Salience Versus Proportional Reasoning: Rethinking the Mechanism Behind Graphical Display Effects

Two experiments examined predictions from two separate explanations for previously observed display effects for communicating low‐probability risks: foreground:background salience and proportional reasoning. According to foreground:background salience, people's risk perceptions are based on the relative salience of the foreground (number of people harmed) versus the background (number of people at risk), such that calling attention to the background makes the risk seem smaller. Conversely, the proportional reasoning explanation states that what matters is whether the respondent attends to the proportion, which conveys how small the risk is. In Experiment 1, we made the background more salient via color and bolding; in contrast to the foreground:background salience prediction, this manipulation did not influence participants' risk aversion. In Experiment 2, we separately manipulated whether the foreground and the background were displayed graphically or numerically. In keeping with the proportional reasoning hypothesis, there was an interaction whereby participants given formats that displayed the foreground and background in the same modality (graphs or numbers, thereby making the proportion easier to form) saw the probability as smaller and were less risk averse than participants given the information in different modalities. There was also a main effect of displaying the background graphically, providing some support for foreground:background salience. In total, this work suggests that the proportional reasoning account provides a good explanation of many display effects related to communicating low‐probability risks, although there is some role for foreground:background salience as well. Copyright © 2018 John Wiley & Sons, Ltd.     

不同回避动机强度的消极情绪对类比推理的影响

通过控制负性情绪的不同回避动机强度,采用经典四项比例式的推理任务,探究不同回避动机强度的负性情绪对类比推理的影响。研究结果发现:(1)不同回避动机强度的负性情绪(悲伤和恐惧)均会导致推理任务的正确率下降;(2)在低回避动机强度情绪(悲伤)下完成推理任务的反应时比高回避动机强度情绪(恐惧)下更长。结论:不同回避动机强度的负性情绪均会对类比推理产生消极作用,高回避动机强度的负性情绪下完成推理任务的速度更快,但正确率较低,这可能是由于注意窄化和情绪的动机强度通过工作记忆影响了推理过程。     

The Influence of Reasoning with Emergent Quantities on Students' Generalizations

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns, procedures, and rules, while instruction encouraging a focus on quantities supported generalizations about relationships, connections between situations, and dynamic phenomena, such as the nature of constant speed. An examination of the similarities and differences in students' generalizations revealed that the type of quantitative reasoning in which students engaged ultimately proved more important in influencing their generalizing than a mere focus on quantities versus numbers. In order to develop powerful, global generalizations about relationships, students had to construct ratios as emergent quantities relating two initial quantities. The role of emergent-ratio quantities is discussed as it relates to pedagogical practices that can support students' abilities to correctly generalize.     

不同趋近动机强度的积极情绪对类比推理的影响——来自ERP的证据

实验采用类比推理的经典四项比例式"A:B::C:D",选择两种有难度差异的类推题目(同形、反义)作为实验任务,用情绪图片诱发情绪,采用事件相关电位(event-related potentials,ERPs)技术,探究欲求(高动机强度)、愉悦(低动机强度)和中性情绪影响类比推理的差异及脑机制。结果发现:(1)图式生成阶段:N400、P300和LNC被诱发,情绪在LNC上的主效应不显著;(2)类比映射阶段:N400和LNC成分被诱发,情绪在LNC上的主效应显著。LNC幅值:欲求情绪(高动机强度)愉悦情绪(低动机强度)中性情绪。结果表明情绪对类比推理的影响主要发生在类比映射阶段。不同趋近动机强度的积极情绪均会降低推理质量,延长推理的反应时,部分支持情绪的动机维度模型。     

