Dealing with Big Numbers: Representation and Understanding of Magnitudes Outside of Human Experience

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed.     

Age-related changes in children's executive functions and strategy selection: A study in computational estimation

Third, fifth, and seventh graders selected the best strategy (rounding up or rounding down) for estimating answers to two-digit addition problems. Executive function measures were collected for each individual. Data showed that (a) children's skill at both strategy selection and execution improved with age and (b) increased efficiency in executive functions contributed significantly to age-related improvement in children's strategy selection skill. These findings have implications for understanding of age-related differences in computational estimation, strategy selection processes, and mechanisms of strategic development in children.     

Computational exploration of metaphor comprehension processes using a semantic space model

Recent metaphor research has revealed that metaphor comprehension involves both categorization and comparison processes. This finding has triggered the following central question: Which property determines the choice between these two processes for metaphor comprehension? Three competing views have been proposed to answer this question: the conventionality view ( Bowdle & Gentner, 2005 ), aptness view ( Glucksberg & Haught, 2006b ), and interpretive diversity view ( Utsumi, 2007 ); these views, respectively, argue that vehicle conventionality, metaphor aptness, and interpretive diversity determine the choice between the categorization and comparison processes. This article attempts to answer the question regarding which views are plausible by using cognitive modeling and computer simulation based on a semantic space model. In the simulation experiment, categorization and comparison processes are modeled in a semantic space constructed by latent semantic analysis. These two models receive word vectors for the constituent words of a metaphor and compute a vector for the metaphorical meaning. The resulting vectors can be evaluated according to the degree to which they mimic the human interpretation of the same metaphor; the maximum likelihood estimation determines which of the two models better explains the human interpretation. The result of the model selection is then predicted by three metaphor properties (i.e., vehicle conventionality, aptness, and interpretive diversity) to test the three views. The simulation experiment for Japanese metaphors demonstrates that both interpretive diversity and vehicle conventionality affect the choice between the two processes. On the other hand, it is found that metaphor aptness does not affect this choice. This result can be treated as computational evidence supporting the interpretive diversity and conventionality views.     

Squeezing, striking, and vocalizing: Is number representation fundamentally spatial?

Numbers are fundamental entities in mathematics, but their cognitive bases are unclear. Abundant research points to linear space as a natural grounding for number representation. But, is number representation fundamentally spatial? We disentangle number representation from standard number-to-line reporting methods, and compare numerical estimations in educated participants using line-reporting with three nonspatial reporting conditions (squeezing, bell-striking, and vocalizing). All three cases of nonspatial-reporting consistently reproduced well-established results obtained with number-line methods. Furthermore, unlike line-reporting—and congruent with the psychophysical Weber–Fechner law—nonspatial reporting systematically produced logarithmic mappings for all nonsymbolic stimuli. Strikingly, linear mappings were obtained exclusively in conditions with culturally mediated elements (e.g., words). These results suggest that number representation is not fundamentally spatial, but builds on a deeper magnitude sense that manifests spatially and nonspatially mediated by magnitude, stimulus modality, and reporting condition. Number-to-space mappings—although ubiquitous in the modern world—do not seem to be rooted directly in brain evolution but have been culturally privileged and enhanced.     

Facilitation by Variation: Right-to-Left Learning of English Yes/No Questions

This study advances the hypothesis that optional structural variation in language facilitates syntactic learning (facilitation‐by‐variation). Support for this is provided by a right‐to‐left‐elaboration acquisition model for English yes/no questions (YNQs). Previous studies have focused on the acquisition of ‘‘inverted’’ YNQs, a cornerstone of nativist theories of language development. Data from five American children (1;3 to 5;1) and their parents show that children hear a range of adult questions (Coming?You coming?Are you coming?), not all inverted. These variants are ordered from structurally least complex noncanonical forms to complex canonical inverted forms. I use state‐of‐the‐art econometric techniques to estimate breakpoints in YNQ time series and show that noncanonical questions emerge early in children’s speech and facilitate acquisition of canonical ones. This incremental structure‐building process relies on an adjunction strategy that augments noncanonical questions with initial auxiliaries and subjects. Development proceeds incrementally from right to left to derive auxiliary‐initial structures.     

疼痛条件下时间目标对时距估计的影响

本研究采用冷压任务引发疼痛,以健康大学生为被试,试图探讨在疼痛条件下时间目标对时距估计的影响。结果发现：疼痛条件下的时距估计值小于非疼痛条件下时距估计值,疼痛条件下具体时间目标的时距估计值显著大于无目标时距估计值。临床上给患者提供具体的时间目标或许有助于他们应对疼痛。     

儿童数字线表征的发展——心理长度的影响

探讨儿童在数字线估计任务中心理长度的发展及其对数量表征模式的影响.选取7~9岁儿童共109名进行数字线估计任务测试,设置了10cm和20cm两种长度条件,要求儿童完成根据位置判断数字任务(position to number,PN任务).结果表明儿童在数字线PN任务中存在心理长度,且7岁儿童心理长度的范围超过10,随着儿童年龄的增长,他们的心理长度范围不断缩小;心理长度范围影响儿童的表征模式,随着心理长度范围的缩小,儿童的数字线表征出现从指数模式到线性模式的变化趋势;与表征模式的发展趋势一致,儿童估计的精确性随年龄增长逐渐提高.     

视觉表象生成系统及其影响因素

视觉表象是在记忆基础上产生的类似知觉的信息表征, 也是人们在日常生活中不可或缺的心理活动之一。本综述介绍了该领域中比较有影响力的表象计算理论模型, 并进一步归纳了视觉表象生成系统的成分及其对应的神经基础。分析结果强调了初级视觉皮层作为“视觉缓冲器”是生成表象的主要机能结构, 以“视觉缓冲器”为基础的表象生成系统的机能受多重因素影响。本综述有助于对视觉表象生成系统形成全面的认识, 促进视觉表象实质的进一步研究。     

Reducing Measurement Error in Student Achievement Estimation

The achievement level is a variable measured with error, that can be estimated by means of the Rasch model. Teacher grades also measure the achievement level but they are expressed on a different scale. This paper proposes a method for combining these two scores to obtain a synthetic measure of the achievement level based on the theory developed for regression with covariate measurement error. In particular, the focus is on ordinal scaled grades, using the SIMEX method for measurement error correction. The result is a measure comparable across subjects with smaller measurement error variance. An empirical application illustrates the method.