Van Rijn 2002 Modeling Developmental Transitions on the Balance Scale Task

Nov 12, 2009 9:33 PM

Periods of relatively stable, rule-like behavior alternated with short transition periods characterize

cognitive development on reasoning tasks like the balance scale task. Each transition gives rise to an

improvement in behavior, until a phase is reached in which performance is ﬂawless or improvement

is not worthwhile given the necessary extra effort. Several computational models have been developed

to capture the developmental phenomena associated with the balance scale task. These models, which

originate fromdifferent computational traditions, explain themain phenomena of development.Recently,

empirical phenomena have been reported that these models cannot easily accommodate. We propose a

computational model that is implemented in ACT-R and that is based on the evaluation of success of

applied knowledge, combinedwith amechanismto construct newknowledge by searching for differences

between the left- and right-hand sides of presented balance scale problems. This model accounts for the

main empirical phenomena as well as for the recently reported empirical phenomena such as learning

without feedback.

The overall picture that emerges from these studies is that children adopt progressively  page 3

more powerful Rules during development, which results in increasingly better performance.

Between transitions, children display stable and consistent behavior on the balance scale task.

During the transition from one Rule to the next, performance is more erratic as some items of

a particular type are already answered correctly, whereas others are still answered according

to the earlier Rule yielding incorrect answers. The exact mechanism of transition may differ

from Rule to Rule.

3.1   Key Structures and mechs of ACT-R archit.

If a chunk or PR has proven successful, its utility will incr in value.

For chucks  this is rep by the activation level.

base level activation is determined by number and recency of past retrievals.

there is also context activation that reflects perceptual saliency.

For production rules, the main parameter is the expected utility. The utility of production

rules is determined by a combination of the proportion of successful completions of goals

and the costs associated with that production rule: Utility = U = P × G − C + σ. In this

equation, P is the proportion of successful applications of the production rule. This proportion

is multiplied by a constant G (20, by default). C reﬂects the cost associated with the execution

of the production rule, expressed in units of time. The last variable in the equation, σ, represents

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