基于关系-表征复杂性模型的数学应用题表征能力测验

基于关系-表征复杂性模型,从每道应用题涉及集合关系的嵌套程度角度事前分析其关系复杂性,编制了难度序列变化的应用题测验,以考察问题表征能力。采用该测验测查了四至七年级共165名学生,考察事前分析的合理性及表征水平随年龄的变化。结果表明:(1)事前分析对两个事后难度指标(错误率和Rasch模型分析的任务难度)的解释率分别为73.7%、78.7%;该测验得分与测查思维水平层次变化的SOLO分类测验上的得分有较高相关(r=0.65)。(2)四年级的应用题表征水平显著低于五、六、七年级,其他三个年级差异不显著;而且随着问题关系复杂性的增加,年级差异增大。这说明基于关系-表征复杂性模型的事前分析是合理的,据此编制的测验能够测查表征水平随年龄的变化。     

儿童图形表征能力测验编制的初步报告

表征能力发展部分地体现为对事物中隐含关系的理解或推理的复杂程度.基于辛自强的"关系-表征复杂性模型",结合Halford的"关系复杂性"理论,通过事前分析任务复杂性确定了难度不同的项目,最终编制成儿童图形表征能力测验,该测验共50个(25类)项目.以265名小学3~6年级儿童为被试,采用计算机呈现方式施测了该测验.结果表明:项目的难度和区分度以及整个测验的重测信度、构想效度、效标关联效度均良好;基于理论的事前任务分析(确定任务的维度数与每个维度内的元素数)对事后任务难度的预测率较高(83.4%).可见,所编制的图形测验能有效测查儿童表征水平.     

关系-表征复杂性模型

基于已有理论和研究背景所提出的关系-表征复杂性模型可以用作任务关系复杂性和儿童对其表征水平的分析框架,对于认知发展研究有较为普遍的意义。本文对关系复杂性(等级复杂性、关系内的和关系间的水平复杂性)、表征复杂性(表征广度、表征深度)以及各自的从属概念进行了理论界定。     

5～9岁儿童在不同复杂性任务上类比推理的发展特点

采用经典的A:B:C:D范式,设计两类难度不同的图片任务,依据关系-表征复杂性模型从等级复杂性和水平复杂性角度分析任务难度.在此基础上,选取5～9岁115名儿童探讨两类任务上类比推理的特点和发展趋势.表明:(1)儿童类比推理呈现多样化特点,主要有:充分意义上掌握了类比推理、部分完成了类比推理、位置关系类比推理、不能类比推理和不确定情况类比推理,其中部分完成了类比推理是复杂任务上所特有的.(2)简单、复杂两类任务上,随着年龄增长,5-9岁儿童充分意义上掌握类比推理的人次比例不断上升,不能类比推理的人次比例不断下降.此外,复杂任务上,随年龄增长,部分完成类比任务的人次比例降低.结果表明,在简单任务上,前运算阶段儿童已具备了类比推理能力;但在复杂任务上,儿童到了具体运算阶段才具备类比推理能力.     

关系-表征复杂性模型的检验

目前有关问题难度的观点多是不全面的,在综合前人研究的基础上提出了关系-表征复杂性模型。在该模型里,区分了问题难度和问题解决难度两个概念,二者的本质分别是关系复杂性和表征复杂性;关系复杂性包括水平复杂性和等级复杂性,表征复杂性相应地包括表征广度和表征深度。以172名小学高年级学生为被试,以长方形面积问题方面的三种测验收集的数据对该模型的内部和外部效度进行了检验,结果表明它能够有效解释问题（解决）难度,区分优、中、差三类学生所能达到的表征复杂性。这说明该模型有理论价值     

关系复杂性理论述评

任务复杂性的分析是发展心理学和心理测量学都非常关注的重要课题。哈尔福德等人提出了评估任务难度的关系复杂性理论,认为任务难度可由相关的变量数量即关系复杂性来确定;关系复杂性越大加工要求也越高,这时可采取概念组块和分解机制来减少复杂性;认知发展阶段可归因于随着年龄的增长能够加工的关系复杂性的增加。虽然该理论得到了很多实验证据的支持,但也存在一些不足。主要不足表现在没有区别问题难度与问题解决难度,对维度层次关系不够重视,以及一些基本的理论问题没有明确阐述。这都是今后进一步研究应解决的问题。     

