A Cross-Linguistic Bayesian Data Analysis of Number Word Learning

• In Event: 3-226 - Number Knowledge Before, During, and After Children’s Mastery of Counting

Integrative Statement

Children's acquisition of number words follows a distinct developmental trajectory (e.g., Wynn, 1992). After memorizing their number words, children slowly begin to map them to quantities of objects. Initially, children gain competence in mapping sets of one to one, then two to two, three to three, and four to four. Instead of repeating this process to learn the meaning of all exact number words, children appear to master the logic of counting at once, recognizing that the cardinality of a set of objects is the last number in their count. This “knower level” pattern of behavior is robust across multiple languages and cultures (e.g., Sarnecka et al., 2007); however, the timing of the trajectory varies. Previous research has explained differences in timing in terms of language specific differences (e.g, plurality/dual markings; Almoammer et al., 2013) or differences in education and cultural utility (e.g., Piantadosi, 2014). Here, we aim to provide convergent evidence for these observations and new insights using a large-scale, cross-linguistic Bayesian data analysis. Despite differences in data availability, education and cultural utility, do children across cultures/languages have the same inductive biases and profile of data usage when learning number word meanings?

Using recent computational models for linking data usage to acquisition distributions (e.g., Hidaka, 2013), we expand an ideal number word learning model to infer the rate in which children use data, the total amount of data children use and the inductive biases children bring to the task of number word learning. To evaluate the model, we compiled data from the Give-N task (Wynn, 1990) from seven difference cultures/languages (English: n=311 , Japanese: n=152 , Mandarin: n=79 , Russian: n=59 , Saudi Arabic: n=83 , Slovenian: n=341 , and Tsimane: n=493). With a much larger sample than previous studies, we set out (i) to confirm if there are language/culture specific differences in the developmental trajectory for number words and (ii) to characterize observed differences in terms of data usage and inductive biases.

Our analysis indicates that there are few differences in the pacing of number word acquisition, but at the coarsest level, knowing a child's knower level and language does not convey significant information about their age. That being said, our analysis does reveal differences in the learning process. Validating our approach, we find that number word learning across different cultures/languages is well explained by an ideal learning model as compared to a baseline multinomial model (BF=10114). Looking at inductive biases, parameter estimates suggest that across languages/cultures, children approach number word learning with the same bias, a preference for simple representations/processes. Turning to data usage, parameter estimates across languages/cultures are on the same order of magnitude, suggesting that effective learning instances for number words are relatively infrequent, at a rate of once every 2-3 months. Interestingly, the order of rates for each language is consistent with corpus analyses of number word frequency. Finally, our model analysis suggests that learners across languages/cultures require on the order of 50 effective learning instances to master the logic of counting.

Authors

• Francis Mollica, University of Rochester
  Presenting Author

• Julian Jara-Ettinger, Yale University
  Non-Presenting Author

• Steven Piantadosi, University of California, Berkeley
  Non-Presenting Author