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 human and non-human animals, conceptual knowledge is partially organized according to low-dimensional geometries that rely on brain structures and computations involved in spatial representations. Recently, two separate lines of research have investigated cognitive maps, that are associated with the hippocampal formation and are similar to world-centered representations of the environment, and image spaces, that are associated with the parietal cortex and are similar to self-centered spatial relationships. I will suggest that cognitive maps and image spaces may be two manifestations of a more general propensity of the mind to create low-dimensional internal models, and may play a role in analogical reasoning and metaphorical thinking. Finally, I will show some data suggesting that the metaphorical relationship between colors and emotions can be accounted for by the structural alignment of low-dimensional conceptual spaces.

Initial social perceptions are often thought to reflect direct “read outs” of facial features. Instead, we outline a perspective whereby initial perceptions emerge from an automatic yet gradual process of negotiation between the perceptual cues inherent to a person (e.g., facial cues) and top-down social cognitive processes harbored within perceivers. This perspective argues that perceivers’ social-conceptual knowledge in particular can have a fundamental structuring role in perceptions, and thus how we think about social groups, emotions, or personality traits helps determine how we visually perceive them in other people. Integrative evidence from real-time behavioral paradigms (e.g., mouse-tracking), multivariate fMRI, and computational modeling will be discussed. Together, this work shows that the way we use facial cues to categorize other people into social groups (e.g., gender, race), perceive their emotion (e.g., anger), or infer their personality (e.g., trustworthiness) are all fundamentally shaped by prior social-conceptual knowledge and stereotypical assumptions. We find that these top-down impacts on initial perceptions are driven by the interplay of higher-order prefrontal regions involved in top-down predictions and lower-level fusiform regions involved in face processing. We argue that the perception of social categories, emotions, and traits from faces can all be conceived as resulting from an integrated system relying on domain-general cognitive properties. In this system, both visual and social cognitive processes are in a close exchange, and initial social perceptions emerge in part out of the structure of social-conceptual knowledge.

Analogical reasoning is a complex ‘high-level’ cognitive process characterised by making inferences based on analogical comparisons. As with other high-level processes, development takes place over a protracted time period and believed to result from changes in multiple ‘lower-level’ systems. In the case of analogical reasoning, changes in systems responsible for conceptual knowledge, task knowledge, inhibition, and working memory have all been causally implicated in development. Whilst there is evidence that each of these systems contributes to development, what the relative contribution of each across development is, and how they interact with each, remain largely unanswered questions. In this presentation, I will describe how cross-sectional trajectory analysis can be used as a complementary method to shed light on these questions.