Several programming models with unascertained parameters and their applications

Several programming models are introduced with the consideration of available unascertained information. In this case, the so‐called unascertained information is some numerical values whose ranges are known but their exact values are not. These models resolve several vital weaknesses of the traditional programming methods to a certain degree. Our study includes considerations of linear and non‐linear programming models with grey parameters, grey 0–1 programming, and satisfactory and quasi‐optimal solutions of grey linear programmings. Finally, some practical applications are given in order to test the applicability of our theory. Copyright © 1999 John Wiley & Sons, Ltd.     

一～四年级小学生发展性计算障碍的亚类型研究

本研究以1~4年级小学生为被试,探讨发展性计算障碍的亚类型.对筛选出的54名发展性计算障碍学生进行聚类分析,结果表明:在小学1~4年级学生中,存在着4种发展性计算障碍的亚类型,分别是听觉型、视觉型、类比型和听觉——类比型,这几种亚类型在数字加工和计算能力不同功能模块上的缺陷模式存在着差异.     

An axiomatization of family resemblance

We invoke concepts from the theory of hypergraphs to give a measure of the closeness of family resemblance, and to make precise the idea of a composite likeness. It is shown that for any positive integer m, for any general term possessing any extent of family resemblance strictly greater than m, there is a taxonomical representation of the term whereby each subordinate taxon has an extent of family resemblance strictly greater than m.     

征兵用数字搜索测验的研制

基于信息加工速度理论自编征兵用数字搜索测验,使用该测验对全国15735名应征青年及190名新兵进行了测量,3个月新兵营训练结束时由228上级对1900名士兵的智力相关工作绩效情况进行了调查,通过对上述数据的分析确定了测验方法及划界分数,并进行了信、效度检验。结果表明:缺失不同数字对题目难度有影响;划界分数为197秒正确应答27题以上;该测验的内部一致性α系数为0.864;预测符合率为95.7%。     

中小学数学教师数感内隐观的调查研究

该研究以131名中小学数学教师为被试,采用调查分析的方法,编制了数感结构选项表,考察了中小学数学教师的数感结构内隐观。结果显示：中小学数学教师的数感结构内隐观所涉及的范围广泛,经因素分析可以把它概括为6个因素。它们分别是：数学运算、数学认知因素、非书面计算能力、理解数与运算的意义、对数的认识与直觉、数符号表征能力。     

Numerosity discrimination in deep neural networks: Initial competence,developmental refinement and experience statistics

Both humans and non‐human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can detect changes in numerosity. These findings are often interpreted as evidence for an innate ‘number sense’. However, recent simulation work has challenged this view by showing that human‐like sensitivity to numerosity can emerge in deep neural networks that build an internal model of the sensory data. This emergentist perspective posits a central role for experience in shaping our number sense and might explain why numerical acuity progressively increases over the course of development. Here we substantiate this hypothesis by introducing a progressive unsupervised deep learning algorithm, which allows us to model the development of numerical acuity through experience. We also investigate how the statistical distribution of numerical and non‐numerical features in natural environments affects the emergence of numerosity representations in the computational model. Our simulations show that deep networks can exhibit numerosity sensitivity prior to any training, as well as a progressive developmental refinement that is modulated by the statistical structure of the learning environment. To validate our simulations, we offer a refinement to the quantitative characterization of the developmental patterns observed in human children. Overall, our findings suggest that it may not be necessary to assume that animals are endowed with a dedicated system for processing numerosity, since domain‐general learning mechanisms can capture key characteristics others have attributed to an evolutionarily specialized number system.     

元回归中效应量的最小个数需求：基于统计功效和估计精度

元回归模型被广泛应用于调节变量的识别。从元分析技术的原理谈起, 介绍了元回归模型, 然后采用蒙特卡洛模拟, 基于统计功效和估计精度探究效应量个数对元回归模型参数估计的影响, 从而确立效应量的最小个数需求。主要研究结果为：(1) Wald-type z检验方法在元回归中易犯I类错误; (2)为达到参数估计要求, 元回归至少需要20个效应量; (3)纳入合适的调节变量能降低对效应量的个数需求。基于研究结果, 提出以下建议：(1)研究者应慎重使用Wald-type z检验方法和CMA软件; (2)研究者至少需要20个效应量, 且应当根据实际情况进一步增加效应量个数; (3)研究者应当积极探索合适的调节变量; (4)未来审稿人可参考最小效应量个数需求对元回归研究进行质量评估。     

Place‐value understanding in number line estimation predicts future arithmetic performance

In multi‐digit numbers, the value of each digit is determined by its position within the digit string. Children's understanding of this place‐value structure constitutes a building block for later arithmetic skills. We investigated whether a number line estimation task can provide an assessment of place‐value understanding in first grade. We hypothesized that estimating the position of two‐digit numbers requires place‐value understanding. Therefore, we fitted a linear function to children's estimates of two‐digit numbers and considered the resulting slope as a measure of children's place‐value understanding. We observed a significant correlation between this slope and children's performance in a transcoding task known to require place‐value understanding. Additionally, the slope for two‐digit numbers assessed at the beginning of grade 1 predicted children's arithmetic performance at the end of grade 1. These results indicate that the number line estimation task may indeed constitute a valid measure for first‐graders' place‐value understanding. Moreover, these findings are hard to reconcile with the view that number line estimation directly assesses a spatial representation of numbers. Instead, our results suggest that numerical processes involved in performing the task (such as place‐value understanding) may drive the association between number line estimation and arithmetic performance.     

Fuzzy computation of teaching performance based on data envelopment analysis method

Data Envelopment Analysis (DEA) is a system analysis method. It is suitable for evaluating the relative efficiency of Decision Making Units (DMU) with multiple input and output indicators, which is subject to no dimensional form of data and does not need to set the parameters. Subordinate colleges are an integral part of a university, and the university’s comprehensive competitiveness can be improved only when each college reaches the optimal state of teaching performance. From the perspective of faculty structure, this paper constructs the evaluation system for the teaching performance of subordinate colleges. In the evaluation system, there are two fuzzy variables, employment quality and quality of enrollment of graduates, so the fuzzy DEA method is adopted. The introduction of fuzzy theory can well solve the problem of fuzzy numbers in input or output. The commonly used fuzzy numbers include triangular fuzzy numbers and trapezoid fuzzy numbers. The triangular one is used in this paper. The research results will help the university strengthen the understanding of subordinate colleges, which is of practical significance to improve the university’s comprehensive competitiveness.     

Asymmetric prefrontal cortex functions predict asymmetries in number space

Little is known about the neuropsychological factors that contribute to individual differences in the asymmetric orientation along the mental number line. The present study documents healthy subjects’ preference for small numbers over large numbers in a random number generation task. This preference, referred to as “small-number bias” (SNB), varied with prefrontal functional lateralization: it was larger in participants with over-proportionately better performance in design fluency compared to letter fluency than in participants with over-proportionately better performance in letter fluency when compared to design fluency. Asymmetries in learning and memory tasks (verbal vs. non-verbal) were not related to direction or size of the SNB. We conclude that hemispheric asymmetries of specifically prefrontal executive functions are predictive of an individual’s lateral orientation bias along the mental number line. Therefore, the focus on parietal contributions to spatial-numerical associations may not be justified. Random number generation may be a helpful method to further explore these associations uncontaminated by the asymmetric involvement of response effectors.