CopyriShr 1996 by the Ameti€n Rrahological Aswiatim, Inc.
0012-1649/96t$3.00
hychology
Dewl@mental
1996. Vol. 32. No. 2.254-262
Are EastAsianVersusAmerican Differencesin Arithmetical
Ability a RecentPhenomenon?
Timothy A. Salthouse
David C. Geary
GeoryiaInstitute of Technology
Universityof Missouri-Columbia
Liu Fan
Guo-PengChen
China Central Institute for EducationalSciences
EastChina Normal Universitv
Youngerand older American and Chineseadults wereadministeredarithmetic, perceptualspeed,
and spatial orientation tests. For the perceptual speed and spatial orientation tests, the younger
adults showedsubstantial performance advantagesover the older adults in both the United States
and China. For the arithmetic tests,the youngerChineseadults outperformedthe older Chinese
adults,but the groupsofyounger and olderAmerican adults had comparablearithmeticalabilities.
Cross-nationalcomparisonsindicatedthat the youngerChineseadults outperformedthe younger
American adults on the arithmetic tests,but not on the perceptualspeedand spatial orientation
tests.The performanceof the olderAmericanand olderChineseadultswascomparablefor all of the
that the advantageofChinese adults over American
ability measures.The overallpattern suggests
adultsin complexarithmetic might be a relativelyrecentphenomenon.
The first systematiccross-nationalstudy of mathematical
abilitieswasconductedin 1964(Hu#n, 1967).The resultsof
this study showedthat American adolescentswere among the
most poorly educatedstudentsin mathematicsin the industrializedworld. In the ensuing30 years,this basicfinding hasbeen
replicatedmany timesand hasbeenshownto be true for nearly
all mathematical
domains,from arithmeticto complexmathematics (Crosswhite,Dossey,Swafford,McKnight, & Cooney,
1985;Lapointe,Mead,& Askew,1992). Differencesbetween
the mathematicaldevel@mentof American children and children from other nations are often times most extreme when
comparisonsare made betweenthe United Statesand East
Asian nations(i.e., China, Korea,Taiwan,& Japan;e.g.,Stevenson,Chen,& Lee, 1993;Stevenson
et al., 1990).tThe consistencyof academicachievementdifferencesbetweenchildren
from the United Statesand children from East Asian nations
has led some scientiststo argue that these diferences stem
Universityof MissouriDavidC. Geary,Departmentof Psychology,
GeoryiaInstiColumbia;Timothy A. Salthouse,Schoolof Psychology,
tute ofTechnology;Guo-PengChen, Department o[Psychology,East
China Normal University,Shanghai,China; Liu Fan, Department of
Psychology,
China Central Institute lor EducationalSciences,Beijing,
China.
The researchwassupportedby Grant I R01-HD2793I from the National Institute of Child Health and Human Developmentand Grant
ACr06826from the National Institute on Aging.
We thank MelissaMoon and Ravindran Sabapathylor their assistancewith data collectionand collation, Zhitang Liu for his assistance
with the translations,and Mark Ashcraft,Donald Kausler',and Robert
Sieglerfor commentson earlierdraftsof this article.
to David
Correspondence
concerningthis article shouldbe addressed
2l0 McAlesterHall, Universityof
C. Geary,Departmentof Psychology,
Missouri.Columbia.Missouri652l l.
largelyfrom a differencein the generalintelligenceofAsian and
Americanindividuals(e.g.,Lynn, 1982;Rushton,1992\.
In this study,we presentevidencethat the advantageofEast
Asian individuals over their American peers in arithmetical
abilitiesprobably did not exist 60 yearsago,and that the more
recent East Asian advantagein arithmetic, and perhapsother
mathematicaldomains, likely reflectssecular changeswithin
the United Statesrather than an EastAsian advantagein intelligence.The hypothesisthat the advantageofEast Asian individuals over their American peersin arithmetic is a relatively
recent phenomenonis basedon two lines of research:crossgenerationalchangesin the arithmetical develqment of American children and differencesin the arithmetical abilities of
youngerand olderAmerican adults.
One dimensionthat distinguishesthe arithmetical develqment
of American children from their EastAsian cohortsis the sqhiv
tication ofthe strategiesusedin problem solving(Fuson& Kwon,
1992a:Gary, Fan,& Bow-Thomas,I 992). For the solvingof simple arithmetic problems,suchas8 + 7, whenan answercannotbe
remembered,American children tend to count mentally or on
theirfi ngen( Gearyet al., I 992;Siegler,I 987). Childrenfrom East
Asian nations,in contrast,typically usea form of decomposition,
in which the digits are decomposedinto smaller setswhich, in
turn, are added together(Fuson & Kwon, 1992a;Geary et al.,
the
1992). Forinstance,to solve8 + 7, thechild might decompose
7 into a 2 arrda 5, and then retrievethe answersto 8 + 2, and l0
* 5. The useofdecompositionappeanto be dependenton a basic
undentandingofsets,and,assuch,shouldprobablybe considered
a conceptuallymore sophisticatedproblem-solvingapproachthan
counting (Fuson & Kwon, 1992a).EastAsian children not only
254
t The mathematicalachievementofchildren from China, Korea,Taiwan, and Japanis generallycomparable( Lapointe et al., 1992;Stevensonetal..1993).
CULTURE AND ARITHMETIC
use develcpmentallyadvanced problem-solving approachesin
comparisonwith their contemporary American peers,they also
memorizethe basicarithmetic facts(e.g.,the addition and subtractiontables)at a much youngerage(e.g.,Gearyet al., 1992).