归纳推理多样性效应的发展及其争论

归纳推理多样性效应指的是在归纳论断中,前提项目数量越多、越多样,将能构成归纳力度越强的推理。已有研究表明成人的归纳推理明显受到前提项目多样性的影响,而幼儿的相关研究却存在着两种对立的观点：一是认为幼儿不能基于多样性进行推理,二是认为5岁左右的幼儿就能够基于多样性进行推理。出现此争论的原因可能与研究方法方面的差异有关,如实验范式与前提组间差异、实验材料类别与概念范畴、属性特征及呈现方式、推理形式;此外,儿童的知识经验也是一个影响因素。未来研究可以结合相关领域的研究范式;深入挖掘影响儿童表现出多样性效应的因素;将任务设计多样化;将实验任务的计分方式多样化;开展相关的应用研究。     

The Effect of Rest Following Massed Practice of Continuous and Discrete Motor Tasks

Theories of the rest-related phenomena of reminiscence and warm-up decrement regard them as independent, being due to different factors. In this study it was found that rest following massed practice of a continuous task increased performance (reminiscence) and rest following massed practice of a discrete task lowered performance (warm-up decrement). The near-zero correlation found between the phenomena indicates that they are indeed independent and task-specific. Implications of the findings for the prediction of the effect of rest, and the fact that much motor learning and performance is task-specific, is discussed.     

Reasoning Continuously: A Formal Construction of Continuous Proofs

We begin with the idea that lines of reasoning are continuous mental processes and develop a notion of continuity in proof. This requires abstracting the notion of a proof as a set of sentences ordered by provability. We can then distinguish between discrete steps of a proof and possibly continuous stages, defining indexing functions to pick these out. Proof stages can be associated with the application of continuously variable rules, connecting continuity in lines of reasoning with continuously variable reasons. Some examples of continuous proofs are provided. We conclude by presenting some fundamental facts about continuous proofs, analogous to continuous structural rules and composition. We take this to be a development on its own, as well as lending support to non-finitistic constructionism.

     

视知觉线索对幼儿小数离散量表征的影响

本研究采用数量辨别任务和数量比较的干扰任务考察了元素累积面积和元素特征丰富度两种视知觉线索对3～6岁幼儿表征4以内离散量的影响。两个任务的被试分别为80名和74名。结果表明,幼儿在辨别小数离散量时并未表现出对元素累积面积的偏好;且幼儿能同时关注累积面积和饼干个数两个维度,从而辨别抽象的数量关系;这种辨别能力有随年龄提高的趋势,不能辨别组以3、4岁幼儿居多,他们辨别方形饼干的数量关系比辨别圆形饼干更容易。当元素累积面积干扰小数量比较时,幼儿数量比较的正确率随数量比例增大而降低,此时幼儿小数量表征不再精确;而当单个元素的知觉特征更鲜明时,即使仍存在元素累积面积干扰,其正确率也不再受数量比例的影响。这说明单个元素的知觉线索与整体知觉线索共同影响小数离散量表征,也提示着幼儿的小数量表征精确性可能并非稳定存在,小数量表征在特定条件下也需要借助模拟数量系统。     

Counselor Ethical Reasoning: Decision‐Making Practice Versus Theory

Counselors’ decision‐making processes have received little attention in the literature. The purpose of this study was to ascertain the ethical decision‐making practices of counselors working in the field. The results of a phenomenological study indicate that linear models and an orientation to professional ethical guidelines learned in graduate training serve as a foundation, yet not a practical guide, in professional ethical decision making. The authors found that 4 themes guide counselors’ ethical decision making: personal values, clients’ best interest, transparency in decision making, and perceptions of formal training and practice. Implications for practice and counselor education are provided, with recommendations for future research.     

小学生非形式推理能力的发展

文章在提出非形式推理评价指标体系的基础上,采用提示访谈法考察了小学生非形式推理能力的发展.结果显示:少数1、2年级小学生处于理由推理水平,多数能够进行反驳推理,3至6年级小学生都能做出反驳推理;三种理由的数量都存在显著的年级差异,功能性理由的数量随年级增长而增多;高年级学生的反驳次数都显著多于低年级学生;低年级学生的推理中断次数和推理错误总次数显著多于高年级,并随年级的增长呈下降趋势.     

