Understanding Students’ Explanations in Geometry Tutoring

Understanding Students’ Explanations in Geometry Tutoring Octav Popescu, Vincent Aleven, and Kenneth Koedinger Human-Computer Interaction Institute Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213 USA octav@cmu.edu, aleven@cs.cmu.edu, koedinger@cmu.edu Abstract Precise Natural Language Understanding is needed in Geometry Tutoring to accurately determine the semantic content of students’ explanations. The paper presents an NLU system developed in the context of the Geometry Explanation Tutor. The system combines unification-based syntactic processing with description logics based semantics to achieve the necessary accuracy level. Solutions to specific semantic problems dealing with equivalence of semantic representations are described. Experimental results on classification accuracy are also presented. 1 Introduction The Geometry Cognitive Tutor is designed to help high school and middle school students learn geometry. As a kind of Cognitive Tutor (Anderson et al. 1995), the system is based on an underlying cognitive model, implemented as an ACT-R production system (Anderson and Lebiere 1998), of both novice and ideal student knowledge. This model is used to monitor student performance and to provide assistance just when students need it and in a context that demands it. Currently the Geometry Cognitive Tutor is in regular use (two days per week) in about 350 schools around the US. The tutor proposes problems to students and checks their solutions step by step. It can also provide context-sensitive hints at each step in solving the problem, as needed. The students are asked to compute various elements of the problem (mostly angle measures) by applying the theorems and definitions they have learned. In case the results are correct, the students are also asked to provide a justification for their results. In the version of the tutor that is currently in use in schools, the justification consists in choosing the right theorem or definition out of a menu. The choice is accepted or rejected by the tutor, accordingly. The use of this tutor in combination with classroom instruction has been shown to lead to improvements in students’ test scores over traditional classroom instruction alone (Koedinger et al. 1997). Experiments have also shown that the use of menu-based justifications help students learn with greater understanding over a tutor that does not ask for justifications (Aleven and Koedinger 2002). However there is room for improvement. Classroom observation shows that some students try to game the system by choosing each item in the menu in turn, until one is accepted. Even when this is not the case, it is possible that simply recognizing the name of the correct theorem or definition out of a menu does not imply that the student is fully knowledgeable about the actual content of the theorem involved. Thus it is plausible that asking the students to express the content of these theorems and definitions in their own words as a form of self- explanation could lead to a deeper level of their understanding. To verify this hypothesis we are currently developing the Geometry Explanation Tutor. This version is based on the Geometry Cognitive Tutor, with the modification that the justification consists …

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