Numeracy

Numeracy is a portmanteau of "numerical literacy", and refers to an ability to reason with numbers and other mathematical concepts. The word was coined in 1959 by the UK Committee on Education, presided over by Sir Geoffrey Crowther. Innumeracy is a lack of numeracy.

In the United States, numeracy it is also known as Quantitative Literacy, and is familiar to math educators and intellectuals. There is also substantial overlap between conceptions of numeracy and conceptions of statistical literacy.

The UK's Department for Education and Skills defines numeracy in their National Strategy documents as follows:

Numeracy is a proficiency which is developed mainly in mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables.

Numeracy in childhood

Mathematics is a core subject in child education. IQ tests include an assessment of numeracy and it can therefore be seen as a key component of intelligence.

There is some evidence that humans may have an inborn sense of number. In one study for example, five-month-old infants were shown two dolls, which were then hidden with a screen. The babies saw the experimenter remove one doll from behind the screen. Without the child's knowledge, a second experimenter could remove or add dolls. When the screen was removed, the infants showed more surprise at an unexpected number (for example, if there were still two dolls). Some researchers have concluded that the babies were able to count, although others doubt this and claim the infants noticed surface area rather than number.

Jean Piaget found that children's concepts of number and quantity developed with age. For example, if an experimenter empties liquid from a short wide container into a tall thin container, a five-year-old typically thinks the quantity of liquid increases, whereas a ten-year-old realizes that the quantity of liquid stays the same.

The TIMSS international study of mathematical achievement tests children at fourth grade (average 10 to 11 years) and eighth grade (average 14 to 15 years) level in 49 countries. The assessment included tests for number, algebra (called patterns and relationships at fourth grade), measurement, geometry, and data. The latest study, in 2003, found that children from Singapore at both grade levels had the highest performance. Hong Kong SAR, Japan, and Taiwan also had high levels of numeracy. The lowest scores were found in South Africa, Ghana, and Saudi Arabia. In most countries, the difference by gender was negligible, but there were exceptions (for example, girls performed significantly better in Singapore and boys performed significantly better in the United States).

Numeracy and employment

A high level of numeracy is required for some jobs, for example: mathematician, physicist, accountant, actuary, financial analyst, engineer, and architect.

Even outside these specialized areas, poor numeracy can reduce employment opportunities and career progress. For example, carpenters and interior designers need to be able to measure, use fractions, and handle budgets.

The Poynter Institute includes numeracy as one of the skills required by competent journalists, and Max Frankel (former executive editor of The New York Times) argues that "deploying numbers skillfully is as important to communication as deploying verbs." However, journalists often show poor numeracy skills; for example, in a study by the Society of Professional Journalists, 58% of job applicants interviewed by broadcast news directors lacked an adequate understanding of statistical materials.

Innumeracy

Innumeracy is a portmanteau of "numerical illiteracy"; it refers to a lack of ability to reason with numbers. The term innumeracy was coined by cognitive scientist Douglas Hofstadter and popularized by mathematician John Allen Paulos in his 1989 book, Innumeracy: Mathematical Illiteracy and its Consequences. Possible causes of innumeracy are poor teaching methods and standards and lack of value placed on mathematical skills. Even prominent and successful people will attest, sometimes proudly, to low mathematical competence, in sharp contrast to the stigma associated with illiteracy.

Paulos outlined some potential consequences of innumeracy:

• Inaccurate reporting of news stories and insufficient skepticism in assessing these stories
• Financial mismanagement and accumulation of consumer debt, specifically related to misunderstanding of compound interest
• Loss of money on gambling, in particular caused by belief in the gambler's fallacy
• Belief in pseudoscience. According to Paulos, "Innumeracy and pseudoscience are often associated, in part because of the ease with which mathematical certainty can be invoked, to bludgeon the innumerate into a dumb acquiescence."
• Poor assessment of risk, for example, refusing to fly by airplane (a relatively safe form of transport) while taking unnecessary risks in a car (where an accident is more likely)
• Limited job prospects

Pathological innumeracy, known as dyscalculia, is often associated with neurological lesions.