In fact,recentstudiessuggestthat only about halfofcontemporary
North American collegestudentsappearto know all of the basic
addition and subtractionfacts(Geary,Frensch,& Wiley, 1993;
Geary& Wiley,l99l;LeRwe, Sadesky,
& Bisanz,in press).
Cross-nationaldifferencesin the frequencywith which decompositionis usedas a problem-solvingstrategyare related,
in part, to differencesin the structure of AsianJanguageand
Englishnumberwords( Fuson& Kwon, 1992a).In Asianlanguages,words for teen valuesare statedten one, ten two, ten
three,and so on, which facilitatesthe child's conceptualunderstandingofthe base-10structureofthe numbersystemas well
as strategydevelopment(Fuson & Kwon, 1992b;Geary, 1994;
Geary,Bow-Thomas,
Fan,& Siegler,1993;Miller, Smith,Zhu,
&Zhang, 1995;Miller & Stigler,1987;Miura, Okamoto,Kim,
Steere,& Fayol,1993).This doesnot appearto be the whole
story,however.2
Descriptivestudiesof the arithmetical development of American children who receivedtheir elementaryschooleducationin the 1930sindicatethat theyfrequentlyused
decompositionasa problem-solvingstrategyand had typically
masteredthe basic arithmetic facts by the end of third grade
(Gesell& Ilg, 1946;Ilg & Ames,l95l ). In this respect,
the arithmeticaldevelopmentof American children 60 yearsagowas
very similar to developmentalsequencesfound in contemporary EastAsian children and greatlyexceededthat of contemporary American children. The cross-generational
changesin
thearithmeticaldevelqment of Americanchildren suggestthat
the advantageof contemporaryEastAsian children over their
American peersin arithmetic reflectsdecreasedarithmetical
abilitiesin Americanchildrenand not an exceptionalfacility
with arithmeticin EastAsianchildren.
In keepingwith the argumentofa cross-generational
decline
in the basicarithmeticalabilitiesof Americansis the findingof
cohort effectsfor performanceon written arithmetic tests(i.e.,
teststhat definethe Numerical Facility factor; Schaie,1983,
1989).Basically,adultswho receivedtheir elementaryschool
educationin the I 940sor later perform more poorly on testsof
arithmetical ability than adults who receivedtheir elementary
schooleducationin the I 920sand I 930s( Schaie,I 993). Moreover,the basicarithmetical skills of American adults has continued to decline for thosewho receivedtheir primary education afterthe 1940s(Schaie,1983).
Results from several,though not all (Salthouse& Coon,
l 994), cognitiveagingstudiescould alsobe interpretedas support for the argument that arithmetic abilities have declined
within the United States(Allen, Ashcraft, & Weber,1992;
Geary& Wiley, 199I ; Gearyet al., 1993). Fbr instance,Geary
et al. contrastedgroupsofyounger (i.e., collegestudents)and
older(M: 72 years)adultson the strategies,and speedofexecuting the underlyingprocesses,
usedto solvesimple (e.g.,8 4) and complex(e.g.,96 - 7) subtractionproblems.The older
adults not only knew more facts,on average,than the younger
adults,they alsoexecutedat leastone basicprocess,trading or
borrowing,much more quickly ( asin 13 - 6) . The resultsof the
Gearyet al. ( 1993) studyand severalothercognitivearithmetic
studiesof youngerand older adults (e.g., Allen et al., 1992;'
255
Geary & Wiley, 1991) standin sharpcontrastto standardfindings in the cognitiveagingliterature. In nearly all other cognitive domains,youngeradults outperform older adults on psychometricability tests,aswell ason tasksthat assess
more basic
processes,such as speed of processingor working memory
(Salthouse,1991,1992,1994).The contrastbetweenthe relative performanceof youngerand olderAmericanadultsin arithmetic in comparisonwith other ability domains (e.g., spatial
ability;e.g.,Salthouse
& Mitchell, l 990) providesa potentially
useful background for contrasting age-relatedperformance
differenceson ability measuresacrossthe United Statesand
EastAsian nations.
If the relativelywell-developed
arithmetical abilities of older
American adults in comparisonwith youngerAmerican adults
reflect a seculartrend within the United States,with declining
generations,then the standardfinding
abilitiesacrosssuccessive
of youngeradultsoutperformingolderadultson cognitivemeasuresshouldbe found for arithmeticin other nations.In this
case,an advantageofyoungeradultsoverolderadultsshouldbe
found for arithmetic testsas well as for testsof other cognitive
abilities. In the United States,a contrastingpattern of older
adultsdoing at leastas well as youngeroneson arithmetic tests
but lesswell in other domainsshouldbe found. On the other
hand, if the strong arithmeticalabilities of older American
adultsreflecttheresultsof cumulativeexperience
with arithmetic, then the arithmeticalabilitiesof youngerand olderadults
shouldbe comparablein othernationsaswell. In this case,the
pattern of youngeradults outperforming older adults in cognitive domainsotherthan arithmetic,in combinationwith older
adultsperformingat leastaswell in arithmetic,shouldbe found
cross-nationally.