智力和元认知技能在发现学习中的作用:任务复杂性的影响

采用自编的计算机模拟发现学习任务,以49名大学生为被试,探讨了在简单和复杂发现学习任务中,智力、元认知技能和学习成绩三者之间的关系。结果发现:在简单任务中,三者关系基本符合混合模型;进行过多的元认知活动,并不能提高学习效果。在复杂任务中,智力对学习成绩起主要预测作用。随着任务复杂性的增加,智力对学习的影响也随之变化,符合难度阈限理论的假设。任务复杂性不同时,智力、元认知技能和发现学习成绩之间的关系也不同,在一定程度上验证了难度阈限扩展理论。     

问题表征与知识建构研究及其意义

人类智能有相互区别又联系的"三重"信息加工、知识建构与智慧生成.以该三重智能构想为基础在信息加工层面研究了问题的表征,提出关系-表征复杂性模型,分别用关系复杂性(包括水平的和等级的复杂性)解释任务难度,用表征复杂性(表征广度和深度)衡量表征能力.在知识获得层面,结合建构主义与认知心理学的技术和微观发生法等思路,可以探讨知识微观建构中可能发生的具体变化,如策略性知识在一般性和特殊性之间循环,程序性知识向概念性知识的转化等.     

小学生数学问题表征发展与流体智力的关系

基于关系一表征复杂性模型编制了复杂程度能序列变化的长方形面积问题,以此测量了4～6年级共310名学生的问题表征水平及其与由瑞文标准推理测验测定的流体智力的关系.结果表明, (1)被试对长方形面积问题的表征水平与流体智力有显著相关; (2)表征复杂性水平随年级的升高而升高.可见,基于该模型所设计的材料能测定随年龄而变化的表征水平.且与经典的流体智力测验结果有稳定的关联.由此体现出该模型的合理性.     

任务难度、决策培训诸因素对群体决策的影响

通过3人群体的人员选拔模拟实验。考察了任务难度、群体结构和决策培训三个变量对群体决策信息取样的影响。结果显示：(1)部分证明了Stasser的信息取样模型,分享信息具有讨论的优势,同时偏好是影响群体决策的中介因素,但是,该模型只适合于任务难度较大的情况;(2)设立具有信息管理作用的领导者这种群体结构在信息取样中没有表现出主效应,它只是通过与决策培训和任务难度一起对信息取样产生影响;(3)策略计划和信息警戒性的决策培训对信息取样有影响,一定程度上提高了非分享信息的讨论比例,然而这种影响仅发生在任务难度小或适中的情况下。决策培训对信息取样的影响发生在讨论的开始部分,并影响了讨论前的个体偏好;(4)群体结构和决策培训具有交互作用,从而影响了群体讨论的信息取样,群体结构和决策培训都受到任务难度的影响。     

Young children's performance on the balance scale: the influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains--transitivity and class inclusion--accounted for 93% of the age-related variance in balance scale scores.     

基于潜在类别分析的6~15岁儿童平衡秤任务认知规则探索

本研究使用自编平衡秤测验测试468名6~15岁儿童,通过潜在类别分析对认知规则进行分类。结果发现,被试使用了规则Ⅰ、规则Ⅰ'、规则Ⅱ、补偿规则、规则Ⅳ、距离优势规则等六种规则;6~9岁儿童主要使用规则Ⅰ;10~13岁儿童主要使用补偿规则;14岁以上儿童主要使用规则Ⅳ;13岁到14岁之间,使用规则Ⅳ的儿童数量呈跳跃式增加。与规则评估技术相比,潜在类别分析用于认知规则研究具有明显优势,最后对运用此方法的前提假设与局限进行了讨论。     

