Number sense

{{Short description|Intuitive grasp of numbers}}

{{Cognitive}}

In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by Stanislas Dehaene in his 1997 book "The Number Sense," but originally named by the mathematician Tobias Dantzig in his 1930 text Number: The Language of Science.

Psychologists believe that the number sense in humans can be differentiated into the approximate number system, a system that supports the estimation of the magnitude, and the parallel individuation system, which allows the tracking of individual objects, typically for quantities below 4.{{cite journal|last=Piazza|first=M.|title=Neurocognitive start-up tools for symbolic number representations|journal=Trends in Cognitive Sciences|year=2010|volume=14|issue=12|doi=10.1016/j.tics.2010.09.008|pages=542–551|pmid=21055996|s2cid=13229498}}

There are also some differences in how number sense is defined in math cognition. For example, Gersten and Chard say number sense "refers to a child's fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons."{{cite web|url=http://www.ldonline.org/article/5838|title=Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities }}{{cite journal|url=http://eric.ed.gov/ERICWebPortal/recordDetail?accno=EJ695626|title=Making Sense of Number Sense: Implications for Children With Mathematical Disabilities|journal=Journal of Learning Disabilities |year=2005 |volume=38 |issue=4 |last1=Berch |first1=Daniel B. |pages=333–339 |doi=10.1177/00222194050380040901 |pmid=16122065 |s2cid=1657049 |url-access=subscription }}{{cite web|url=http://edletter.org/insights/stages.shtml|title=Stages in Development of Number Sense - Harvard Education Letter}}

In non-human animals, number sense is not the ability to count, but the ability to perceive changes in the number of things in a collection.{{cite web|url=http://www.math.twsu.edu/history/topics/num-sys.html#sense|title=Number Systems|website=www.math.twsu.edu}} All mammals, and most birds, will notice if there is a change in the number of their young nearby. Many birds can distinguish two from three.Dantzig, Tobias. Number: The Language of Science. New York: Macmillan Company, 1930.

Researchers consider number sense to be of prime importance for children in early elementary education, and the National Council of Teachers of Mathematics has made number sense a focus area of pre-K through 2nd grade mathematics education.{{cite web|url=http://www.fayar.net/east/teacher.web/math/Illuminations/reflections/prek2/E_NumberSense/index.html|title=Understanding a Child's Development of Number Sense}} An active area of research is to create and test teaching strategies to develop children's number sense. Number sense also refers to the contest hosted by the University Interscholastic League. This contest is a ten-minute test where contestants solve math problems mentally—no calculators, scratch-work, or mark-outs are allowed.{{cite web|url=https://www.uiltexas.org/academics/number-sense|title=UIL Number Sense}}