Multi-Media As a Cognitive Tool

Two of the modalities used to present information to students, namely, animation and verbal representation are in a constant competition in effectiveness, without any persistent winner, except when it comes to conceptual versus procedural knowledge. Here, we present an architecture that combines the two into a multi-media tutoring system. This system is tested and results indicate that combining the two media leads to a cognitive interaction that promotes student learning with no less than 40% from their post classical-classroom session levels. A test for individual differences indicates that this group is almost equally divided between those described as “spatially oriented” and those described as “verbally oriented”. Learning across the two types of learners does not show any significant differences, except with respect to one question. This implies that perhaps, the two media may have ambiguous internal factors that support each other. Additionally, individual learning styles does not seem to be a clear-cut division, and is instead a “preference” of one modality as a primary source of learning, not an only one

LOGICAL AND PSYCHOLOGICAL PARTITIONING OF MIND: DEPICTING THE SAME MAP?

The aim of this paper is to demonstrate that empirically delimited structures of mind are also differentiable by means of systematic logical analysis. In the sake of this aim, the paper first summarizes Demetriou's theory of cognitive organization and growth. This theory assumes that the mind is a multistructural entity that develops across three fronts: the processing system that constrains processing potentials, a set of specialized structural systems (SSSs) that guide processing within different reality and knowledge domains, and a hypecognitive system that monitors and controls the functioning of all other systems. In the second part the paper focuses on the SSSs, which are the target of our logical analysis, and it summarizes a series of empirical studies demonstrating their autonomous operation. The third part develops the logical proof showing that each SSS involves a kernel element that cannot be reduced to standard logic or to any other SSS. The implications of this analysis for the general theory of knowledge and cognitive development are discussed in the concluding part of the paper

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

DISTINGUISHING VISUAL IMAGERY AND SPATIAL REASONING

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73598/1/j.1467-8640.1993.tb00228.x.pd

Reasoning, representing, and generalizing in geometric proof problems among 8th grade talented students

Proof, a key topic in advanced mathematics, also forms an essential part of the formal learning experience at all levels of education. The reason is that the argumentation involved calls for pondering ideas in depth, organizing knowledge, and comparing different points of view. Geometry, characterized by the interaction between the visual appearance of geometric elements and the conceptual understanding of their meaning required to generate precise explanations, is one of the foremost areas for research on proof and argumentation. In this qualitative analysis of the arguments formulated by participants in an extracurricular mathematics stimulus program, we categorized students’ replies on the grounds of reasoning styles, representations used, and levels of generality. The problems were proposed in a lesson on a quotient set based on the similarity among triangles created with Geogebra and the responses were gathered through a Google form. By means a content analysis, the results inform about the reasoning style, the scope of the argumentation, and the representation used. The findings show that neither reasoning styles nor the representations used conditioned the level of generality, although higher levels of argumentation were favored by harmonic and analytical reasoning and the use of algebraic representations

Touch and vision: some considerations for diagrammatical reasonning

[Abstract] Some of the spatial properties of surfaces can be translated by touch as well as vision. Both blind and clearsighted people can equally perceive corners and edges; their minds being equally capable of recognizing objects or arrangements of these. A fundamental difference, however, must be kept in mind: while most of the time the visual system readily homogenizes sensitive data through unity constructing, the haptic system usually «makes experiments» across time, which can be unified by a rule of interpretation only afterwards. Those are two different kinds of logic: visually knowing an object — or arrangement of objects — is to perceive it from general to particular, and tactilely knowing an object — or arrangement of objects — is to perceive it from particular to general. In this paper, with the theoretical background of peircean semiotics, we address the issue of how touch [predominantly inductive] and vision [predominantly deductive] are complementary perceptual/critical senses ecologically connected. Such senses can be intersemiotically translated, as outline drawings demonstrate. A map produced for clearsighted and blind persons will be examined in an attempt to show how diagrammatical reasoning can be developed from predominantly deductive or inductive cognitive processes, and possibly share common representations for haptic and visual systems

A survey of qualitative spatial representations

Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work

Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file

Arrow Symbols: Theory for Interpretation

People often sketch diagrams when they communicate successfully among each other. Such an intuitive collaboration would also be possible with computers if the machines understood the meanings of the sketches. Arrow symbols are a frequent ingredient of such sketched diagrams. Due to the arrows’ versatility, however, it remains a challenging problem to make computers distinguish the various semantic roles of arrow symbols. The solution to this problem is highly desirable for more effective and user-friendly pen-based systems. This thesis, therefore, develops an algorithm for deducing the semantic roles of arrow symbols, called the arrow semantic interpreter (ASI). The ASI emphasizes the structural patterns of arrow-containing diagrams, which have a strong influence on their semantics. Since the semantic roles of arrow symbols are assigned to individual arrow symbols and sometimes to the groups of arrow symbols, two types of the corresponding structures are introduced: the individual structure models the spatial arrangement of components around each arrow symbol and the inter-arrow structure captures the spatial arrangement of multiple arrow symbols. The semantic roles assigned to individual arrow symbols are classified into orientation, behavioral description, annotation, and association, and the formats of individual structures that correspond to these four classes are identified. The result enables the derivation of the possible semantic roles of individual arrow symbols from their individual structures. In addition, for the diagrams with multiple arrow symbols, the patterns of their inter-arrow structures are exploited to detect the groups of arrow symbols that jointly have certain semantic roles, as well as the nesting relations between the arrow symbols. The assessment shows that for 79% of sample arrow symbols the ASI successfully detects their correct semantic roles, even though the average number of the ASI’s interpretations is only 1.31 per arrow symbol. This result indicates that the structural information is highly useful for deriving the reliable interpretations of arrow symbols

An Automated System for Chromosome Analysis

The design, construction, and testing of a complete system to produce karyotypes and chromosome measurement data from human blood samples, and to provide a basis for statistical analysis of quantitative chromosome measurement data are described