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Article Excerpt
The purpose of this article is to provide five empirically-derived guidelines for knowledge map construction tools that facilitate problem solving. First, the combinational representation principle proposes that conceptual and corresponding procedural knowledge should be represented together (rather than separately) within the knowledge map. Second, the contextual enhancement principle proposes that the learner should provide information regarding the context of the problem within the knowledge map. Third, the spatial flexibility principle proposes that the space where learners represent concepts should be flexible and not artificially constrained. Fourth, the property association principle proposes that the magnitude of association between the concept and associated processes should be classified by the learner within the knowledge map. Fifth, the multiple representation principle proposes that the knowledge map construction tool should have the capacity to represent concepts through multiple modalities. The article presents a prototype of a new knowledge map construction tool that incorporates each of these principles.
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Using external representations through symbols and objects to illustrate a learner's knowledge and the structure of that knowledge can facilitate complex cognitive processing during problem-solving (Vekiri, 2002; Zhang, 1997). Such external representations can help a learner elaborate the problem statement, transform its ambiguous status to an explicit condition, constrain unnecessary cognitive work, and create possible solutions (Kosslyn, 1989; Scaife, & Rogers, 1996). Larkin (1989) argued that an external representation supports human problem-solving by reducing the complexity of a problem and its associated mental workload. Moreover, Bauer and Johnson-Laird (1993) showed that diagrams helped learners solve a problem more effectively and efficiently.
Potential instructional uses of external knowledge representations include the following: (a) clarification or elaboration of a learner's own conceptual understanding of a problem space (Stoyanov, 1997); (b) communication of a learner's conceptual understanding to others (Okebukola, 1992); and, (c) evaluation of a learner's conceptual understanding. The focus here is the first use: that is, the learners' use of external representations to aid in their interpretation and understanding of concepts and procedures, as a way to facilitate problem solving. The purpose of this article is to provide empirically-derived guidelines for designing such external representations (i.e., knowledge maps) to facilitate performance in solving complex problems. Later, a prototype of a computer-based tool that incorporates these principles is presented.
KNOWLEDGE REPRESENTATIONS AND LEARNING
There are numerous forms of representation that facilitate learners in externalizing their internal knowledge structure during problem solving. Examples include the following (Kosslyn, 1989; Vekiri, 2002):
1. graphs that compare the relations among variables;
2. charts that illustrate the flow of discrete events;
3. maps that arrange symbolic objects spatially; and
4. diagrams that show relationships through objects and lines.
Of these external representations, knowledge maps that connect concepts (i.e., "nodes") through labeled (or sometimes unlabeled) arrows (i.e., "links") have been found to be particularly very highly effective for problem solving (Jonassen, Beissner, & Yacci, 1993).
The theoretical rationale for knowledge mapping is based in part on Ausubel's assimilation theory (Ausubel, 1968), which suggested that learners think about concepts as well as the relations among them when they process information. The learner links new concepts to more generalized concepts that are already stored in his or her internal cognitive structures. Another theory underlying the knowledge map is semantic networking theory (Collins & Loftus, 1975), which hypothesizes that human memory is organized semantically. These existing networks of concepts, referred to as "schemas," are linked with new knowledge when learners form new connections to them.
Specifically, the knowledge map is an externalized graphical representation that describes the relations among nodes by use of bi-directional links that define properties among the nodes (Fisher, 2000a). For example, an arrow labeled "has," from the node labeled "Mary" to the node labeled "pencils" represents the sentence "Mary has pencils." Figure 1 is the graphical representation of this sentence.
[FIGURE 1 OMITTED]
Depending on researchers' preferences or computer software conventions, such maps are sometimes referred to as "cluster maps," "mind maps," "concept circle diagrams," "concept maps," "semantic networks," or "conceptual graphs" (Fisher, 2000a). The links of cluster maps and mind maps, for example, are unlabeled whereas concept maps, semantic networks, and the links of conceptual graphs are labeled. Moreover, different types of maps serve different educational purposes. For instance, concept circle diagrams illustrate larger categories into which smaller concepts are grouped. Irrespective of their names, these forms have the common characteristics that they assign and link important concepts with labeled or unlabelled lines.
There are several ways in which knowledge maps can support learning in general. First, learners can construct knowledge maps for representing their understanding in a domain. By creating a knowledge map during the learning process, they can reconceptualize, elaborate, and refine concepts that they already know. Second, this process can facilitate their recognition of patterns and relationships...
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