Watching another person take actions to complete a goal and making inferences about that person's knowledge is a relatively natural task for people. This ability can be especially important in educational settings, where the inferences can be used for assessment, diagnosing misconceptions, and providing informative feedback. In this paper, we develop a general framework for automatically making such inferences based on observed actions; this framework is particularly relevant for inferring student knowledge in educational games and other interactive virtual environments. Our (...) approach relies on modeling action planning: We formalize the problem as a Markov decision process in which one must choose what actions to take to complete a goal, where choices will be dependent on one's beliefs about how actions affect the environment. We use a variation of inverse reinforcement learning to infer these beliefs. Through two lab experiments, we show that this model can recover people's beliefs in a simple environment, with accuracy comparable to that of human observers. We then demonstrate that the model can be used to provide real-time feedback and to model data from an existing educational game. (shrink)

Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how to solve the equation and the ways in which they might answer incorrectly offers the opportunity to obtain a more nuanced perspective of their algebra skills. To automatically make sense of step‐by‐step solutions, we (...) propose a Bayesian inverse planning model for equation solving that computes an assessment of a learner's skills based on her pattern of errors in individual steps and her choices about what sequence of problem‐solving steps to take. Bayesian inverse planning builds on existing machine learning tools to create a generative model relating (mis)‐understandings to equation solving choices. Two behavioral experiments demonstrate that the model can interpret people's equation solving and that its assessments are consistent with those of experienced teachers. A third experiment uses this model to tailor guidance for learners based on individual differences in misunderstandings, closing the loop between assessing understanding, and using that assessment within an educational technology. Finally, because the bottleneck in applying inverse planning to a new domain is in creating the model of possible student misunderstandings, we show how to combine inverse planning with an existing production rule model to make inferences about student misunderstandings of fraction arithmetic. (shrink)

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are more concrete and familiar, and they are more similar to physical objects and everyday experience. The complementary computational characteristics of grounded and abstract representations lead to trade‐offs in problem‐solving performance. In prior research with (...) high school students solving relatively simple problems, Koedinger and Nathan (2004) demonstrated performance benefits of grounded representations over abstract representations—students were better at solving simple story problems than the analogous equations. This article extends this prior work to examine both simple and more complex problems in two samples of college students. On complex problems with two references to the unknown, a “symbolic advantage” emerged, such that students were better at solving equations than analogous story problems. Furthermore, the previously observed “verbal advantage” on simple problems was replicated. We thus provide empirical support for a trade‐off between grounded, verbal representations, which show advantages on simpler problems, and abstract, symbolic representations, which show advantages on more complex problems. (shrink)

The work presented here investigates the process by which one group of individuals solves the problem of detecting deceptions created by other agents. A field experiment was conducted in which twenty-four auditors (partners in international public accounting firms) were asked to review four cases describing real companies that, unknown to the auditors, had perpetrated financial frauds. While many of the auditors failed to detect the manipulations in the cases, a small number of auditors were consistently successful. Since the detection of (...) frauds occurs infrequently in the work of a given auditor, we explain success by the application of powerful heuristics gained from experience with deceptions in everyday life. These heuristics implement a variation of Dennett's intentional stance strategy, which is based on interpreting detected inconsistencies in the light of the Deceiver's (i.e., management's) goals and possible actions. We explain failure to detect deception by means of perturbations (bugs) in the domain knowledge of accounting needed to apply these heuristics to the specific context of financial statement fraud. We test our theory by showing that a computational model of fraud detection that employs the proposed heuristics successfully detects frauds in the cases given to the auditors. We then modify the model by introducing perturbations based on the errors made by each of the auditors in the four cases. The resulting models account for 84 of the 96 observations (i.e., 24 auditors × four cases) in our data. (shrink)

The work presented here investigates the process by which one group of individuals solves the problem of detecting deceptions created by other agents. A field experiment was conducted in which twenty‐four auditors (partners in international public accounting firms) were asked to review four cases describing real companies that, unknown to the auditors, had perpetrated financial frauds. While many of the auditors failed to detect the manipulations in the cases, a small number of auditors were consistently successful. Since the detection of (...) frauds occurs infrequently in the work of a given auditor, we explain success by the application of powerful heuristics gained from experience with deceptions in everyday life. These heuristics implement a variation of Dennett's intentional stance strategy, which is based on interpreting detected inconsistencies in the light of the Deceiver's (i.e., management's) goals and possible actions. We explain failure to detect deception by means of perturbations (bugs) in the domain knowledge of accounting needed to apply these heuristics to the specific context of financial statement fraud. We test our theory by showing that a computational model of fraud detection that employs the proposed heuristics successfully detects frauds in the cases given to the auditors. We then modify the model by introducing perturbations based on the errors made by each of the auditors in the four cases. The resulting models account for 84 of the 96 observations (i.e., 24 auditors × four cases) in our data. (shrink)