Rule transition on the balance scale task: a case study in belief change

For various domains in proportional reasoning cognitive development is characterized as a progression through a series of increasingly complex rules. A multiplicative relationship between two task features, such as weight and distance information of blocks placed at both sides of the fulcrum of a balance scale, appears difficult to discover. During development, children change their beliefs about the balance scale several times: from a focus on the weight dimension (Rule I) to occasionally considering the distance dimension (Rule II), guessing (Rule III), and applying multiplication (Rule IV; Siegler, 1981). Because of the detailed empirical findings the balance scale task has become a benchmark task for computational models of proportional reasoning. In this article, we present a large empirical study (N = 420) of which the findings provide a challenge for computational models. The effect of feedback and the effect of individually adapted training items on rule transition were tested for children using Rule I or Rule II. Presenting adapted training items initiates belief revision for Rule I but not for Rule II. The experience of making mistakes (by providing feedback) induces a change for both Rule I and Rule II. However, a delayed posttest shows that these changes are preserved after 2 weeks only for children using Rule I. We conclude that the transition from Rule I to Rule II differs from the transition from Rule II to a more complex rule. Concerning these empirical findings, we will review performance of computational models and the implications for a future belief revision model.

It is one Thing, to show a Man that he is in an Error, and another, to put him in possession of Truth. John Locke

     

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。     

What response times tell of children's behavior on the balance scale task

Analysis of accuracy of responses to balance scale problems gives a global idea of the cognitive processes that underlie problem-solving behavior on this task. We show that response times (RTs) provide additional detailed information about the kind and duration of these processes. We derive predictions about the RTs from Siegler's (1981) model for the balance scale task, including the counterintuitive prediction that young adults are slower than children in solving particular balance scale problems. The predictions were tested in a study in which 191 6- to 22-year-old participants were presented with a computerized balance scale task. RTs were analyzed with regression models. In addition to qualitative differences between items, we also modeled quantitative differences between items in the regression models. Analyses supported the predictions and provided additional knowledge on the rules. Rule II was reformulated as a rule that always involves the encoding, but not always the correct application of the distance cue. RTs provided evidence for the use of a buggy-rule and not an addition-rule. Finally, a relation between rule inconsistency and increased RT was found.     

逻辑－信念冲突与推理难度对逻辑和信念判断的影响

双加工理论框架下的平行竞争模型和默认干涉模型对推理过程中启发式和分析式加工的启动次序和相互作用的性质提出了不同假设。本研究通过考察被试在信念判断和逻辑判断两种指导语下解决不同难度和不同类型推理问题的正确率和反应时,对两个模型的预测进行了检验。实验结果表明,解决简单问题时,问题类型对信念判断有显著影响,对逻辑判断无显著影响;解决复杂问题时,问题类型对逻辑判断的影响显著大于对信念判断的影响。实验结果支持平行竞争模型的假设,即两类加工在推理过程中同时启动,共同竞争最终的推理反应。     

Influence curves for factor loadings

Influence curves for the initial and rotated loadings are derived for the maximum likelihood factor analysis (MLFA) model. Cook's distances based on the empirical influence curves of factor loadings are proposed for the identification of influential observations. The distances are shown to be invariant under scale transformation and factor rotation. We find that an observation with a very large Cook's distance based on the sample influence curve may not necessarily exert an excessive influence on the factor loadings pattern but may change the ordering of the factors. The issue of the switching of factors is also studied by means of the empirical influence curve and factor scores.     

Towards better computational models of the balance scale task: a reply to Shultz and Takane

In contrast to Shultz and Takane [Shultz, T.R., & Takane, Y. (2007). Rule following and rule use in the balance-scale task. Cognition, in press, doi:10.1016/j.cognition.2006.12.004.] we do not accept that the traditional Rule Assessment Method (RAM) of scoring responses on the balance scale task has advantages over latent class analysis (LCA): RAM is similar to a very restricted form of LCA. The apparent shortcomings of LCA are also less severe than they suggest. Via new simulations we show that LCA detects small classes reliably. We also counter their concerns regarding the torque difference effect and we underline the problems connectionist models have with correctly responding to balance items. Despite these differences in opinion we agree with Shultz and Takane on the possible avenues for future research.