Analogical reasoning is a common reasoning tool for learning and problem-solving. Existing research has extensively studied children’s reasoning when comparing, or choosing from ready-made analogies. Relatively less is known about how children come up with analogies in authentic learning environments. Design education provides a suitable context to investigate how children generate analogies for creative learning purposes. Meanwhile, the frequent use of visual analogies in design provides an additional opportunity to understand the role of spatial reasoning in design-by-analogy. Spatial reasoning is one of the most studied human cognitive factors and is critical to the learning of science, technology, engineering, arts, and mathematics (STEAM). There is growing interest in exploring the interplay between analogical reasoning and spatial reasoning. In this talk, I will share qualitative findings from a case study, where a class of 11-to-12-year-olds in the Netherlands participated in a biomimicry design project. These findings illustrate (1) practical ways to support children’s analogical reasoning in the ideation process and (2) the potential role of spatial reasoning as seen in children mapping form-function relationships in nature analogically and adaptively to those in human designs.

Metaphor is a pervasive phenomenon in language and cognition. To date, the vast majority of psycholinguistic research on metaphor has focused on noun-noun metaphors of the form An X is a Y (e.g., My job is a jail). Yet there is evidence that verb metaphor (e.g., I sailed through my exams) is more common. Despite this, comparatively little work has examined how verb metaphors are processed. In this talk, I will propose a novel account for verb metaphor comprehension: verb metaphors are understood in the same way that analogies are—as comparisons processed via structure-mapping. I will discuss the predictions that arise from applying the analogical framework to verb metaphor and present a series of experiments showing that verb metaphoric extension is consistent with those predictions.

In cognitive development, learning more than the input provides is a central challenge. This challenge is especially evident in learning the meaning of numbers. Integers – and the quantities they denote – are potentially infinite, as are the fractional values between every integer. Yet children’s experiences of numbers are necessarily finite. Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input. However, retrieving proper analogy requires cognitive supports. In this talk, I seek to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning. To examine these hypotheses, I will present a series of educational intervention studies with third-to-fifth graders. Results showed that a short, unsupervised intervention of spatial alignment between integers and fractions on number lines produced broad and durable gains in fractional magnitudes. Additionally, training on conceptual knowledge of fractions – that fractions denote magnitude and can be placed on number lines – facilitates explicit analogical reasoning. Together, these studies indicate that analogies can play an important role in rational number learning with the help of number lines as schemas. These studies shed light on helpful practices in STEM education curricula and instructions.

In this presentation, we will discuss adaptations of historical examples of mathematical research to bring out some of the intuitive judgments that accompany the working practice of mathematicians when reasoning by analogy. The main epistemological claim that we will aim to illustrate is that a central part of mathematical training consists in developing a quasi-perceptual capacity to distinguish superficial from deep analogies. We think of this capacity as an instance of Hadamard’s (1954) discriminating faculty of the mathematical mind, whereby one is led to distinguish between mere “hookings” (77) and “relay-results” (80): on the one hand, suggestions or ‘hints’, useful to raise questions but not to back up conjectures; on the other, more significant discoveries, which can be used as an evidentiary source in further mathematical inquiry. In the second part of the presentation, we will present some recent applications of this epistemological framework to mathematics education projects for middle and high schools in Italy.

Dominant theories of analogical thinking postulate that making an analogy consists in discovering that two superficially different situations share isomorphic systems of similar relations. According to this perspective, the comparison between the two situations may eventually lead to the construction of a schema, which retains the structural aspects they share and deletes their specific contents. We have developed a new approach to analogical thinking, whose purpose is to explain a particular type of analogies: those in which the analogs are exemplars of a schema-governed category (e.g., two instances of robbery). As compared to standard analogies, these comparisons are noteworthy in that a well-established schema (the schema-governed category) mediates each one of the subprocesses involved in analogical thinking. We argue that the category assignment approach is able to provide a better account of how the analogical subprocesses of retrieval, mapping, re-representation, evaluation and inference generation are carried out during the processing of this specific kind of analogies. The arguments presented are accompanied by brief descriptions of some of the studies that provided support for this approach.

