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.

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.

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 paper considers three key issues: the question of whether diagrams make certain tasks easier (and whether this is desirable from an educational point of view), the generalisation and transfer of diagrammatic skills once learnt, and the possible problems associated with simultaneously learning domain knowledge and a novel representational system. The paper then considers a number of sub-issues, and concludes by highlighting areas of particular interest for future AI research.

Cognitive Processing, 2013

Thinking often entails interacting with cognitive tools. In many cases, notably design, the predominant tool is the page. The page allows externalizing, organizing, and reorganizing thought. Yet, the page has its own properties that by expressing thought affect it: path, proximity, place, and permanence. The effects of these properties were evident in designs of information systems created by students Paths were interpreted as routes through components. Proximity was used to group subsystems. Horizontal position on the page was used to express temporal sequence and vertical position to reflect real-world spatial position. The permanence of designs on the page guided but also constrained generation of alternative designs. Cognitive tools both reflect and affect thought.

2004

This paper explores the role of diagrams in a specific problem solving process. Two types of tests were administered to 194, 12 year old students, each of which consisted of six non-routine problems that could be solved with the use of a diagram. In Test A students were asked to respond to the problems in any way they whished whereas in Test B problems were accompanied by diagrams and students were asked to solve these problems with the use of the specific diagrams presented. The results revealed that there was no statistical significant difference between the two tests. The result also revealed that it was not the same group of students that were successful in the two tests.

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.

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.

for the learning of mathematics, 1994

It is widely claimed that drawing diagrams or pictures is helpful for solving problems in general [e.g. Gick, 1989], for solving mathematical problems in particular [e.g. Hembree, 1992; Kersh & McDonald, 1991; Lakin & Simon, 1987], and that this kind of activity is considered to be one of the problem-solving strategies [e g. Charles eta/, 1985; Eicholz et a/., 1985] Its usefulness lies, we think, in the fact that it can show relationships among elements in the problem clearly For example, Nickerson, Perkins & Smith [1985] state:

Proceedings of the 30th Annual Conference of the …, 2008

Although diagrams are considered as effective personal tools for solving problems, applied research in education has identified a widespread problem: that students lack spontaneity in diagram use. One way to address this problem was reported by : their findings indicate the effectiveness of using peer instruction to enhance students' spontaneous use of diagrams. However, it was not clear from their study whether actual interaction is necessary, and whether formulation of explanations in using diagrams to solve problems would in itself be sufficient. The present study sought to clarify the role of communication in enhancing the spontaneous use of diagrams, and involved 5 days of experimental classes for 59 participants in the 8 th grade. Two conditions were used: one where participants really interacted with each other in peer instruction sessions (the experimental condition), and another where the participants formulated explanations but were not involved in peer instruction interactions. At post test, both quantity and quality of diagrams spontaneously produced by participants in the experimental condition were higher than those in the control condition, suggesting that the communication process involved in actual interactions with peers is a critical factor. This result supports the notion that using diagrams as communication tools results in their internalization as personal tools for problem solving.

Thinking with Diagrams, 2001

Visual programming languages aim to broaden the use of diagrams within the software industry, to the extent that they are integrated into the programming language itself. As a result, they provide an ideal opportunity to study the benefits of diagrams as an external representation during problem solving: not only is programming a challenging problem-solving activity, but the effect of diagram usage can be directly assessed by comparing performance while using a visual programming language to performance with a standard textual language. There have been several misconceptions amongst visual language researchers regarding the role of diagrams in software design, but these are being addressed by empirical studies and by new theories of notation design derived from studies of visual programming. Based on this research, the authors are able to recommend several new directions for research into thinking with diagrams.