We assessed
thesepossibilitiesby administeringa batteryof
psychometric
ability teststo groupsofyoungerand olderadults
in mainlandChina and the United States.Specifically,
we administeredmeasuresof numericalfacility,perceptualspeed,
and spatialorientation.By administeringteststhat spanthree
ability domains,we were able to determine if age-relatedperformancedifferencesemergedacrossnations.as well as across
domains,and whetherdifferentpatternsemergedfor the numerical facility,in comparisonwith the perceptualspeedand spatial
orientation,measures.Stevensonand his colleagues( Stevenson
et al., I 985) found no spatialability differencesfor fi rst- or fi fthgradeAmericanand Chinese(i.e., Taiwan)children.For the
perceptualspeedtests,the scoresofthe American and Chinese
fifth graderswere comparable,but the American first graders
outperformedtheir same-age
Chinesepeers.The overallpattern
suggestedno systematicdifferencesin the overall intelligence
ofChinese,Japanese,and American children, eventhough the
Chineseand Japanesechildren substantiallyoutperformedthe
American children on a mathematicsachievementtest.By administering perceptualspeedand spatial orientation tests,as
well as arithmetic tests,we could attempt to replicatethe Stevensonet al. finding for adults and test the hypothesisthat the
2 Presumably,differencesin the structureof numberwordsin English
and Asian languageswould result in national differencesin the initial
acquisitionof number and arithmetic concepts,but they should not
result in national differencesonce basicarithmetic has beenmastered
(Ackerman.1988).
cEARY sALTHousE, CHEN, AND EAN
256
advantageof East Asian individuals over Americans in basic
mathematics stems from an East Asian advantagein intelligence(e.g.,Lynn, 1982). If Chineseadultsare more intelligent
than American adults, then both the youngerand the older Chineseadults shouldoutperform their same-ageAmerican peers
on all, or nearlyall, of the ability measures.
Method
differencein physical health. In keepingwith this position wasthe findingthat reported health statuswasnot significantly correlated with performanceon any of the ability testsin any of the samples(ps > .05).
The two correlations that approachedconventional significancelevels
(ps < .10 and > .05) werefound for the samplesof younger(r - .33,
betweenhealth statusand performanceon the Card Rotations Test) and
older ( r = .30, betweenhealth status and performance on the Identical
Pictures Test) Chinese adults. In both cases,the worse the reported
health, the better the performance on the ability test.
Participants
Ability Measures
The participantswere66 younger(42 female,24male) and 44 older
( 36 female,8 male;agerange: 57 to 85 years)adults from the United
States,and 40 younger(20 female,20 male) and 40 older (20 female,
20 male;agerange= 60 to 77 years)adultsfrom China. The 66 younger
American adults were recruited from an undergraduate psychology
courseat the Universityof Missouri-Columbia and receivedpartial
coursecredit for participatingin the experiment.The older American
adultswerefrom Atlanta, Georgia,and wererecruitedthrough a senior
citizensgroup,which receiveda donationin their namefor their participation. In China, the youngeradultswererecruitedfrom undergraduatecourses( primarily in the socialsciences)at EastChina Normal University,Shanghai,China, and the older adults were recruited through
advertisemenls
or referralfrom Shanghai,China. Both the youngerand
older Chineseadults were paid a small fee for participating in the
experiment.
Beforebeing administeredthe psychometrictests,describedbeloq
all participantswereaskedto provideinformation on gender,age,years
ofeducation, and to report their health statuson a | (excellent)to 5
(bad) Likert-type scale.Descriptivestatisticsfor age,education,and
reported health are presentedin Table l. A 2 (nation) x 2 (cohort:
youngervs. older) analysisofvariance (ANOVA) revealednonsignificant nation,cohort, and Nation x Cohort effectsfor yearsofeducation
(ps > . l0). Forage,significantnation,-F(I, I 86) : 42.17,p <.00 l, and
Nation X Cohort,lf(l' 186) = 28.02,p <.0001, effectswerefound.
Post hoc comparisons(Tirkey's honestlysignificantdifference;HSD)
indicatedno significantmeanagedifferencefor the youngergroups(p
> .05), but the olderAmericanadultsweresignificantlyolderthan their
Chinesepeen(p < .05).
For reportedhealthstatus,significantnation, F( I , I 7 I ) : 143.77, p
< .001,andcohort,F( l, l'l l\ = 19.48,p < .001,effectswerefound,but
the Nation x Cohort interactionwasnot significant,F( I, l7 I ) = 3.'17,
p > .05.Overall,youngeradultsreportedb€tterhealththan olderadults,
althoughthe mean differenceswere not large(0.2 in the U.S. sample
and 0.7 in the Chinesesample), and the American adultsreportedbetter healththan the Chineseadults.The national differencein reported
health status might be due to the tendencyof Americansto endorse
extremescores( I in this case)on Likert{ype scalesmore frequently
than do Asians(Chen, Lee, & Stevenson,1995), ratherthan an actual
All participants were administered a battery of psychometric tests
that spannedthe Numerical Facility, PerceptualSpeed,and Spatial Orientation ability facton (Ekstrom, French, & Harman, 1976). Both
forms for each test were administered, and the total score for each test
wasthe sum of both forms.
Numerical facility. Four arithmetic testswere usedto representthe
numericalfacility construct.Two ofthese,the Addition Testand Addition and Subtraction Correction, were from the Educational Testing
tests( Ekstromet al., I 976) ' and
Service( ETS) kit of factor-referenced
the other two tests,SimpleSubtractionand ComplexSubtraction'were
usedbasedon a previouscognitiveagingstudy( i.e.,Gearyet al.' I 993).
Eachform of the Addition Testallows2 min to solveasmany complex
addition problems(e.g., 19 + 8 + 27) as possible.Addition and Subtraction Correction requiresparticipantsto indicate whetherthe pre-sentedanswerfor addition ( e.g., | | + 23 34 C | ) or subtraction( e.g.'
