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
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 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