A million is more than a thousand: Children\u27s acquisition of very large number words

Very large numbers words such as “hundred,” “thousand,” “million,” “billion,” and “trillion” pose a learning problem for children because they are sparse in everyday speech and children\u27s experience with extremely large quantities is scarce. In this study, we examine when children acquire the relative ordering of very large number words as a first step toward understanding their acquisition. In Study 1, a hundred and twenty-five 5–8-year-olds participated in a verbal number comparison task involving very large number words. We found that children can judge which of two very large numbers is more as early as age 6, prior to entering first grade. In Study 2, we provided a descriptive analysis on the usage of very large number words using the CHILDES database. We found that the relative frequency of large number words does not change across the years, with “hundred” uttered more frequently than others by an order of magnitude. We also found that adults were more likely to use large number words to reference units of quantification for money, weight, and time, than for discrete, physical entities. Together, these results show that children construct a numerical scale for large number words prior to learning their precise cardinal meanings, and highlight how frequency and context may support their acquisition. Our results have pedagogical implications and highlight a need to investigate how children acquire meanings for number words that reference quantities beyond our everyday experience

The Nature of Representations of Number in Early Childhood: Numerical Comparison as a Case Study

What is the nature of non-verbal representations of number? Broadly speaking, non-verbal representations of number can be divided into two categories: representations of particular numerosities and representations of unspecified numerosities. However, studies of representations of number do not only call for investigations into the representations of numerosities. As philosophers of mathematics (i.e., structuralists) have pointed out, the essence of number lies in numerical relations. Using numerical comparison as a case study, this dissertation asks questions about the nature of the non-verbal representations of particular numerosities and unspecified numerosities. Research in the last few decades has found evidence for a non-verbal representation of particular numerosities – the approximate number system (ANS). The ANS encodes number as approximate numerical magnitudes, and is a dedicated system for representing number. While there is much evidence that the ANS can be used to represent numerical relations, little is known about whether a separate system for representing small sets of individual objects – parallel individuation – can also be used to represent number. In Chapter 2, I ask whether the parallel individuation system can support numerical comparison. In two experiments, children between the ages of 2 ½ and 4 ½ years old were asked to compare either exclusively small sets ( 6) on the basis of number. The results of these studies suggest that parallel individuation supports numerical comparison prior to the acquisition of numerical language. In addition to representations of particular numerosities, humans are also capable of representing unspecified number. For example, we understand that the numerical statement ‘x + 1 > x’ is true without representing the particular value of x. But when does this representation develop? In Chapter 3, I ask at what age children begin to show the capacity to reason about unspecified numerosities. In three experiments, children between the ages of 3 and 6 years were asked to reason about the effects of numerical and non-numerical transformations on the numerosity of a set. These sets were large enough to be outside the range of parallel individuation and involved comparisons that are not computable by the ANS (Experiment 3), or were hidden so that the specific numerosity was unavailable (Experiments 4 and 5). After the transformation, children were asked whether there were more objects in the set. The results of these studies suggest that the ability to represent unspecified numerosities emerges at around age 4, and is fully in place by ages 5 to 6. Together, these studies provide evidence that 1) in addition to the ANS, parallel individuation is one of the developmental roots of the representation of numerical relations and 2) the numerical reasoning principles that operate over representations of unspecified numerosities may develop later than computations that operate over representations of particular numerosities

Sources of Individuation in Mandarin Chinese, a Classifier language

PACLIC / The University of the Philippines Visayas Cebu College Cebu City, Philippines / November 20-22, 200

Individuation: Number marking languages vs. classifier languages

Book chapter from the Oxford Handbook of Grammatical Numbe

The development of numerical comparison in 2- to 4-year-olds

<p>Cognitive Science 2012</p

What's on the book shelf?

<p>Canadian Developmental Psychology Conference in Ottawa</p