No abstract

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 corresponding physical representations. We argue for an independent pathway to learning "big" multi-digit symbolic numbers that focuses on the symbol system itself. Across five experiments using both betweenand within-subject designs, we asked preschoolers to identify written multi-digit numbers with their spoken names in a two-alternative-choice-test or to indicate the larger quantity between two written numbers. Results showed that preschoolers could reliably map spoken number names to written forms and compare the magnitudes of two written multi-digit numbers. Importantly, these abilities were not related to their non-symbolic representation of quantities. These findings have important implications for numerical cognition, symbolic development, teaching, and education.

The level of detail (LoD) concept in CityGML (City Geography Markup Language), which indicates how closely the model mirrors its real-world counterpart, has been accepted and applied widely in various applications, including the 3D modeling of buildings. However, with an increasing number of human activities occurring in the indoor environment, the standardized LoD definition appears to be insufficient because of its narrow classifications for interior features, which can be presented only in LoD4. In view of this drawback, an extended indoor LoD (ILoD) specification is proposed, particularly for indoor spaces, allowing the existing LoD to become a more precise outdoor LoD (OLoD) by exploiting the advantages of two other international standards: Industry foundation classes (IFC) and IndoorGML. In this paper, the interior space is divided into distinct systems of three semantic aspects (structure, connectivity, and volume); the approach can be considered the guiding ideology to define the detailed indoor levels following a concrete theoretical realization based on extending the UML diagram of CityGML’s building model. Moreover, a continuous and seamless full LoD (FLoD) set obtained by combining various OLoDs and ILoDs is subsequently listed to realize the full specification for 3D building models. Furthermore, to demonstrate the proposed specification and prove the applicability of the building model at different LoDs, a practical experiment is conducted.

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.

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 instructions that help them see the relational correspondences between the map and the space. In 4 experiments, 3-year-olds completed a map reading task in which they were asked to find hidden objects in a miniature room, using a corresponding map. We manipulated the availability of guided alignment (showing children the analogical mapping between maps and spaces; Experiments 1, 2, and 3a), the format of guided alignment (gesture or relational language; Experiment 2), and the iconicity of maps (Experiments 3a and 3b). We found that (a) young children's difficulties in map reading follow from known patterns of analogical development-for example, focusing on object similarity over relational similarity; and (b) guided alignment based on analogical reasoning led to substantially better performance. Results also indicated that children's map reading performance was affected by the format of guided alignment, the iconicity of the maps, and the order of tasks. The results bear on the developmental mechanisms underlying young children's learning of spatial representations and also suggest ways to support this learning. (PsycINFO Database Record