:
35 l0 20 C I) problemsis correct(C) or incorrect(l). Eachform
ofAddition and SubtractionCorrectionallows2 min. For eachform of
the Simple Subtraction(e.g.,8 - 4) and ComplexSubtraction(e.g.'78
- 9) tests,participantswereallowed I min to solveas many problems
aspossible.
Each form ofthe Addition Testconsistsof60 vertically placedthreeaddendproblems.Forty-eightoftheseconsistofdoubledigit addends( e.g.'
12+ 42 + 53), oneproblemconsistsofthree singledigitaddends(i.e., 8
+ 3 + 7), and the rcmaining problems consistof a mix of single-and
doubledigit addends( e.g., 19 + 8 + 27) . Addition and SubtractionCorrection consistsof a mixture of 60 horizontally pres€nteddoubledigit addendsor doubledigit minuendsand subtrahends,asillustratedabora.The
Simple Subtraction test consistsof 72 singledigit minuendsand subtraansu,en(e.g.,5 - 2). The items for the Simple
hendswith nonnegative
Subtractiontest include the 36 problemsdefined by the combination of
the integprsI to 9 (excludingtie problems,e.9.,I - I ); eachproblemis
presentedtwice. The Complex Subtraaion test consistsof 56 problems
(e.9.,57 - 3);28
with doubledigitminuendsand singledigitsubtrahends
(e.9.,
9)'
35
oftheseproblemsrequirea borrowor trade
Perceptualspeed. Two testsfrom the ETS battery were usedto representthe perceptualspeedconstruct: the Number ComparisonTest
and the IdenticalPicturesTest( Ekstromet al., 1976). For eachform of
Table I
DescriptiveSlatisticsfor the U.S.and ChineseSamples
United Stales
Variable
Age
Yearsofeducation
Health status
M
20.1
14.0
1.5
SD
3.'7
0.6
0.5
M
72.'7
14.7
l.'7
Older
Younger
Older
Younger
SD
M
SD
5.7
t9.4
14.3
2.4
t.2
0.8
0.6
z-)
o.'7
Note. Health statuswasratedon a | (excellent)to 5 (bail Likert-typescale.
M
65.6
14.4
3.1
SD
4.3
2.5
0.6
CULTURE AND ARITHMETIC
both tests,participantswereallowedL5 min to solveasmany problems
as possible.For the Number ComparisonTest,pairs of digit strings,
ranging from 3 to 13 digits, are presented.The task is to indicate
whetherthe digit stringsdiffer.The IdenticalPicturesTestrequiresparticipants to indicatewhich of five alternativepictures is identical to a
comparisonpicture.
Spatial orientation. Three testswere usedto representthe spatial
orientationconstruct:the Card RotationsTestand the CubeComparisonsTest,both from the ETS battery,aswell asthe Mental RotationTest
( Ekstromet al., I 976;Vandenberg
& Kuse,I 978). For eachform of all
threetests,participantswereallowed3 min to solveasmany problems
aspossible.The Card RotationsTestrequiresthe rotation offigures in
two-dimensionalspace,whereasthe Mental Rotation Testrequiresthe
rotation offigures in three-dimensionalspace.The CubeComparisons
Testrequiresthe rotationofdrawingsofcubes,someofwhich needto
berotatedin two-dimensionalspace,othersin three-dimensional
space.
Procedure
Translation. For all measures.the test stimuli wereidenticalin the
Englishand Chineseversions.To ensurecomparability,an experienced
translatorfirst translatedthe Englishinstructionsinto Chinese.The
Chineseversionwasthen back-translatedinto Englishby anotherexperiencedtranslatorwho wasnot familiarwith the Englishinstructions.
Discrepanciesbetweenthe original Englishinstructionsand the backtranslatedinstructionswere then discussedbetweenDavid C. Geary
and the two translators,
which resultedin a secondChineseversionof
the instructions.To ensurethat theseinstructionswereclear.we then
administered
the Chineseversionsof all ability measures
to two individualswho werenot familiarwith eitherthe Englishor Chineseversionsofthe tests.Both individualsindicatedthat the instrucrionswere
readilyunderstandable.
Administration. All ability measureswereadministered,either individuallyor in smallgroups,understandardinstructionsfor both the U.S.
andChinesesamples.All participantswerefirst administeredthe numerical facilitytests,followedin turn by the perceptualspeedandspatialorientationmeasures.
Theentiretestingsession
lastedabout50 min.
Results
For easeof presentation,
the resultsare discussedin three
generalsections.In the first, the factor structure ofthe psychometric battery is assessed
for the American and Chinesesamples.National and cohort ( i.e.,youngervs.older) differenceson
the ability testsare describedin the secondsection,and issues
concerningdifferencesin the intelligenceof the samplesand
sampleselectivityareaddressed
in the final section.
Factor Structure
The factorstructureof the ability testswasassessed
by means
of a confirmatoryfactor analysis(Jiireskog,1969), usingthe
CALIS programavailablethroughSAS(SAS Institute,1990).
For eachsample,partial covariancematriceswereobtainedby
partialing the linear,quadratic,and cubic agetrends from performanceon the ability tests.A three-factor*Numerical Facility, PerceptualSpeed,and SpatialOrientation-model wasthen
fitted to the covariancematrices.For theseanalyses,the indicators for each factor were identical to those describedin the
Method section(e.g.,the PerceptualSpeedfactor was defined
by the Number Comparison Test and the Identical Pictures
Test).The factorswereallowedto correlate,and all nondefining
factor loadingswere fixed at 0. The adequacyof such models
257
canbe assessed
by meansof a goodness-of-fit
index (GFI), with
valuesgreaterthan .90 typically consideredacceptable( Bentler
&Bonett,1980).
