The Development of Procedural and Conceptual Knowledge in Computational Estimation

Children in Grades 4, 6, and 8 and adults estimated answers to multiplication problems. The problems varied in the number of digits: 1 x 2 (e.g., 8 x 18), 1 X 3 (e.g., 5 x 144), 2 x 2 (e.g., 22 x 91), and 2 x 3 (e.g., 45 x 164). Few children in Grade 4 could estimate. Most sixth and eighth graders provided reasonable estimates, however, even on difficult (e.g., 2 x 3) problems. Estimation performance improved with age, with adults producing more accurate estimates than children, but the most striking developmental changes were in the conceptual knowledge used to perform this estimation task. From Grade 6, students seemed to understand the role of the simplification principle in estimation. Children reduced complex problems through rounding and prior compensation to produce reasonable estimates. Only adults seemed to have a good grasp of the principle of proximity, however, understanding that it is important for the estimate to be reasonably close to the actual answer. Adults produced exact-answer solutions on simple problems and adjusted their preliminary estimates closer to the actual answer postcompensation). We propose a process model of estimation based on Siegler's model of strategy choice in simple arithmetic.     

Dynamics Versus Development in Numerosity Estimation: A Computational Model Accurately Predicts a Developmental Reversal

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model—a situation in which children's estimates of numerosity would be better than those of adults. Consistent with the model simulations, task contexts led to a clear developmental reversal: children made more adult-like, linear estimates when to-be-estimated numbers were descending over trials (i.e., backward condition), whereas adults became more like children with logarithmic estimates when numbers were ascending (i.e., forward condition). In addition, adults’ estimates were subject to inter-trial differences regardless of stimulus order. In contrast, children were not able to use the trial-to-trial dynamics unless stimuli varied systematically, indicating the limited cognitive capacity for dynamic updates. Together, the model adequately predicts both developmental and trial-to-trial changes in number-line tasks.     

A unitary Neo-Piagetian/Neo-Eriksonian model of development: Fundamental assumptions and meta-issues

The article briefly reviews a stage model of change in human development that integrates a Neo-Piagetian model and a Neo-Eriksonian model into one unitary stage model across the lifespan (as presented in Young, 2011). The model suggests a generic model of stages in change. The article explores the fundamental assumptions underlying the model as well as considering meta-issues. The article adds to the book by describing the Neo-Eriksonian stages as reflections of a social “participatory” process. It adds to the change process in development by describing it as possibly reflecting “punctuated disequilibrium.” Finally, it adds a “multiple psychodynamics” model.     

估算:来自心理学的声音

估算(computational estimation),是指个体懂得什么情况下无法或不必作准确计算,并应用相关知识和策略给出近似答案的能力,它特别适用于解决日常实际问题。估算已是当前国际小学数学教育中比较重视的一种能力。教育部最新颁布的《九年义务教育全日制小学数学教学大纲(试用修订版)》中增加了这样的教学要求．要使学生“具有估算意识和初步的估算能力”,并指出,“估算在日常生活中有广泛的应用,在各年级应适当加强估算”,同时提出,“要重视培养学生估算的习惯和能力”。但是估算教学的心理依据到底怎样呢？     

六年级儿童的估算水平与策略

借鉴Lemaire与Siegler提出的儿童认知策略的一般概念框架,运用自编的估算题目对210名小学六年级儿童的估算能力进行了初步分析。结果表明;小学六年级儿童具有一定的估算能力,只是所给估算答案明显受到数字类型和运算规则的交互影响;他们会运用多种估算策略,但各种策略的使用频率、执行速度和准确性都存在明显差异。文章还对儿童估算策略的评估做了深入讨论。     

数学学业不良儿童的估算情感特点研究

运用自编估算测试材料,通过与学优生相比较,考察了数学学业不良儿童的估算情感特点及与估算能力的关系,被试为40名小学六年级学生。结果表明:1.学业不良儿童的估算情感总分明显低于学优儿童,学业不良儿童在数学自信心和估算情感认同这两个维度上表现较为消极。2.学业不良儿童的估算情感认同与他们的估算成绩之间关系更为密切。     

数学焦虑、问题形式对乘法估算的影响

采用由研究者所修订的数学焦虑量表和自行设计的估算问题,通过对大学生被试进行团体测验,考察了在纯数字运算和应用题两种情境中数学焦虑对估算加工的影响以及估算中的问题大小效应。结果显示：（1）数学焦虑情绪在纯数字与应用题两种情境下都对估算有显著影响;（2）情境对估算准确率影响显著,纯数字情境下的估算准确率显著高于应用题情境;（3）在应用题情境估算中发现明显的问题大小效应,在纯数字情境估算中却未发现该效应。     

