A Bayesian Model of Pedagogical Reasoning

Much of learning and reasoning occurs in pedagogical situations – situations in which teachers choose examples with the goal of having a learner infer the concept the teacher has in mind. In this paper, we present a model of teaching and learning in pedagogical settings which predicts what examples teachers should choose and what learners should infer given a teachers’ examples. We present experimental results affirming the predictions of the pedagogical model and discuss future directions. Much of human learning and reasoning goes on in pedagogical settings. In schools, teachers impart their knowledge to students about mathematics, science, and literature through examples and problems. From early in life, parents teach children words for objects and actions, and cultural and personal preferences through subtle glances and outright admonitions. Pedagogical settings – settings where one agent is choosing information to transmit to another agent for the purpose of communicating a concept – dominate human learning and reasoning. If learners’ assumptions about how teachers sample information reflected this purposeful sampling, then learners might be able to make much stronger inferences in pedagogical situations. Sampling assumptions are assumptions that a learner makes about the source of data, in order to better interpret the evidence for statistical learning. Recent research suggests that even infants are sensitive to the sampling processes that underlie observed data (Xu & Tenenbaum, 2007) and young children make qualitatively different inferences when data are sampled by a teacher (Gergely, Egyed, & Kiraly, 2007). Consider a simple example which we call the rectangle game: a game where the teacher thinks of a rectangle on a board, and tries to communicate that concept to a learner by choosing to label points inside and/or outside the rectangle (cf. Tenenbaum, 1999). In the rectangle game, the learner’s job is to try to infer, given the labeled examples chosen by the teacher, what rectangle the teacher is thinking of. Figure 1 presents potential teacher and learner scenarios. In each case, there seem to be choices which are obviously better than others. As a person trying to teach someone the Copyright c © 2008, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. O O O O O O X