儿童数控技能(childrens numerical skills)

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peopleappeartoborntopute.thenumericalskillsofchildrendevelopsoearlyandsoinexorablythatitiseasytoimagineaninternalclockofmathematicalmaturityguidingtheirgrowth.notlongafterlearningtowalkandtalk,theycansetthetablewithimpressauracy---oneknife,onespoon,onefork,foreachofthefivechairs.

soontheyarecapableofnothingthattheyhaveplacedfiveknives,spoonsandforksonthetableand,abitlater,thatthisamountstofifteenpiecesofsilverware.havingthusmasteredaddition,theymoveontosubtraction.itseemsalmostreasonabletoexpectthatifachildweresecludedonadesertislandatbirthandretrievedsevenyearslater,heorshecouldenterasecondenterasecond-grademathematicsclasswithoutanyseriousproblemsofintellectualadjustment.

ofcourse,thetruthisnotsosimple.thiscentury,theworkofcognitivepsychologistshasilluminatedthesubtleformsofdailylearningonwhichintellectualprogressdepends.childrenwereobservedastheyslowlygrasped-----or,asthecasemightbe,bumpedinto-----conceptsthatadultstakeforquantityisunchangedaswaterpoursfromashortglassintoatallthinone.

psychologistshavesincedemonstratedthatyoungchildren,askedtocountthepencilsinapile,readilyreportthenumberofblueorredpencils,butmustbecoaxedintofindingthetotal.suchstudieshavesuggestedthattherudimentsofmathematicsaremasteredgradually,andwitheffort.theyhavealsosuggestedthattheveryconceptofabstractnumbers------theideaofaoneness,

atwoness,athreenessthatappliestoanyclassofobjectsandisaprerequisitefordoinganythingmoremathematicallydemandingthansettingatable-----isitselffarfrominnate