探测认知发展的非连续性:思路与方法

认知发展是连续性的还是非连续性的是发展心理学中一个重要理论问题.目前研究者逐渐认识到发展既有连续性的也有非连续性的,因而关键的问题是什么情况下是非连续性的,什么情况下是连续性的.该问题的回答与非连续性的检测标准有很大关系.本研究详细介绍了考察发展非连续性的三种思路和方法:量表图分析和多重任务法;Rasch模型分析和Saltus模型分析;突变理论的应用.最后,强调了影响发展非连续性问题探讨的一些因素.     

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

     

Stagewise cognitive development: an application of catastrophe theory.

In this article an overview is given of traditional methodological approaches to stagewise cognitive developmental research. These approaches are evaluated and integrated on the basis of catastrophe theory. In particular, catastrophe theory specifies a set of common criteria for testing the discontinuity hypothesis proposed by Piaget. Separate criteria correspond to distinct methods used in cognitive developmental research. Such criteria are, for instance, the detection of spurts in development, bimodality of test scores, and increased variability of responses during transitional periods. When a genuine stage transition is present, these criteria are expected to be satisfied. A revised catastrophe model accommodating these criteria is proposed for the stage transition in cognitive development from the preoperational to the concrete operational stage.     

The role of surface discontinuity and shape in 4-month-old infants' object segregation

This research examined whether 4-month-old infants use a discontinuity in an object's front surface to visually segregate a display into two separate objects, and whether object shape enables its use. In Experiment 1, infants saw a three-dimensional display composed of two parts with distinctly different shapes. Two groups of infants saw a display in which these two shapes were divided by a visible discontinuity in the front surface (i.e., a boundary between the two objects). One of these groups saw the display move apart at the discontinuity when a gloved hand pulled one object; the second group saw the two objects move together as a single unit. A third group saw a modified version of this display that had no discontinuity present. The results suggested that infants regarded the discontinuity as an indication that the display could be composed of more than one object. In Experiment 2, infants saw the same display, but with a shape that did not highlight the discontinuity. The infants in this study showed no evidence of using the discontinuity. Together, the findings suggest that 4-month-old infants use the surface discontinuity between two objects as an indication that multiple objects could be present in a display, but only when scanning the outer edges of the display leads them to attend to it.     

A connectionist model of a continuous developmental transition in the balance scale task

A connectionist model of the balance scale task is presented which exhibits developmental transitions between ‘Rule I’ and ‘Rule II’ behavior [Siegler, R. S. (1976). Three aspects of cognitive development. Cognitive Psychology,8, 481–520.] as well as the ‘catastrophe flags’ seen in data from Jansen and van der Maas [Jansen, B. R. J., & van der Maas, H. L. J. (2001). Evidence for the phase transition from Rule I to Rule II on the balance scale task. Developmental Review, 21, 450–494]. The model extends a connectionist model of this task [McClelland, J. L. (1989). Parallel distributed processing: Implications for cognition and development. In R. G. M. Morris (Ed.), Parallel distributed processing: Implications for psychology and neurobiology (pp. 8–45). Oxford: Clarendon Press] by introducing intrinsic variability into processing and by allowing the network to adapt during testing in response to its own outputs. The simulations direct attention to several aspects of the experimental data indicating that children generally show gradual change in sensitivity to the distance dimension on the balance scale. While a few children show larger changes than are characteristic of the model, its ability to account for nearly all of the data using continuous processes is consistent with the view that the transition from Rule I to Rule II behavior is typically continuous rather than discrete in nature.     

背景线索对视觉客体连续性表征的影响

该研究考察了背景线索连续性对客体心理表征连续性的作用。采用2（目标客体运动形式：连续和不连续）×2（引导线索运动形式：连续和不连续）两因素被试内设计,12名被试参加实验。结果发现,目标客体在时空上不连续时,连续线索条件下对颜色变化检测反应时小于线索不连续条件;目标客体在时空上连续运动时,不连续线索条件下对目标颜色变化的检测反应时高于线索连续条件。因此,不连续背景线索对物理层面上连续运动客体的表征有干扰影响：连续背景线索对物理层面上不连续运动客体的表征有促进作用。这说明特殊的时空条件如背景线索引导会对客体表征连续性产生重要影响。     

