The relationship between non-symbolic multiplication and division in childhood.

Publisher: Sage in association with Experimental Psychology Society Country of Publication: England NLM ID: 101259775 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1747-0226 (Electronic) Linking ISSN: 17470218 NLM ISO Abbreviation: Q J Exp Psychol (Hove) Subsets: MEDLINE

Publication: 2018- : London : Sage in association with Experimental Psychology Society
Original Publication: London : Informa Healthcare

Mathematics* ; Social Class*; Concept Formation/*physiology ; Learning/*physiology ; Problem Solving/*physiology; Child ; Female ; Humans ; Male ; Photic Stimulation

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b - b = a). The current study examines children's ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and were then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8*4/4) or did not (e.g., 8*4/2). Children's performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a*b/b structure, suggesting that they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems.

Cogn Psychol. 2013 Jun;66(4):380-404. (PMID: 23770623)
Psychol Sci. 2004 Nov;15(11):776-81. (PMID: 15482450)
Psychol Sci. 2013 Oct;24(10):2013-9. (PMID: 23921769)
Psychol Sci. 2007 Aug;18(8):740-5. (PMID: 17680947)
J Exp Child Psychol. 2011 Feb;108(2):278-92. (PMID: 20974477)
PLoS One. 2012;7(5):e37426. (PMID: 22616007)
Infancy. 2009 Mar 4;14(2):244-262. (PMID: 32693466)
Psychon Bull Rev. 2009 Apr;16(2):225-37. (PMID: 19293088)
Cognition. 2003 Jan;86(3):201-21. (PMID: 12485738)
Can J Exp Psychol. 2000 Jun;54(2):105-16. (PMID: 10881394)
PLoS Biol. 2007 Dec;5(12):e328. (PMID: 18092890)
Anim Cogn. 2012 Jul;15(4):699-710. (PMID: 22526693)
Psychophysiology. 2012 Nov;49(11):1481-91. (PMID: 23046492)
J Exp Child Psychol. 2009 Aug;103(4):532-45. (PMID: 19167015)
Infancy. 2018 May-Jun;23(3):310-324. (PMID: 32884496)
Front Psychol. 2013 Jun 10;4:325. (PMID: 23772216)
J Cogn Neurosci. 2009 Nov;21(11):2217-29. (PMID: 19016605)
Cognition. 2006 Jan;98(3):199-222. (PMID: 15876429)
Cereb Cortex. 2016 Feb;26(2):748-763. (PMID: 25715283)
Psychol Sci. 2001 May;12(3):238-43. (PMID: 11437307)
J Exp Child Psychol. 2016 Feb;142:66-82. (PMID: 26513326)
Cogn Sci. 2014 Jan-Feb;38(1):101-27. (PMID: 23855416)
Dev Psychol. 2014 Jan;50(1):108-12. (PMID: 23647413)
Cortex. 2013 Nov-Dec;49(10):2674-88. (PMID: 23890692)
PLoS One. 2009;4(3):e4786. (PMID: 19274079)
Dev Psychol. 2008 Sep;44(5):1466-77. (PMID: 18793077)
J Exp Child Psychol. 2012 Aug;112(4):361-77. (PMID: 22575845)
Cognition. 2010 Jul;116(1):33-41. (PMID: 20381023)
J Exp Child Psychol. 2013 Mar;114(3):375-88. (PMID: 23201156)
J Exp Child Psychol. 2006 Aug;94(4):349-62. (PMID: 16674969)
Proc Natl Acad Sci U S A. 2005 Sep 27;102(39):14116-21. (PMID: 16172388)
J Exp Child Psychol. 2003 Jun;85(2):89-102. (PMID: 12799163)
Br J Dev Psychol. 2012 Jun;30(Pt 2):344-57. (PMID: 22550952)
Dev Sci. 2015 Jan;18(1):38-49. (PMID: 24589420)
J Exp Child Psychol. 2009 Aug;103(4):400-8. (PMID: 19285683)
Dev Sci. 2013 Jul;16(4):610-21. (PMID: 23786478)
Nature. 2008 Oct 2;455(7213):665-8. (PMID: 18776888)
Cogn Dev. 2013 Jul;28(3):272-289. (PMID: 24049245)
Dev Sci. 2014 Jul;17(4):506-24. (PMID: 25089322)
Can J Exp Psychol. 2003 Dec;57(4):321-30. (PMID: 14710869)
Psychon Bull Rev. 2001 Dec;8(4):698-707. (PMID: 11848588)
J Exp Child Psychol. 1999 Nov;74(3):194-212. (PMID: 10527554)
Nature. 2007 May 31;447(7144):589-91. (PMID: 17538620)
J Exp Child Psychol. 2013 Dec;116(4):829-38. (PMID: 24076381)
Proc Natl Acad Sci U S A. 2012 Jul 10;109(28):11116-20. (PMID: 22733748)
J Exp Psychol Anim Behav Process. 1983 Jul;9(3):320-34. (PMID: 6886634)
Dev Psychol. 2009 Nov;45(6):1583-94. (PMID: 19899916)
Public Health Rep. 2006 Jan-Feb;121(1):51-9. (PMID: 16416698)
Cognition. 2008 Jun;107(3):932-45. (PMID: 18281029)
Child Dev. 2011 Jul-Aug;82(4):1224-37. (PMID: 21679173)
J Exp Child Psychol. 2009 Aug;103(4):441-54. (PMID: 19289237)
J Exp Psychol Gen. 1998 Dec;127(4):377-97. (PMID: 9857493)
J Deaf Stud Deaf Educ. 2009 Spring;14(2):260-77. (PMID: 18948568)
Cognition. 2010 Aug;116(2):204-16. (PMID: 20537618)
Dev Sci. 2006 Sep;9(5):F50-8. (PMID: 16911437)
Front Psychol. 2013 Jul 19;4:444. (PMID: 23882245)
PLoS One. 2016 Sep 02;11(9):e0147734. (PMID: 27588944)
J Exp Child Psychol. 2009 May;103(1):17-29. (PMID: 18513738)

R15 HD065629 United States HD NICHD NIH HHS

Keywords: Cognitive development; Division; Inversion; Memory; Multiplication; Number; Quantity

Date Created: 20160217 Date Completed: 20170317 Latest Revision: 20240324

20240324

PMC5228418

10.1080/17470218.2016.1151060

26880261