A rational cascade from teaching explains strategy discovery in development: The case of early addition

Without being taught, children learning addition discover strategies that are faster and less error-prone than those in their repertoire. Leading explanations of strategy discovery propose metacognitive mechanisms where children iteratively rewrite their existing strategies. Departing from this tradition, we propose that children make discoveries through a combination of reconstructive imitation during teaching, followed by rational inference under basic performance pressures. We instantiate our proposal with a model of Bayesian program induction with a prior for algorithmic simplicity and a likelihood that first encodes a pressure of mimicry (teaching phase), and then a pressure for speed and/or accuracy (individual practice phase). Regardless of whether the pressure is to respond faster or more accurately, the model robustly captures the long-observed developmental trajectory of strategy discovery.