Application of the category adjustment model in temporal, spatial, and abstract magnitude at the billions scale

Application of the Category Adjustment Model in Temporal, Spatial, and Abstract Magnitude at the Billions Scale Ilyse Resnick (ilyse.resnick@temple.edu) Department of Psychology, 1701 N. 13 th Street Philadelphia, PA 19122 USA Thomas F. Shipley (tshipley@temple.edu) Department of Psychology, 1701 N. 13 th Street Philadelphia, PA 19122 USA Abstract The current study examines the generalization of the Category Adjustment Model (CAM) across scales along two dimensions: time and distance. Participants were presented with geologic time and astronomical distance information either conventionally or using the hierarchical alignment model. Participants provided with hierarchically structured magnitude information for time and distances were more accurate on similar estimations at large scales than participants given the same content in a conventional manner. Patterns in event and distance estimation, along with overall group differences, are consistent with the CAM; suggesting people use hierarchically organized categorical information when estimating across scales and dimensions, and providing salient category boundary information improves estimation. Findings suggest a common representation of scale information for temporal, spatial, and abstract (numeric) magnitudes. Patterns of abstract magnitude estimations are consistent with segmented linear models of scale representation. Implications of the CAM in scale representation and the hierarchical alignment model in education are discussed. Keywords: Category Adjustment Alignment; Scale Representation Model; Hierarchical Introduction The Category Adjustment Model (CAM) is an adaptive Bayesian account for the pattern of systematic biases observed in recall of metric quantities due to category membership (Huttenlocher, Hedges, & Prohaska, 1988; Huttenlocher, Hedges, Vevea, 2000). The CAM posits 1D, 2D, and 3D magnitudes are stored in a hierarchical combination of metric and categorical information. In the absence of lower-level information (e.g., precise metric information), people use higher-level categories to aide in estimation. Variation in estimation, therefore, occurs due to imprecision of category boundaries. Recall is biased towards the ‘prototype’ of the respective category. For example, when recalling the position of an object in a circular display, participants naturally divide the circle into mental quadrants and the recalled location is biased towards the center (or prototype) of the relevant quadrant (Huttenlocher, Hedges, & Duncan, 1991). The CAM predicts recall patterns on a range of dimensions (e.g., fatness of fish, grayness of squares, and lengths of lines (Huttenlocher, et al., 2000), events (Huttenlocher, et al., 1988), and even social dimensions such as perception of facial expressions (Roberson, Damjanovic, & Pilling, 2007) and judgments of gender and ethnicity (Huart, Corneille, & Becquart, 2005)). However, there is limited research examining the CAM’s predictive capability for a given dimension (such as temporal and spatial scales) across different scales (such as from human scales through to scales outside of human perception). Science education research has identified conceptual categories for spatial and temporal scales outside of human perception (e.g., Trend, 2001; Tretter, Jones, Andre, Negishi, & Minogue, 2006), suggesting people may conceptualize magnitude information at relatively small and large temporal and spatial scales using a combination of metric and categorical information. Resnick, et al. (2012) experimentally assessed the role of categories in estimations of large temporal magnitudes. Participants who were provided with salient hierarchically organized event boundaries fostered a linear representation of events on the Geologic Time Scale compared to those who received the same information about the events without the salient hierarchical structure. Aligned with the CAM, this finding suggests the use of hierarchically organized category boundaries in the representation of events at larger temporal scales. The current study aims to add to this relatively sparse literature by examining the generalization of the CAM across scales and dimensions. Two main objectives are to replicate research on memory for large temporal magnitudes (geologic time), and extend research to another dimension: space. Astronomical distance (a spatial magnitude at a large scale) was chosen for two reasons. There is already extensive research on CAM and spatial distance; demonstrating spatial distances at familiar scales are stored in a combination of metric and categorical information (e.g., Huttenlocher, et al., 1991; Huttenlocher, et al., 2000). Additionally, while the precise nature of the relationship is unclear, there is a systematic relationship between time and distance (e.g., Clark, 1973; Gentner, 2001), suggesting that time and distance at human scales are represented and estimated in the same way. Thus, if temporal and spatial dimensions across familiar and relatively larger scales are represented in a similar way, an analogous pattern of memory performance would be expected.