Analogical reasoning –learning about new things by relating it to previous knowledge– lies at the heart of human intelligence and creativity and forms the core of educational practice. Children start creating and using analogies early on, making incredible progress moving from associative processes to successful analogical reasoning. For example, if we ask a four-year-old “Horse belongs to stable like chicken belongs to …?” they may use association and reply “egg”, whereas older children will likely give the intended relational response “chicken coop” (or other term to refer to a chicken’s home). Interestingly, despite state-of-the-art AI-language models having superhuman encyclopedic knowledge and superior memory and computational power, our pilot studies show that these large language models often make mistakes providing associative rather than relational responses to verbal analogies. For example, when we asked four- to eight-year-olds to solve the analogy “body is to feet as tree is to …?” they responded “roots” without hesitation, but large language models tend to provide more associative responses such as “leaves”. In this study we examine the similarities and differences between children's and six large language models' (Dutch/multilingual models: RobBERT, BERT-je, M-BERT, GPT-2, M-GPT, Word2Vec and Fasttext) responses to verbal analogies extracted from an online adaptive learning environment, where >14,000 7-12 year-olds from the Netherlands solved 20 or more items from a database of 900 Dutch language verbal analogies.

Analogies between old and new concepts are common during classroom instruction. While previous studies of transfer focus on how features of initial learning guide later transfer to new problem solving, less is known about how to best support analogical transfer from previous learning while children are engaged in new learning episodes. Such research may have important implications for teaching and learning in mathematics, which often includes analogies between old and new information. Some existing research promotes supporting learners' explicit connections across old and new information within an analogy. In this talk, I will present evidence that instructors can invite implicit analogical reasoning through warm-up activities designed to activate relevant prior knowledge. Warm-up activities "close the transfer space" between old and new learning without additional direct instruction.

Space is the universal donor for relations" (Gentner, 2014). This quote is the foundation of my talk. I will explore how and why visual representations and analogies are related, and why. I will also explore how considering the relation between analogy and spatial reasoning can shed light on why and how spatial thinking is correlated with learning in STEM fields. For example, I will consider children’s numbers sense and learning of the number line from the perspective of analogical reasoning.

Previous experiments have shown that a comparison of two written narratives highlights their shared relational structure, which in turn facilitates the retrieval of analogous narratives from the past (e.g., Gentner, Loewenstein, Thompson, & Forbus, 2009). However, analogical retrieval occurs across domains that appear more conceptually distant than merely different narratives, and the deepest analogies use matches in higher-order relational structure. The present study investigated whether comparison can facilitate analogical retrieval of higher-order relations across written narratives and abstract symbolic problems. Participants read stories which became retrieval targets after a delay, cued by either analogous stories or letter-strings. In Experiment 1 we replicated Gentner et al. who used narrative retrieval cues, and also found preliminary evidence for retrieval between narrative and symbolic domains. In Experiment 2 we found clear evidence that a comparison of analogous letter-string problems facilitated the retrieval of source stories with analogous higher-order relations. Experiment 3 replicated the retrieval results of Experiment 2 but with a longer delay between encoding and recall, and a greater number of distractor source stories. These experiments offer support for the schema induction account of analogical retrieval (Gentner et al., 2009) and show that the schemas abstracted from comparison of narratives can be transferred to non-semantic symbolic domains.

How and why are analogies spontaneously generated? Despite the prominence of analogy in learning and reasoning, there is little research on whether and how analogy is spontaneously generated in everyday settings. Here we fill this gap by gathering parents' answers to children's real questions, and examining analogy use in parental explanations. Study 1 found that parents used analogy spontaneously in their explanations, despite no prompt nor mention of analogy in the instruction. Study 2 found that these analogical explanations were rated highly by parents, schoolteachers, and university students alike. In Study 3, six-year-olds also rated good analogical explanations highly, but unlike their parents, did not rate them higher than causal, non-analogical explanations. We discuss what makes an analogy a good explanation, and how theories from both explanation and analogy research explain one’s motivation for spontaneously generating analogies.

Engineering designers practice design-by-analogy (DbA) during concept generation to retrieve knowledge from external sources or memory as inspiration to solve design problems. DbA is a tool for innovation that involves retrieving analogies from a source domain and transferring the knowledge to a target domain. While DbA produces innovative results, designers often come up with analogies by themselves or through serendipitous, random encounters. Computational support systems for searching analogies have been developed to facilitate DbA in systematic design practice. However, many systems have focused on a query-based approach, in which a designer inputs a keyword or a query function and is returned a set of algorithmically determined stimuli. In this presentation, a new analogical retrieval process that leverages a visual interaction technique is introduced. It enables designers to explore a space of analogies, rather than be constrained by what’s retrieved by a query-based algorithm. With an exploration-based DbA tool, designers have the potential to uncover more useful and unexpected inspiration for innovative design solutions.

