Editing Numeracy (section)

==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>