a. Intrinsic features of the domains compared

In this subsection we review the literature on analogical reasoning and its development, with a special focus on the features of the domains compared which affect analogical reasoning. These factors are mainly surface features of the domains compared, like their concreteness (i.e., the amount of information irrelevant to the task they bring), the saliency of the relational structure, the depth of the relational structure of the domains in itself, and the distinctiveness of the goal object from the rest of the domain, as well as the surface and structural similarity of the two domains compared. For the factors which were tested both in adults and children, it seems that they affect their ability to reason by analogy similarly, but at different degrees.

Surface features of the materials compared

The properties of the domains which are used is an unavoidable source of variations in adults' reasoning, as the saliency of certain features of these domains will attract the attention of the subject, when other will not retain his attention, and generally will bias the representation of the domains in some configurations. These biases can be congruent with

59 what is important for the solution of the problem, or not, which will lead to facilitation or difficulties to solve the problem.

Mature reasoning

A clue of the effect of surface features of the domains compared on transfer were obtained by Didierjean & Nogry (2004) by manipulating the difficulty of the solution of a source problem by varying its presentation and observing how participants were affected in their transfer of this solution to an analogous target problem. The authors showed that varying the difficulty to solve the source problem by making the structure of these elements more or less salient (i.e., present both in the diagram given and the verbal explanation, or only in the diagram) impacted the way participants encoded the source: simple source problems (i.e., when the relational structure was obvious) were encoded more shallowly and resulted in poorer transfer, when more difficult ones (i.e., with less salient structural features) were encoded in depth, resulting in more transfer of these abstract principles to the target problems.

Another surface factor affecting analogical reasoning is the concreteness of the elements composing the domains which are compared. Kaminski, Sloutsky, & Heckler (2013) defined concreteness as the quantity of information brought by a specific instance of a concept. Using this metric, they showed that the less concrete the instances analogically compared are (i.e., the less superfluous information they convey), the more transfer the participants do. However, when helped in the alignment of the two domains, the difference between concrete and generic (i.e., not concrete) instances vanishes. This was interpreted by the authors as concreteness affecting mapping: the concreteness (i.e., the amount of information brought by the material) is an obstacle in the alignment of the two domains, the non-alignable extraneous information masking the similarity between the structures of the two domains.

The systematicity (i.e., the fact that first-order relations are connected or not by higher-order relations) of the source domain also guides the analogical matches that are drawn by participants. Clement & Gentner's (1991) results show that participants rated more similar two analogous facts that were part of stories that had higher degrees of structural similarity than stories that were only similar in the fact that had to be compared (see materials in Figure 1). Similarly, participants were more prone to infer facts in the target domain that were parts

60 of more global structures than isolated facts at the level of structural consistency between the two domains. Thus, the embedding of a fact in a relational structure influences both analogical judgments and inference.

Figure 1: Materials used by Clement & Gentner (1991)

These different studies show the effect of surface features is present at different levels in adult analogical reasoning. It can influence encoding, mapping and transfer.

Reasoning development

Children are also affected by the perceptual features of the material used to assess analogical abilities. Rattermann & Gentner (1998a, Experiment 1) used visually rich (i.e., concrete, as defined by Kaminski et al., 2013) or sparse (i.e., generic) objects in a triad mapping task (see Figure 2) using size as the relational frameworks in the domains to be compared. Three-, 4- and 5-year-olds were tested in this task and performed better in the

61 sparse than in the rich condition. This suggests that concreteness (as defined by Kaminski et al. (2013), see above) also affects children's performance.

Figure 2: Materials from Rattermann & Gentner 1998a

A related study by Paik & Mix (2006) explored the effect of the distinctiveness between the objects to be matched with the other objects of the domains compared on 3- and 4-year-olds. Making the solution and the matching object in the source more distinctive from the other objects in their respective domains made children have better performances in a simple mapping task, but had the opposite effect in a cross-mapping task (when similar objects have different roles in the two domains). Vasilyeva & Bowers (2006) also have data that could be explained by the distinctiveness of the elements to be matched. They gave 3- to 6-year-olds a spatial mapping task using isosceles triangles as maps. They found that children were better able to find the target object on the basis of the map indication when it was the distinctive angle that was used to hide it than when it was one of the two identical angles.

