Editing Numeracy

{{Short description|Ability to apply numerical concepts}}
{{About|the ability to apply numerical concepts|the academic journal|Numeracy (journal)}}
{{Redirect|Innumeracy|the book|Innumeracy (book)}}
[[File:Math games - Big Brother Mouse activity day.jpg|thumb|Children in [[Laos]] have fun as they improve numeracy with "Number Bingo". They roll three dice, construct an equation from the numbers to produce a new number, then cover that number on the board, trying to get [[Connect Four|four in a row]].]]
[[File:Number bingo improves math skills LPB Laos.jpg|thumb|Number bingo improves math skills. LPB Laos.]]
'''Numeracy''' is the ability to understand, [[reason]] with, and apply simple numerical concepts; it is the numerical counterpart of [[literacy]].<ref>{{cite journal |last=Brooks |first=M. |author2=Pui |title=Are individual differences in numeracy unique from general mental ability? A closer look at a common measure of numeracy. |journal=Individual Differences Research |year=2010 |volume=8 |series=4 |pages=257–265}}</ref> The charity [[National Numeracy]] states: "Numeracy means understanding how mathematics is used in the real world and being able to apply it to make the best possible decisions...It's as much about thinking and reasoning as about 'doing sums'". Basic numeracy skills consist of comprehending fundamental [[arithmetic]]al operations 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 to possess at least basic numeric knowledge. Substantial aspects of numeracy also include [[number sense]], operation sense, computation, [[measurement]], [[geometry]], [[probability]] and [[statistics]].{{citation needed|date=July 2020}} A numerically [[literacy|literate]] person can manage and respond to the mathematical demands of life.<ref>{{cite web |author=Statistics Canada |title=Building on our Competencies: Canadian Results of the International Adult Literacy and Skills Survey |url=http://www.nald.ca/library/research/booc/booc.pdf |publisher=Statistics Canada |page=209 |archive-url=https://web.archive.org/web/20110927003001/http://www.nald.ca/library/research/booc/booc.pdf |archive-date=2011-09-27 }}</ref><ref name="PetersBook" />

By contrast, '''innumeracy''' (the lack of numeracy) can have a negative impact. Numeracy has an influence on healthy behaviors, financial literacy, and career decisions. Therefore, innumeracy may negatively affect economic choices, financial outcomes, health outcomes, and life satisfaction.<ref name=PetersBook>{{Cite book|last=Peters|first=Ellen|title= Innumeracy in the wild: Misunderstanding and misusing numbers |publisher=Oxford University Press |year=2020}}</ref><ref name="Gerardi2012">{{cite journal|last1=Gerardi|first1=K.|last2=Goette|first2=L.|last3=Meier|first3=S.|year=2013|title=Numerical ability predicts mortgage default|journal=Proceedings of the National Academy of Sciences|volume=110|issue=28|pages=11267–11271|bibcode=2013PNAS..11011267G|doi=10.1073/pnas.1220568110|pmc=3710828|pmid=23798401|doi-access=free}}</ref><ref name="Banks2010">{{cite journal|last1=Banks|first1=J.|last2=O'Dea|first2=C.|last3=Oldfield|first3=Z.|year=2010|title=Cognitive Function, Numeracy and Retirement Saving Trajectories*|journal=The Economic Journal|volume=120|issue=548|pages=F381–F410|doi=10.1111/j.1468-0297.2010.02395.x|pmc=3249594|pmid=22228911}}</ref> It also may distort risk perception in health decisions.<ref name="Reyna2009" /> Greater numeracy has been associated with reduced susceptibility to [[Framing effect (psychology)|framing effects]], less influence of nonnumerical information such as mood states, and greater sensitivity to different levels of numerical risk.<ref name="Peters2012">{{cite journal |last1=Weller |first1=J.A. |last2=Dieckmann |first2=N.F. |last3=Tusler |first3=M. |last4=Mertz |first4=C.K. |last5=Burns |first5=W.J. |last6=Peters |first6=E. |doi=10.1002/bdm.1751 |title=Development and Testing of an Abbreviated Numeracy Scale: A Rasch Analysis Approach |journal=Journal of Behavioral Decision Making |volume=26 |issue=2 |pages=198–212 |year=2013 |pmid= 32313367|pmc= 7161838|citeseerx=10.1.1.678.6236}}</ref> [[Ellen Peters (professor)|Ellen Peters]] and her colleagues argue that  achieving the benefits of numeric literacy, however, may depend on one's numeric [[self-efficacy]] or confidence in one's skills.<ref name="peterstompkins">{{cite journal |last1=Peters |first1=E. |last2=Tompkins |first2=M.K. |last3=Knoll |first3=M. |last4=Ardoin |first4=S.P. |last5=Shoots-Reinhard |first5=B.  |last6=Meara |first6=A.S. |title=Despite high objective numeracy, lower numeric confidence relates to worse financial and medical outcomes |journal=Proceedings of the National Academy of Sciences |volume=116 |issue=39 |pages=19386–19391 |year=2019|doi=10.1073/pnas.1903126116 |pmid=31501338 |pmc=6765274 |bibcode=2019PNAS..11619386P |doi-access=free }}</ref>

