c. Developmental hypotheses of analogical reasoning

The following subsection presents the main hypotheses about the development of analogical reasoning, i.e., the Relational Shift Hypothesis (Gentner & Rattermann, 1991), the Relational Primacy Hypothesis (Goswami, 1991, 1992), and the Relational Complexity Hypothesis (Halford, Wilson, & Phillips, 1998; Halford, 1993).

The Relational Shift Hypothesis

Gentner & Rattermann (1991) introduced the “relational shift” hypothesis about the development of analogical reasoning. According to them, a relational shift occurs during childhood: children first process the similarity between objects and only after a developmental change are they able to process similarity between relations. Several findings by Gentner and other researchers support this hypothesis. Gentner (1988) reported results about the interpretation of metaphors in children. She found that 5-year-olds preferentially interpreted

55 metaphors in terms of featural similarity, whereas adults mainly used relational similarity to express the meaning of metaphors. Nine-year-olds gave in-between explanations, using both relational and object similarity, thus, apparently showing a state of saccade between the two types of focus. Similar findings were obtained by Billow (1975) in 5- to 13-year-olds. In a similar vein, Gentner & Toupin (1985, 1986) showed that children aged 6 were not affected by higher-level relations (i.e., a moral), only by the surface similarity between the objects, when performing a mapping task, whereas 9-year-old children were affected both by surface and higher-order relational similarity. The same effect of surface similarity was found in 5-year-olds in an analogy problem-solving task (Holyoak, Junn, & Billman, 1984). Children were affected by the physical resemblance of the objects to be matched.

However, as mentioned by Richland et al. (2006) and Thibaut et al. (2010a), the reason for this shift remains unclear. Several hypothesis are proposed by Gentner &

Rattermann (1991): a general maturational process such as the one proposed by Piaget et al.

(1977), increase in domain knowledge, or the acquisition of mapping strategies. These different accounts lead to different predictions. The general ability account predicts a general change in cognitive abilities at a certain age. The domain-knowledge account, favored by Gentner and colleagues, predicts differences between the acquisition of the ability to map structures from different domains, depending on the degree of expertise of the child in these domains. The strategy-learning account predicts both differences in the time of the shift between more or less familiar domains, and cross-domain facilitation due to strategy learning.

Note, however, that these three explanations are not mutually exclusive. Whenever the performances of children increase through age, there is still room for improvement in the tasks used to assess reasoning ability. Thus, part of the improvement might be due to better knowledge of conceptual domains, to better strategies, or to domain general cognitive abilities.

Another explanation of this shift was given by Bulloch & Opfer (2009) who argued the relational shift was the effect of the learning of a the difference in the predictive value of superficial similarity versus relational similarity in different contexts through development.

Thus, children's use of relational matches in a generalization task should increase when relational similarity is highly predictive, but should decrease in a domain where superficial similarity is more predictive. The results they observed in a generalization task using offspring (a domain in which relational similarity is more predictive) and prey (in which superficial similarity is more predictive) in 3-, 4-, 5-year-olds, and adults support their

56 interpretation. Three- and 4-year-olds made relational matches more often than 5-year-olds and adults in the context of prey problems, but less than them in the context of offspring. This effect is mainly due to learning over time as 3-year-olds showed the same pattern in a repeated measure setting, when they were given feedback on their answers.

The Relational Primacy Hypothesis

Goswami and her colleagues argued for an inherent capability of even young children and infants to use relational similarity to drive their inferences about the world (Brown, 1990;

Goswami & Brown, 1990a, 1990b; Goswami, 1991, 1992; Vosniadou, 1988). However, even if children are able to reason by analogy early in life, qualitative changes, such as metacognitive processes, occur throughout development. Goswami and Brown (1990b) tested children aged 3, 4 and 6 in a causal A:B::C:? forced-choice task (using, as foils, the same object as C with an incorrect relation, a different object with the correct relation, a mere-appearance match, and a thematic/category match) and assessing their knowledge of the causal relations in a control task. They found that, with age, the knowledge of the causal relations increased, and that the analogical performances increased accordingly. The majority of the errors made were children choosing the correct object, but associated with the wrong relation. This view of analogical reasoning development is supported by children's early ability to solve reasoning problems when surface similarity supports the mapping between the different domains (Chen, Sanchez, & Campbell, 1997; Holyoak et al., 1984), when a proper representation of the problem has been encoded (Brown, Kane, & Echols, 1986), or when the relational similarity between the problems to be compared is highlighted (Brown, Kane, &

Long, 1989; Crisafi & Brown, 1986).

Relational Complexity

The relational complexity theory (Halford et al., 1998) posits that what limits the analogical comparisons that can be made is the relational complexity of the domains to be compared. Relational complexity is defined as the number of dimension relations have at the same time (i.e., the number of arguments a relational predicate takes). For example, reasoning about speed as a function of distance over time involves a ternary relation, where speed, distance and time are three arguments in this relational structure. Thus, what is limited in

57 working memory capacity is the number of arguments feeding a relation which can be handled at the same time, called the arity of a relation. Complex concepts often involve more than four dimensions. To deal with these concepts, one has two possibilities: chunking several dimensions into a single one (but the detailed relations within the structures chunked cannot be accessed) or segmenting the concepts into several sub-concepts involving lower dimension relations. Thus the effective complexity is the lowest dimensionality allowed by chunking and segmentation that has to be processed without loss of information. The relational complexity that can be handled increases through development: unary relations can be processed by one year of age, binary relation by two (only binary relations have to be handled in proportional, A:B::C:? problems), ternary relations by five, and quaternary relations by 11.

The relational complexity theory is supported by several findings. First, children display an early competence (before the age of 5) in the classical A:B::C:? task when appropriate material and experiment procedure are used (Goswami & Brown, 1990a; Singer-Freeman, 2005). Nevertheless, when the relational complexity is increased above the threshold of binary relations, young children have lower performances (Doumas, Morrison, &

Richland, 2009; Hosenfeld, van der Maas, & van den Boom, 1997a, 1997b; Richland et al., 2006). Performance is far from perfect when only binary relations are used in such tasks at early stages of development, which suggest that other factors than the clarity of the relations used play a role in the development of analogy making, such as the executive component of working memory (Richland et al., 2006; Thibaut, French, & Vezneva, 2010a, 2010b, see subsection IV.b. for a description), and knowledge accretion (Brown, 1990; Goswami &

Brown, 1990b).

Conclusion

These different hypotheses focus on different factors in analogical reasoning development, but are not strictly mutually exclusive. It is even likely that knowledge accretion, metacognitive aspects, working memory capacity and its executive component play distinct roles in the development of analogical reasoning. These different factors might even interact as it is suggested, for instance, by current views of executive functions as being dependent on their substrate, i.e., the representations they operate on (Chevalier, 2010). Thus further work should aim at investigating these interactions in the development of analogical reasoning.

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