Lei Yuan

University of Colorado Boulder | CUB · Department of Psychology and Neuroscience

Children’s early accuracy on place value (PV) tasks longitudinally predicts their later multidigit calculation skills. However, another window into children’s emerging base-ten concepts is the pattern of errors—‘smart errors’—they exhibit on these measures. Past research has speculated that these smart errors—similar to invented spelling—might refl...

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....

Place value concepts were measured longitudinally from kindergarten (2017) to first grade (2018) in a diverse sample (n = 279; Mage = 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 co...

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 evid...

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...

Numerous studies from developmental psychology have suggested that human symbolic representation of numbers is built upon the evolutionally old capacity for representing quantities that is shared with other species. Substantial research from mathematics education also supports the idea that mathematical concepts are best learned through their corre...

Across science, education, and business, we process and communicate data visually. One bedrock finding in data visualization research is a hierarchy of precision for perceptual encodings of data (e.g., that encoding data with Cartesian positions allows more precise comparisons than encoding with sizes). But this hierarchy has only been tested for s...

Across science, education, and business, we process and communicate data visually. One bedrock finding in data visualization research is a hierarchy of precision for perceptual encodings of data, e.g., that encoding data with Cartesian positions allows more precise comparisons than encoding with sizes. But his hierarchy has only been tested for sin...

Sustained visual attention is crucial to many developmental outcomes. We demonstrate that, consistent with the developmental systems view, sustained visual attention emerges from and is tightly tied to sensory motor coordination. We examined whether changes in manual behavior alter toddlers' eye gaze by giving one group of children heavy toys that...

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 sym...

We propose that map reading can be construed as a form of analogical mapping. We tested 2 predictions that follow from this claim: First, young children's patterns of performance in map reading tasks should parallel those found in analogical mapping tasks; and, second, children will benefit from guided alignment instructions that help them see the...

Perceiving not just values, but relations between values, is critical to human cognition. We tested the predictions of a proposed mechanism for processing categorical spatial relations between two objects—the shift account of relation processing—which states that relations such as ‘above’ or ‘below’ are extracted by shifting visual attention upward...

Testing Response Keys (Experiment 5). (DOCX)

Additional analysis of Experiment 1. (DOCX)

Additional analysis of Experiment 3. (DOCX)

Replicating the Spatial Template Recognition Task (Experiment 4). (DOCX)

Full analysis of Experiment 1. (DOCX)

Additional analysis of Experiment 2a. (DOCX)

The frequent and fluent use of symbols is a distinguishing characteristic of human thought and communication. Symbols free us from the bounds of our own direct experience and allow us to learn about the world from others. To use a symbol, children need to (1) understand the intention that led to the creation and use of the symbol, and (b) how the s...

Visual spatial relations are the foundation for encoding information in graphs, diagrams, and maps. While successfully using these displays requires that we extract, remember, and integrate these relations, there is little existing work measuring how many we can store. Some related types of visual information seem to be robustly encoded, such as th...