==Representation of numbers==
Humans have evolved to mentally represent numbers in two major ways from observation (not formal math).<ref name=pmid15242690>{{cite journal |last1=Feigenson |first1=Lisa |last2=Dehaene |first2=Stanislas |last3=Spelke |first3=Elizabeth |title=Core systems of number |journal=Trends in Cognitive Sciences |date=July 2004 |volume=8 |issue=7 |pages=307–314 |doi=10.1016/j.tics.2004.05.002 |pmid=15242690 |s2cid=17313189 }}</ref> These representations are often thought to be innate<ref name="Izard2008">{{cite journal |last1=Izard |first1=V. |last2=Sann |first2=C. |last3=Spelke |first3=E.S. |last4=Streri |first4=A. |title=Newborn infants perceive abstract numbers |doi=10.1073/pnas.0812142106 |journal=Proceedings of the National Academy of Sciences |volume=106 |issue=25 |pages=10382–10385 |year=2009 |pmid=19520833 |pmc=2700913 |bibcode=2009PNAS..10610382I |doi-access=free }}</ref> (see [[Numerical cognition]]), to be shared across human cultures,<ref name=pmid18511690>{{cite journal |last1=Dehaene |first1=S. |last2=Izard |first2=V. |last3=Spelke |first3=E. |last4=Pica |first4=P. |title=Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures |doi=10.1126/science.1156540 |journal=Science |volume=320 |issue=5880 |pages=1217–1220 |year=2008 |pmid=18511690 |pmc=2610411|bibcode=2008Sci...320.1217D }}</ref> to be common to multiple species,<ref name="Nieder2005">{{cite journal |last1=Nieder |first1=A. |title=Counting on neurons: The neurobiology of numerical competence |doi=10.1038/nrn1626 |journal=Nature Reviews Neuroscience |volume=6 |issue=3 |pages=177–190 |year=2005 |pmid=15711599 |s2cid=14578049 }}</ref> and not to be the result of individual learning or cultural transmission. They are:
# Approximate representation of numerical magnitude, and
# Precise representation of the quantity of individual items.

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.<ref name=pmid18511690/> 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.<ref name=pmid18511690/>

Precise representations of distinct items demonstrate that people are more accurate in estimating amounts and distinguishing differences when the numbers are relatively small (see [[Subitizing]]).<ref name=pmid18511690/> 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.<ref name=pmid18511690/>

Both systems—approximate representation of magnitude and precise representation quantity of individual items—have limited power. For example, neither allows representations of [[fractions]] or [[negative number]]s. More complex representations require education. However, achievement in school mathematics correlates with an individual's unlearned approximate [[number sense]].<ref>{{cite journal |last1=Halberda |first1=J. |last2=Mazzocco |first2=M.L.M.M. |last3=Feigenson |first3=L. |doi=10.1038/nature07246 |title=Individual differences in non-verbal number acuity correlate with maths achievement |journal=Nature |volume=455 |issue=7213 |pages=665–668 |year=2008 |pmid=18776888 |bibcode=2008Natur.455..665H |s2cid=27196030 }}</ref>