类比数量表征的线索:离散量还是连续量

运用Stroop研究范式,对30名成人被试的类比数量表征线索进行了研究。结果发现:在类比数量的小数和大数段上,不存在表征线索的分化;在个数任务中不出现Stroop效应,但被试在强不一致条件下的错误率显著高于强一致条件下的错误率;在累积面积任务中出现Stroop效应,且在弱不一致、强不一致条件下的反应时、错误率都显著高于强一致、弱一致条件下的反应时、错误率。以上结果表明被试在进行类比数量表征时,可以同时提取离散量线索和连续量线索,但是对离散量线索的抑制要难于对连续量线索的抑制。     

On the Role of Mathematics in Explaining the Material World: Mental Models for Proportional Reasoning

Contemporary psychological research that studies how people apply mathematics has largely viewed mathematics as a computational tool for deriving an answer. The tacit assumption has been that people first understand a situation, and then choose which computations to apply. We examine an alternative assumption that mathematics can also serve as a tool that helps one to construct an understanding of a situation in the first place. Three studies were conducted with 6th-grade children in the context of proportional situations because early proportional reasoning is a premier example of where mathematics may provide new understanding of the world. The children predicted whether two differently-sized glasses of orange juice would taste the same when they were filled from a single carton of juice made from concentrate and water. To examine the relative contributions and interactions of situational and mathematical knowledge, we manipulated the formal features of the problem display (e.g., diagram vs. photograph) and the numerical complexity (e.g., divisibility) of the containers and the ingredient ratios. When the problem was presented as a diagram with complex numbers, or “realistically” with easy numbers, the children predicted the glasses would taste different because one glass had more juice than the other. But, when the problem was presented realistically with complex numbers, the children predicted the glasses would taste the same on the basis of empirical knowledge (e.g., “Juice can't change by itself”). And finally, when the problem was presented as a diagram with easy numbers, the children predicted the glasses would taste the same on the basis of proportional relations. These complex interactions illuminate how mathematical and empirical knowledge can jointly constrain the construction of a new understanding of the world. We propose that mathematics helped in the case of successful proportional reasoning because it made a complex empirical situation cognitively tractable, and thereby helped the children construct mental models of that situation. We sketch one aspect of the mental models that are constructed in the domain of quantity—a preference for specificity—that helps explain the current findings.     

Heuristic Value of Eclecticism in Theory Development: The Case of Piagetian-Vygotskian <Emphasis Type="Italic">dialogue</Emphasis> about Proportional Reasoning

Køppe’s proposition of four layers in theoretical building are used here in the exploration of a specific case of eclectic combination, the use of Piagetian and Vygotskian general approaches to the analysis of proportional reasoning as a cognitive mathematical ability. It is proposed here that the eclectic consideration of these contributions depends on the consideration of their specificity, in the sense that they highlight different aspects of the phenomenon under scrutiny, and also on the consideration of the coherence between this eclectic convergence and premises in terms of schools of thought under which each contribution is framed. We conclude proposing in accordance to S. Køppe’s proposal that eclecticism can be valuable and heuristic in theory development, but this contribution will depend largely on the effort in establishing careful relations between the four layers of theory-building.     

不同任务类型条件下4～6年级儿童比例推理策略的表现

随机选取小学4~6年级被试86名,从辅助策略、比例推理策略的策略选择和策略效用三方面,通过五种类型的天平任务考察儿童比例推理策略的表现。结果表明:(1)儿童最常使用手指动作辅助加工基本数量信息。辅助策略的使用率随年龄增长而减少,五年级开始使用出声思维,反映出元认知能力的发展。(2)在正式学习比例知识之前,各年级儿童都能使用两种以上策略,也能根据任务难度自发产生新策略,具备策略选择的多样性和适应性。其中,三个年级均能使用定性比例推理策略(双维策略,IIIA策略,补偿策略),表明儿童初步认识了距离和重量两个维度的共变关系。此外,六年级儿童能使用"运货车策略"将冲突问题灵活地化解为简单问题。(3)儿童的错误策略表现为:在冲突任务中盲目使用补偿策略、简单策略或加法策略。(4)分层回归分析表明,在控制年龄后,儿童的一般推理能力越高,其对重量策略的依赖性越低,且可能更容易发掘距离维度的意义,其使用运货车策略的频次更多。此外,一般推理能力对解决冲突类天平任务的正确次数有正向预测作用。     

