Numeric Cognition and Number-Word Learning: Insights from Models and Correlations

What is the right way to think about the process of number-word learning and exactly how does it relate to all of the different kinds of concurrent non-conceptual development, especially forms of non-verbal numeric cognition? How do we model number-word learning and these other processes? The following is a series of seven articles that helps build up an answer.;Chapters 1, 3, 5 and 6 take a simple correlational approach. They suggest that number-word learning is related to overall vocabulary and spontaneous attention to number, but not approximate number system (ANS) acuity. This paints a picture of number-word learning as a linguisticly-supported process, and also suggests that being willing to frequently attend to number is perhaps more important than being good at it. Chapter 3 presents the surprising result that exposure to a second language is not correlated with the executive function component of an ANS task, despite the fact that it correlates with many other executive function measures.;Chapters 2, 4 and 7 take a modeling approach. In chapter 2, a model by Lee and Sarnecka is adapted to work (to a very good approximation) in an excel sheet. This model describes how children with different levels of number-word knowledge will perform when they are asked to give a certain number of items to a prop. Chapter 4 presents a model of how rapid numeric estimates of large sets are computed. The model selects a group of 7 items, estimates their area, estimates the total area of the display and computes the following: Numeric Estimate = (Total Area / Sample Area) * 7. This fits human data better in certain described cases. Chapter 7 models how children with limited number-word knowledge would apply the ANS to an estimation task. We did this in order to look for certain statistical features that should be present if children really are using the ANS for that task. These projects serve as working demonstrations of the assertion that modeling approaches can lead to fundamental new theoretical insights into numeric cognition.