Numeracy

"Innumeracy" redirects here. For the book of same name, see Innumeracy (book).

Numeracy is the ability to reason with numbers and other mathematical concepts. A numerically literate person can manage and respond to the mathematical demands of life.^[1] Aspects of numeracy include number sense, operation sense, computation, measurement, geometry, probability and statistics.

The portmanteau of "numerical literacy" was coined in 1959 by the UK Committee on Education, presided over by Sir Geoffrey Crowther.^[2] Innumeracy is a lack of numeracy.^[3]

In the United States numeracy 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 Children, Schools and Families 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.

— Department for Education and Skills (UK)

The (US) National Center for Education Statistics, in its 1993 Report of the National Adult Literacy Survey^[4] defines quantitative literacy as:

The knowledge and skills required to apply arithmetic operations, either alone or sequentially, using numbers embedded in printed material (e.g., balancing a checkbook, completing an order form).

— National Center for Education Statistics

The latter definition captures the sense of proficiency in the application mathematical knowledge to everyday tasks implicit in the former definition of numeracy, but it lacks the depth of "a repertoire," and the sense that an "inclination" to apply mathematics is a central part of numeracy/quantitative literacy. The differences in depth and extent in these definitions is natural; just as with literacy, numeracy measurements vary depending on the context.

Others have drawn a distinction between numeracy and mathematics as a language or system of thought, arguing that too narrow a focus on working with numbers neglects abstract reasoning.^[5]

Representation of numbers

Humans mentally represent numbers in two major ways from observation (not formal math).^[6] These representations are innate; they are not the result of individual learning or cultural transmission. They are

1. Approximate representations of numerical magnitude, and
2. Precise representations of distinct individuals.

Both systems have limited expressive power; for instance, neither allows fractions nor negative numbers to be represented. Further representations require arduous processes that are probably only achieved through education. Achievement in school mathematics is related to unlearned mathematical ability (specifically, our approximate number sense).^[7]

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 pull one doll from behind the screen. Without the child's knowledge, a second experimenter could remove, or add dolls, unseen behind the screen. 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.^[8]

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 has tested 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).^[9]

In studies^{[citation needed]} of gender and choice of science careers, age is also found to be related with gender. Thus at some ages, girls perform better with science subjects like mathematics, and at other ages, boys. This was true in the USA and is generally thought to affect career and school-course choices in school-age children.

Numeracy and employment

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

Even outside these specialized areas, poor numeracy can reduce employment opportunities and career progress.^[10] For example, carpenters and interior designers need to be able to measure, use fractions, and handle budgets.^[11]

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.^[12]

Innumeracy

Innumeracy is a neologism coined by analogue with 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.^[13]

Paulos outlined some potential consequences of innumeracy:^[13]

• 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.

See also

• Numerosity adaptation effect
• Oracy
• QuickSmart

Notes

1. ^ Statistics Canada. "Building on our Competencies: Canadian Results of the International Adult Literacy and Skills Survey". Statistics Canada. p. 209. http://www.nald.ca/library/research/booc/booc.pdf. 
2. ^ Fowler's Modern English Usage, R.W. Burchfield, ed.
3. ^ Definition from answers.com
4. ^ National Center for Education Statistics (NCES). Adult Literacy in America. Report of the National Adult Literacy Survey (NALS). Washington, DC: U.S. Department of Education, 1993.
5. ^ (Bullock 1994), (Steen 2001)
6. ^ doi:10.1016/j.tics.2004.05.002 http://www.wjh.harvard.edu/~lds/pdfs/feigenson2004.pdf
7. ^ doi:10.1038/nature07246
8. ^ Numbers in Mind
9. ^ Trends in International Mathematics and Science Study
10. ^ Parsons S. & Bynner J. (1997). Numeracy and employment Education + Training, Volume 39, Number 2, 1997 , pp. 43–51(9) Publisher: Emerald Group Publishing Limited
11. ^ Orr, Tamra B. (2002) Paradon me…do you speak numeracy? Career World, Sept, 2002
12. ^ Scanlan, Chip (2004). Why Math Matters Poynter Online, September 8, 2004.
13. ^ ^{a b} John Allen Paulos (1989). Innumeracy: Mathematical Illiteracy and its Consequences. Hill and Wang.

• Bullock, James O. (October 1994), "Literacy in the Language of Mathematics", The American Mathematical Monthly 101 (8): 735–743, JSTOR 2974528 
• Steen, Lynn Arthur (2001), "Mathematics and Numeracy: Two Literacies, One Language", The Mathematics Educator (Journal of the Singapore Association of Mathematics Educators) 6 (1): 10–16, http://www.stolaf.edu/people/steen/Papers/twolits.html 

External links

• Berlin Advanced Numeracy Test