工作记忆对类比推理的影响

该实验采用2(类比推理类型)×6(组别)双因素实验设计来探讨工作记忆与类比推理之间的关系,尤其关注工作记忆的各个子成分对类比推理的影响。控制组的被试只需完成类比推理测验,而实验组的被试是在双任务的条件下进行实验。结果表明,工作记忆是影响类比推理的一个重要因素。在图形类比推理中,主要有视空间模板中的空间成分,语音回路中的发音成分以及中央执行器的参与;在言语类比推理中,则是视空间模板中的空间成分起主要作用。     

Development of Conditional Reasoning: A Longitudinal Study

This study examines the development of conditional reasoning within a longitudinal design. Two age cohorts were assessed each year for 3 years. One cohort began the investigation as 6th-grade students (M = 11 years, 6 months of age); the other cohort began as 8th-grade students (M =13 years, 8 months of age). At each measurement point, each participant completed 5 reasoning problems consisting of modified versions of the Wason Selection Task (Overton, 1990). Results demonstrated a significant improvement in reasoning performance for each cohort. Furthermore, participants performed better when "if-then" propositions were formulated with the antecedent phrase specifying an action and the consequent specifying a condition, than they did when the antecedent specified a condition and the consequent an action. The results are consistent with the position that the development of logical thinking moves toward the integration of inferential schemes into a systematic network, and that this network is not consistently available before adolescence.     

幼儿非形式推理能力的发生与发展

针对在儿童非形式推理能力发生研究中评价标准不一和研究结果中发生年龄不同的问题,在论证并提出幼儿非形式推理发生评价标准的基础上,采用提示访谈法对333名3-6岁幼儿的非形式推理做了考察。结果显示:幼儿的我方推理普遍在3岁3个月～3岁9个月发生;他方推理普遍在4岁～4岁6个月发生;反驳推理普遍在4岁9个月～6岁发生。幼儿在推理过程中提出的理由数量随年龄的增长而增多,年龄差异显著,但无显著性别差异。研究中建立的评价指标体系可以有效测量幼儿非形式推理的发生和发展。     

因果信息在贝叶斯推理中的作用:问题情境的调节

以大学生为被试,考察因果信息在不同贝叶斯推理问题中的作用。结果表明:(1)问题情境的主效应显著(F(1,122)=16.33,p0.05,η~2=0.120),因果信息的主效应不显著((F(1,122)=1.161,p=0.283,η~2=0.01),但问题类型和因果信息的交互作用显著(F(1,122)=4.757,p0.05,η~2=0.038)。(2)不同类型的问题上因果信息的作用是不同的。具体表现为,在乳癌问题中,增加了因果信息,被试的正确率明显提高(χ~2(1)=6.759,p0.05,V=0.607),而在中彩问题中没有因果信息的推理成绩反而更好(χ~2(1)=1.864,p=0.221,V=0.167)。     

Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables

Multinomial processing tree models assume that discrete cognitive states determine observed response frequencies. Generalized processing tree (GPT) models extend this conceptual framework to continuous variables such as response times, process-tracing measures, or neurophysiological variables. GPT models assume finite-mixture distributions, with weights determined by a processing tree structure, and continuous components modeled by parameterized distributions such as Gaussians with separate or shared parameters across states. We discuss identifiability, parameter estimation, model testing, a modeling syntax, and the improved precision of GPT estimates. Finally, a GPT version of the feature comparison model of semantic categorization is applied to computer-mouse trajectories.