For the initial models, the GFI values were .88 and .89
(actually.899) for the U.S.and Chinesesamples,respectively.
The estimation of two correlated residuals(i.e., allowing the
unique variancefor two setsofability teststo correlate)for the
U.S.sampleand onecorrelatedresidualfor the Chinesesample
yieldedacceptableGFI valuesfor both the U.S. (GFI : .91)
and Chinese(GFI : .92) samples.rThe factor patternswere
highly similar acrossthe two samples,with a coefficientof congruence(Gorsuch,1983) of .99 for the NumericalFacilityfactor, and .95 and .96, respectively,for the PerceptualSpeedand
Spatial Orientation factors. Thus, with very slight modifications, the expectedthree-factorstructureofthe ability testswas
confirmedfor both the U.S.and Chinesesamples.
Ab i I it y Tbst Perfor manc e
Mean ability test scoresacrossnation and cohort are shown
in Thble2. To facilitatethe discussion
ofthe results,we present
the analysesseparatelyfor each of the ability constructs.For
eachof the respectivesetsof ability tests,national and cohort
differenceswere initially assessed
by meansof a multivariate
analysisof variance(MANOVA). SignificantMANOVAswere
followedup by 2 ( nation) X 2 (cohort)ANOVAs;simplemeans
werecontrastedby meansof the HSD procedure.
Numerical facility. The MANOVA for the four arithmetic
testsrevealed
significant
nation,F(4, 178): 30.65,p < .001;cohort, F(4, 178): 45.67,p < .001;and Nation X Cohort,F(4,
178) - 18.98,p < .001,effects.The ANOVAsrevealed
that the
nation,cohort,and Nation X Cohorteffectsweresignificant(ps <
.05) for the SimpleSubtraction,ComplexSubtraction,and Addition and SubtractionCorrection tests.For the Addition Test,the
Nation X Cohort interactionwassignificant(p < .001), but the
main effectsfor nationandcohortwerenot (ps > .20).0
For the Addition test,comparisonsof simplemeansindicated
that the older Americanadults and the youngerChineseadults
had comparablemeanscores(p > .05), which weresignificantly
higherthan the meanscoresfor the youngerAmerican adults and
the olderChineseadults(ps < .05). The meanscoreof the youngerAmericanadultswas,in turn, significantlyhigherthan that of
'In the U.S.sample,the correlatedresidualswerebetweenthe Identical PicturesTestand the Card RotationsTest(.42) and betweenthe
Addition Testand the Mental RotationTest(-.43). For the Chinese
sample,the correlatedresidualwasbetweenAddition and Subtraction
Correctionandthe NumberComparisonTest(.42). Tablesof the standardized factor loadings,factor correlations,and correlatedresiduals
are availablefrom David C. Geary on request.
4 A MANOVA confirmedthat therewereno genderdifferencesor Cohort X Genderinteractionsfor the numericalfacility testsfor eitherthe
U.S.or Chinesesamples(ps > . l0 ). For the perceptualspeedand spatial orientation tests.there were no Gender X Cohort interactionsin
eithersample(ps > .10). For the Chinesesample,the only significant
(p < .05) genderdifference,which favored men, was for the Mental
Rotation Test.For the U.S. sample,men outperformedwomen on the
Mental RotationTest and the Cube ComparisonsTest (ps <.05),
whereaswomen outperformedmen on the Number ComparisonTest
(p<.ol).
258
CHEN, AND FAN
GEARY SALTHOUSE,
Thble2
Mean Ability kst ScoresAcrossGroup and Nation
United States
China
Younger
Test
Numerical Facility
Addition
Simplesubtraction
Complex subtraction
Addition/subtraction
PerceptualSpeed
Number comparison
Identicalpictures
SpatialOrientation
Card rotations
Cubecomparisons
Mental rotation test
M
Younger
M
SD
SD
M
SD
M
,sD
36.7
I 18.3
3 5 .l
67.1
8.7
r9.0
9.s
t5.2
45.6
99.l
3s.8
56.9
t4.4
22.7
lo.7
t4.2
46.6
134.2
58.6
99.4
9. t
r 3.3
tO.1
t4.8
33.t
96.2
36.9
57.9
16.l
3t.6
17.3
24.8
54.I
73.4
9.1
12.7
41.3
40.9
r1.6
7.5
55.4
63.3
r2.l
l r.E
38.4
46.6
17.4
12.6
l r5-9
16.8
15.3
25.5
9.7
9.6
59.8
4.6
4.1
29.8
5.4
6.4
94.7
13.7
13.9
27.9
8.7
9.9
58.3
3.6
3.3
42.1
6.2
5.1
the olderChines€adults(p < .05). For the SimpleSubraction test
and Mdition and Subtraction Correction, the youngerChinese
adultsoutperformedall othergroups(ps < .05). The performance
of the older American and older Chinesegroupswzrscomparable
(ps > .05) but was significantly lorrcr than that of the youngsr
American adults (ps < .05). For the Complex Subtraction test,
the performanceofthe two oldergroupsand the group ofyounger
Americanadultswascomparable(ps > .05) but wassignificantly
lourcrthan that of the youngerChineseadults(ps < .05). Finally,
partialing agein the comparisonof the two oldergroupsto adjust
for the significantagedifferencedid not alter the resultsfor any of
the arithmetic tests.
