What Constitutes an Effective Representation?
This paper presents a taxonomy of 19 cognitive criteria for judging what constitutes effective representational systems, particularly for knowledge rich topics. Two classes of cognitive criteria are discussed. The first concerns access to concepts by read
- PDF / 1,384,252 Bytes
- 15 Pages / 439.37 x 666.142 pts Page_size
- 85 Downloads / 191 Views
Abstract. This paper presents a taxonomy of 19 cognitive criteria for judging what constitutes effective representational systems, particularly for knowledge rich topics. Two classes of cognitive criteria are discussed. The first concerns access to concepts by reading and making inferences from external representations. The second class addresses the generation and manipulation of external representations to fulfill reasoning or problem solving goals. Suggestions for the use of the classification are made. Examples of conventional representations and Law Encoding Diagrams for the conceptual challenging topic of particle collisions are provided throughout. Keywords: External representation Mental representation Cognition Knowledge domains Law encoding diagrams Algebraic expressions Tables Particle collisions Problem solving
1 Introduction What constitutes an effective representation? Here representations include abstract (non-figurative) encodings and presentations of information, such as tables, formal notations, maps, diagrams and interfaces to computers. The title question is important because the design of representations may have a dramatic impact on cognitive processes at different times scales – from perception on the order seconds, to problem solving over minutes, learning lasting hours and days, and discovery taking years. For example, isomorphic representations of the Tower of Hanoi problem can increase problem solution times by up to 16 times [20]. An empirical study [7] on the mechanics problem from Larkin and Simon’s [21] seminal paper showed a six-fold benefit for diagrams over sentential representations. A computational study [12] on the topic of particle collisions showed how diagrams (such as that in Fig. 1A, below) might have been instrumental to the discovery of certain conservation laws in physics. So, this paper addresses the title question from a cognitive perspective, with a particular focus on representations for knowledge rich topics. The question is challenging in cognitive terms. A cognitive answer must integrate: (a) considerations of the nature of external representations (ER); (b) considerations of the nature of the internal mental representations (IR); (c) investigate the rich and complex relations between the two – how ERs and IRs work together to encode knowledge. ERs may in themselves be complex [15, 17]. IRs are also complex [22] and must be examined in relation to the information processing capabilities of the human cognitive architecture [23], including visual perception, mental imagery, propositional © Springer International Publishing Switzerland 2016 M. Jamnik et al. (Eds.): Diagrams 2016, LNAI 9781, pp. 17–31, 2016. DOI: 10.1007/978-3-319-42333-3_2
18
P.C-H. Cheng
(verbal/logical) reasoning and spatial reasoning, which involve memory encoding and retrieval processes at many levels [28]. To be clear on terminology: an ER is a particular physically rendered instance of a representation in the external environment; an IR comprises the information associated with
Data Loading...
