Categories, definitions and mathematics : student reasoning about objects in analysis

This thesis has two integrated components, one theoretical and one investigative. The theoretical component considers human reason about categories of objects. First, it proposes that the standards of argumentation in everyday life are variable, with emphasis on direct generalisation, whereas standards in mathematics are more fixed and require abstraction of properties. Second, it accounts for the difficulty of the transition to university mathematics by considering the impact of choosing formal definitions upon the nature of categories and argumentation. Through this it unifies established theories and observations regarding student behaviours at this level. Finally, it addresses the question of why Analysis seems particularly difficult, by considering the relative accessibility of its visual representations and its formal definitions. The investigative component is centred on a qualitative study, the main element of which is a series of interviews with students attending two different first courses in Real Analysis. One of these courses is a standard lecture course, the other involves a classroom-based, problem-solving approach. Grounded theory data analysis methods are used to interpret the data, identifying behaviours exhibited when students reason about specific objects and whole categories. These behaviours are linked to types of understanding as distinguished in the mathematics education literature. The student's visual or nonvisual reasoning style and their sense of authority, whether "internal" or "external" are identified as causal factors in the types of understanding a student develops. The course attended appears as an intervening factor. A substantive theory is developed to explain the contributions of these factors. This leads to improvement of the theory developed in the theoretical component. Finally, the study is reviewed and the implications of its findings for the teaching and learning of mathematics at this level are considered

Directional adposition use in English, Swedish and Finnish

Directional adpositions such as to the left of describe where a Figure is in relation to a Ground. English and Swedish directional adpositions refer to the location of a Figure in relation to a Ground, whether both are static or in motion. In contrast, the Finnish directional adpositions edellä (in front of) and jäljessä (behind) solely describe the location of a moving Figure in relation to a moving Ground (Nikanne, 2003). When using directional adpositions, a frame of reference must be assumed for interpreting the meaning of directional adpositions. For example, the meaning of to the left of in English can be based on a relative (speaker or listener based) reference frame or an intrinsic (object based) reference frame (Levinson, 1996). When a Figure and a Ground are both in motion, it is possible for a Figure to be described as being behind or in front of the Ground, even if neither have intrinsic features. As shown by Walker (in preparation), there are good reasons to assume that in the latter case a motion based reference frame is involved. This means that if Finnish speakers would use edellä (in front of) and jäljessä (behind) more frequently in situations where both the Figure and Ground are in motion, a difference in reference frame use between Finnish on one hand and English and Swedish on the other could be expected. We asked native English, Swedish and Finnish speakers’ to select adpositions from a language specific list to describe the location of a Figure relative to a Ground when both were shown to be moving on a computer screen. We were interested in any differences between Finnish, English and Swedish speakers. All languages showed a predominant use of directional spatial adpositions referring to the lexical concepts TO THE LEFT OF, TO THE RIGHT OF, ABOVE and BELOW. There were no differences between the languages in directional adpositions use or reference frame use, including reference frame use based on motion. We conclude that despite differences in the grammars of the languages involved, and potential differences in reference frame system use, the three languages investigated encode Figure location in relation to Ground location in a similar way when both are in motion. Levinson, S. C. (1996). Frames of reference and Molyneux’s question: Crosslingiuistic evidence. In P. Bloom, M.A. Peterson, L. Nadel & M.F. Garrett (Eds.) Language and Space (pp.109-170). Massachusetts: MIT Press. Nikanne, U. (2003). How Finnish postpositions see the axis system. In E. van der Zee & J. Slack (Eds.), Representing direction in language and space. Oxford, UK: Oxford University Press. Walker, C. (in preparation). Motion encoding in language, the use of spatial locatives in a motion context. Unpublished doctoral dissertation, University of Lincoln, Lincoln. United Kingdo

Proceedings of the 1st Doctoral Consortium at the European Conference on Artificial Intelligence (DC-ECAI 2020)

1st Doctoral Consortium at the European Conference on Artificial Intelligence (DC-ECAI 2020), 29-30 August, 2020 Santiago de Compostela, SpainThe DC-ECAI 2020 provides a unique opportunity for PhD students, who are close to finishing their doctorate research, to interact with experienced researchers in the field. Senior members of the community are assigned as mentors for each group of students based on the student’s research or similarity of research interests. The DC-ECAI 2020, which is held virtually this year, allows students from all over the world to present their research and discuss their ongoing research and career plans with their mentor, to do networking with other participants, and to receive training and mentoring about career planning and career option

Retrieval, reuse, revision and retention in case-based reasoning

El original está disponible en www.journals.cambridge.orgCase-based reasoning (CBR) is an approach to problem solving that emphasizes the role of prior experience during future problem solving (i.e., new problems are solved by reusing and if necessary adapting the solutions to similar problems that were solved in the past). It has enjoyed considerable success in a wide variety of problem solving tasks and domains. Following a brief overview of the traditional problem-solving cycle in CBR, we examine the cognitive science foundations of CBR and its relationship to analogical reasoning. We then review a representative selection of CBR research in the past few decades on aspects of retrieval, reuse, revision, and retention.Peer reviewe

Artificial Intelligence and Human Error Prevention: A Computer Aided Decision Making Approach: Technical Report No. 4: Survey and Analysis of Research on Learning Systems from Artificial Intelligence

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryU.S. Department of Transportation / DOT FA79WA-4360 ABFederal Aviation Administratio

Concepts as Correlates of Lexical Labels. A Cognitivist Perspective, 274 s.

This is a submitted manuscript version. The publisher should be contacted for permission to re-use or reprint the material in any form. Final published version, copyright Peter Lang: https://doi.org/10.3726/978-3-653-05287-9The study of language becomes particularly attractive when it is not practised as an isolated descriptive enterprise, but when it has wide-ranging implications for the study of the human mind. Such is the spirit of this book. While categorisation may be the single most basic cognitive process in organisms, and as an area of inquiry, it is fundamental to Cognitive Science as a whole, at the other end of the spectrum, high-level cognition is organised and permeated by language, giving rise to categories that count and function as concepts. Working from considering the philosophical assumptions of the cognitivist perspective, this study offers an argument for a very productive understanding of the relation between concepts, categories, and their theoretical models

Instructional strategies in explicating the discovery function of proof for lower secondary school students

In this paper, we report on the analysis of teaching episodes selected from our pedagogical and cognitive research on geometry teaching that illustrate how carefully-chosen instructional strategies can guide Grade 8 students to see and appreciate the discovery function of proof in geometr

An investigation into figurative language in the ‘LOLITA' NLP system

The classical and folk theory view on metaphor and figurative language assumes that metaphor is a rare occurrence, restricted to the realms of poetry and rhetoric. Recent results have, however, unarguably shown that figurative language of various complexity exhibits great systematicity and is pervasive in everyday language and texts. If the ubiquity of figurative language cannot be disputed, however, any natural language processing (NLP) system aiming at processing text beyond a restricted scope has to be able to deal with figurative language. This is particularly true if the processing is to be based on deep techniques, where a deep analysis of the input is performed. The LOLITA NLP system employs deep techniques and, therefore, must be capable of dealing with figurative input. The task of natural language (NL) generation is affected by the naturalness of figurative language, too. For if metaphors are frequent and natural, NL generation not capable of handling figurative language will seem restricted and its output unnatural. This thesis describes the work undertaken to examine the options for extending the LOLITA system in the direction of figurative language processing and the results of this project. The work critically examines previous approaches and their contribution to the field, before outlining a solution which follows the principles of natural language engineering