Prior studies of A:B::C:D verbal analogies have identified several factors that affect performance, including the semantic similarity between source and target domains (semantic distance), the semantic association between the C-term and incorrect answers (distracter salience), and the type of relations between word pairs (e.g., categorical, compositional, and causal). However, it is unclear how these stimulus properties affect performance when utilized together. Moreover, how do these item factors interact with individual differences such as crystallized intelligence and creative thinking? Several studies reveal interactions among these item and individual difference factors impacting verbal analogy performance. For example, a three-way interaction demonstrated that the effects of semantic distance and distracter salience had a greater impact on performance for compositional and causal relations than for categorical ones (Jones, Kmiecik, Irwin, & Morrison, 2022). Implications for analogy theories and future directions are discussed.

Extensive research on science teaching has shown the effectiveness of analogies as a didactic tool which, when appropriately and effectively used, facilitates the learning process of abstract concepts. This seminar does not contradict the efficacy of such a didactic use of analogies in this seminar but switches attention and interest on their heuristic use in approaching and understanding of what previously unknown. Such a use of analogies derives from research with 10 to 17 year-olds, who, when asked to make predictions in novel situations and to then provide explanations about these predictions, they self-generated analogies and used them by reasoning on their basis. This heuristic use of analogies can be used in science teaching in revealing how students approach situations they have not considered before as well as the sources they draw upon in doing so.

Individuals vary widely in how they categorize novel phenomena. This individual variation has led canonical theories in cognitive and social science to suggest that communication in large social networks leads populations to construct divergent category systems. Yet, anthropological data indicates that large, independent societies consistently arrive at similar categories across a range of topics. How is it possible for diverse populations, consisting of individuals with significant variation in how they view the world, to independently construct similar categories? Through a series of online experiments, I show how large communication networks within cultures can promote the formation of similar categories across cultures. For this investigation, I designed an online “Grouping Game” to observe how people construct categories in both small and large populations when tasked with grouping together the same novel and ambiguous images. I replicated this design for English-speaking subjects in the U.S. and Mandarin-speaking subjects in China. In both cultures, solitary individuals and small social groups produced highly divergent category systems. Yet, large social groups separately and consistently arrived at highly similar categories both within and across cultures. These findings are accurately predicted by a simple mathematical model of critical mass dynamics. Altogether, I show how large communication networks can filter lexical diversity among individuals to produce replicable society-level patterns, yielding unexpected implications for cultural evolution. In particular, I discuss how participants in both cultures readily harnessed analogies when categorizing novel stimuli, and I examine the role of communication networks in promoting cross-cultural similarities in analogy-making as the key engine of category formation.

Building conceptual abstractions from sensory information and then reasoning about them is central to human intelligence. Abstract reasoning both relies on, and is facilitated by, our ability to make analogies about concepts from known domains to novel domains. Structure Mapping Theory of human analogical reasoning posits that analogical mappings rely on (higher-order) relations and not on the sensory content of the domain. This enables humans to reason systematically about novel domains, a problem with which machine learning (ML) models tend to struggle. We introduce a two-stage neural net framework, which we label Neural Structure Mapping (NSM), to learn visual analogies from Raven's Progressive Matrices, an abstract visual reasoning test of fluid intelligence. Our framework uses (1) a multi-task visual relationship encoder to extract constituent concepts from raw visual input in the source domain, and (2) a neural module net analogy inference engine to reason compositionally about the inferred relation in the target domain. Our NSM approach (a) isolates the relational structure from the source domain with high accuracy, and (b) successfully utilizes this structure for analogical reasoning in the target domain.

Affectively charged analogies are commonly used in literature and art, but also in politics and argumentation. There are reasons to think we may process these analogies differently. Notably, analogical reasoning is a complex process that requires the use of cognitive resources, which are limited. In the presence of affectively charged content, some of these resources might be directed towards affective processing and away from analogical reasoning. To investigate this idea, I investigated effects of affective charge on differences in brain activity evoked by sound versus unsound analogies. The presentation will detail the methods and results for two such experiments, one in which participants saw analogies formed of neutral and negative words and one in which they were created by combining conditioned symbols. I will also briefly discuss future research aiming to investigate the effects of analogical reasoning on brain activity related to affective processing.

