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<Paper uid="W04-0911">
  <Title>Lexical-Semantic Interpretation of Language Input in Mathematical Dialogs</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
PEDAGOGICAL
KNOWLEDGE
USER
MODEL
LEARNING
ENVIRONMENT
MATHEMATICAL
PROOF ASSISTANT
DIALOG MANAGER
GENERATION
PROOF MANAGER
ANALYSIS
MATHEMATICAL
KNOWLEDGE
(MBASE)
ACTIVEMATH OMEGA
RESOURCES
LINGUISTIC DIALOG
RESOURCES
TUTORING
RESOURCES /
MANAGER
USER
</SectionTitle>
    <Paragraph position="0"> proofs. The PM builds and maintains a representation of constructed proofs and communicates with the MPA to evaluate the appropriateness of the student's contributions for the proof construction.</Paragraph>
    <Paragraph position="1"> Dialog Manager: We employ the Information-State (IS) Update approach developed in the TRINDI project2 Tutorial Manager (TM): This component incorporates extensions to handle tutorialspecific dialog moves, such as hinting. Knowledge Resources: This includes pedagogical knowledge (teaching strategies), and mathematical knowledge.</Paragraph>
    <Paragraph position="2"> In order to empirically investigate the use of natural language in mathematics tutoring, we collected and analyzed a corpus of dialogs with a simulated tutoring system.</Paragraph>
    <Paragraph position="3"> 24 subjects with varying educational background and little/fair prior mathematical knowledge participated in a Wizard-of-Oz experiment (Benzm&amp;quot;uller et al., 2003b). The experiment consisted of 3 phases: (i) preparation and pre-test (on paper), (ii) tutoring session (mediated by a WOz tool (Fiedler and Gabsdil, 2002)), (iii) post-test and evaluation questionnaire (on paper). At the tutoring session, they were asked to prove 3 theorems3: (i) K((A [ B) \</Paragraph>
    <Paragraph position="5"> A K(B), then B K(A). The subjects were instructed to enter proof steps, rather than complete proofs at once, to encourage interaction with the system. The subjects and the tutor were free in formulating their turns.4  ematical symbols, while literals were typed on the keyboard. The collected corpus consists of 66 dialog logfiles, containing on average 12 turns. The total number of sentences is 1115, of which 393 are student sentences. The students' turns consisted on average of 1 sentence, the tutor's of 2. More details on the corpus itself and annotation efforts that guide the development of the system components can be found in (Wolska et al., 2004).</Paragraph>
  </Section>
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