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Learning to think and communicate with diagrams: 14 questions to consider
Artificial Intelligence Review, 2001
This paper looks at the particular role which diagrammatic representations, and external representations more generally, play within an educational context. In particular, it considers the way in which the demands on diagrammatic representational systems in educational settings differ with respect to other settings (e.g. professional): in some instances, these demands are increased, while in others, the demands are markedly different.
The use of diagrams as external aids to facilitate cognitive abilities is not new. This paper looks into cognitive studies for insight into when, why and how diagrams are effective in problem solving. A case study examines the use of diagrammatic representations as thinking tools and tools for communicating information. The purpose is to examine whether diagramming could be used as a design method, as part of the designer's creative process.
A Practice-Based Approach to Diagrams
Visual Reasoning with Diagrams, 2013
In this article, I propose an operational framework for diagrams. According to this framework, diagrams do not work like sentences, because we do not apply a set of explicit and linguistic rules in order to use them. Rather, we become able to manipulate diagrams in meaningful ways once we are familiar with some specific practice, and therefore we engage ourselves in a form of reasoning that is stable because it is shared. This reasoning constitutes at the same time discovery and justification for this discovery. I will make three claims, based on the consideration of diagrams in the practice of logic and mathematics. First, I will claim that diagrams are tools, following some of Peirce's suggestions. Secondly, I will give reasons to drop a sharp distinction between vision and language and consider by contrast how the two are integrated in a specific manipulation practice, by means of a kind of manipulative imagination. Thirdly, I will defend the idea that an inherent feature of diagrams, given by their nature as images, is their ambiguity: when diagrams are 'tamed' by the reference to some system of explicit rules that fix their meaning and make their message univocal, they end up in being less powerful.
Cognitive Science Approaches To Understanding Diagrammatic Representations
Thinking with Diagrams, 2001
Through a wide variety of approaches cognitive science has given us various important insights into the nature of diagrammatic representations. This paper surveys the findings, issues and approaches to diagrammatic representations in cognitive science. Important current issues that are highlighted include: the relation between the parts of the representational system that are internal to the mind and in external visual media that presents the diagram; the use of multiple representations which is typical of real contexts of diagram use; the benefits of diagrams in terms of (i) computational offloading, (ii) re-representation and (iii) graphical constraining.
Functional Roles for the Cognitive Analysis of Diagrams in Problem Solving
2002
This paper proposes that a novel form of cognitive analysis for diagrammatic representations is in terms of the functional roles that they can play in problem solving. Functional roles are capacities or features that a diagram may possess, which can support particular forms of reasoning or specific problem solving tasks. A person may exploit several functional roles of a single diagram in one problem. A dozen functional roles have been identified, which can be considered as a framework to bridge the gulf between (i) studies of the properties of diagrams in themselves and (ii) investigations of human reasoning and problem solving with diagrammatic representations. The utility of the framework is demonstrated by examining how the functional roles can explain why certain diagrams facilitate problem solving in thermodynamics. The thermodynamics diagrams are interesting, in themselves, as examples of complex cognitive artefacts that support a variety of sophisticated forms of reasoning.
Mental Representations of Diagrams, Views about Diagrams, and Problem Solving
palm.mindmodeling.org
This study investigated people's mental representations of diagrams and whether these related to views about diagrams and problem solving performance. The participants were 93 undergraduate students who were asked to complete a questionnaire which included free writing on the topic of diagrams, and problem solving. Analysis of the statements and ideas that the students wrote revealed four categories through which diagrams may be mentally represented: uses/purposes, exemplars, personal opinions, and structure. Personal opinions responses were found to negatively correlate with views about the usefulness of diagrams, and with experiences and confidence in using diagrams. In contrast, responses about the uses/purposes of diagrams positively correlated with confidence in using diagrams. Evidence was also found suggesting that, among students studying math, greater knowledge about the uses/purposes of diagrams facilitated better problem solving performance.
CHREST+ : Investigating How Humans Learn to Solve Problems Using Diagrams
This paper describes the underlying principles of a computer model, CHREST+, which learns to solve problems using diagrammatic representations. Although earlier work has determined that experts store domain-specific information within schemata, no substantive model has been proposed for learning such representations. We describe the different strategies used by subjects in constructing a diagrammatic representation of an electric circuit known as an AVOW dia- gram, and explain how these strategies fit a theory for the learnt representations. Then we describe CHREST+, an ex- tended version of an established model of human perceptual memory. The extension enables the model to relate informa- tion learnt about circuits with that about their associated AVOW diagrams, and use this information as a schema to im- prove its efficiency at problem solving.
Cognitive conditions of diagrammatic reasoning
Semiotica, 2000
In the first part of this paper, I delineate Peirce's general concept of diagrammatic reasoning from other usages of the term that focus either on diagrammatic systems as developed in logic and AI or on reasoning with mental models. The main function of Peirce's form of diagrammatic reasoning is to facilitate individual or social thinking processes in situations that are too complex to be coped with exclusively by internal cognitive means. I provide a diagrammatic definition of diagrammatic reasoning that emphasizes the construction of, and experimentation with, external representations based on the rules and conventions of a chosen representation system. The second part starts with a summary of empirical research regarding cognitive effects of working with diagrams and a critique of approaches that use 'mental models' to explain those effects. The main focus of this section is, however, to elaborate the idea that diagrammatic reasoning should be conceptualized as a case of 'distributed cognition.' Using the mathematics lesson described by Plato in his Meno, I analyze those cognitive conditions of diagrammatic reasoning that are relevant in this case.
Diagrammatic reasoning: Abstraction, interaction, and insight
Pragmatics & Cognition, 2015
Many types of everyday and specialized reasoning depend on diagrams: we use maps to find our way, we draw graphs and sketches to communicate concepts and prove geometrical theorems, and we manipulate diagrams to explore new creative solutions to problems. The active involvement and manipulation of representational artifacts for purposes of thinking and communicating is discussed in relation to C.S. Peirce’s notion ofdiagrammatical reasoning. We propose to extend Peirce’s original ideas and sketch a conceptual framework that delineates different kinds of diagram manipulation: Sometimes diagrams are manipulated in order to profile known information in an optimal fashion. At other times diagrams are explored in order to gain new insights, solve problems or discover hidden meaning potentials. The latter cases often entail manipulations that either generate additional information or extract information by means of abstraction. Ideas are substantiated by reference to ethnographic, experim...