Building complex number words: How and when do children learn the meaning of multipliers.
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Number words or numerals are built using a compositional system, wherein a small number of words can be combined in multiple ways to represent many different numbers. Children not only have to learn the rules for combining numerals, but must also map certain combinations to specific arithmetic functions. One such combination involves a class of words called multipliers that are used in a multiplicative structure (e.g. “two hundred” maps to “two times one hundred”). How and when do children learn this mapping? There have been two contrasting theories of acquisition: (1) That the compositional rules themselves provide all the necessary tools in order to create the mapping (Hurford, 1975) or (2) the rules are learned by rote and children only make the mapping via explicit instruction and experience with real world objects (Fuson, 1990). To test these theories, 99 children between 4.5 and 6.5 years old were trained on a novel numeral phrase that either did (Experiment 1) or did not (Experiment 2) use a multiplier structure. With all other stimuli remaining the same, more children (43% vs. 10%) were able to determine the novel word was a multiplier when in the correct structure. Other possible avenues for learning this mapping, including being taught the place value system (Experiment 3) and experience counting (Experiment 4), did not fully explain why children did better with the correct syntax. Although the results of these experiments cannot entirely discount the theory put forth by Fuson, they do support Hurford’s theory that it is the rules themselves which allow children to map meaning onto complex numerals.