Research shows that experts, as well as novices, can generate and use multiple variations of analogies (Ball, Ormerod, & Morley, 2004; Beveridge & Parkins, 1987; Blanchette & Dunbar, 2001; Christensen & Schunn, 2005; Clement J. , 1981) during insight and creative problem solving. However, while not all generated analogies are potent, how do these experts choose the right ones for their problems? How can one tell whether a proposed concept is authentic? How can the analogy be evaluated and validated with regard to the analogous relationships between source and target? In another biometic example, the Zimbabwean architect Mick Pearce (Beatley, 2012), before designing the largest retail and office complex in Harare, studied termite mounds with a view to figuring out how to minimise the cost of air-conditioning in such a
massive building. The architect was confident that the inferences from the analogy would help him find a solution allowing him to build a sustainable, self-sufficient architectural complex. The validity of analogy here was deductible from the inspired context (Clement J. J., 2008). This micro crowded living habitat idea gave the architect confidence through analogy appropriateness. To find a solution for the building’s sustainability, Pearce learned from termites and looked mostly at how the principles from these living organisms can be transferred into engineering. The use of the termite mound analogy solution saved the owner of the building more than $3.5 million in energy costs in its first five years (Beatley, 2012); however, this is not an indication that the architect knew exactly that that would be the case when he chose this particular analogy as inspiration for his design.
Indisputably, most of the analogies used in creative problem solving are intuitive, often deeply entangled with the personality and identity of their creator. Some of these analogies may lead to highly-optimised solutions, but we can never demonstrate why and how exactly they were chosen, or if the resulting solutions are the best. The triple role of analogy (providing insights into a problem solution, explanation tools, and informing the design process) in most of creative activities and situations makes it difficult for us to deduct or generalise a validation path.
Another view on the analogy evaluation process is described in a study by Forbus et al. (1997) and was presented at the Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society. This model is rather an extension of Gentner’s structure- mapping theory (1983) that is based on comparing structural correspondences through the mapping of distinct symbolic relationships identified in the source and target. Depending on the nature of overlapping correspondences, the evaluation of mapping provides an estimate of match quality.
The authors claim that their model of analogical inference is the first to match the models of mapping and retrieval (Holyoak & Koh, 1987; Hummel & Holyoak, 2005) at a level of generality. Based on their experimental studies and case-based reasoning examples (Falkenhainer, Forbus, & Gentner, 1986; 1989; Gentner, 1986), they provide evidence of how structural evaluation of analogical inferences can be used to estimate a promising inference by its form and the mapping that generated the analogy (Keane, 1994). In their experiments, they used an MAC/FAC retrieval model (Forbus, Gentner, & Law, 1995) to retrieve the likely needs cases with the highest score support for
optimal advice for the problems that intermediate thermodynamics students faced. Students used a brief description of the problem as an input in the CyclePad application and then, based on that description, the expert mode modified the design and suggested how to fix the problem in “watch me” mode.
They found that CyclePad provided the optimal advice for students in problem solving tasks when they chose analogical inferences generated by the CyclePad application which had the highest scores.
The authors aimed to measure the structural evaluation of candidate inferences in two stages: support and extrapolation. Support would answer the question of how much structural support an analogical inference derives from the mapping that generated it, and extrapolation, consequently, relates to how far an analogical inference goes beyond the support lent by the mapping (Forbus K. D., Gentner, Everett, & Wu, 1997).
Although this model is plausible and contributes to the literature, it turns out that it is domain-specific and that one can rely only on the database of similar problem solving cases from CyclePad or other similar applications. It is also unlikely that the model alone can predict genuine solutions to real-world problems, which are more complex than simple algorithm calculations. Not every possible combination of natural objects mappings and correspondences is equally probable, and even if it were possible for them to be computed in the future, the interpretations of those constructs sometimes differ drastically between the human brain and computer algorithmic output.
An analogical bridging model for analogy evaluation proposed by Clement (2008) includes evidence that experts are capable of imagining and inventing new forms, representations, and new concepts beyond simple algorithms that derive from structural mapping.
The evidence that he provided is based on the case studies of invented representations that have been constructed by participants to find solutions to the given problems. One of the tasks given to participants (Clement J. J., 2008, p. 48) was to solve the Wheel Problem (see A in Figure 3.1): “You are given the task of rolling a heavy wheel up a hill. Does it take more, less, or the same amount of force to roll the wheel when you push at x, rather than at y?” The participants were told to solve the problem “in any way that you can” without any suggestions about any specific problem solving methods or strategies to employ. In this study, seven experts in technical fields participated (advanced doctoral students or professors), three of whom used analogy to find the
solution to the problem. Of the three who used analogy, two used the bridging method. After generating the lever analogy (see B in Figure 3.1) as a potential solution to the wheel problem and having doubts about the result, a participant generated an in- between analogy (see C in Figure 3.1) in the form of a spooked rimless wheel.
Figure 3.1 Bridging analogy for “Wheel Problem” from Clement’s (2008) book
This bridging analogy captures an array of levers at different angles that gave the participant confidence in the validity of the original analogy, and in effect, in the problem solution.
It seems that in order to evaluate an analogous case, one has to generate one or multiple (reported in the same study) intermediary analogies that share features with both the problem and the original analogy, regardless of whether they may be dependent on mapping or discrete symbols or not. Although the author uses close-domain analogy in his studies, the bridging model can be applied to any domain when evaluating an analogy’s relationship between a problem and an analogous case. It is claimed that many of the bridging analogy examples in this study are innovative and creative, and that the analogy is not retrieved from memory or past experiences; however, in his wheel problem case study, Clement used a small pool of participants, with a small range in participants’ educational levels, thus making it difficult to deduct common credible patterns. The model also lacks a satisfying explanation for the usefulness of such transitive analogies. All of these models are creative and useful developments in analogy construction. Our work lies at the cross section of the methods discussed above, as we integrate the theoretical framework with the formal practice-based techniques.
of visual analogies specifically for particular problem solving tasks to sort out how we can construct better and more effective analogies for learning and problem solving.
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