Problem Solving of Elementary Mathematics Based on Co-reference between Drill Text and Dialogue with Teacher

Tsutomu ENDO, Hidehiro OHKI, Tsuneo KAGAWA

Department of Computer Science and Intelligent Systems, Oita University

Dannoharu, Oita 870-11, Japan

e-mail: endo@csis.oita-u.ac.jp

A dialogue plays an important role in learning how to solve a problem and forming a concept. In primary education, the dialogue between students and a teacher is the major part of the educational activity. A textbook, drill text, and figures on a blackboard are used for students to understand teacher's utterance easily. Sentences of the text are written in the spoken language to associate it with the dialogue. The spoken language has such problems as deviation from grammar, ellipsis, or occurrence of anaphoric forms. Reference to the text and figures will be useful in solving those problems. In realizing a problem solving process using text together with dialogue, it is necessary to understand the mutual relation between natural language expressions and picture expressions in the text, make each less ambiguous by referring to the other, transform one expression into another, and associate the text with the dialogue. This research intends to develop a problem solving system based on co-reference between drill texts and dialogue with a teacher, focusing on first grade mathematics. We are now designing a prototype system which consists of a number of interpreting modules that try to interpret components of the text. These modules use a variety of knowledge modules according to the structural and semantic features of the components concerned, and they communicate with each other if necessary. This year we investigated the following issues.

(1)Analyzing the problem sentences in textbooks, drill texts, and guidebooks, and expected utterances in the problem solving process.

(2)Representing the structure at any level from the character strings or primitive pictures to the interpretation. The sentence is described by the case structure, and the problem picture by the picture descriptive structure. The command sequence for problem solving are finally generated by co-reference of both structures.

(3)Improving on the knowledge modules such as discriminating of data type, planning, character recognition, natural language processing, and picture recognition.

(4)Designing a dialogue control module. The system passes the right of control to this module when a knowledge module fails in interpreting the text component. It generates a suitable question according to both the attributes of the component and the situation that the module is used.

Keywords: text understanding, problem solving, elementary mathematics, distributed processing, cooperative understanding, dialogue