The importance of reasoning by analogy has been widely investigated and documented in science. Reasoning by analogy (a.k.a. analogical reasoning) is the type of thinking that involves arguments between two objects, systems of objects or concepts that
highlight accepted similarities between the two to support the claim that some more similarities exist. Solving a problem through analogy occurs when one finds a known concept or situation and applies it to a problem that has similarities with that concept or situation. Processes include identifying properties of objects, identifying relationships between objects, relationships between the relationships of objects, keeping all of these in mind or storing them for further manipulations, and evaluations to formulate answers (Goswami U. , 1992; Sternberg R. J., 1999) are associated with analogical reasoning. The more complex an analogy, the more difficult it is to meet the prerequisites of solving it. Efficiency in solving an analogy (Duit, 1991; Christensen & Schunn, 2005; Ball, Ormerod, & Morley, 2004) depends on working memory (Paivio, Rogers, & Smythe, 1968) components, storage capacity, executive functioning, evaluation, and decision-making capabilities.
Research in cognitive psychology shows that analogising is a skill that develops over time. According to Piagetian’s theorists, young children develop their analogical reasoning skills during the “formal-operational” (at 11-12 years of age) period of reasoning; however, a number of authors (Vosniadou, 1989; Gentner, 1989; Goswami U. , 1992) argue that the shift occurs much earlier than that and children’s analogising improves as they acquire more knowledge.
Knowledge-based views do predict improvements in children’s performance, and they might recognise relational similarity, but the shift is not global, and mostly depends on children’s ability to understand conceptual relations between the source and target. The process of analogising involves the transfer of structural and/or conceptual information from a source domain to a target problem.
Studies on analogical transfer have identified three main stages: (i) encoding the source and target analogues, (ii) retrieval of the source by the target, and (iii) mapping the source to the target (Gick & Holyoak, 1983; Weisberg, 1988). According to Chen (2002), there are three distinctive types of similarities between problems, structural, procedural and superficial, that share causal relationships in terms of some of their components, procedures to enforce the solution principles into explicit operations, and solution-irrelevant details. Differences between the problems’ similarities play an important role at each stage. For example, easily recognised similarities between the structures and/or principles derived from the source during the encoding stage may lead problem solvers to successful mapping, consequently generating more accurate
solutions. Gick and Holyoak (1983) conducted several investigations on the role of analogy in creative problem solving and found that subjects more often solved a problem when they were told that the previous problem was related. It appears that most participants have difficulty locating the analogues, but once an analogue is discovered they can apply it quite effectively to the problem they face.
2.4.1 Structure-Mapping Theory
Structure-mapping theory (Gentner, 1983), models of similarity, analogy, and metaphor in perceptual and conceptual tasks, particularly, describe how the meaning of analogies is derived from the meaning of their parts. Its strength in explaining analogy comprehension resides in its identification of two principles for mapping knowledge from the source to the target domain. The systematicity principle (Gentner, 1986) states that connected knowledge is preferred over independent facts; and the structural consistency principle suggests one-to-one mapping between each part of the target and each part of the source, as well as between each of the attributes of these two parts. The system of matching objects, their attributes and relations is what Gentner called aligned structure (Gentner & Medina, 1998). Relevant in this structure is the distinction between alignable differences and nonalignable differences. The former involve correspondence between non-identical objects while the latter refer to the lack of, or wrong correspondence, between non-identical objects (Gentner, 1986).
The theory also emphasises the distinction between surface and structural analogies. Whereas the former relates to the easily accessible aspects of object properties, the latter target the higher order relationships based on relevant but less accessible properties. Although surface analogies are easier to understand, they do not guarantee the transfer of structural relations between the source and target domain, while the opposite is true for the structural analogies.
Whereas a wealth of research has explored the role of analogies and metaphors in comprehension, learning and problem solving (Duit, 1991; Novick & Holyoak, 1991), the process of transferring meaning from a source to a target domain has been predominantly explored through conceptual metaphors. We argue that the current research bias is regrettable given that, as described by Lakoff (1993), metaphor is not a figure of a speech but a mode of thought (Forceville, 2002), and we advocate that visual metaphors need to be rigorously explored.
3
Visual Analogies: Static and Dynamic
The value of visual analogies in problem solving has been extensively researched, with most of the work focusing on their benefits (Goldschmidt & Smolkov, 2006; Smith & Blankenship, 1991; Dundar, 1995), but less investigated is how visual analogies are actually developed.
Efforts to address the bias towards conceptual metaphors have led to research in visual analogies including those for computer displays, diagrams (Jones, 1993) to capture complex systems (Tversky, Morrison, & Betancourt, 2002), or animated arrows to hint insight problem solving (Beveridge & Parkins, 1987). Such interest in visual analogies is linked to the arguable superiority effect of pictures over words for memory and cognition. The dual-code theory proposed by Paivio (1971) suggested that pictures, by evoking both imaginal and verbal codes, are likely to be redundantly encoded. Nelson’s sensory–semantic model (1984) suggested that pictures are more memorable because they provide more distinctive representations, whereas Gestalt psychologists have long advocated the role of perceptual factors in metaphor transfer (Kogan, Connor, Gross, & Fava, 1980).
Weldon et al. (1989) showed that pictures can be categorised more quickly than words (Potter & Faulconer, 1975), and produce more elaborate codes (Craik & Lockhart, 1972). In addition, diagrams are particularly useful for attracting attention and sustaining motivation, structuring content and representing visuospatial information (Tversky, Morrison, & Betancourt, 2002).