**Numeracy** is the ability to reason and to apply simple numerical concepts.^{[1]} Basic numeracy skills consist of comprehending fundamental arithmetics like addition, subtraction, multiplication, and division. For example, if one can understand simple mathematical equations such as 2 + 2 = 4, then one would be considered possessing at least basic numeric knowledge. Substantial aspects of numeracy also include number sense, operation sense, computation, measurement, geometry, probability and statistics. A numerically literate person can manage and respond to the mathematical demands of life.^{[2]}

By contrast, **innumeracy** (the lack of numeracy) can have a negative impact. Numeracy has an influence on career decisions, and risk perception towards health decisions. For example, innumeracy distorts risk perception towards health decisions^{[3]} and may negatively affect economic choices.^{[4]}^{[5]} "Greater numeracy has been associated with reduced susceptibility to framing effects, less influence of nonnumerical information such as mood states, and greater sensitivity to different levels of numerical risk".^{[6]}

# Representation of numbers

Humans have evolved to mentally represent numbers in two major ways from observation (not formal math).^{[7]} These representations are often thought to be innate^{[8]} (see Numerical cognition), to be shared across human cultures,^{[9]} to be common to multiple species,^{[10]} and not to be the result of individual learning or cultural transmission. They are:

Approximate representations of numerical magnitude imply that one can relatively estimate and comprehend an amount if the number is large (see Approximate number system). For example, one experiment showed children and adults arrays of many dots.^{[7]} After briefly observing them, both groups could accurately estimate the approximate number of dots. However, distinguishing differences between large numbers of dots proved to be more challenging.^{[7]}

Precise representations of distinct individuals demonstrate that people are more accurate in estimating amounts and distinguishing differences when the numbers are relatively small (see Subitizing).^{[7]} For example, in one experiment, an experimenter presented an infant with two piles of crackers, one with two crackers the other with three. The experimenter then covered each pile with a cup. When allowed to choose a cup, the infant always chose the cup with more crackers because the infant could distinguish the difference.^{[7]}

Both systems—approximate representation of magnitude and precise representation quantity of individual items—have limited power.

# Definitions and assessment

Fundamental (or rudimentary) numeracy skills include understanding of the real number line, time, measurement, and estimation.^{[3]} Fundamental skills include basic skills (the ability to identify and understand numbers) and computational skills (the ability to perform simple arithmetical operations and compare numerical magnitudes).

More sophisticated numeracy skills include understanding of ratio concepts (notably fractions, proportions, percentages, and probabilities), and knowing when and how to perform multistep operations.^{[3]} Two categories of skills are included at the higher levels: the analytical skills (the ability to understand numerical information, such as required to interpret graphs and charts) and the statistical skills (the ability to apply higher probabilistic and statistical computation, such as conditional probabilities).

A variety of tests have been developed for assessing numeracy and health numeracy.^{[3]}^{[6]}^{[12]}^{[13]}^{[14]}^{[15]}^{[16]}

# Childhood influences

The first couple of years of childhood are considered to be a vital part of life for the development of numeracy and literacy.^{[17]} There are many components that play key roles in the development of numeracy at a young age, such as Socioeconomic Status (SES), parenting, Home Learning Environment (HLE), and age.^{[17]}

# Socioeconomic status

Children who are brought up in families with high SES tend to be more engaged in developmentally enhancing activities.^{[17]} These children are more likely to develop the necessary abilities to learn and to become more motivated to learn.^{[17]} More specifically, a mother's education level is considered to have an effect on the child's ability to achieve in numeracy. That is, mothers with a high level of education will tend to have children who succeed more in numeracy.^{[17]}

A number of studies have, moreover, proved that the education level of mother is strongly correlated with the average age of getting married. To be more precise, females who entered the marriage later, tend to have greater autonomy, chances for skills premium and level of education (i.e. numeracy). Hence, they were more likely to share this experience with children.^{[18]}

# Parenting

Parents are suggested to collaborate with their child in simple learning exercises, such as reading a book, painting, drawing, and playing with numbers.

