Numeracy
Encyclopedia
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. 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
. Innumeracy is a lack of numeracy.
In the United States
numeracy is also known as Quantitative Literacy and is familiar to math
educators
and intellectual
s. 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:
The (US) National Center for Education Statistics
, in its 1993 Report of the National Adult Literacy Survey defines quantitative literacy as:
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.
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
).
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 infant
s 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.
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
).
In studies 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.
, physicist
, accountant
, actuary
, Risk Analyst, financial analyst
, engineer
, and architect
.
Even outside these specialized areas, poor numeracy can reduce employment opportunities and career progress. For example, carpenter
s 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.
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:
Pathological innumeracy, known as dyscalculia
, is often associated with neurological
lesion
s.
Literacy
Literacy has traditionally been described as the ability to read for knowledge, write coherently and think critically about printed material.Literacy represents the lifelong, intellectual process of gaining meaning from print...
person can manage and respond to the mathematical demands of life. 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
Geoffrey Crowther, Baron Crowther
Geoffrey Crowther, Baron Crowther was a British economist, journalist, educationalist and businessman. He was editor of The Economist from 1938 to 1956.-Early life and education:...
. Innumeracy is a lack of numeracy.
In the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
numeracy is also known as Quantitative Literacy and is familiar to math
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
educators
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
and intellectual
Intellectual
An intellectual is a person who uses intelligence and critical or analytical reasoning in either a professional or a personal capacity.- Terminology and endeavours :"Intellectual" can denote four types of persons:...
s. There is also substantial overlap between conceptions of numeracy and conceptions of statistical literacy
Statistical literacy
Statistical literacy is a term used to describe an individual's or group's ability to understand statistics. Statistical literacy is necessary for citizens to understand material presented in publications such as newspapers, television, and the Internet. Numeracy is a prerequisite to being...
.
The UK's Department for Children, Schools and Families
Department for Children, Schools and Families
The Department for Children, Schools and Families was a department of the UK government, between 2007 and 2010, responsible for issues affecting people in England up to the age of 19, including child protection and education...
defines numeracy in their National Strategy documents as follows:
The (US) National Center for Education Statistics
National Center for Education Statistics
The National Center for Education Statistics is the part of the United States Department of Education's Institute of Education Sciences that collects, analyzes, and publishes statistics on education and public school district finance information in the United States...
, in its 1993 Report of the National Adult Literacy Survey defines quantitative literacy as:
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
Literacy
Literacy has traditionally been described as the ability to read for knowledge, write coherently and think critically about printed material.Literacy represents the lifelong, intellectual process of gaining meaning from print...
, 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.
Representation of numbers
Humans mentally represent numbers in two major ways from observation (not formal math). These representations are innate; they are not the result of individual learning or cultural transmission. They are- Approximate representations of numerical magnitude, and
- 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
Number sense
In mathematics education, number sense can refer to "an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations." Many other definitions exist, but are similar to the one given...
).
Numeracy in childhood
MathematicsMathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
is a core subject in child education
Education
Education in its broadest, general sense is the means through which the aims and habits of a group of people lives on from one generation to the next. Generally, it occurs through any experience that has a formative effect on the way one thinks, feels, or acts...
. 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 infant
Infant
A newborn or baby is the very young offspring of a human or other mammal. A newborn is an infant who is within hours, days, or up to a few weeks from birth. In medical contexts, newborn or neonate refers to an infant in the first 28 days after birth...
s 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.
Jean Piaget
Jean Piaget
Jean Piaget was a French-speaking Swiss developmental psychologist and philosopher known for his epistemological studies with children. His theory of cognitive development and epistemological view are together called "genetic epistemology"....
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
Singapore
Singapore , officially the Republic of Singapore, is a Southeast Asian city-state off the southern tip of the Malay Peninsula, north of the equator. An island country made up of 63 islands, it is separated from Malaysia by the Straits of Johor to its north and from Indonesia's Riau Islands by the...
at both grade levels had the highest performance. Hong Kong SAR, Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
, and Taiwan
Taiwan
Taiwan , also known, especially in the past, as Formosa , is the largest island of the same-named island group of East Asia in the western Pacific Ocean and located off the southeastern coast of mainland China. The island forms over 99% of the current territory of the Republic of China following...
also had high levels of numeracy. The lowest scores were found in South Africa
South Africa
The Republic of South Africa is a country in southern Africa. Located at the southern tip of Africa, it is divided into nine provinces, with of coastline on the Atlantic and Indian oceans...
, Ghana
Ghana
Ghana , officially the Republic of Ghana, is a country located in West Africa. It is bordered by Côte d'Ivoire to the west, Burkina Faso to the north, Togo to the east, and the Gulf of Guinea to the south...
, and Saudi Arabia
Saudi Arabia
The Kingdom of Saudi Arabia , commonly known in British English as Saudi Arabia and in Arabic as as-Sa‘ūdiyyah , is the largest state in Western Asia by land area, constituting the bulk of the Arabian Peninsula, and the second-largest in the Arab World...
. 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
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
).