工作记忆中央执行成分对估算表现的影响

工作记忆中央执行成分在计算加工的诸多过程中发挥重要影响。以82名大学生为被试,采用双任务实验范式考察工作记忆中央执行成分对估算表现的影响。结果发现：1）估算过程需要中央执行成分的参与,增加中央执行成分负荷会导致估算准确率下降;2）无论是否增加中央执行负荷,问题大小效应在估算中均不明显;3）乘法个位数大小顺序会影响估算值的准确性,在有中央执行负荷时数字顺序效应明显。     

The Neurodynamics of Cognition: A Tutorial on Computational Cognitive Neuroscience

Computational Cognitive Neuroscience (CCN) is a new field that lies at the intersection of computational neuroscience, machine learning, and neural network theory (i.e., connectionism). The ideal CCN model should not make any assumptions that are known to contradict the current neuroscience literature and at the same time provide good accounts of behavior and at least some neuroscience data (e.g., single-neuron activity, fMRI data). Furthermore, once set, the architecture of the CCN network and the models of each individual unit should remain fixed throughout all applications. Because of the greater weight they place on biological accuracy, CCN models differ substantially from traditional neural network models in how each individual unit is modeled, how learning is modeled, and how behavior is generated from the network. A variety of CCN solutions to these three problems are described. A real example of this approach is described, and some advantages and limitations of the CCN approach are discussed.     

中央执行负荷对成人估算策略运用的影响

随机选取128名大学生为被试, 运用选择/无选法研究范式, 考察了不同中央执行负荷对估算策略运用的影响。结果发现：(1)中央执行负荷不影响策略分布; (2)策略运用条件、中央执行负荷影响策略执行。主次一致任务, 负荷对策略执行反应时的影响随负荷强度增大而增大, 对策略执行精确度影响不大; 而对主次不一致任务, 低负荷对策略执行反应时及精确度影响都不明显; (3)策略运用条件、中央执行负荷影响策略选择。负荷强度对策略选择反应时起重要作用, 只有当次级任务负荷高时, 干扰作用才明显; (4)成人的策略选择适应性受负荷强度的影响。无负荷条件下个体策略适应性更好。     

创造性思维计算模型研究综述

本文综述了已有的创造性思维计算模型,根据其采用的计算方法进行分类,分析这些方法的优缺点,对创造性思维的计算模拟方法进行了展望。     

CaMeRa: A Computational Model of Multiple Representations

This research aims to clarify, by constructing and testing a computer simulation, the use of multiple representations in problem solving, focusing on their role in visual reasoning. The model is motivated by extensive experimental evidence in the literature for the features it incorporates, but this article focuses on the system's structure. We illustrate the model's behavior by simulating the cognitive and perceptual processes of an economics expert as he teaches some well-learned economics principles while drawing a graph on a blackboard. Data in the experimental literature and concurrent verbal protocols were used to guide construction of a linked production system and parallel network, CaMeRa (Computation with Multiple Representations), that employs a "Mind's Eye" representation for pictorial information, consisting of a bitmap and associated node-link structures. Propositional list structures are used to represent verbal information and reasoning. Small individual pieces from the different representations are linked on a sequential and temporary basis to form a reasoning and inferencing chain, using visually encoded information recalled to the Mind's Eye from long-term memory and from cues recognized on an external display. CaMeRa, like the expert, uses the diagrammatic and verbal representations to complement one another, thus exploiting the unique advantages of each.     

The Effect of Prominence and Cue Association on Retrieval Processes: A Computational Account

We present a comprehensive empirical evaluation of the ACT‐R–based model of sentence processing developed by Lewis and Vasishth (2005) (LV05). The predictions of the model are compared with the results of a recent meta‐analysis of published reading studies on retrieval interference in reflexive‐/reciprocal‐antecedent and subject–verb dependencies (Jäger, Engelmann, & Vasishth, 2017). The comparison shows that the model has only partial success in explaining the data; and we propose that its prediction space is restricted by oversimplifying assumptions. We then implement a revised model that takes into account differences between individual experimental designs in terms of the prominence of the target and the distractor in memory‐ and context‐dependent cue‐feature associations. The predictions of the original and the revised model are quantitatively compared with the results of the meta‐analysis. Our simulations show that, compared to the original LV05 model, the revised model accounts for the data better. The results suggest that effects of prominence and variable cue‐feature associations need to be considered in the interpretation of existing empirical results and in the design and planning of future experiments. With regard to retrieval interference in sentence processing and to the broader field of psycholinguistic studies, we conclude that well‐specified models in tandem with high‐powered experiments are needed in order to uncover the underlying cognitive processes.     