==Definitions and assessment==
Fundamental (or rudimentary) numeracy skills include understanding of the real number line, time, measurement, and estimation.<ref name="Reyna2009">{{cite journal |last1=Reyna |first1=V.F. |last2=Nelson |first2=W.L. |last3=Han |first3=P.K. |last4=Dieckmann |first4=N.F. |title=How numeracy influences risk comprehension and medical decision making |doi=10.1037/a0017327 |journal=Psychological Bulletin |volume=135 |issue=6 |pages=943–973 |year=2009 |pmid=19883143 |pmc=2844786}}</ref> 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.<ref name="Reyna2009" /> 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.<ref name="Reyna2009" /><ref name="Peters2012"/><ref name="Schwartz1997">{{cite journal |last1=Schwartz |first1=L.M. |last2=Woloshin |first2=S. |last3=Black |first3=W.C. |last4=Welch |first4=H.G. |title=The Role of Numeracy in Understanding the Benefit of Screening Mammography |doi=10.7326/0003-4819-127-11-199712010-00003 |journal=Annals of Internal Medicine |volume=127 |issue=11 |pages=966–972 |year=1997 |pmid=9412301 |s2cid=19412405 }}</ref><ref name="Lipkus2001">{{cite journal |last1=Lipkus |first1=I.M. |last2=Samsa |first2=G. |last3=Rimer |first3=B.K. |doi=10.1177/0272989X0102100105 |title=General Performance on a Numeracy Scale among Highly Educated Samples |journal=Medical Decision Making |volume=21 |issue=1 |pages=37–44 |year=2001 |pmid=11206945 |s2cid=25249366 }}</ref><ref name="Cokely2012">{{cite journal |last1=Cokely |first1=E.T. |last2=Galesic |first2=M. |last3=Schulz |first3=E. |last4=Ghazal |first4=S. |last5=Garcia-Retamero |first5=R. |year=2012 |title=Measuring risk literacy: The Berlin Numeracy Test |url=http://journal.sjdm.org/11/11808/jdm11808.pdf |journal=Judgment and Decision Making |volume=7 |issue=1 |pages=25–47 |doi=10.1017/S1930297500001819 |s2cid=11617465 }}</ref><ref>{{cite journal |last1=Schapira |first1=M.M. |last2=Walker |first2=C.M. |last3=Cappaert |first3=K.J. | last4=Ganschow |first4=P.S. |last5=Fletcher |first5=K.E. |last6=McGinley |first6=E.L. |last7=Del Pozo |first7=S. |last8=Schauer |first8=C. |last9=Tarima |first9=S. |last10=Jacobs |first10=E.A. |doi=10.1177/0272989X12447239 |title=The Numeracy Understanding in Medicine Instrument: A Measure of Health Numeracy Developed Using Item Response Theory |journal=Medical Decision Making |volume=32 |issue=6 |pages=851–865 |year=2012 |pmid=22635285 |pmc=4162626}}</ref><ref>{{cite journal |last1=Fagerlin |first1=A. |last2=Zikmund-Fisher |first2=B.J. |last3=Ubel |first3=P.A. |last4=Jankovic |first4=A. |last5=Derry |first5=H.A. |last6=Smith |first6=D.M. |doi=10.1177/0272989X07304449 |title=Measuring Numeracy without a Math Test: Development of the Subjective Numeracy Scale |journal=Medical Decision Making |volume=27 |issue=5 |pages=672–680 |year=2007 |pmid=17641137 |s2cid=30150256 }}</ref> Different tests have been developed to evaluate health numeracy. Two of these tests that have been found to be "reliable and valid" are the GHNT-21 and GHNT-6.<ref>{{Cite journal|last1=Osborn|first1=Chandra Y.|last2=Wallston|first2=Kenneth A.|last3=Shpigel|first3=Adam|last4=Cavanaugh|first4=Kerri|last5=Kripalani|first5=Sunil|last6=Rothman|first6=Russell L.|date=June 2013|title=Development and Validation of the General Health Numeracy Test (GHNT)|journal=Patient Education and Counseling|volume=91|issue=3|pages=350–356|doi=10.1016/j.pec.2013.01.001|issn=0738-3991|pmc=3644342|pmid=23433635}}</ref>

==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.<ref name="CiampaOsborn2010">{{cite journal |last1=Ciampa |first1=Philip J. |last2=Osborn |first2=Chandra Y. |last3=Peterson |first3=Neeraja B. |last4=Rothman |first4=Russell L. |title=Patient Numeracy, Perceptions of Provider Communication, and Colorectal Cancer Screening Utilization |journal=Journal of Health Communication |date=13 December 2010 |volume=15 |issue=sup3 |pages=157–168 |doi=10.1080/10810730.2010.522699 |pmid=21154091 |pmc=3075203 }}</ref> 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.<ref name="CiampaOsborn2010" />

==Socioeconomic status==
Children who are brought up in families with high SES tend to be more engaged in developmentally enhancing activities.<ref name="CiampaOsborn2010" /> These children are more likely to develop the necessary abilities to learn and to become more motivated to learn.<ref name="CiampaOsborn2010" /> 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.<ref name="CiampaOsborn2010" />

