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Syntax and Semantics in Leaming to Subtract
A lapanese Perspective
Levels of Description in the Analysis of Addition
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ability abstract action addition and subtraction addition problems analysis answer arithmetic arrays Baoulé basic blocks borrowing bugs cardinal Category child child’s classes of problems column conceming concepts concrete construct context counting algorithms counting words counting-on cues decrement diagrams difﬁculty Dioula Educational entities equation errors example ﬁeld ﬁgural ﬁnal ﬁnd ﬁndings ﬁngers ﬁrst addend ﬁve Fuson Gelman goal Groen initial Interviewer inversion and compensation inversion problem involves IV problems keeping-track leaming marbles mathematical Mathematics Education meaning minuend motor unit items Nesher number facts number word numerosity objects pattem preschool Psychology quantity reﬂect relationship repair rules represent representation Research second addend semantic sequence signiﬁcant skills speciﬁc strategies structure student substage subtraction problems subtraction word problems symbolic syntactic tasks theory tion top digit transformation types unary operation understanding University of Wisconsin-Madison unschooled variables verbal arithmetic verbal problems young children zero