Numeracy

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

Numeracy is defined as the ability to reason and to apply simple numerical concepts.[1] Basic numeracy skills consist of comprehending fundamental mathematics 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] However, the lack of numeracy or innumeracy can have a negative impact if the skills are absent. Numeracy has an influence on career professions, literacy, and risk perception towards health decisions.

Contents

Representation of numbers

Humans have evolved to mentally represent numbers in two major ways from observation (not formal math).[3] 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.

Approximate representations of numerical magnitude imply that one can relatively estimate and comprehend an amount, if the number is large. For example, children and adults were given dot arrays composed of many dots.[3] After briefly reviewing them, both groups could roughly estimate the number of dots close to the correct number. However, distinguishing amount differences with larger numbers is more challenging.[3]

Precise representations of distinct individuals demonstrate that people are more accurate in estimating amounts and distinguish amount differences, when the numbers are relatively smaller.[3] For example, infants were presented with 2 piles of crackers.[3] One pile had 2 crackers and the other pile had 3 crackers.[3] Cups then covered both piles of crackers.[3] When given the option to choose a cup, the infant always chose the cup containing the most crackers because the infant could distinguish the subtle difference.[3]

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).[4]

Numeracy during childhood

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.[5] 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.[5]

Socioeconomic Status

Children who are brought up in families with high SES tend to be more engaged in developmentally enhancing activities.[5] These children are more likely to develop the necessary abilities to learn and to become more motivated to learn.[5] 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.[5]

Parenting

Parents are suggested to collaborate with their child in simple learning exercises, such as reading a book, painting, drawing, and playing with numbers. On a more expressive note, the act of using complex language, being more responsive towards the child, and establishing warm interactions are recommended to parents with the confirmation of positive numeracy outcomes.[5] When discussing beneficial parenting behaviors, a feedback loop is formed because pleased parents are more willing to interact with their child, which in essence promotes better development in the child.[5]

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.[6] 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.[6]

Age

Age is accounted for when discussing the development of numeracy in children.[6] Children under the age of 5 have the best opportunity to absorb basics numeracy skills.[6] After the age of 7, acknowledgement of basic numeracy skills become less influential.[6] For example, a study was conducted to compare the reading and mathematic abilities between children, 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 at age 5, than between the groups at age 7. This reveals that the younger you are the greater chance you have to retain more information, like numeracy.

Literacy and Numeracy

There seems to be a relationship between literacy and numeracy, 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.[7] 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]

Numeracy and employment

Numeracy has a huge impact on employment.[9] In a work environment, numeracy can be a controlling factor affecting career achievements and failures.[9] 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.[10] For example, carpenters and interior designers need to be able to measure, use fractions, and handle budgets.[11] 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.[12]

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 conducted under a significant time frame, which calls for quick and concise thinking. 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 reassures us that an applicant's results are reliable and accurate.[13]

These psychometric numerical reasoning tests first became prevalent during the 1980s, following the pioneering work of psychologists, such as P.Kline. In 1986, P. Kline's published a book entitled, "A handbook of test construction: Introduction to psychometric design," which explained that psychometric testing could provide reliable and objective results. These findings could then be used to effectively assess a candidate's abilities in numeracy. In the future, psychometric numerical reasoning tests will continue to be used in employment assessments to fairly and accurately differentiate and evaluate possible employment applicants.

Innumeracy

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

Patterns and Differences

The root cause of innumeracy varies. Innumeracy has been seen in those suffering from poor education and childhood deprivation of numeracy.[14] Innumeracy is apparent in children during the transition of numerical skills obtained before schooling and the new skills taught in the education departments because of their memory capacity to comprehend the material.[14] Patterns of innumeracy have also been observed depending on age, gender, and race.[15] Older adults have been associated with lower numeracy skills than younger adults.[16] Men have been identified to have higher numeracy skills than women.[9] Some studies seem to indicate young people of African heritage tend to have lower numeracy skills.[15] The Trends in International Mathematics and Science Study (TIMSS) in which children at fourth-grade (average 10 to 11 years) and eighth-grade (average 14 to 15 years) from 49 countries were tested on mathematical comprehension. The assessment included tests for number, algebra (also 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. Countries like Hong Kong SAR, Japan, and Taiwan also shared high levels of numeracy. The lowest scores were found in countries like South Africa, Ghana, and Saudi Arabia. Another finding showed a noticeable difference between boys and girls with some exceptions. For example, girls performed significantly better in Singapore, and boys performed significantly better in the United States.[3]

Theory

There is a theory that innumeracy is more common than illiteracy when dividing cognitive abilities into two separate categories. David C. Geary, a notable cognitive developmental and evolutionary psychologist from the University of Missouri, created the terms "biological primary abilities" and "biological secondary abilities."[14] Biological primary abilities evolve over time and are necessary for survival. Such abilities include speaking a common language or knowledge of simple mathematics.[14] Biological secondary abilities are attained through personal experiences and cultural customs, such as reading or high level mathematics learned through schooling.[14] Literacy and numeracy are similar in the sense that they are both important skills used in life. However, they differ in the sorts of mental demands each makes. Literacy consists of acquiring vocabulary and grammatical sophistication, which seem to be more closely related to memorization, whereas numeracy involves manipulating concepts, such as in calculus or geometry, and builds from basic numeracy skills.[14] This could be a potential explanation of the challenge of being numerate.[14]

