A comprehensive model of development on the balance-scale task

We present a new model of children's performance on the balance-scale task, one of the most common benchmarks for computational modeling of psychological development. The model is based on intuitive and torque-rule modules, each implemented as a constructive neural network. While the intuitive module recruits non-linear sigmoid units as it learns to solve the task, the second module can additionally recruit a neurally-implemented torque rule, mimicking the explicit teaching of torque in secondary-school science classrooms. A third, selection module decides whether the intuitive module is likely to yield a correct response or whether the torque-rule module should be invoked on a given balance-scale problem. The model progresses through all four stages seen in children, ending with a genuine torque rule that can solve untrained problems that are only solvable by comparing torques. The model also simulates the torque-difference effect and the pattern of human response times, faster on simple problems than on conflict problems. The torque rule is more likely to be invoked on conflict problems than on simple problems and its emergence requires both explicit teaching and practice. Overlapping waves of rule-based stages are also covered by the model. Appendices report evidence that constructive neural networks can also acquire a genuine torque rule from examples alone and show that Latent Class Analysis often finds small, unreliable rule classes in both children and computational models. Consequently, caution in using Latent Class Analysis for rule diagnosis is suggested to avoid emphasis on rule classes that cannot be replicated.