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

Tsutomu ENDO, Hidehiro OHKI, and Tsuneo KAGAWA

Department of Computer Science and Intelligent Systems, Oita University
Dannoharu, Oita 870-11, JAPAN

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 them 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 asynchronously communicate with each other if necessary. This year we investigated the following issues.

{(1) Designing problem solving of a drill text.}
Problem sentences in the text are described by the case structure, and problem pictures by the picture descriptive form. The command sequence for problem solving of the text is finally generated by co-reference of both descriptions. When ambiguities arise or attempts to generate the command sequence fail in that process, the system tries to communicate with a teacher using a dialogue control module. Each command is described by the frame-like representation which has such slots as super-frame, case-frame, parameters, or procedures. The parameter slot consists of such facets as type, role, concept, constraints, or value.

{(2) Analyzing dialogue development in problem solving process.}
A system takes the initiative in having a dialogue with a teacher, because the goal of the system is to solve a problem in a drill text. Utterance functions of the system are request for confirmation, request for information (or question), request for paraphrase, and giving information (or answer). Each utterance has its own activation conditions and its own effects, which are new dialogue states. For example, a sentence of request for confirmation is generated when the system succeeded in inferring an unknown parameter value or a new command candidate using information of command frame, or in solving the problem by executing the generated command sequence. Teacher's utterance makes a pair with system's one, and then has a function such as agreement/disagreement, answer, paraphrase, or question. There can be three types of surface structure of response pairs in a dialogue. One is a sequential type, in which a response pair appears sequentially. The second is a nested one, in which one pair is embedded in other pair. The third is a multiple one, in which an utterance in a pair has more than one function, or more than one sentence.

{(3) Developing the dialogue control module.}
Language generation from the problem solving system should take extraction of linguistic information, conjunction of sentences, and naturalness into consideration. Propositional information of an utterance is extracted from both the case-frame slot of the class command frame and the print-name facet of the instance one. Some templates are prepared for typical events in command generating process. Modal information such as affirmation, negation, or question is set up based on the situation or condition of command generating process. For example, affirmation is extracted when new events occurred after executing a procedure given by the teacher. Suitable morphemes are attached to the proposition according to the modal information. The types of conjunction are conjunctive and embedded. Various kinds of rhetorical operations will contribute more or less to naturalness of sentences. Ellipsis, thematization, and focus are considered to make sentences cohere to each other. An old entity in the current utterance can be a theme or focus, and new one is most likely to be the focus of the next utterance. In Japanese, the syntactic case marker of "wa" is attached to the focused element, which is moved to the head of the sentence.

{(4) Implementing an experimental dialogue system.}
An experimental system was implemented on SPARC station. The dictionary, rules, and programs were written in PROLOG. The case structures of problem sentences and picture descriptive forms of problem pictures are stored in the disk file in advance. A part of a dialogue is as follows:

S: nanino kazuwo kazoerunodesuka. (What may I count?)
T: wakuno nakano monodesu. (Objects in the rectangle.)
S: sono nakaniwa iroirona monoga arimasu. nanino kazuwo kazoerunodesuka.
(There are various kinds of object in it. What may I count?)
T: onazi nakamano kazuwo kazoemasu. mazu chuurippuno kazuwo kazoenasai.
(You should count same kind of objects. First of all, count the tulips.)
S: chuurippuno kazudake maruwo kakunodesune.
(May I draw as many circles as the number of tulips?)
T: soudesu. (Yes, you may.)
S: maruwa dokoni kakunodesuka. (Where may I draw circles?)

In above dialogue, S and T indicate the utterance of the system and the teacher respectively.

Keywords: text understanding, problem solving, elementary mathematics, cooperative understanding, dialogue, utterance function, natural language generation