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abstract Asian asked base ten blocks base ten responses block representations Block Responses canonical chi-square child children counting children who count children's ability Chinese circling task construct conventional number conventional written counting string counting words CSD responses current study decade errors decade words Educational Psychology English number language English speakers entire number example experimenter five-tens Fuson Gelman groups of tens indicate individual digits initial responses instruction Kamii Kirs low counters Mathematics Mathematics Education mistakes multiunitary Noncanonical Nonstandard notation systems number language structure number understanding number words Numbers 14 numerical knowledge one-to-one responses place value poor counters pretest quantity regular counters regular counting group regular group regular language regular number language represented Resnick shown in Figure skipping errors Stigler subjects tally marks two-digit numbers U.S. children understanding of number understanding of two-digit unitary conceptual structure whole number written and spoken written number system young children