A number of studies have, moreover, proved that the education level of the mother is strongly [[correlated]] with the average age of getting married. More precisely, 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.<ref>{{cite journal |last1=Joerg |first1=Baten |last2=Mikołaj |first2=Szołtysek |last3=Monica |first3=Campestrini |title='Girl Power' in Eastern Europe? The human capital development of Central-Eastern and Eastern Europe in the seventeenth to nineteenth centuries and its determinants |journal=European Review of Economic History |date=14 December 2016 |doi=10.1093/ereh/hew017 |s2cid=51963985 |url=http://pdfs.semanticscholar.org/8ec8/de479e466e0c9cf567baef1353ee65eb4b47.pdf |archive-url=https://web.archive.org/web/20190228165111/http://pdfs.semanticscholar.org/8ec8/de479e466e0c9cf567baef1353ee65eb4b47.pdf |archive-date=28 February 2019 }}</ref>

==Parenting==
Parents are advised 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{{clarify|date=July 2020}}, 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.<ref name="CiampaOsborn2010" /> 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.<ref name="CiampaOsborn2010" />

==Home-learning environment==
Along with parenting and SES, a strong [[Homeschooling|home-learning]] environment increases the likelihood of the child being prepared for comprehending complex mathematical schooling.<ref name="MelhuishPhan2008">{{cite journal |last1=Melhuish |first1=Edward C. |last2=Phan |first2=Mai B. |last3=Sylva |first3=Kathy |last4=Sammons |first4=Pam |last5=Siraj-Blatchford |first5=Iram |last6=Taggart |first6=Brenda |title=Effects of the Home Learning Environment and Preschool Center Experience upon Literacy and Numeracy Development in Early Primary School |journal=Journal of Social Issues |date=March 2008 |volume=64 |issue=1 |pages=95–114 |doi=10.1111/j.1540-4560.2008.00550.x |s2cid=18460752 }}</ref> 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.<ref name="MelhuishPhan2008"/>

==Age==
Age is accounted for when discussing the development of numeracy in children.<ref name="MelhuishPhan2008"/> Children under the age of 5 have the best opportunity to absorb basic numeracy skills.<ref name="MelhuishPhan2008" /> After the age of seven, achievement of basic numeracy skills become less influential.<ref name="MelhuishPhan2008" /> For example, a study was conducted to compare the reading and mathematical abilities between children of ages five and seven, 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 five than between the groups aged seven. This reveals that those of younger ages have an opportunity to retain more information, like numeracy. According to Gelman and Gallistel in The Child's Understanding of Number, 'children as young as 2 years can accurately judge numerosity provided that the numerosity is not larger than two or three'. Children as young as three have been found to understand elementary mathematical concepts.<ref>{{Cite book|last=Hughes|first=Martin|title=Children and Number|publisher=Wiley-Blackwell|year=1986|isbn=978-0-631-13581-4}}</ref> Kilpatrick and his colleagues state 'most preschoolers show that they can understand and perform simple addition and subtraction by at least 3 years of age'.<ref>{{Cite book |author=Jeremy Kilpatrick |author2=Jane Swafford |author3=Bradford Findell |title=Adding + it up: helping children learn mathematics|date=2001|publisher=National Academy Press|isbn=0-309-06995-5|oclc=248386156}}</ref> Lastly, it has been observed that pre-school children benefit from their basic understanding of 'counting, reading and writing of numbers, understanding of simple addition and subtraction, numerical reasoning, classifying of objects and shapes, estimating, measuring, [and the] reproduction of number patterns'.<ref>{{Cite journal|last1=Ewers-Rogers|first1=Jennifer|last2=Cowan|first2=Richard|date=January 1996|title=Children as Apprentices to Number|journal=Early Child Development and Care|volume=125|issue=1|pages=15–25|doi=10.1080/0300443961250102|issn=0300-4430}}</ref>