In all, the youngerChineseadults outperformedtheir American peerssubstantiallyon all four arithmetic tests.The advantageofthe youngerChineseadults overthe youngerAmerican
adultswasabout I standarddeviationfor the Addition Testand
the Simple Subtractiontest, and more than 2 standarddeviations for the Complex Subtractionand the Addition and Subtraction Correctiontests.In contrast,for threeofthe four arithmetic tests,there was no significantnational differencefor the
oldergroups.The one testthat did showa significantdifference
acrossthe older groups,that is, the Addition Test,favoredthe
Americanparticipants.In fact, for the Addition Test,the mean
performanceofthe olderAmericanadultswascomparablewith
that of the youngerChineseadults, and about 0.75 standard
deviationsabovethe meanof the youngerAmericanadults.
Another way to highlight and summarizethe overallpattern
is by meansofstandardscores.Here,for eachofthe four arithmetic tests,the overallmeanwassetat 0 and the standarddeviation at l. The resultingz scoreswerethen summedto create
an overall performancescore for the numerical facility construct. On the basisofthe cognitiveagingliterature,this procedure might be expectedto yield mean scoresabovethe overall
meanfor the youngergroups,and scoresbelowthe overallmean
for the older groups.Indeed,the left sectionofFigure I shows
exactly this pattern for the Chineseparticipants; that is, the
meanperformanceof the youngerChineseadults is abovethe
overallmean,whereasthe meanperformanceof the older Chineseadults is below the overall mean. In contrast, the mean
performanceof both the youngerAmerican adults and the older
American adultsis belowthe overallmean.
Perceptualspeed. For the perceptual speedtests,the initid
MANOVA revealeda nonsignificant main effect for nation,
F(2,l8l) < l, p > .25, but significant
cohort,F(2, l8l):
102.23,p < .00l, and Nation X Cohort, F( 2, I 8 I ) : 16.39,p <
.001, effects.The ANOVAsconfirmedthat the advantageof the
youngeradults over the older adults wassignificant for both the
Number ComparisonTestand the IdenticalPicturesTest(ps <
.00l ). Comparisonsof simple meansindicatedthat theseagerelateddiferencesweresignificantin both the U.S.and Chinese
samples(ps < .05). The Nation X Cohort interactionwasnot
significantfor the Number ComparisonTest,F( I , I 84) : | .21,
p > .25, but wassignificantfor the ldentical PicturesTest,.F( I,
interaction,the
182) : 21.13,p < .001.With this cross-over
youngerAmerican adults outperformedtheir Chinesepeen (p
< .05), whereasthe older Chineseadults outperformedtheir
American peers(p < .05). However,partialing agefrom performanceon the Identical PicturesTesteliminated the advantage
of the olderChineseadultsoverthe olderAmericanadults,F( I,
7 8 \ : r . 1 3p, > . 2 5 .
The overall pattern is summarizedin the middle sectionof
Figure l. In keepingwith the expectedcognitive-agingpattern,
it can be seenthat for both the U.S. and Chinesesamples,the
mean for the youngeradultsis abovethe overallmean,whereas
the meanfor the olderadultsis belowthe overallmean.
Spatial orientation. For the spatialtests,the MANOVA revealeda nonsignificantmain effectfor nation,F( 3, I 84 ) : 2.29,
p > .05,and a nonsignificantNation X Cohort interaction,f( 3,
184) : 1.74,, > . I 0. The main effectfor cohort wassignificant,
howeveqf(3, 184) : 48.98,p < .001.For both the American
and Chinesesamples,the advantageof the youngeradults over
the older adults was significantfor all three spatialtests(ps <
.05). The overallpattern is summarizedin the right sectionof
Figure I and, again,showsthat for both the U.S. and Chinese
samples,the mean for the youngeradults is abovethe overall
mean, and the mean for the older adults is below the overall
mean.
259
CULTURE AND ARITHMETIC
m
r
Legend
Young€rgroup
Oldergroup
o
o
o
C)
CJ)
E
(5
E
I
I
c
(U
a
U.S.
Chlna
NumetlcalFadllty
U.S.
China
PerccpludSpeed
U.S.
China
SpatialOrienlrdon
Figure I . Standardscoresacrosscohort and nation for the numericalfacility,perceptualspeed,and spatial
orientationabilitydomains.
ment that there were no systematicability differencesacross
the Chineseand American samples.The significantNation X
Eventhough the pattern ofresults shownin Figure I is conAbility X Cohorteffect,,F(2, 185) = 20.05,p <.0001, indicated
sistentwith the position that there has beena relativelyrecent
a selectiveage-relateddifferenceacrossthe Chineseand Amerideclinein the arithmetical abilities of Americans,two related
can samplesfor at leastone of the ability domains.
issuesneed to be addressedbefore such an argument can be
Follow-up ANOVAs within each ability domain indicated
madewith any certainty.The first concernswhetherthe advanthat the main effect for nation was not significant for any of
tageofthe youngerChineseadults overthe youngerAmerican
the ability domains:numericalfacility,f'( l, 186)< l, p > .50;
adults in arithmetic could be attributable to differencesin the
perceptualspeed,F( l, 186): 1.97,p> .15;and spatialorienintelligenceof the Chineseand American samples,and the sectation,F( I, I 86) : 1.76, p > .l 5. The Nation X Cohort effect
ond concernswhetherthe youngerChineseadults are simply a
wasnot significantfor the perceptualspeed,F( l, 186) = 2.98,
more highly selectedgroup than the youngerAmericanadults.