The start-stop procedure: Estimation

In four experiments investigating human timing, subjects produced estimates of sample durations by bracketing their endpoints. On each trial, subjects reproduced a sample duration by pressing a button before the estimated sample duration elapsed (start time) and releasing it after the estimated duration elapsed (stop time). From these responses, middle time (start + stop/2) and spread time (stop — start) were calculated, representing the point of subjective equality and the difference limen, respectively. In all experiments, subjects produced middle times that varied directly with sample duration. In Experiment 2, middle times lengthened when feedback was withheld. Consistent with Weber timing, spread times, as well as the standard deviation of middle times, varied directly with middle time (Experiments 1, 3, and 4). On the basis of an internal clock model of timing (Gibbon & Church, 1990), the data permitted inferences regarding memory processes and response threshold. Correlations between start and stop times and between start and spread times agreed with earlier findings in animals suggesting that the variance of temporal estimates across trials is based in part upon the selection of a single temporal memory sample from a reference memory store and upon one or two threshold samples for initiating and terminating each estimate within a trial.     

Relationship Development in Selling: A Cognitive Analysis

Recent research has suggested that trust and relationship-building contribute to the effectiveness of salespeople. This paper reviews the literature on the cognitive selling paradigm and the influence of knowledge structures on the relationship-building process. Next, two recent studies (Anglin 1990; Szymanski 1987) which investigated knowledge, relationship development, and sales performance are reviewed. The findings from these studies imply that a fundamental difference may exist in the manner in which higher and lower performing salespeople perceive the selling process. Higher performers placed greater emphasis on establishing “trust” and also preferred to find out information about the prospect before reciprocating with information about themselves. Lower performers, on the other hand, preferred to disclose information about themselves before obtaining personal information about the prospect.     

意向性的计算解释

当代心智哲学和认知科学中,意向性是颇受关注且又不断引发争论的中心概念之一。直观上,意向性系指心智状态或过程具有的"关于性",即心智的内容是关于或表征某种东西的。许多哲学家认为,意向性是大多数(甚至所有)心智状态的标志。倘若意向性确是一种真实的现象,则以理解心智现象为己任的认知科学,就有责任用科学上合适的方式来解释心智状态的这一特质。     

Approximate Semantic Transference: A Computational Theory of Metaphors and Analogies

In this paper we start from the assumption that in a metaphor, or an analogy, some terms belonging to one domain (source domain) are used to refer to objects other than their conventional referents belonging to a possibly different domain (target domain). We describe a formalism, which is based on the First Order Predicate Calculus, for representing the knowledge structure associated with a domain and then develop a theory of Constrained Semantic Transference [CST] which allows the terms and the structural relationships of the source domain to be transferred coherently across to the target domain. We show how metaphors and analogies can be characterized in CST in such a way that many of their cognitive properties con be explained. We then propose a theory of Approximate Semantic Transference [AST] which is a computational version of CST and is derived from it by replacing the coherency requirement with approximate coherency. We show how AST can be used as a basis for designing models of cognitive processes involved in comprehending metaphors and analogies.     

Concepts as Semantic Pointers: A Framework and Computational Model

The reconciliation of theories of concepts based on prototypes, exemplars, and theory‐like structures is a longstanding problem in cognitive science. In response to this problem, researchers have recently tended to adopt either hybrid theories that combine various kinds of representational structure, or eliminative theories that replace concepts with a more finely grained taxonomy of mental representations. In this paper, we describe an alternative approach involving a single class of mental representations called “semantic pointers.” Semantic pointers are symbol‐like representations that result from the compression and recursive binding of perceptual, lexical, and motor representations, effectively integrating traditional connectionist and symbolic approaches. We present a computational model using semantic pointers that replicates experimental data from categorization studies involving each prior paradigm. We argue that a framework involving semantic pointers can provide a unified account of conceptual phenomena, and we compare our framework to existing alternatives in accounting for the scope, content, recursive combination, and neural implementation of concepts.