==Literacy==
There seems to be a relationship between [[literacy]] and numeracy,<ref name="Bullock1994">{{citation |title=Literacy in the Language of Mathematics |first=James O. |last=Bullock |journal=[[The American Mathematical Monthly]] |volume=101 |issue=8<!--| number = 8--> |date=October 1994 |pages=735–743 |jstor=2974528 |doi=10.2307/2974528}}</ref><ref name="Steen2001">{{citation |title=Mathematics and Numeracy: Two Literacies, One Language |journal=The Mathematics Educator |volume=6 |number=1 |year=2001 |pages=10–16 |first=Lynn Arthur |last=Steen}}</ref> 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.<ref>{{cite journal |last=Purpura |first=David |author2=Hume, L. |author3=Sims, D. |author4=Lonigan, C. |title=Early literacy and early numeracy: The value of including early literacy skills in the prediction of numeracy |journal=[[Journal of Experimental Child Psychology]] |year=2011 |volume=110 |issue=4 |pages=647–658 |doi=10.1016/j.jecp.2011.07.004 |pmid=21831396}}</ref> 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.<ref>[https://www.sciencenews.org/article/numbers-mind Numbers in Mind]</ref>

==Employment==
Numeracy has a huge impact on employment.<ref name="Brooks 2010 257–265">{{cite journal |last=Brooks |first=M. |author2=Pui, S. |title=Are individual differences in numeracy unique from general mental ability? A closer look at a common measure of numeracy |journal=Individual Differences Research |year=2010 |volume=8 |series=4 |pages=257–265}}</ref> In a work environment, numeracy can be a controlling factor affecting career achievements and failures.<ref name="Brooks 2010 257–265"/> Many professions require individuals to have well-developed numerical skills: for example, [[mathematician]], [[physicist]], [[accountant]], [[actuary]], [[financial analyst]], [[engineer]], and [[architect]]. This is why a major target of the UN's [[Sustainable Development Goal 4]] is to substantially increase the number of youths who have relevant skills for decent work and employment<ref>{{Cite web|title=SDG4's 10 targets|url=https://www.campaignforeducation.org/en/who-we-are/the-international-education-framework-2/the-sustainable-development-goal-4/sdg4s-10-targets/|access-date=2020-09-22|website=Global Campaign For Education|language=en-US}}</ref> because, even outside these specialized areas, the lack of numeracy skills can reduce employment opportunities and promotions, resulting in unskilled manual careers, low-paying jobs, and even unemployment.<ref>{{cite journal | last1 = Ciampa | first1 = Philip J. | last2 = Osborn | first2 = Chandra Y. | last3 = Peterson | first3 = Neeraja B. | last4 = Rothman | first4 = Russell L. | year = 2010 | title = Patient Numeracy, Perceptions of Provider Communication, and Colorectal Cancer Screening Utilization | journal = Journal of Health Communication | volume = 15 | issue = Suppl 3 | pages = 157–168 | doi = 10.1080/10810730.2010.522699 | pmid = 21154091 | pmc = 3075203 }}</ref> For example, carpenters and interior designers need to be able to measure, use fractions, and handle budgets.<ref>{{cite journal | last1 = Melhuish | first1 = Edward C. | last2 = Phan | first2 = Mai B. | last3 = Sylva | first3 = Kathy | last4 = Sammons | first4 = Pam | last5 = Siraj-Blatchford | first5 = Iram | last6 = Taggart | first6 = Brenda | year = 2008 | title = Effects of the Home Learning Environment and Preschool Center Experience upon Literacy and Numeracy Development in Early Primary School | journal = Journal of Social Issues | volume = 64 | issue = 1| pages = 95–114 | doi = 10.1111/j.1540-4560.2008.00550.x | s2cid = 18460752 }}</ref> Another example of 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 [[verb]]s". 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.<ref>Scanlan, Chip (2004). "[http://www.poynter.org/column.asp?id=52&aid=71048 Why Math Matters] {{Webarchive|url=https://web.archive.org/web/20090114185500/http://www.poynter.org/column.asp?id=52&aid=71048 |date=2009-01-14 }}" ''Poynter Online'', September 8, 2004.</ref>

To assess job applicants, [[Psychometrics|psychometric]] numerical reasoning tests have been created by [[occupational psychologist]]s, who are involved in the study of numeracy. These tests are used to assess ability to comprehend and apply numbers. They are sometimes administered with a time limit, so that the test-taker must 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{{citation needed|date=December 2019}}

These tests first became prevalent during the 1980s, following the pioneering work of psychologists, such as P.&nbsp;Kline, who published a book in 1986 entitled ''A handbook of test construction: Introduction to psychometric design'', which explained that psychometric testing could provide reliable and objective results, which could be used to assess a candidate's numerical abilities.

