Abstract
We propose and test three statistical models for the analysis of children’s responses to the balance scale task, a seminal task to study proportional reasoning. We use a latent class modelling approach to formulate a rule-based latent class model (RB LCM) following from a rule-based perspective on proportional reasoning and a new statistical model, the Weighted Sum Model, following from an information-integration approach. Moreover, a hybrid LCM using item covariates is proposed, combining aspects of both a rule-based and information-integration perspective. These models are applied to two different datasets, a standard paper-and-pencil test dataset (N = 779), and a dataset collected within an online learning environment that included direct feedback, time-pressure, and a reward system (N = 808). For the paper-and-pencil dataset the RB LCM resulted in the best fit, whereas for the online dataset the hybrid LCM provided the best fit. The standard paper-and-pencil dataset yielded more evidence for distinct solution rules than the online data set in which quantitative item characteristics are more prominent in determining responses. These results shed new light on the discussion on sequential rule-based and information-integration perspectives of cognitive development.
Highlights
Two types of cognitive processing are often considered, and fiercely debated, in theoretical discussions of cognitive development: sequential rule-based processes (RB) versus informationintegration (InI) based processes
We present three measurement models: a latent class model (LCM) following from the RB perspective, a WSM following from an InI perspective and a hybrid LCM that combines both RB and InI effects
The LCMs based on the paper-and-pencil dataset replicated, in general, the class structure found by JM
Summary
Two types of cognitive processing are often considered, and fiercely debated, in theoretical discussions of cognitive development: sequential rule-based processes (RB) versus informationintegration (InI) based processes. These two types of processing are contrasted in other areas in (cognitive) psychology. In the study of information-integration in category learning [1] and in the study of explicit and implicit learning [2]. Pothos [3] provides a discussion of the rules versus similarity distinction in cognition, and Kahneman [4] provides an broad overview and examples of dual route models, explicit versus implicit, in psychology.
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