Encouraging versatile thinking in algebra using the computer

In this article we formulate and analyse some of the obstacles to understanding the notion of a variable, and the use and meaning of algebraic notation, and report empirical evidence to support the hypothesis that an approach using the computer will be more successful in overcoming these obstacles. The computer approach is formulated within a wider framework ofversatile thinking in which global, holistic processing complements local, sequential processing. This is done through a combination of programming in BASIC, physical activities which simulate computer storage and manipulation of variables, and specific software which evaluates expressions in standard mathematical notation. The software is designed to enable the user to explore examples and non-examples of a concept, in this case equivalent and non-equivalent expressions. We call such a piece of software ageneric organizer because if offers examples and non-examples which may be seen not just in specific terms, but as typical, or generic, examples of the algebraic processes, assisting the pupil in the difficult task of abstracting the more general concept which they represent. Empirical evidence from several related studies shows that such an approach significantly improves the understanding of higher order concepts in algebra, and that any initial loss in manipulative facility through lack of practice is more than made up at a later stage

A Constraint Programming Approach for Mining Sequential Patterns in a Sequence Database

Constraint-based pattern discovery is at the core of numerous data mining tasks. Patterns are extracted with respect to a given set of constraints (frequency, closedness, size, etc). In the context of sequential pattern mining, a large number of devoted techniques have been developed for solving particular classes of constraints. The aim of this paper is to investigate the use of Constraint Programming (CP) to model and mine sequential patterns in a sequence database. Our CP approach offers a natural way to simultaneously combine in a same framework a large set of constraints coming from various origins. Experiments show the feasibility and the interest of our approach

Focusing for Pronoun Resolution in English Discourse: An Implementation

Anaphora resolution is one of the most active research areas in natural language processing. This study examines focusing as a tool for the resolution of pronouns which are a kind of anaphora. Focusing is a discourse phenomenon like anaphora. Candy Sidner formalized focusing in her 1979 MIT PhD thesis and devised several algorithms to resolve definite anaphora including pronouns. She presented her theory in a computational framework but did not generally implement the algorithms. Her algorithms related to focusing and pronoun resolution are implemented in this thesis. This implementation provides a better comprehension of the theory both from a conceptual and a computational point of view. The resulting program is tested on different discourse segments, and evaluation and analysis of the experiments are presented together with the statistical results.Comment: iii + 49 pages, compressed, uuencoded Postscript file; revised version of the first author's Bilkent M.S. thesis, written under the supervision of the second author; notify Akman via e-mail ([email protected]) or fax (+90-312-266-4126) if you are unable to obtain hardcopy, he'll work out somethin

Gathering Statistics to Aspectually Classify Sentences with a Genetic Algorithm

This paper presents a method for large corpus analysis to semantically classify an entire clause. In particular, we use cooccurrence statistics among similar clauses to determine the aspectual class of an input clause. The process examines linguistic features of clauses that are relevant to aspectual classification. A genetic algorithm determines what combinations of linguistic features to use for this task.Comment: postscript, 9 pages, Proceedings of the Second International Conference on New Methods in Language Processing, Oflazer and Somers ed

Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories

The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like alethic and deontic modalities, indexicals, higher-order quantification, among others. Harnessing the high expressive power of Church's type theory as a meta-logic to semantically embed a combination of quantified non-classical logics, our work pushes existing boundaries in knowledge representation and reasoning. We demonstrate that intuitive encodings of complex ethical theories and their automation on the computer are no longer antipodes.Comment: 14 page