==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 (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 causes of innumeracy vary. Innumeracy has been seen in those suffering from poor education and childhood deprivation of numeracy.<ref name="Lefevre2000">{{cite journal |last1=Lefevre |first1=Jo-Anne|author1-link=Jo-Anne LeFevre |title=Research on the development of academic skills: Introduction to the special issue on early literacy and early numeracy. |journal=Canadian Journal of Experimental Psychology |date=2000 |volume=54 |issue=2 |pages=57–60 |doi=10.1037/h0088185 |pmid=10881390 }}</ref> Innumeracy is apparent in children during the transition between numerical skills obtained before schooling and the new skills taught in the education departments because of their memory capacity to comprehend the material.<ref name="Lefevre2000" /> Patterns of innumeracy have also been observed depending on age, gender, and race.<ref name="Donelle2007" /> Older adults have been associated with lower numeracy skills than younger adults.<ref name="Donelle2007">{{cite journal |last=Donelle |first=L. |author2=Hoffman-Goetz, L. |author3=Arocha, J.F. |title=Assessing health numeracy among community-dwelling older adults |journal=Journal of Health Communication |year=2007 |volume=12 |issue=7 |series=7 |pages=651–665 |doi=10.1080/10810730701619919 |pmid=17934942|s2cid=20421979 }}</ref> Men have been identified to have higher numeracy skills than women.<ref name="Brooks 2010 257–265"/> Some studies seem to indicate young people of African heritage tend to have lower numeracy skills.<ref name="Donelle2007" /> 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{{clarify|date=July 2020}} 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.<ref name=pmid18511690/>

==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".<ref name="Lefevre2000" /> Biological primary abilities evolve over time and are necessary for survival.  Such abilities include speaking a common language or knowledge of simple mathematics.<ref name="Lefevre2000" /> Biological secondary abilities are attained through personal experiences and cultural customs, such as reading or high level mathematics learned through schooling.<ref name="Lefevre2000" /> 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.<ref name="Lefevre2000" /> This could be a potential explanation of the challenge of being numerate.<ref name="Lefevre2000" />

==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".<ref>{{cite journal |last1=Golbeck |first1=AL |last2=Ahlers-Schmidt |first2=CR |last3=Paschal |first3=AM |last4=Dismuke |first4=SE |year=2005 |title=A definition and operational framework for health numeracy |journal=American Journal of Preventive Medicine |volume=29 |issue=4 |pages=375–376 |doi=10.1016/j.amepre.2005.06.012 |pmid=16242604}}</ref> 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. For instance, health numeracy also requires the ability to understand probabilities or relative frequencies in various numerical and graphical formats, and to engage in [[Bayesian inference]], while avoiding errors sometimes associated with Bayesian reasoning (see [[Base rate fallacy]], [[Conservatism (Bayesian)]]). Health numeracy also requires understanding terms with definitions that are specific to the medical context. For instance, although 'survival' and 'mortality' are complementary in common usage, these terms are not complementary in medicine (see [[five-year survival rate]]).<ref name="Welch2000">{{cite journal |last1=Welch |first1=H.G. |last2=Schwartz |first2=L.M. |last3=Woloshin |first3=S. |doi=10.1001/jama.283.22.2975 |title=Are Increasing 5-Year Survival Rates Evidence of Success Against Cancer? |journal=JAMA |volume=283 |issue=22 |pages=2975–2978 |year=2000 |pmid=10865276 }}</ref><ref name="Gigerenzer2007">{{cite journal |last1=Gigerenzer |first1=G. |last2=Gaissmaier |first2=W. |last3=Kurz-Milcke |first3=E. |last4=Schwartz |first4=L.M. |last5=Woloshin |first5=S. |title=Helping Doctors and Patients Make Sense of Health Statistics |doi=10.1111/j.1539-6053.2008.00033.x |journal=Psychological Science in the Public Interest |volume=8 |issue=2 |pages=53–96 |year=2007 |pmid=26161749 |doi-access=free |hdl=11858/00-001M-0000-0025-7CFC-A |hdl-access=free }}</ref> Innumeracy is also a very common problem when dealing with risk perception in health-related behavior; it is associated with patients, physicians, journalists and policymakers.<ref name="Donelle2007" /><ref name="Gigerenzer2007" /> 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.<ref name="CiampaOsborn2010" /><ref name=LagBauger>{{cite journal |last1=Låg |first1=T. |last2=Bauger |first2=L. |last3=Lindberg |first3=M. |last4=Friborg |first4=O. |title=The role of numeracy and intelligence in health-risk estimation and medical data interpretation |journal=Journal of Behavioral Decision Making |volume=30 |issue=2 |pages=95–108 |year=2014 |doi=10.1002/bdm.1788}}</ref>  For example, if a patient has been diagnosed with breast cancer, being innumerate may hinder her ability to comprehend her physician's recommendations, or even the severity of the health concern or even the likelihood of treatment benefits.<ref name="Lipkus2010">{{cite journal |last1=Lipkus |first1=I.M. |last2=Peters |first2=E. |last3=Kimmick |first3=G. |last4=Liotcheva |first4=V. |last5=Marcom |first5=P. |title=Breast cancer patients' treatment expectations after exposure to the decision aid program, Adjuvant Online: The influence of numeracy. | journal=Medical Decision Making |volume=30 |issue=4 |pages=464–473|year=2010 |doi=10.1177/0272989X09360371|pmid=20160070 |pmc=3616375 }}</ref> One study found that people tended to overestimate their chances of survival or even to choose lower-quality hospitals.<ref name="Brooks 2010 257–265" /> Innumeracy also makes it difficult or impossible for some patients to read medical graphs correctly.<ref>{{cite journal |last1=Hess |first1=R. |last2=Visschers |first2=V.H.M. |last3=Siegrist |first3=M. |last4=Keller |first4=C. |title=How do people perceive graphical risk communication? The role of subjective numeracy |doi=10.1080/13669877.2010.488745 |journal=Journal of Risk Research |volume=14 |pages=47–61 |year=2011 |s2cid=146594087 }}</ref> Some authors have distinguished graph literacy from numeracy.<ref name="Galesic2011">{{cite journal |last1=Galesic |first1=M. |author-link=Mirta Galesic |last2=Garcia-Retamero |first2=R. |year=2010 |title=Graph Literacy: A Cross-Cultural Comparison |journal=Medical Decision Making |volume=31 |issue=3 |pages=444–457 |doi=10.1177/0272989X10373805 |pmid=20671213 |s2cid=32662502|hdl=11858/00-001M-0000-0024-F299-8 |hdl-access=free }}</ref> Indeed, many doctors exhibit innumeracy when attempting to explain a graph or statistics to a patient. 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 harm to health.

