No abstract

This study examined whether singular/plural marking in a language helps children learn the meanings of the words 'one,' 'two,' and 'three.' First, CHILDES data in English, Russian (which marks singular/plural), and Japanese (which does not) were compared for frequency, variability, and contexts of number-word use. Then young children in the USA, Russia, and Japan were tested on Counting and Give-N tasks. More English and Russian learners knew the meaning of each number word than Japanese learners, regardless of whether singular/plural cues appeared in the task itself (e.g., "Give two apples" vs. "Give two"). These results suggest that the learning of "one," "two" and "three" is supported by the conceptual framework of grammatical number, rather than that of integers.

A task commonly used to assess young children's number knowledge is the Give-N task, in which an experimenter asks the child to generate sets of a given number. Typically, children find small sets easier to produce than large ones. The present study analyzes children's incorrect responses (i.e., errors) on the Give-N task. Logically, there are two types of incorrect response possible: (a) performance errors, and (b) guesses. Performance errors occur when the child knows the meaning of the number word requested, but makes a mistake in producing the set. Guesses occur when the child does not know what the number word means. New analyses of three previously published datasets (280 children total) found that most errors were guesses, with some evidence of performance error appearing for high number words only. Results support the “knower-levels” theory of number development.

This paper examines what children believe about unmapped number words - those number words whose exact meanings children have not yet learned. In Study 1, 31 children (ages 2-10 to 4-2) judged that the application of five and six changes when numerosity changes, although they did not know that equal sets must have the same number word. In Study 2, 15 children (ages 2-5 to 3-6) judged that six plus more is no longer six, but that a lot plus more is still a lot. Findings support the hypothesis that children treat number words as referring to specific, unique numerosities even before they know exactly which numerosity each word refers to.

Children’s understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and this has often been interpreted as evidence of a change in the child’s psychological representation of integer quantities. The present article presents theoretical and empirical evidence that the change in number-line performance actually reflects the development of measurement skills used in the task. We compare 2 versions of the number-line task: the bounded version used in the literature and a new, unbounded version. Results indicate that it is only children’s performance on the bounded task (which requires subtraction or division) that changes markedly with age. In contrast, children’s performance on the unbounded task (which requires only addition) remains fairly constant as they get older. Thus, developmental changes in performance on the traditional bounded number-line task likely reflect the growth of task-specific measurement skills rather than changes in the child’s understanding of numerical quantities.