# Home-learning environment

Along with parenting and SES, a strong home-learning environment increases the likelihood of the child being prepared for comprehending complex mathematical schooling.^{[19]} For example, if a child is influenced by many learning activities in the household, such as puzzles, coloring books, mazes, or books with picture riddles, then they will be more prepared to face school activities.^{[19]}

# Age

Age is accounted for when discussing the development of numeracy in children.^{[19]} Children under the age of 5 have the best opportunity to absorb basic numeracy skills.^{[19]} After the age of 7, achievement of basic numeracy skills become less influential.^{[19]} For example, a study was conducted to compare the reading and mathematic abilities between children of ages 5 and 7, each in three different mental capacity groups (underachieving, average, and overachieving). The differences in the amount of knowledge retained were greater between the three different groups aged 5 than between the groups aged 7. This reveals that those of younger ages have an opportunity to retain more information, like numeracy.

# Literacy

There seems to be a relationship between literacy and numeracy,^{[20]}^{[21]} which can be seen in young children. Depending on the level of literacy or numeracy at a young age, one can predict the growth of literacy and/ or numeracy skills in future development.^{[22]} 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.^{[23]}

# Employment

Numeracy has a huge impact on employment.^{[24]} In a work environment, numeracy can be a controlling factor affecting career achievements and failures.^{[24]} Many professions require individuals to have a well-developed sense of numeracy, for example: mathematician, physicist, accountant, actuary, Risk Analyst, financial analyst, engineer, and architect. Even outside these specialized areas, the lack of proper numeracy skills can reduce employment opportunities and promotions, resulting in unskilled manual careers, low-paying jobs, and even unemployment.^{[25]} For example, carpenters and interior designers need to be able to measure, use fractions, and handle budgets.^{[26]} Another example pertaining to numeracy influencing employment was demonstrated at the Poynter Institute. The Poynter Institute has recently included numeracy as one of the skills required by competent journalists. Max Frankel, former executive editor of The New York Times, argues that "deploying numbers skillfully is as important to communication as deploying verbs". Unfortunately, it is evident that journalists often show poor numeracy skills. 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.^{[27]}

With regards to assessing applicants for an employment position, psychometric numerical reasoning tests have been created by occupational psychologists, who are involved in the study of numeracy. These psychometric numerical reasoning tests are used to assess an applicants' ability to comprehend and apply numbers. These tests are sometimes administered with a time limit, resulting in the need for the test-taker to think quickly and concisely. Research has shown that these tests are very useful in evaluating potential applicants because they do not allow the applicants to prepare for the test, unlike interview questions. This suggests that an applicant's results are reliable and accurate.^{[28]}

These psychometric numerical reasoning tests first became prevalent during the 1980s, following the pioneering work of psychologists, such as P. Kline.

# Innumeracy and dyscalculia

The term *innumeracy* is a neologism, coined by analogy with illiteracy. *Innumeracy* refers to a lack of ability to reason with numbers. The term was coined by cognitive scientist Douglas Hofstadter; however, it was popularized in 1989 by mathematician John Allen Paulos in his book Innumeracy: Mathematical Illiteracy and its Consequences

Developmental dyscalculia refers to a persistent and specific impairment of basic numerical-arithmetical skills learning in the context of normal intelligence.

# Patterns and differences

The root cause of innumeracy varies.

# Theory

There is a theory that innumeracy is more common than illiteracy when dividing cognitive abilities into two separate categories.

# Innumeracy and risk perception in health decision-making

Health numeracy has been defined as "the degree to which individuals have the capacity to access, process, interpret, communicate, and act on numerical, quantitative, graphical, biostatistical, and probabilistic health information needed to make effective health decisions".^{[31]} The concept of health numeracy is a component of the concept of health literacy. Health numeracy and health literacy can be thought of as the combination of skills needed for understanding risk and making good choices in health-related behavior.

Health numeracy requires basic numeracy but also more advanced analytical and statistical skills.

Different presentation formats of numerical information, for instance natural frequency icon arrays, have been evaluated to assist both low-numeracy and high-numeracy individuals.^{[30]}^{[36]}^{[37]}^{[38]}^{[39]}

# Evolution of numeracy

In the field of economic history, numeracy is often used to assess human capital at times when there was no data on schooling or other educational measures. Using a method called age-heaping, researchers like Professor Jörg Baten study the development and inequalities of numeracy over time and throughout regions. For example, Baten^{[40]} and Hippe find a numeracy gap between regions in western and central Europe and the rest of Europe for the period 1790–1880. At the same time, their data analysis reveals that these differences as well as within country inequality decreased over time. Taking a similar approach, Baten and Fourie^{[41]} find overall high levels of numeracy for people in the Cape Colony (late 17th to early 19th century).

In contrast to these studies comparing numeracy over countries or regions, it is also possible to analyze numeracy within countries.