


It is unlikely that the person writing the AQA exam paper, who suggested giving the girls thirty-six pounds’ pocket money, was trying to give an unrealistic number; in his or her mind that seemed a plausible amount. The runners whose speed and distance we must represent on graphs do not perform super-heroic feats and run tens of thousands of miles in minutes; they run conceivable distances of 400 metres. It is equally unlikely that the examiner was trying to trip up the children in tower blocks to whom thirty-six pounds was an inconceivable amount to give to any two children, let alone a five- and a seven-year-old.


This is not a problem with a perpetrator. It is, however, a problem from which we can understand two things. First, we can deduce something about the social class and context of those who set the papers: the process of writing a maths exam paper takes a year and a half, and the paper is taken through numerous checks and reviews, including an evaluation by specialists on visually impaired students and the British Association of Teachers of the Deaf who are responsible for deciding whether ‘certain words or images could make the question more difficult for some students’. The fact that the paper is checked for accessibility with that degree of rigour and yet it occurs to no-one that, for many sitting the paper, thirty-six pounds is not a credible figure for pocket money suggests the degree of social separation between those setting the paper and many of the students sitting it.


Which brings me to the heart of my argument: these maths papers encapsulate some of the, often insurmountable, disadvantages someone from a less privileged background faces when attempting academic success. The signals that any exam, assessment or interview send to our subconscious brain are important, often pivotal in the outcome of the exam. In a study conducted by psychologists Claude Steele and Joshua Aronson, white and black graduate students sat an exam. Prior to the exam, some of the black students were asked to indicate their race on the answer page, while members of the control group were not. Merely answering this question correlated with statistically significant lower test scores.


In the chapter on psychological ‘priming’ from his book, Blink, Malcolm Gladwell explains the sensitivity of the unconscious mind to information given prior to and during a test. In another experiment, one group of students was asked to list attributes they associated with professors for ten minutes whilst the other group was asked to list attributes associated with soccer hooligans. The ‘professor’ group averaged 55.6% and the ‘soccer hooligan’ group scored 42.6%. Students were randomly assigned so the groups were evenly matched in ability; the difference was attributable only to one group thinking about being intelligent for ten minutes, while the other was thinking of the characteristics associated with drunk and violent sports fans.



The relevance of these studies to the AQA maths paper is clear: the influence of subconscious signals to the brain is significant, therefore the wording and content of a question that suggests that the paper was designed for students with a radically different economic and social background could be expected to have a significant effect on the performance of students from a lower economic background. It is not simply the extra mental effort it takes to carry out a calculation where the figures do not tally with one’s own perception of the world; it is that the disparity between what the paper ‘expects’ the economic background of the student to be and their economic reality sends the subconscious a message of alienation; the subconscious acts on the belief that the paper is for more economically advantaged students.


The student sitting the paper in which infants are lavished with limitless funds, popcorn costs five pounds a bucket, and private gardens boast dimensions more appropriate to playgrounds, will be primed with the message that the paper is not aimed at them and that the world of mathematics is not for them.


I was excited to hear that the John Locke Institute is launching a scheme this year to match high-performing alumni with promising young students from less privileged backgrounds, who will benefit from extra help and encouragement, especially in maths. Often the barriers poorer students face, though, are all but invisible to the rest of us. We need to develop a sensitivity to these unconscious discouragements, to raise the possibilities and aspirations for those students whose potential will otherwise remain unfulfilled.


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