Discontinuities in function learning

Existing process of models of function learning mostly assume that function learning is a gradual and continuous process (polynomial rule model: Koh and Meyer (1991); EXtrapolation Association Model (EXAM): DeLosh et al. (1997); Population Of Linear Experts (POLE): Kalish et al. (2004)). In contrast, Brehmer (1974) proposed a two-staged hypothesis testing theory of function learning. The first stage involves discovering a suitable rule, and the second stage is concerned with learning the parameters of the rule. Although this theory has not been quantitatively formalized, it differs from the other theories by positing a discontinuity when the learner transitions from discovering a rule to applying a rule. In this extended abstract, we present preliminary evidence of such discontinuities. In a replication of McDaniel et al. (2014), we identified a subset of participants that demonstrated abrupt decreases in error over the course of the experiment. Our computational simulations of existing process models further confirmed that gradual update mechanisms are insufficient to account for these observed discontinuities.