In studies 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: mathematicianMathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, accountant
Accountant
An accountant is a practitioner of accountancy or accounting , which is the measurement, disclosure or provision of assurance about financial information that helps managers, investors, tax authorities and others make decisions about allocating resources.The Big Four auditors are the largest...
, actuary
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
, Risk Analyst, financial analyst
Financial analyst
A financial analyst, securities analyst, research analyst, equity analyst, or investment analyst is a person who performs financial analysis for external or internal clients as a core part of the job.-Job:...
, engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
, and architect
Architect
An architect is a person trained in the planning, design and oversight of the construction of buildings. To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the...
.
Even outside these specialized areas, poor numeracy can reduce employment opportunities and career progress. For example, carpenter
Carpenter
A carpenter is a skilled craftsperson who works with timber to construct, install and maintain buildings, furniture, and other objects. The work, known as carpentry, may involve manual labor and work outdoors....
s and interior designers need to be able to measure, use fractions, and handle budgets.
The Poynter Institute
Poynter Institute
The Poynter Institute is a non-profit school for journalism located in St. Petersburg, Florida. The school's mission statement says that "The Poynter Institute is a school dedicated to teaching and inspiring journalists and media leaders. It promotes excellence and integrity in the practice of...
includes numeracy as one of the skills required by competent journalists, and Max Frankel
Max Frankel
Max Frankel is a Pulitzer Prize-winning journalist.Frankel came to the United States in 1940. He attended Columbia College and began part-time work for The New York Times in his sophomore year. He received his B.A. degree in 1952 and an M.A. in American government from Columbia in 1953.He joined...
(former executive editor of The New York Times
The New York Times
The New York Times is an American daily newspaper founded and continuously published in New York City since 1851. The New York Times has won 106 Pulitzer Prizes, the most of any news organization...
) 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
Society of Professional Journalists
The Society of Professional Journalists , formerly known as Sigma Delta Chi, is one of the oldest organizations representing journalists in the United States. It was established in April 1909 at DePauw University, and its charter was designed by William Meharry Glenn. The ten founding members of...
, 58% of job applicants interviewed by broadcast news directors lacked an adequate understanding of statistical materials.
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 HofstadterDouglas Hofstadter
Douglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...
and popularized by mathematician John Allen Paulos
John Allen Paulos
John Allen Paulos is a professor of mathematics at Temple University in Philadelphia who has gained fame as a writer and speaker on mathematics and the importance of mathematical literacy...
in his 1989 book, Innumeracy: Mathematical Illiteracy and its Consequences
Innumeracy (book)
Innumeracy: Mathematical Illiteracy and its Consequences is a 1988 book by mathematician John Allen Paulos about "innumeracy", a term he embraced to describe the mathematical equivalent of illiteracy — incompetence with numbers rather than words...
. 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 reportingJournalismJournalism is the practice of investigation and reporting of events, issues and trends to a broad audience in a timely fashion. Though there are many variations of journalism, the ideal is to inform the intended audience. Along with covering organizations and institutions such as government and...
of news stories and insufficient skepticismSkepticismSkepticism has many definitions, but generally refers to any questioning attitude towards knowledge, facts, or opinions/beliefs stated as facts, or doubt regarding claims that are taken for granted elsewhere...
in assessing these stories - Financial mismanagement and accumulation of consumer debtConsumer debtIn economics, consumer debt is outstanding debt of consumers, as opposed to businesses or governments. In macroeconomic terms, it is debt which is used to fund consumption rather than investment...
, specifically related to misunderstanding of compound interestCompound interestCompound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding... - Loss of money on gambling, in particular caused by belief in the gambler's fallacyGambler's fallacyThe Gambler's fallacy, also known as the Monte Carlo fallacy , and also referred to as the fallacy of the maturity of chances, is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process, future deviations in the opposite direction are...
- Belief in pseudosciencePseudosciencePseudoscience is a claim, belief, or practice which is presented as scientific, but which does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status...
. 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 riskRiskRisk is the potential that a chosen action or activity will lead to a loss . The notion implies that a choice having an influence on the outcome exists . Potential losses themselves may also be called "risks"...
, 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 prospectsCareerCareer is defined by the Oxford English Dictionary as a person's "course or progress through life ". It is usually considered to pertain to remunerative work ....
Pathological innumeracy, known as dyscalculia
Dyscalculia
Dyscalculia is a specific learning disability involving innate difficulty in learning or comprehending simple arithmetic. It is akin to dyslexia and includes difficulty in understanding numbers, learning how to manipulate numbers, learning maths facts, and a number of other related symptoms...
, is often associated with neurological
Neurology
Neurology is a medical specialty dealing with disorders of the nervous system. Specifically, it deals with the diagnosis and treatment of all categories of disease involving the central, peripheral, and autonomic nervous systems, including their coverings, blood vessels, and all effector tissue,...
lesion
Lesion
A lesion is any abnormality in the tissue of an organism , usually caused by disease or trauma. Lesion is derived from the Latin word laesio which means injury.- Types :...
s.