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Language can affect cognition, but through what mechanism? Substantial past research has focused on how labeling can elicit categorical representation during online processing. We focus here on a particularly powerful type of language—relational language—and show that relational language can enhance relational representation in children through an embodied attention mechanism. Four-year-old children were given a color-location conjunction task, in which they were asked to encode a two-color square, split either vertically or horizontally (e.g., red on the left, blue on the right), and later recall the same configuration from its mirror reflection. During the encoding phase, children in the experimental condition heard relational language (e.g., “Red is on the left of blue”), while those in the control condition heard generic non-relational language (e.g., “Look at this one, look at it closely”). At recall, children in the experimental condition were more successful at choosing the correct relational representation between the two colors compared to the control group. Moreover, they exhibited different attention patterns as predicted by the attention shift account of relational representation (Franconeri et al., 2012). To test the sustained effect of language and the role of attention, during the second half of the study, the experimental condition was given generic non-relational language. There was a sustained advantage in the experimental condition for both behavioral accuracies and signature attention patterns. Overall, our findings suggest that relational language enhances relational representation by guiding learners’ attention, and this facilitative effect persists over time even in the absence of language. Implications for the mechanism of how relational language can enhance the learning of relational systems (e.g., mathematics, spatial cognition) by guiding attention will be discussed. 

Very few questions have cast such an enduring effect in cognitive science as the question of “symbol-grounding”: Do human-invented symbol systems have to be grounded to physical objects to gain meanings? This question has strongly influenced research and practice in education involving the use of physical models and manipulatives. However, the evidence on the effectiveness of physical models is mixed. We suggest that rethinking physical models in terms of analogies, rather than groundings, offers useful insights. Three experiments with 4- to 6-year-old children showed that they can learn about how written multi-digit numbers are named and how they are used to represent relative magnitudes based on exposure to either a few pairs of written multi-digit numbers and their corresponding names, or exposure to multi-digit number names and their corresponding physical models made up by simple shapes (e.g., big-medium-small discs); but they failed to learn with traditional mathematical manipulatives (i.e., base-10 blocks, abacus) that provide a more complete grounding of the base-10 principles. These findings have implications for place value instruction in schools and for the determination of principles to guide the use of physical models. 

Examining how informal knowledge systems change after formal instruction is imperative to understanding learning processes and conceptual development and to implementing effective educational practices. We used network analyses to determine how the organization of informal knowledge about multidigit numbers in kindergartners ( N = 279; mean age = 5.76 years, SD = 0.55; 135 females) supports and is transformed by a year of in-school formal instruction. The results show that in kindergarten, piecemeal knowledge about the surface properties of reading and writing multidigit numbers and the use of base-10 units to determine large quantities are strongly associated with each other and connected in a stringlike manner to other emerging skills. After a year of instruction, each skill becomes connected to the “hub” abilities of reading and writing multidigit numbers, which also become strongly connected to more advanced knowledge of base-10 principles. These findings provide new insights into how partial knowledge provides the backbone on which explicit principles are learned.

 

Place value concepts were measured longitudinally from kindergarten (2017) to first grade (2018) in a diverse sample (n = 279;M_age = 5.76 years,SD = 0.55; 135 females; 41% Black, 38% White, 8% Asian, 12% Latino). Children completed three syntactic tasks that required an explicit understanding of base‐10 symbols and three approximate tasks that could be completed without this explicit understanding. Approximate performance was significantly better in both age groups. A factor analysis confirmed that syntactic and approximate tasks tapped separate latent variables in kindergarten, but not in first grade. Path analyses indicated that only kindergarten approximate performance predicted overall first‐grade place value understanding. These findings suggest that explicit understanding of base‐10 principles develops from implicit, partial knowledge of multidigit numbers.

 

The number‐line task has been extensively used to study the mental representation of numbers in children. However, studies suggest that proportional reasoning provides a better account of children’s performance. Ninety 4‐ to 6‐year‐olds were given a number‐line task with symbolic numbers, with clustered dot arrays that resembled a perceptual scaling task, or with spread‐out dot arrays that involved numerical estimation. Children performed well with clustered dot arrays, but poorly with symbolic numbers and spread‐out dot arrays. Performances with symbolic numbers and spread‐out dot arrays were highly correlated and were related to counting skill; neither was true for clustered dot arrays. Overall, results provide evidence for the role of mental representation of numbers in the symbolic number‐line task.

 

We argue that analogical reasoning, particularly Gentner's (1983, 2010) structure‐mapping theory, provides an integrative theoretical framework through which we can better understand the development of symbol use. Analogical reasoning can contribute both to the understanding of others’ intentions and the establishment of correspondences between symbols and their referents, two crucial components of symbolic understanding. We review relevant research on the development of symbolic representations, intentionality, comparison, and similarity, and demonstrate how structure‐mapping theory can shed light on several ostensibly disparate findings in the literature. Focusing on visual symbols (e.g., scale models, photographs, and maps), we argue that analogy underlies and supports the understanding of both intention and correspondence, which may enter into a reciprocal bootstrapping process that leads children to gain the prodigious human capacity of symbol use.