Taken together, these results about surface features of the domains compared suggest that adults as well as children are affected in their ability to perform a mapping between two domains by the intrinsic visual characteristics of the objects constituting them: the amount of information given by the scene, but also the similarity within the domain and how easily the relational structure is inferred from the visual characteristics of the objects.

62 Similarity between sources and targets

We saw that the intrinsic features of the materials within domains affect analogical reasoning in both children and adults. However another kind of features, the similarity between the domains, also impacts the way people compare different domains.

Mature reasoning

The spontaneous retrieval of a source in long term memory, despite its everyday usefulness, is a notoriously difficult task (Gick & Holyoak, 1980, 1983), and is also affected by several low level factors, like surface and structural similarity between the two analogs.

Holyoak & Koh (1987, Experiment 2) presented different analogical sources, varying either the structural (i.e., the constraints on the application of a solution to the problem) or the surface (i.e., the resemblance of the apparatus used to solve the problem) similarity, or both structural and surface similarity between the source and the target domains, but all sharing the same solution to the problem. They observed higher rates of correct, spontaneous application of the previously seen solution to a new, analogous problem in the condition where the to-be-retrieved source was similar both on the structural and surface dimensions. A decrease in similarity on either or both of these dimensions impaired participants spontaneous retrieval.

This suggests that retrieval is dependent on both these similarity properties. Similar evidence comes from Gentner & Landers (1985). They designed a set of scenarios similar to the targets either in their first-order relations, or in both their first-order relations and their surface properties, or in both their first-order and their higher-order relations. Participants reminded more source stories that shared surface similarity in addition to analogous first-order relations, and to a lower extent stories that shared both first- and higher-order relations, than stories only similar in their first-order relation. Wharton et al. (1994) also showed that retrieval was affected by structural similarity when a competition arose between different potential analogs sharing either surface or structural similarity with the current story. However, although surface similarity can be helpful for accessing a previously encountered analog (Gentner &

Landers, 1985; Holyoak & Koh, 1987), it can also be detrimental, as shown by Ross (1987, 1989). He showed that using source and target domains with same objects in different roles impaired participants' ability to retrieve a previously seen example to solve the current problem.

63 Both structural and surface similarities affect the mapping of one domain on the other, even if there are dissimilarities in their effects. Holyoak & Koh (1987) showed that in addition to affecting the retrieval of the source, structural similarity had an impact on the ability to draw an analogy (i.e., to transfer an already seen solution to a new problem after being given a hint to use the source story as an analog of the problem at hand). However, the surface similarity did not seem to have any effect on the use of the source after being given this hint. Nevertheless, Ross (1987, 1989) showed that surface similarity can be detrimental not only on the retrieval of a source (as presented above) but also on the use of the source, when it is pitted against structural similarity (i.e., when elements are similar in the source and target domains but do not play the same role, referred to as cross-mapping in the remainder of this dissertation).

Gentner, Rattermann, & Forbus (1993) also showed that surface similarity had differential effects on retrieval and analogical inference in adults. Participants were asked to retrieve previously encountered stories from a large set, using target stories, and to judge how much the inferences from one story of the set could be inferred analogically in another story of the set. They rated higher the inferential power of structurally similar than superficially similar stories, but retrieval was more linked to surface than structural similarity, which led the authors to conclude to a dissociation between the information that is used to retrieve analogs in long term memory and the information that is used to reason by analogy and to infer information in a new domain from another one.

From a wider perspective, the retrieval of a source analog is also altered by the similarity between the contexts of exploration of the source and target analogs. Spencer &

Weisberg (1986) showed that the change of experimenter between the presentation of the source and the target analogs decreased the spontaneous retrieval of the source's solution for the solution of the target problem.