p > .05,or spatialorientation,F( I, I 86) : 1.19,p > .25,scores,
Intelligence. If the advantageofthe youngerChineseadults
but washighly significantfor the numericalfacility scores,F( l,
overtheir same-age
American peersfor the arithmetic testswas
I 86) : 20.05,p < .0001. For numericalfacility, the overallperrelatedto an EastAsian advantagein intelligence,then both the
formance
of the youngerand older American g.roupsdid not
youngerand olderChineseadultsshouldhaveshownan advan(p
>
differ
.05), but the youngerChineseadults outperformed
tageovertheir same-age
American peerson all, or nearlyall, of
the olderChineseadults(p < .05). The overallpatternconfirms
the ability measures.This wasclearly not the case.Except for
a selectiveage-relatedperformancedifferenceacrossthe Chithe finding of youngerChineseadults outperforming younger
nese and American samplesfor the numerical facility tests.
American adults on the arithmetic tests,comparisonsfor the
Moreover,as noted earlier,the pattern of no overall national
remainingability tests,aswell as for the groupsof older adults,
differencein ability test scoresacrossthe three domainsis conrevealedeither no national differencesor a slight American adsistentwith the view that the EastAsian and American samples
vantage,in keepingwith the findingsofStevensonet al. ( 1985)
usedin this study werecomparablein terms of overalllevelsof
for comparisonsof Chineseand American children.
intelligence.
Nevertheless,
to further assess
the possibilityofability differSampleselectivity. The issueof sampleselectivityis particencesacrossour Chineseand American samples,we analyzed
ularly important for the youngersamples,becausecontempothe overallpatternof performanceon the psychometrictestsby
rary Chineseuniversitiesare more selective,on average,than
meansof a mixed-designANOVA. Here, the z scoresfor the
are contemporaryunivenities in the United States;this is less
threeability domains( i.e.,the meanof the z scoresfor the indiofan issuefor our older samplesgiventhat collegeattendance
vidual testsin eachdomain) servedasa within-subjectsvariable
(ability), and nation and cohort servedas between-subjects wasrelativelyunusualin both countriesearlierin this century.
Evenif the youngersamplesare comparablein terms of general
variables.With this analysis,there were two crucial tests:the
abilities, it is possiblethat the largeadvantageofthe younger
Nation X Ability interactionandthe Nation X Ability X Cohort
interaction. The finding of a nonsignificantNation X Ability
Chineseadultsoverthe youngerAmerican adultsin arithmetic
interaction,,F'(2,185)< l, p>.50, is consistent
with the arguwas somehowrelated to the selectioncriteria (e.g., types of
I ntelligence and Selectivily
,
I
260
GEARY SALTHOUSE,CHEN, AND FAN
0.8
0.6
I
o
o
o.4
b
() o.2
CA
E(!
0
E 4.2
g
cn 4.4
{.6
{.8
U.S.
China
NumericalFadlity
U.S.
China
PerceptualSpeed
U.S.
China
Spatial Orientation
Figure 2. Within-nation standardscorecomparisonsof the relativeperformanceof the youngerand older
groupsfor the numericalfacility,perceptualspeed,and spatialorientationability domains.
I
I
tests)associatedwith admissionto the two respectiveuniversities.5We haveno wayof directly testingthis possibility.
However,within-nation comparisonsof the relative advanrage
ofyoungeradultsoverolderadultsacrossthe threeability domains
allow usto indirectly testthis possibility.Becausethe performance
ofthe groupsofolderChineseandolderAmericanadultswascomparableacrossall three ability domains,and becausethesegroups
werecomparablein terms of mean levelsof education,their performancecan providea benchmarkagainstwhich the relativeperformance of their same-nationyoungerpe€rscan be assessed.
If
the youngerChinesesamplewereselectedsuchthat they had unusuallyhigh arithmeticalabilities,then the youngerChineseadults
should showa largeradvantageover the older Chineseadults on
the arithmetic tests,relative to the perceptualspeedand spatial
orientationtests.Ifthe samplesare roughlyequivalent,then the
relative advantageof the youngeradults over same-nationolder
adultsshouldbe similar acrossthe Chineseand American samples
and acrossthe three ability domains.In keepingwith the central
hypothesisofthis study,the only exceptionshouldbe for the comparisonofthe numerical facility scoresfor the groupsofyounger
and olderAmericans.
Figure 2 showsthe within-nation standardscorecomparisons
acrossthe youngerand oldergroupsfor the numerical facility, perceptualspeed,and spatialorientation constructs.Scoresabovethe
mean of 0 indicate an advantageof younger adults over older
adultsin termsof standarddeviationunits.For the Chinesesamples,the advantageofthe youngeradults overthe older adultswas
highly similar acrossall three ability domains and rangedfrom
0.52 to 0.60 standarddeviations.Similarly,the advanrage
of the
youngerAmerican adultsoverthe olderAmerican adultswas0.55
and 0.50 standarddeviationsfor the perceptualspeedand spatial
orientationscores,respectively.
The only comparisonthat doesnot
fit with the overallpattem is the relativelycomparablenumerical
facility scoresofthe youngerand olderAmerican adults(the mean
difference was 0.07 standard deviations). The overall pattern
seemsto be consistentwith the view that the greaterselectivityof
Chineseuniversitiesin comparisonwith American universitieshas
not resultedin unusuallyhigh arithmetical abilities in our sample
ofyounger Chineseadults.6Ifanything, the overallpattem is consistentwith the view that the arithmetical abilities of the younger
American adults is unusuallylow. This is not to saythat the sampleswe havecomparedin this study are representativeof the general populationsof the United Statesand China; they almost certainly are not. The point is that when we contrastgroupsof comparably,and relativelywell, educatedyoungerand older Chinese
and American adults,the "value," in terms of fosteringthe acquisition of basicarithmetic skills, of educationin the United States
appearsto havechangedoverthe pas 60 yean.