Different presentation formats of numerical information, for instance natural frequency icon arrays, have been evaluated to assist both low-numeracy and high-numeracy individuals.<ref name="Donelle2007" /><ref name="Ancker2006">{{cite journal |last1=Ancker |first1=J.S. |last2=Senathirajah |first2=Y. |last3=Kukafka |first3=R. |last4=Starren |first4=J.B. |title=Design Features of Graphs in Health Risk Communication: A Systematic Review |doi=10.1197/jamia.M2115 |journal=Journal of the American Medical Informatics Association |volume=13 |issue=6 |pages=608–618 |year=2006 |pmid=16929039 |pmc=1656964}}</ref><ref name="GarciaRetamero2012">{{cite journal |last1=Garcia-Retamero |first1=R. |last2=Okan |first2=Y. |last3=Cokely |first3=E.T. |title=Using Visual Aids to Improve Communication of Risks about Health: A Review |doi=10.1100/2012/562637 |journal=The Scientific World Journal |volume=2012 |pages=1–10 |year=2012 |pmid=22629146 |pmc=3354448 |doi-access=free }}</ref><ref name="Hoffrage2000">{{cite journal |last1=Hoffrage |first1=U. |last2=Lindsey |first2=S. |last3=Hertwig |first3=R. |last4=Gigerenzer |first4=G. |title=Medicine: Communicating Statistical Information |doi=10.1126/science.290.5500.2261 |journal=Science |volume=290 |issue=5500 |pages=2261–2262 |year=2000 |pmid=11188724 |hdl=11858/00-001M-0000-0025-9B18-3 |s2cid=33050943 |hdl-access=free }}</ref><ref name="Galesic2009">{{cite journal |last1=Galesic |first1=M. |last2=Garcia-Retamero |first2=R. |last3=Gigerenzer |first3=G. |doi=10.1037/a0014474 |title=Using icon arrays to communicate medical risks: Overcoming low numeracy |journal=Health Psychology |volume=28 |issue=2 |pages=210–216 |year=2009 |pmid=19290713 |hdl=11858/00-001M-0000-0024-F6BE-3 |s2cid=10545246 |hdl-access=free }}</ref> Other data formats provide more assistance to low-numeracy people.<ref name=PetersBook /><ref name=PetersDieckmannDixon>{{cite journal |last1=Peters | first1=E. |last2=Dieckmann |first2=N. |last3=Dixon |first3=A. |last4=Hibbard |first4=J.H. |last5=Mertz |first5=C.K. |title=Less is more in presenting quality information to consumers |journal=Medical Care Research & Review |volume=64 |issue=2 |pages=169–190 |year=2007 |doi=10.1177/10775587070640020301| pmid=17406019 | s2cid=1001326 }}</ref><ref name=PetersDieckmannVastfjall>{{cite journal |last1=Peters | first1=E. |last2=Dieckmann |first2=N. |last3=Våstfjåll |first3=D. |last4=Mertz |first4=C.K. |last5=Slovic |first5=P. |last6=Hibbard |first6=J.H. |title=Bringing meaning to numbers: The impact of evaluative categories on decisions |journal=Journal of Experimental Psychology: Applied |volume=15 |issue=3 |pages=213–227 |year=2009 |doi=10.1037/a0016978| pmid=19751072 | s2cid=11035873 }}</ref>

