Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction.
Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this task successfully with all the signatures of adults' nonsymbolic number representations: accuracy modulated by the ratio of the sum and the comparison quantity, equal performance for within- and cross-modality tasks and for addition and comparison tasks, and performance superior to that of a matched subtraction task. The findings provide clear evidence for nonsymbolic numerical operations on abstract numerical quantities in children who have not yet been taught formal arithmetic.
Barth
Hilary
H
Department of Psychology, Wesleyan University, Middletown, CT 06459, USA. hbarth@wesleyan.edu
Beckmann
Lacey
L
Spelke
Elizabeth S
ES
D000161:Acoustic Stimulation; D001307:Auditory Perception; D002648:Child; D002675:Child, Preschool; D032882:Comprehension; D003210:Concept Formation; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics; D010364:Pattern Recognition, Visual; D011340:Problem Solving
Cognition. 2003 Jan;86(3):201-21
12485738
Proc Natl Acad Sci U S A. 2006 Feb 28;103(9):3486-9
16492785
Cognition. 2006 Jan;98(3):199-222
15876429
Cogn Psychol. 2006 Mar;52(2):130-69
16364281
Trends Cogn Sci. 2000 Feb;4(2):59-65
10652523
Cognition. 2004 Sep;93(2):B59-68
15147939
J Exp Psychol Gen. 1994 Sep;123(3):284-96
7931093
Cognition. 2008 Mar;106(3):1221-47
17678639
Dev Sci. 2007 Jan;10(1):104-9
17181707
Cognition. 2000 Jan 10;74(1):B1-B11
10594312
J Exp Psychol Anim Behav Process. 2000 Jan;26(1):31-49
10650542
Psychol Sci. 2002 Sep;13(5):395-401
12219804
Percept Psychophys. 1982 Aug;32(2):163-70
7145586
Percept Psychophys. 2007 Oct;69(7):1185-203
18038956
Proc Biol Sci. 2003 Jul 22;270(1523):1441-6
12965007
Psychol Sci. 2001 May;12(3):238-43
11437307
Psychol Bull. 2002 Mar;128(2):278-94
11931520
Psychol Sci. 2003 Sep;14(5):396-401
12930467
Cognition. 2003 Aug;89(1):B15-25
12893126
Psychol Sci. 2004 Nov;15(11):776-81
15482450
Child Dev. 2005 Sep-Oct;76(5):978-88
16149996
Percept Psychophys. 2007 Nov;69(8):1324-33
18078224
Trends Cogn Sci. 2004 Jul;8(7):307-14
15242690
Cognition. 2006 Jan;98(3):B57-66
16115616
Dev Sci. 2006 Jan;9(1):33-9
16445393
J Deaf Stud Deaf Educ. 2006 Spring;11(2):139-43
16306180
Proc Natl Acad Sci U S A. 2005 Sep 27;102(39):14116-21
16172388
Psychol Sci. 2001 May;12(3):244-6; discussion 247
11437308
J Exp Child Psychol. 2004 Jan;87(1):57-84
14698689
Science. 2006 Sep 8;313(5792):1431-5
16960005
Brain Res. 2006 Aug 23;1106(1):177-188
16828717
Science. 2004 Oct 15;306(5695):499-503
15486303
Dev Sci. 2005 Sep;8(5):409-19
16048513
Nature. 2007 May 31;447(7144):589-91
17538620
Cognition. 2007 Nov;105(2):395-438
17208214
Cognition. 2008 May;107(2):650-62
18061156
Cognition. 2005 Oct;97(3):315-25
16260264