Discussion
By providing a comparisonof the psychometricabilities of
youngerand older American and Chineseadults, the present
study provided a unique perspectiveon cross-nationaldifferencesin basic mathematicalabilities, and it suggeststhat the
often cited advantageof EastAsian individualsoverindividuals
in the United Statesin mathematics(e.9., Stevensonet al.,
1990;Stevenson
et al., 1993) might not haveexisted,at leastfor
arithmetic, 60 yearsago.The two most important outcomesof
5 Studentsat the Universityof Missouri-Columbia
are a relatively
selectgroup. Of all of the studentstaking the American CollegeTest
(ACT), their meanACT scoreof 25 is at the 83rd percentilenationally.
6 Any differencesin the selectivityofthe two universitieswould likely
be most evidentfor complexmathematics,not the basicskills assessed
in this study.
261
CULTURE AND ARITHMETIC
the study that support this claim are (a) the pattern ofage-related ability differenceswithin the U.S. and Chinesesamples
and (b) the comparisonsof the abilities of same-agegroups
acrossthe U.S.and Chinesesamples.
For the former, the same age-relatedperformancepatterns
were found in both the U.S. and Chinesesamplesfor the perceptualspeedand spatialorientationmeasures.Consistentwith
expectationsderivedfrom cognitiveaging research(e.g., Salthouse,1994),for both the U.S.andChinesesamples,
the younger adults showedconsistentand substantialperformanceadvantagesovertheir oldersame-nationpeers.Moreover,the magnitudeofthe performanceadvantageofthe youngeradultsover
the olderadultsfiorthe perceptualspeedand spatialorientation
measureswasessentiallythe samefor the Chineseand Americansamples.Forthe numericalfacility measures,this samepattern wasevidentin the Chinesesamplebut not in the U.S.sample. For the U.S. sample,the older adults showedhigher mean
scoresthan the youngeradults for one numerical facility test,
therewas no meandifferencefor anothertest,and the younger
group outperformedthe older group for the two remaining numericalfacility tests.In comparisonwith their performanceon
the perceptualspeedand spatial orientation tests,the performanceof the youngerAmericanson the arithmetic testswas
ratherpoor.
The cross-nationalcomparisonsof the younger and older
groupsalso showeddifferent patternswith the numerical facility, in relation to the perceptualspeedand spatialorientation,
measures.In keepingwith othercross-nationalstudiesof mathet al., I 993), the youngerChiematicalabilities( e.g.,Stevenson
neseadultshad a consistentand substantialadvantageovertheir
same-ageAmerican peersin arithmetic. However,it cannot be
arguedthat the advantageofthe youngerChineseadults over
the youngerAmerican adults in arithmetic is due to a Chinese
facility with arithmetic, becauseno such national difference
wasevidentfor the older groups.In fact, with the exceptionof
the Addition Test,which showedan American advantage,the
performance of the older American and the older Chinese
adultswascomparable.
Nor is it likely that the advantageof the youngerChinese
adults over their American peersin arithmetic was due to a
difference,favoringthe Asian adults, in the intelligenceofthe
two samples.With the exceptionof the performanceof the two
youngergroupson the numericalfacility tests,the psychometric
performanceof the Chineseand American adults wascomparable. This pattern is consistentwith studiesof EastAsian and
et al., 1985) and arguesagainst
Americanchildren( Stevenson
the position that the advantageof East Asian individuals over
Americansin mathematicsis largelydue to an EastAsian advantagein intelligence(e.g.,Lynn, 1982).Finally,althoughit
cannotbe statedwith completecertainty,giventhat the pattern
of age-relatedperformancedifferencesin the Chinesesample
was highly similar acrossthe numerical facility, perceptual
speed,and spatialorientation domains,it doesnot appearthat
theseresultsare due to a selectiveand unusually high level of
arithmeticalabilitiesin the youngerChineseadults.
Indeed,whencomparedagainstthe advantagethat the younger adults haveovertheir same-nationpeerson the perceptual
speedand spatialorientationmeasuresand the advantageofthe
youngerChineseadultsoverthe olderChineseadultson the nu-
merical facility tests,the finding of comparablearithmetic skills
of the youngerand older American adultsappearsto be due to
poorly developedarithmetic skills in the youngerAmericans.
This view is in keepingwith the apparentdeclinein the arithmetical abilities of American children over the past 60 or so
years(e.g.,Gesell& Ilg, 1946).The combinationof what appearsto be comparablearithmeticalskillsof Americanchildren
60 yearsagoandcontemporaryEastAsianchildren and no consistentarithmetical ability differencescomparingolder Amerithat the youngerAmerican and older Chineseadults suggests
canadultsshouldbe capableofachievingthe samelevelofcompetencyin arithmetic, and perhapsother mathematicalareas,
astheir contemporaryEastAsian peers.Stateddifferently,it ap.
pearsthat many contemporaryAmerican collegestudentsare
performingbetweenI and 2 standarddeviationsbelowtheir potential in basicarithmetic.
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Received
Rbruary 3, 1995
RevisionreceivedMay 19, 1995
AcceptedMay 24, 1995 r