==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 [[Whipple's index|age-heaping]], researchers like Professor [[Jörg Baten]] study the development and inequalities of numeracy over time and throughout regions. For example, Baten<ref>{{cite journal |last1=Baten |first1=Jörg |last2=Hippe |first2=Ralph |title=The early regional development of human capital in Europe, 1790–1880 |journal=Scandinavian Economic History Review |date=2012 |volume=60 |issue=3 |pages=254–289|doi=10.1080/03585522.2012.727763 |s2cid=154669586 |url=http://www.cliometrie.org/images/wp/AFC_WP_07-2011.pdf}}</ref> 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<ref>{{cite journal |last1=Baten |first1=Jörg |last2=Fourie |first2=Johan |title=Numeracy of Africans, Asians, and Europeans during the early modern period: new evidence from Cape Colony court registers |journal=The Economic History Review |date=2015 |volume=68 |issue=2 |pages=632–656 |doi=10.1111/1468-0289.12064|hdl=10.1111/1468-0289.12064 |s2cid=51961313 |hdl-access=free }}</ref> 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. For example, Baten, Crayen and Voth<ref>{{cite journal |last1=Baten |first1=Jörg |last2=Crayen |first2=Dorothee |last3=Voth |first3=Hans-Joachim |title=Numeracy and the impact of high food prices in industrializing Britain, 1780–1850 |journal=Review of Economics and Statistics |date=2014 |volume=96 |issue=3 |pages=418–430 |doi=10.1162/REST_a_00403 |s2cid=3518364 |url=http://www.zora.uzh.ch/id/eprint/100551/1/rest_a_00403.pdf}}</ref> look at the effects of war on numeracy in [[England]], and Baten and Priwitzer<ref>{{cite journal |last1=Baten |first1=Jörg |last2=Priwitzer |first2=Stefan |title=Social and intertemporal differences of basic numeracy in Pannonia (first century BCE to third century CE) |journal=Scandinavian Economic History Review |date=2015 |volume=63 |issue=2 |pages=110–134 |doi=10.1080/03585522.2015.1032339|s2cid=51962193 }}</ref> find a "military bias" in what is today western [[Hungary]]: people opting for a military career had - on average - better numeracy indicators (1 BCE to 3[[Common Era|CE]]).

==See also==

{{div col|colwidth=30em}}
* [[Acalculia]]
* [[Approximate number system]]
* [[Bayesian inference]]
* [[Dyscalculia]]
* [[Graphicacy]]
* [[Health literacy]]
* [[Literacy]]
* [[National Numeracy Network]]
* [[Number sense]]
* [[Numeracy bias]]
* [[Numerical cognition]]
* [[Numerosity adaptation effect]]
* [[Oracy]]
* [[Subitizing]]
{{div col end}}

==Notes==
{{reflist|2}}

==External links==
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*[http://www.riskliteracy.org The Berlin Numeracy Test]
*[https://www.cdc.gov/healthliteracy/training/page5756.html CDC Health Literacy Resources]
*[http://www.ahrq.gov/professionals/quality-patient-safety/quality-resources/tools/literacy/index.html Agency for Healthcare Research and Quality Health Literacy Measurement tools]
*[http://haberlah.edublogs.org/2017/07/17/importance-of-being-numerate/ Australian blog post reviewing the increasing importance of teaching numeracy skills]

{{Literacy}}
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[[Category:Literacy]]
[[Category:Mathematics education]]
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