Social learning and analogical reasoning both provide exponential opportunities for learning. These skills have largely been studied independently, but my future research asks how combining skills across previously independent domains could add up to more than the sum of their parts. Analogical reasoning allows individuals to transfer learning between contexts and opens up infinite opportunities for innovation and knowledge creation. Its origins and development, so far, have largely been studied in purely cognitive domains. Constraining analogical development to non-social domains may mistakenly lead researchers to overlook its early roots and limit ideas about its potential scope. Building a bridge between social learning and analogy could facilitate identification of the origins of analogical reasoning and broaden its far-reaching potential. In this talk, I propose that the early emergence of social learning, its saliency, and its meaningful context for young children provides a springboard for learning. In addition to providing a strong foundation for early analogical reasoning, the social domain provides an avenue for scaling up analogies in order to learn to learn from others via increasingly complex and broad routes.

Although analogical reasoning has been assumed to involve insight and its associated “aha!” experience, the relationship between these phenomena has never been directly probed empirically. In this study we investigated the relationship between representational change and the “aha!” experience during analogical reasoning. A novel set of verbal analogy stimuli were developed for use as an insight task. Across two experiments, participants reported significantly stronger aha moments and showed greater evidence of representational change on trials with more semantically distant analogies. Further, the strength of reported aha moments was correlated with the degree to which participants’ descriptions of the analogies changed over the course of each trial. Lastly, we probed the individual differences associated with a tendency to report stronger "aha" experiences, particularly related to mood, curiosity, and reward responsiveness. The findings shed light on the affective components of analogical reasoning and suggest that measuring affective responses during such tasks may elucidate novel insights into the mechanisms of creative analogical reasoning.

Analogies are widely used by teachers and coaches of different movement disciplines, serving a role during the learning phase of a new skill, and honing one’s performance to a competitive level. In previous studies, analogies improved motor control in various tasks and across age groups. Our study aimed to evaluate the efficacy of analogies throughout the learning process, using kinematic measures for an in-depth analysis. We tested whether applying analogies can shorten the motor learning process and induce insight and skill improvement in tasks that usually demand many hours of practice. The experiment included a drawing task, in which subjects were asked to connect four dots into a closed shape, and a mirror game, in which subjects tracked an oval that moved across the screen. After establishing a baseline, subjects were given an analogy, explicit instructions, or no further instruction. We compared their improvement in overall skill, accuracy, and speed. Subjects in the analogy and explicit groups improved their performance in the drawing task, while significant differences were found in the mirror game only for slow movements between analogy and controls. In conclusion, analogies are an important tool for teachers and coaches, and more research is needed to understand how to apply them for maximum results. They can rapidly change motor control and strategy but may also affect only some aspects of a movement and not others. Careful thought is needed to construct an effective analogy that encompasses relevant movement facets, as well as the practitioner’s personal background and experience.

Humans can adapt to a novel task on our first try. By contrast, artificial intelligence systems often require immense amounts of data to adapt. In this talk, I will discuss my recent work (https://www.pnas.org/content/117/52/32970) on creating deep learning systems that can adapt on their first try by exploiting relationships between tasks. Specifically, the approach is based on transforming a representation for a known task to produce a representation for the novel task, by inferring and then using a higher order function that captures a relationship between the tasks. This approach can be interpreted as a type of analogical reasoning. I will show that task transformation can allow systems to adapt to novel tasks on their first try in domains ranging from card games, to mathematical objects, to image classification and reinforcement learning. I will discuss the analogical interpretation of this approach, an analogy between levels of abstraction within the model architecture that I refer to as homoiconicity, and what this work might suggest about using deep-learning models to infer analogies more generally.

