Acquisition of children's addition strategies: A model of impasse-free, knowledge-level learning

When children learn to add, they count on their fingers, beginning with the simple Sum Strategy and gradually developing the more sophisticated and efficient Min strategy. The shift from Sum to Min provides an ideal domain for the study of naturally occurring discovery processes in cognitive skill acquisition. The Sum -to- Min transition poses a number of challenges for machine-learning systems that would model the phenomenon. First, in addition to the Sum and Min strategies, Siegler and Jenkins (1989) found that children exhibit two transitional strategies, but not a strategy proposed by an earlier model. Second, they found that children do not invent the Min strategy in response to impasses, or gaps in their knowledge. Rather, Min develops spontaneously and gradually replaces earlier strategies. Third, intricate structural differences between the Sum and Min strategies make it difficult, if not impossible, for standard, symbol-level machine-learning algorithms to model the transition. We present a computer model, called Gips , that meets these challenges. Gips combines a relatively simple algorithm for problem solving with a probabilistic learning algorithm that performs symbol-level and knowledge-level learning, both in the presence and absence of impasses. In addition, Gips makes psychologically plausible demands on local processing and memory. Most importantly, the system successfully models the shift from Sum to Min , as well as the two transitional strategies found by Siegler and Jenkins.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46917/1/10994_2004_Article_BF00993172.pd

A comparative evaluation of socratic versus didactic tutoring

While the effectiveness of one-on-one human tutoring has been well established, a great deal of controversy surrounds the issue of which features of tutorial dialogue separate effective uses of dialogue in tutoring from those that are less effective. In this paper we present a formal comparison of Socratic versus Didactic style tutoring that argues in favor of the Socratic tutoring style

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453