Back حساب ذهني Arabic Congak BEW Càlcul mental Catalan Kopfrechnen German Νοεροί υπολογισμοί Greek Cálculo mental Spanish Buruzko kalkulu Basque محاسبه ذهنی Persian Päässälasku Finnish Calcul mental French
Mental calculation (also known as mental computation [1]) consists of arithmetical calculations made by the mind, within the 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 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, [2] specifically perhaps, the phonological loop, in the context of addition calculations (only). [3] Mental flexibleness 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 patterns, combined with algorithms process. [4]
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. [5] People with an unusual fastness with reliably correct performance of mental calculations of sufficient relevant complexity are prodigies or savants. [6] 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. [7]
In a survey of children in England it was found that mental imagery was used for mental calculation. [8] By neuro-imaging, brain activity in the parietal lobes of the right hemisphere was found to be associated with mental imaging. [9]
The teaching of mental calculation as an element of schooling, with a focus in some teaching contexts on mental strategies [10]
- ^ Alistair McIntosh (2004). "Mental Computation: A strategies approach" (PDF). amsi.org.au. University of Tasmania: Department of Education. ISBN 1920865209.
- ^ Hope, John Alfred (1984). Characteristics of unskilled, skilled and highly skilled mental calculators (Thesis). University of British Columbia. doi:10.14288/1.0096641.
- ^ Noël, Marie-Pascale; Désert, Michel; Aubrun, Anne; Seron, Xavier (January 2001). "Involvement of short-term memory in complex mental calculation". Memory & Cognition. 29 (1): 34–42. doi:10.3758/BF03195738. PMID 11277462.
- ^ Timo Flückiger; Elisabeth Rathgeb-Schnierer (February 2022). "Capturing flexibility in mental calculation". hal.science. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12): HAL – via John Threlfall Flexible Mental Calculation doi:10.1023/A:1020572803437.
- ^ Clawson, C.C. (1994). "The Genius Calculators". The Mathematical Traveler. Springer. doi:10.1007/978-1-4899-6014-6_14. ISBN 978-0-306-44645-0.
- ^ Fehr, Thorsten; Weber, Jochen; Willmes, Klaus; Herrmann, Manfred (April 2010). "Neural correlates in exceptional mental arithmetic—About the neural architecture of prodigious skills". Neuropsychologia. 48 (5): Abstract. doi:10.1016/j.neuropsychologia.2010.01.007.
- ^ Bousfield, W. A.; Barry, Jr., H. (April 1933). "The Visual Imagery of a Lightning Calculator". The American Journal of Psychology. 45 (2). University of Illinois Press: JSTOR: 233. doi:10.2307/1414296.
- ^ Chris Bills; Eddie Gray. "THE USE OF MENTAL IMAGERY IN MENTAL CALCULATION" (PDF). Education Resources Information Center. University of Warwick: Institute of Education Sciences. p. 97.
What is apparent is that these children have shown a preference for concrete or abstract visual images in both calculation and non calculation contexts.
- ^ O'Boyle, Michael W.; et al. (October 2005). "Mathematically gifted male adolescents activate a unique brain network during mental rotation". Cognitive Brain Research. 25 (2): 583–587. doi:10.1016/j.cogbrainres.2005.08.004. PMID 16150579.
- ^ Thompson, Ian (November 1999). "Mental Calculation Strategies for Addition and Subtraction. Part 1". Mathematics in School. 28 (5): 2–4. JSTOR 30215422.
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