Abstract. Probabilistic and learned approaches to student modeling are attractive because of the uncertainty surrounding the student skills assessment and because of the need to automatize the process. Item to item structures readily lend themselves to probabilistic and fully learned models because they are solely composed of observable nodes, like answers to test questions. Their structure is also well grounded in the cognitive theory of knowledge spaces. We study the effectiveness of two Bayesian frameworks to learn item to item structures and to use the induced structures to predict item outcome from a subset of evidence. One approach, POKS, relies on a naive Bayes framework whereas the other is based on the Bayesian network learning and inference framework. Both approaches are assessed over their predictive ability and their computational efficiency in different experimental simulations. The results from simulations over three data sets show that they both can effectively perform accurate predictions, but POKS generally displays higher predictive power than the Bayesian network. Moreover, the simplicity of POKS translates to a time efficiency of one to three orders of magnitude greater than the Bayesian network runs. We furhter explore the use of the item to item approach for handling concepts mastery assessment. The approach investigated consist in augmenting an initial set of observations, based on inferences with the item to item structure, and feed the augmented set to a Bayesian network containing a number of concepts. The results show that augmented set can effectively improve predictive power of a Bayesian network for item outcome, but that improvement does not transfer to the concept assessment in this particular experiment. We discuss different explanations for the results and outline future research avenues.
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects. QED-Tutrix is an intelligent tutor for geometry offering an interface to help high school students in the resolution of demonstration problems. It focuses on specific goals: 1) to allow the student to freely explore the problem and its figure, 2) to accept proofs elements in any order, 3) to handle a variety of proofs, which can be customized by the teacher, and 4) to be able to help the student at any step of the resolution of the problem, if the need arises. The software is also independent from the intervention of the teacher. QED-Tutrix offers an interesting approach to geometry education, but is currently crippled by the lengthiness of the process of implementing new problems, a task that must still be done manually. Therefore, one of the main focuses of the QED-Tutrix' research team is to ease the implementation of new problems, by automating the tedious step of finding all possible proofs for a given problem. This automation must follow fundamental constraints in order to create problems compatible with QED-Tutrix: 1) readability of the proofs, 2) accessibility at a high school level, and 3) possibility for the teacher to modify the parameters defining the "acceptability" of a proof. We present in this paper the result of our preliminary exploration of possible avenues for this task. Automated theorem proving in geometry is a widely studied subject, and various provers exist. However, our constraints are quite specific and some adaptation would be required to use an existing prover. We have therefore implemented a prototype of automated prover to suit our needs. The future goal is to compare performances and usability in our specific use-case between the existing provers and our implementation.
Abstract. We present a method for text compression, which relies on pruning of a syntactic tree. The syntactic pruning applies to a complete analysis of sentences, performed by a French dependency grammar. Sub-trees in the syntactic analysis are pruned when they are labelled with targeted relations. Evaluation is performed on a corpus of sentences which have been manually compressed. The reduction ratio of extracted sentences averages around 70%, while retaining grammaticality or readability in a proportion of over 74%. Given these results on a limited set of syntactic relations, this shows promise for any application which requires compression of texts, including text summarization.
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