In this talk, I will present the results of two recent systematic reviews and meta-analyses related to analogical reasoning and metaphor processing in autism, together with the results of a study that investigated verbal analogical reasoning and metaphor processing in the same sample of participants. Both metaphors and analogies rely on exploiting similarities, and they necessitate contextual processing. Nevertheless, our findings relating to metaphor processing and analogical reasoning showed distinct patterns. Whereas analogical reasoning emerged as a relative strength in autism, metaphor processing was found to be a relative weakness. Additionally, both meta-analytic studies investigated the relations between the level of intelligence of participants included in the studies, and the effect size of group differences between the autistic and typically developing (TD) samples. These analyses suggested in the case of analogical reasoning that the relative advantage of ASD participants might only be present in the case of individuals with lower levels of intelligence. By contrast, impairments in metaphor processing appeared to be more pronounced in the case of individuals with relatively lower levels of (verbal) intelligence. In our experimental study, we administered both verbal analogies and metaphors to the same sample of high-functioning autistic participants and TD controls. The two groups were matched on age, verbal IQ, working memory and educational background. Our aim was to understand better the similarities and differences between processing analogies and metaphors, and to see whether the advantage in analogical reasoning and disadvantage in metaphor processing is universal in autism.

Analogies, broadly defined, map novel concepts onto familiar concepts, making them essential for perception, reasoning, and communication. We argue that analogy-building served a critical role in the evolution of cumulative culture, by allowing humans to learn and transmit complex behavioural sequences that would otherwise be too cognitively demanding or opaque to acquire. The emergence of a protolanguage consisting of simple labels would have provided early humans with the cognitive tools to build explicit analogies and to communicate them to others. This focus on analogy-building can shed new light on the coevolution of cognition and culture, and addresses recent calls for better integration of the field of cultural evolution with cognitive science. This talk will address what cumulative cultural evolution is, how we define analogy-building, how analogy-building applies to cumulative cultural evolution, how analogy-building fits into language evolution, and the implications of analogy-building for causal understanding and cognitive evolution.

It is generally acknowledged that analogy is a core mechanism of human cognition, but paradoxically, analogies based on structural similarities would rarely be implemented spontaneously (e.g. without an explicit invitation to compare two representations). The scarcity of deep spontaneous analogies is at odds with the demonstration that familiar concepts from our daily-life are spontaneously used to encode the structure of our experiences. Based on this idea, we will present experimental works highlighting the predominant role of structural similarities in analogical retrieval. The educational stakes lurking behind the tendency to encode the problem’s structures through familiar concepts will also be addressed.

Research on analogical processing and reasoning has provided strong evidence that the use of adequate educational analogies has strong and positive effects on the learning of mathematics. In this talk I will show some experimental results suggesting that analogies based on spatial representations might be particularly effective to improve mathematics learning. Since fostering mathematics learning also involves addressing psychosocial factors such as the development of mathematical anxiety, providing social incentives to learn, and fostering engagement and motivation, I will argue that one area to explore with great potential to improve math learning is applying analogical research in the development of learning games aimed to improve math learning. Finally, I will show some early prototypes of an educational project devoted to developing games designed to foster the learning of early mathematics in kindergarten children.

Learning by analogy is a powerful tool children’s developmental repertoire, as well as in educational contexts such as mathematics, where the key knowledge base involves building flexible schemas. However, noticing and learning from analogies develops over time and is cognitively resource intensive. I review studies that provide insight into the relationship between mechanisms driving children’s developing analogy skills, highlighting environmental inputs (parent talk and prior experiences priming attention to relations) and neuro-cognitive factors (Executive Functions and brain injury). I then note implications for mathematics learning, reviewing experimental findings that show analogy can improve learning, but also that both individual differences in EFs and environmental factors that reduce available EFs such as performance pressure can predict student learning.

In 1955, John McCarthy and colleagues proposed an AI summer research project with the following aim: “An attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves.” More than six decades later, all of these research topics remain open and actively investigated in the AI community. While AI has made dramatic progress over the last decade in areas such as vision, natural language processing, and robotics, current AI systems still almost entirely lack the ability to form humanlike concepts and abstractions. Some cognitive scientists have proposed that analogy-making is a central mechanism for conceptual abstraction and understanding in humans. Douglas Hofstadter called analogy-making “the core of cognition”, and Hofstadter and co-author Emmanuel Sander noted, “Without concepts there can be no thought, and without analogies there can be no concepts.” In this talk I will reflect on the role played by analogy-making at all levels of intelligence, and on prospects for developing AI systems with humanlike abilities for abstraction and analogy.