Hence, both structural and surface similarity between the domains compared have consequences on adults' analogical reasoning, but affect different processes: surface and contextual similarity seem to have a greater impact on retrieval than on mapping and transfer, which is the reverse of the effect of structural similarity. Differential effects of the two kinds of similarity are also observed depending on the fact that this similarity supports the relational alignment between the two domains or if it is pitted against this alignment on a relational basis.

64 Reasoning development

Children's analogical reasoning is also influenced by superficial and structural similarity between the source and the target domains. Holyoak, Junn, & Billman (1984) used a problem solving task, known as the Genie problem. In this task, they have to transfer the solution used by the genie to solve a similar problem themselves. Changing the source story in its surface similarity (adding a new character) or in the primary goal the genie was pursuing lessened dramatically the number of transfers of 6-year-olds when compared to a control group using higher surface and structural similarity.

Similar findings were obtained by Gentner & Toupin (1985, 1986). They asked 4-6- and 8-10-year-olds first to act out stories with toy dolls and then to act them out a second time with different characters. They varied the systematicity of the stories by adding or not a moral to them. The superficial similarity was also manipulated as the children had to act out the stories with different toy dolls the second time, these toy dolls having high superficial similarity and same roles, no superficial similarity, or high superficial similarity but different roles (referred as cross-mapping). Performances of the younger children were generally lower than those of the older group. Both ages were negatively affected by the decrease of superficial similarity, and even more dramatically by the cross-mapping condition in both high and low systematicity conditions. However, a difference between the two systematicity conditions appeared only in the low superficial similarity and cross-mapping conditions in older children, suggesting a developmental trend toward the use of systematicity in analogical reasoning and that it helped them overcome the most difficult mapping condition (i.e., cross-mapping). Kotovsky & Gentner (1996, Experiment 1) found converging evidence using a mapping task between triads of geometrical forms varying on the dimension of the relational structure (e.g., size, color) and the polarity of the relation (e.g., a big-small-big pattern in the source corresponding to a big-small-big pattern in the target [same polarity], or to a small-big-small pattern [different polarity]). They found main effects of both these kinds of similarity and that the ability to handle more superficially dissimilar materials developed between 4 and 8 years of age. Convergent findings come from another study by Chen (1996) which explored surface and structural similarities. Chen also manipulated procedural similarity of the implementation of the solutions (adding water or combining different items with the same goal) and surface similarity in the source and target (Chen, 1996; Experiment 2) and found a

65 significant effect of this kind of similarity on 5-to-8-year-olds, with higher similarity supporting mapping between elements to be matched.

Thus, what might negatively affect very young children's ability to transfer a solution from one problem to another might be their inability to notice this similarity between the structures of the two problems. Crisafi & Brown (1986; Experiment 2 & 3) explored this issue in 2-3-year-olds. Children who were given hints that the two problems were the same outperformed those who did not have any explicit clue of the two problem's similarity from the experimenter. This finding was reliable, even in highly superficially dissimilar problems.

Daehler & Chen (1993) further explored which similarity aspects were determinant in children's use of a source to solve a target problem. They varied the similarity between the source and the target in several ways: resemblance between the main characters of the stories, the main themes, or the goal objects, and tested 5- and 7-year-olds. The younger group's transfer rate and reaction time were mainly affected by the goal object similarity and marginally by the theme similarity between the two domains. The older group was not affected by the manipulations of these types of similarities. Thus, goal object similarity seems to be crucial in young children’s ability to solve problems by analogy.

The effect of similarity between the source and target domains is one of the most reliable finding in the analogical reasoning literature. This similarity can be helpful, especially when testing very young children, when it supports the matching between the objects and relations in the domains compared. However, it is detrimental when this similarity leads to inconsistent mapping (e.g., in the cross-mapping task).

IV.b. Features of the mental representations and the influence of the