Editing Mental calculation (section)

{{short description|Arithmetical calculations using only the human brain}}
{{Redirect|Human calculator|the systematic use of people for routine calculations|Human computer}}
[[File:Mental calculation at primary school.jpg|thumb|Mental calculation has long been a component of mathematical education.]]
'''Mental calculation''' (also known as [[Mind|mental]] [[computation]]<ref>{{cite web|author=Alistair McIntosh
|url=https://amsi.org.au/wp-content/uploads/sites/15/2014/03/Module-1.pdf|website=amsi.org.au|title=Mental Computation: A strategies approach|date=2004|publisher=[[University of Tasmania]]: Department of Education|access-date=|isbn=1920865209|archive-url=|archive-date=}}</ref>) consists of [[arithmetic]]al [[calculation]]s made by the [[mind]], within the [[human brain|brain]], with no help from any supplies (such as pencil and paper) or devices such as a [[calculator]]. People may use mental calculation when computing tools are not available, when it is faster than other means of calculation (such as conventional educational institution methods), or even in [[Mental calculator#Champion mental calculators|a competitive context]]. Mental calculation often involves the use of specific techniques devised for specific types of problems. Many of these techniques take advantage of or rely on the [[decimal]] numeral system.

Capacity of [[short-term memory]] is a necessary factor for the successful acquisition of a calculation,<ref>{{Cite thesis|last1=Hope |first1=John Alfred|date=1984|title=Characteristics of unskilled, skilled and highly skilled mental calculators|doi=10.14288/1.0096641|publisher=[[University of British Columbia]]}}</ref> specifically perhaps, the [[phonological loop]], in the context of addition calculations (only).<ref>{{Cite journal|last1= Noël|first1=Marie-Pascale|last2=Désert|first2= Michel |last3=Aubrun |first3= Anne|last4=Seron |first4=Xavier |date=January 2001|title=Involvement of short-term memory in complex mental calculation|journal=[[Memory & Cognition]] |volume=29 |issue=1 |pages=34–42 |doi=10.3758/BF03195738 |pmid=11277462 }}</ref> [[Cognitive flexibility|Mental flexible]]ness contributes to the probability of successful completion of mental effort - which is a concept representing adaptive use of knowledge of rules or ways any number associates with any other and how multitudes of numbers are meaningfully associative, and certain (any) number [[pattern]]s, combined with [[algorithm]]s process.<ref>{{cite web|author1=Timo Flückiger|author2=Elisabeth Rathgeb-Schnierer|url=https://hal.science/hal-03746661/document|website=hal.science|title=Capturing flexibility in mental calculation|date=February 2022|publisher=Twelfth Congress of the European Society for Research in Mathematics Education (CERME12): [[HAL (open archive)|HAL]]|access-date=|url-status=|archive-url=|via=John Threlfall ''Flexible Mental Calculation'' doi:10.1023/A:1020572803437}}</ref>

It was found during the eighteenth century that children with powerful mental capacities for calculations developed either into very capable and successful scientists and or mathematicians or instead became a counter example having experienced personal [[retardation]].<ref>{{Cite book|last1=Clawson  |first1=C.C.|date=1994|chapter= The Genius Calculators|title=The Mathematical Traveler|publisher= Springer|pages=|isbn=978-0-306-44645-0|doi=10.1007/978-1-4899-6014-6_14}}</ref> People with an unusual fastness with reliably correct performance of mental calculations of sufficient relevant complexity are [[Child prodigy|prodigies]] or [[savants]].<ref>{{Cite journal|last1=Fehr |first1=Thorsten |last2=Weber|first2=Jochen |last3=Willmes |first3=Klaus |last4= Herrmann|first4=Manfred |date=April 2010|title=Neural correlates in exceptional mental arithmetic—About the neural architecture of prodigious skills|journal=[[Neuropsychologia]]|volume= 48    |issue=5|pages=Abstract|doi=10.1016/j.neuropsychologia.2010.01.007 }}</ref> By the same token, in some contexts and at some time, such an exceptional individual would be known as a: [[lightning]] calculator, or a [[genius]].<ref>{{Cite journal|last1=Bousfield  |first1=W. A. |last2=Barry, Jr.|first2=H.|url=https://www.jstor.org/stable/i261742|date=April 1933|title=The Visual Imagery of a Lightning Calculator|journal=[[The American Journal of Psychology]]|volume=45  |issue=2|page=233|doi=10.2307/1414296|publisher=[[University of Illinois Press]]: [[JSTOR]]|url-access=subscription}}</ref>

In a survey of children in England it was found that [[mental imagery]] was used for mental calculation.<ref>{{cite web|author1=Chris Bills|author2=Eddie Gray|location= [[University of Warwick]]|url=https://files.eric.ed.gov/fulltext/ED452032.pdf#page=91|website=[[Education Resources Information Center]]|title=<small>THE USE OF MENTAL IMAGERY IN MENTAL CALCULATION</small>|date=|publisher=[[Institute of Education Sciences]]|page=97 |access-date=|url-status=|archive-url=|quote=What is apparent is that these children have shown a preference for concrete or abstract visual images in both calculation and non calculation contexts.}}
</ref> By [[neuro-imaging]], brain activity in the [[parietal lobes]] of the right hemisphere was found to be associated with mental imaging.<ref>{{cite journal |  first=Michael W. |  last=O'Boyle |display-authors=etal | title=Mathematically gifted male adolescents activate a unique brain network during mental rotation | journal=[[Cognitive Brain Research]] | date=October 2005 | volume=25 | issue=2 | pages=583–587 | doi=10.1016/j.cogbrainres.2005.08.004| pmid=16150579 }}</ref>

The teaching of mental calculation as an element of [[schooling]], with a focus in some teaching contexts on mental strategies  <ref>{{Cite journal|last1= Thompson|first1=Ian |date=November 1999|title=Mental Calculation Strategies for Addition and Subtraction. Part 1|url=https://www.jstor.org/stable/30215422|journal=[[Mathematics in School]]|volume= 28|issue=5 |pages=2–4 |jstor=30215422 }}</ref>