Magdalena Wolska

Analysis of Mixed Natural and Symbolic Input in Mathematical Dialogs

Discourse in formal domains, such as mathematics, is characterized by a mixture of telegraphic natural language and embedded (semi-)formal symbolic mathematical expressions. We present language phenomena observed in a corpus of dialogs with a simulated tutorial system for proving theorems as evidence for the need for deep syntactic and semantic analysis. We propose an approach to input understanding in this setting. Our goal is a uniform analysis of inputs of different degree of verbalization: ranging from symbolic alone to fully worded mathematical expressions.

Toward evaluation of writing style: finding overly repetitive word use in student essays

Automated essay scoring is now an established capability used from elementary school through graduate school for purposes of instruction and assessment. Newer applications provide automated diagnostic feedback about student writing. Feedback includes errors in grammar, usage, and mechanics, comments about writing style, and evaluation of discourse structure. This paper reports on a system that evaluates a characteristic of lower quality essay writing style: repetitious word use. This capability is embedded in a commercial writing assessment application, CriterionSM. The system uses a machine-learning approach with word-based features to model repetitious word use in an essay. System performance well exceeds several baseline algorithms. Agreement between the system and a single human judge exceeds agreement between two human judges.

Interpreting semi-formal utterances in dialogs about mathematical proofs

Dialogs in formal domains, such as mathematics, are characterized by a mixture of telegraphic natural language text and embedded formal expressions. Analysis methods for this kind of setting are rare and require empirical justification due to a notorious lack of data, as opposed to the richness of presentations found in genre-specific textbooks. In this paper, we focus on interpretation techniques for major phenomena observed in a recently collected corpus of tutorial dialogs on proving mathematical theorems. We combine analysis techniques for mathematical formulas and for natural language expressions, supported by knowledge about domain-relevant lexical semantics and by representations relating informal vocabulary to precise domain terms. Interpreting these expressions in a competent manner is not only important for the use in tutorial systems, but also for supporting domain experts through improving the accessibility and usability of formal systems.

Handling errors in mathematical formulas

In tutorial systems, effective progress in teaching the problem-solving target is frequently hindered by expressive sloppiness and low-level errors made by the student, especially in conventionalized expressions such as formulas. In order to improve the effectiveness of tutorial systems in teaching higher-level skills, we present a fault-tolerant formula interpreter that aims at finding plausibly intended, formally correct specifications from student statements containing formal inaccuracies. The interpretation consists of local changes based on categorization of errors, a fault-tolerant structure building, and testing contextually-motivated alternations. The error interpretation component is intended to enhance the analysis component of a tutorial system that teaches mathematical proving skills.

Word problems: a review of linguistic and numerical factors contributing to their difficulty

Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group.

DiaWOz-II: a tool for wizard-of-Oz experiments in mathematics

We present DiaWOz-II, a configurable software environment for Wizard-of-Oz studies in mathematics and engineering. Its interface is based on a structural wysiwyg editor which allows the input of complex mathematical formulae. This allows the collection of dialog corpora consisting of natural language interleaved with non-trivial mathematical expressions, which is not offered by other Wizard-of-Oz tools in the field. We illustrate the application of DiaWOz-II in an empirical study on tutorial dialogs about mathematical proofs, summarize our experience with DiaWOz-II and briefly present some preliminary observations on the collected dialogs.

Natural language dialog with a tutor system for mathematical proofs

Natural language interaction between a student and a tutoring or an assistance system for mathematics is a new multi-disciplinary challenge that requires the interaction of (i) advanced natural language processing, (ii) flexible tutorial dialog strategies including hints, and (iii) mathematical domain reasoning. This paper provides an overview on the current research in the multi-disciplinary research project Dialog, whose goal is to build a prototype dialog-enabled system for teaching to do mathematical proofs. We present the crucial sub-systems in our architecture: the input understanding component and the domain reasoner. We present an interpretation method for mixed-language input consisting of informal and imprecise verbalization of mathematical content, and a proof manager that supports assertion-level automated theorem proving that is a crucial part of our domain reasoning module. Finally, we briefly report on an implementation of a demo system.

Interpreting Semi-formal Utterances in Dialogs about Mathematical Proofs

Dialogs in formal domains, such as mathematics, are characterized by a mixture of telegraphic natural language text and embedded formal expressions. Analysis methods for this kind of setting are rare and require empirical justification due to a notorious lack of data, as opposed to the richness of presentations found in genre-specific textbooks. In this paper, we focus on dedicated interpretation techniques for major phenomena observed in a recently collected corpus on tutorial dialogs in proving mathematical theorems. We combine analysis techniques for mathematical formulas and for natural language expressions, supported by knowledge about domain-relevant lexical semantics and by representations relating vague lexical to precise domain terms.

A Classification of Dialogue Actions in Tutorial Dialogue

In this paper we present a taxonomy of dialogue moves which describe the actions that students and tutors perform in tutorial dialogue. We are motivated by the need for a categorisation of such actions in order to develop computational models for tutorial dialogue. As such, we build both on existing work on dialogue move categorisation for tutorial dialogue as well as dialogue taxonomies for general dialogue. Our taxonomy has been prepared by analysing a corpus of tutorial dialogues on mathematical theorem proving. We also detail an annotation experiment in which we apply the taxonomy and discuss idiosyncrasies in the data which influence the decisions in the dialogue move classification.

Lexical-semantic interpretation of language input in mathematical dialogs

Discourse in formal domains, such as mathematics, is characterized by a mixture of telegraphic natural language and embedded (semi-)formal symbolic mathematical expressions. Due to the lack of empirical data, little is known about the suitability of input analysis methods for mathematical discourse in a dialog setting. We present an input understanding method for a tutoring system teaching mathematical theorem proving. The adopted deep analysis strategy is motivated by the complexity of the language phenomena observed in a corpus collected in a Wizard-of-Oz experiment. Our goal is a uniform input interpretation, in particular, considering different degrees of formality of natural language verbalizations.