Year-one children thinking about and writing ‘large’ quantities / Niños de primer grado pensando en y anotando cantidades ‘grandes’

Abstract

We studied how year-one children in primary school think about and with numbers when they use verbal expressions and numerical notations to suggest ‘very large’ quantities in different contexts of meaning (tokens, an elderly person’s age, stars). We individually interviewed 63 children from schools in Río Negro, Argentina. The analysis identified the different ways children approached the tension that exists between stability and innovation. Context seems to influence the answers given by many of the children who were interviewed. The results showed five cognitive trajectories: in the first two, children did not demonstrate any innovation in their notations. Children in the remaining trajectories (84% of respondents) conducted a kind of numerical ‘take off’ in at least one of the tasks. Knowledge of the number series does not guarantee an easy approach to writing ‘large’ quantities but it does seem to favour a strategy of greater cognitive flexibility.     

A physical critique of physical causation

The conserved quantities theory of causation (CQTC) attempts to use physics as the basis for an account of causation. However, a closer examination of the physics involved in CQTC reveals several critical failures. Some of the conserved quantities in physics cannot be used to distinguish causal interactions. Other conserved quantities cannot always be the properties of fields or particles. Finally, CQCT does not account for causal interactions that are static. I would like to thank Fred Kronz, Cory Juhl, Joshua Dever, and two anonymous referees for their many helpful suggestions and comments.     

New perspectives on the expression of quantity

The expression of quantity is central to many acts of communication, both formal and casual. Expressions of quantity, whether in numbers and percentages or in language, are used to convey information about frequency, certainty, risk, and degrees of association. It has typically been supposed that the many linguistic expressions that convey quantities are merely vague ways of indicating information that would be better conveyed by numbers and percentages, whenever possible. However, we show that such a view is too simplistic and is misleading. Language expressions can be more informative than numerical information alone. Language expressions carry built-in perspectives that affect the inferences and decisions made by listeners and readers. We also show that information presented through numbers (e.g., the depiction of fat content of foods) is not necessarily neutral, but also induces perspective. Failure to recognize effects of perspective may have led to some false conclusions about how people attribute causation.     

Counting by Identity: A Reply to Liebesman

David Liebesman (AJP, 2015) argues that we never count by identity. He generalizes from an argument that we don't do so with sentences indicating fractions, or with measurement sentences on their supposed count readings. In response, I argue that measurement sentences aren't covered by the thesis that we count by identity, in part because they don't have count readings. Then I use the data to which Liebesman appeals, in his argument that we don't count by identity using measurement sentences, in order to rebut his argument that we don't count by identity using sentences indicating fractions.     

表面相似性与共享标签知识对智障儿童数量表征的影响

采用给数取物任务和数量比较任务,考察表面相似性与共享标签知识对96名7～16岁智障儿童数量表征的影响。研究结果表明：（1）智障儿童数量表征能力随着年龄增长而提高,11～13岁和14～16岁智障儿童完成数量比较任务的正确率显著高于7～10岁;（2）智障儿童在高表面相似物体下完成数量比较任务的正确率显著高于低表面相似物体下的正确率;（3）擅长使用数字标签的智障儿童,在数量比较任务的表现显著优于不擅长组。     

First- and Second-Order Logic of Mass Terms

Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.     

Calibration of phase field parameters demonstrated on kinetics of a shrinking single grain

The phase field method is frequently employed to simulate evolution of rather complex microstructures. In order to accurately describe the real kinetics of a specific material system, the phase field parameters must be calibrated to standard thermodynamic quantities such as interface mobilities or interface energies. This letter presents a convenient method, based on thermodynamic modelling of shrinking of a single grain embedded in single crystal (matrix), how to calibrate the phase field parameters. It also shows, how the required thermodynamic quantities can be met by proper rescaling of a phase field simulation carried out for given phase field parameters.     

Anchors aweigh: a demonstration of cross-modality anchoring and magnitude priming

Research has shown that judgments tend to assimilate to irrelevant "anchors." We extend anchoring effects to show that anchors can even operate across modalities by, apparently, priming a general sense of magnitude that is not moored to any unit or scale. An initial study showed that participants drawing long "anchor" lines made higher numerical estimates of target lengths than did those drawing shorter lines. We then replicated this finding, showing that a similar pattern was obtained even when the target estimates were not in the dimension of length. A third study showed that an anchor's length relative to its context, and not its absolute length, is the key to predicting the anchor's impact on judgments. A final study demonstrated that magnitude priming (priming a sense of largeness or smallness) is a plausible mechanism underlying the reported effects. We conclude that the boundary conditions of anchoring effects may be much looser than previously thought, with anchors operating across modalities and dimensions to bias judgment.     

Common Representations of Abstract Quantities

ABSTRACT— Representations of abstract quantities such as time and number are essential for survival. A number of studies have revealed that both humans and nonhuman animals are able to nonverbally estimate time and number; striking similarities in the behavioral data suggest a common magnitude-representation system shared across species. It is unclear, however, whether these representations provide animals with a true concept of time and number, as posited by Gallistel and Gelman (2000) . In this article, we review the prominent cognitive and neurobiological models of timing and counting and explore the current evidence suggesting that nonhuman animals represent these quantities in a modality-independent (i.e., abstract) and ordered manner. Avenues for future research in the area of temporal and mathematical cognition are also discussed.