Innumeracy and Risk Perception in Health Decision-making

Innumeracy is also a very common problem when dealing with risk perception in health-related behavior.[15] This is known as health numeracy.[15] Health numeracy is 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."[15] Those who lack or have limited health numeracy skills run the risk of making poor health-related decisions because of an inaccurate perception of information.[5] For example, if a patient has been diagnosed with breast cancer, being innumerate may hinder the patient's ability to comprehend her physician's recommendations or even the severity of the health concern. People tend to overestimate their chances of survival or even choose lower quality hospitals.[9] This innumeracy also makes it difficult or impossible for some patients to read medical graphs correctly.[17] Indeed, many doctors exhibit innumeracy when attempting to explain a graph or statistics to a patient. Once again, a misunderstanding between a doctor and patient due to either the doctor, patient, or both being unable to comprehend numbers effectively could result in serious health consequences. Possible solutions to poor health numeracy include physicians identifying and recognizing a patient's numerical strengths and weaknesses in order to convey the information appropriately.[15]

See also

Notes

  1. ^ Brooks, M; Pui (2010). "Are individual differences in numeracy unique from general mental ability? A closer look at a common measure of numeracy.". Individual Differences Research. 4 8: 257–265.
  2. ^ 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.
  3. ^ a b c d e f g h i doi:10.1016/j.tics.2004.05.002 http://www.wjh.harvard.edu/~lds/pdfs/feigenson2004.pdf
  4. ^ doi:10.1038/nature07246
  5. ^ a b c d e f g h Ciampa, Philip J.; Osborn, Chandra Y.; Peterson, Neeraja B.; Rothman, Russell L. (2010). "Patient Numeracy, Perceptions of Provider Communication, and Colorectal Cancer Screening Utilization". Journal of Health Communication 15 (sup3): 157–168. doi:10.1080/10810730.2010.522699. ISSN 1081-0730.
  6. ^ a b c d e Melhuish, Edward C.; Phan, Mai B.; Sylva, Kathy; Sammons, Pam; Siraj-Blatchford, Iram; Taggart, Brenda (2008). "Effects of the Home Learning Environment and Preschool Center Experience upon Literacy and Numeracy Development in Early Primary School". Journal of Social Issues 64 (1): 95–114. doi:10.1111/j.1540-4560.2008.00550.x. ISSN 0022-4537.
  7. ^ Purpura, David; Hume, L; Sims, D; Lonigan, C (2011). "Early literacy and early numeracy: The value of including early literacy skills in the prediction of numeracy". Journal of Experimental Child Psychology 110 (4): 647–658. doi:10.1016/j.jecp.2011.07.004.
  8. ^ Numbers in Mind
  9. ^ a b c d Brooks, M.; Pui, S. (2010). "Are individual differences in numeracy unique from general mental ability? A closer look at a common measure of numeracy". Individual Differences Research. 4 8: 257–265.
  10. ^ Ciampa, Philip J.; Osborn, Chandra Y.; Peterson, Neeraja B.; Rothman, Russell L. (2010). "Patient Numeracy, Perceptions of Provider Communication, and Colorectal Cancer Screening Utilization". Journal of Health Communication 15 (sup3): 157–168. doi:10.1080/10810730.2010.522699. ISSN 1081-0730.
  11. ^ Melhuish, Edward C.; Phan, Mai B.; Sylva, Kathy; Sammons, Pam; Siraj-Blatchford, Iram; Taggart, Brenda (2008). "Effects of the Home Learning Environment and Preschool Center Experience upon Literacy and Numeracy Development in Early Primary School." Journal of Social Issues 64 (1): 95–114. doi:10.1111/j.1540-4560.2008.00550.x. ISSN 0022-4537.
  12. ^ Scanlan, Chip (2004). Why Math Matters Poynter Online, September 8, 2004.
  13. ^ Thomas Andrews (2009). Psychometric Numerical Tests & Employment Psychometric numerical reasoning tests, December 2011.
  14. ^ a b c d e f g Lefevre, Jo-Anne (2000). "Research on the development of academic skills: Introduction to the special issue on early literacy and early numeracy.". Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale 54 (2): 57–60. doi:10.1037/h0088185. ISSN 1878-7290.
  15. ^ a b c d e f Donelle, Lorie; Hoffman-Goetz, Laurie; Arocha, Jose F. (2007). "Assessing Health Numeracy Among Community-Dwelling Older Adults". Journal of Health Communication 12 (7): 651–665. doi:10.1080/10810730701619919. ISSN 1081-0730.
  16. ^ Donelle, L.; Hoffman-Goetz, L., & Arocha, J.F. (2007). "Assessing health numeracy among community-dwelling older adults". Journal Of Health Communication. 7 12: 651–665. doi:10.1080/10810730701619919.
  17. ^ Hess, R.; Visschers, V., Siegrist, M., & Keller, C. (2011). "How do people perceive graphical risk communication? The role of subjective numeracy". Journal Of Risk Research. 1 14: 47–61. doi:10.1080/13669877.2010.488745.

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