Stochastic catastrophe analysis of switches in the perception of apparent motion

Dynamical phenomena such as bistability and hysteresis have been found in a number of studies on perception of apparent motion. We show that new developments in stochastic catastrophe theory make it possible to test models of these phenomena empirically. Catastrophe theory explains discontinuous changes in responses caused by continuous changes in experimental parameters. We propose catastrophe models for two experimental paradigms on perception of apparent motion and present experiments that support these models. We test these models by using an algorithm for fitting stochastic catastrophe models. We derive from catastrophe theory the prediction that a dynamical phenomenon called divergence is necessary when hysteresis is found. This new prediction is supported by the data.     

Anxiety‐induced performance catastrophes: Investigating effort required as an asymmetry factor

Two studies are reported that test the hypothesis that previous support for the cusp catastrophe model of anxiety and performance, and the hysteresis effect in particular, could have been due to a complex interaction between cognitive anxiety and effort required rather than between cognitive anxiety and physiological arousal. We used task difficulty to manipulate effort required in a letter transformation task. Experiment 1 (N=32) used high levels of trait anxiety together with a competitive environment to induce state anxiety. Experiment 2 (N=20) used a competitive environment with social pressure and ego threat instructions to induce high levels of worry. Both studies revealed significant three‐way interactions as hypothesized with follow‐up tests showing some support for the hysteresis hypothesis in Study 1, and strong support for the hysteresis hypothesis in Study 2. The findings support a processing efficiency theory explanation of anxiety‐induced performance catastrophes and indicate that two cusp catastrophe models of performance may exist; one that incorporates the interactive effects of cognitive anxiety and physiological arousal upon performance and the other that incorporates the interactive effects of cognitive anxiety and effort required upon performance.     

Explaining social contagion in sport applying Heider's balance theory: First experimental results

A sudden collective collapse of an entire sport team is often described in terms of the social contagion of weak performance. Two experiments studied this phenomenon against the backdrop of balance theory. Experiment 1 examined whether false negative feedback on a partner's performance during a team task would lead to compensatory mechanisms as predicted by balance theory. Results showed that perceived negative performance in the partner was compensated by devaluing the relationship to the partner. Experiment 2 replicated Experiment 1 and investigated the impact of physical self-esteem. Results showed that persons with strong physical self-esteem devalued the situational value of the relationship when they perceived their partner's performance to be negative. Experiment 2 also investigated objective performance. Although failing to attain statistical significance, there was a tendency for the perceived sudden decline in the partner's performance to be contagious. It is concluded that balance theory offers promising insights into the interpersonal dynamics of social contagion.     

The dynamics of development on the Dimensional Change Card Sorting task

A widely used paradigm to study cognitive flexibility in preschoolers is the Dimensional Change Card Sorting (DCCS) task. The developmental dynamics of DCCS performance was studied in a cross-sectional design (N = 93, 3 to 5 years of age) using a computerized version of the standard DCCS task. A model-based analysis of the data showed that development on the DCCS task is best described as a discontinuous change in performance on the post-switch phase of the task. In addition to a perseveration group and a switch group, a transitional group that showed shifts between perseverating and switching during the post-switch trials could be distinguished. Computational models of performance and development on the DCCS task cannot, in their current forms, explain these results. We discuss how a catastrophe model of the developmental changes in task performance could be used to generate specific hypotheses about the variables that control development of DCCS performance.     

The development of children's rule use on the balance scale task

Cognitive development can be characterized by a sequence of increasingly complex rules or strategies for solving problems. Our work focuses on the development of children's proportional reasoning, assessed by the balance scale task using Siegler's (1976, 1981) rule assessment methodology. We studied whether children use rules, whether children of different ages use qualitatively different rules, and whether rules are used consistently. Nonverbal balance scale problems were administered to 805 participants between 5 and 19 years of age. Latent class analyses indicate that children use rules, that children of different ages use different rules, and that both consistent and inconsistent use of rules occurs. A model for the development of reasoning about the balance scale task is proposed. The model is a restricted form of the overlapping waves model (Siegler, 1996) and predicts both discontinuous and gradual transitions between rules.     

Key pecking in pigeons produced by pairing keylight with inaccessible grain

In Experiment I, keylight was paired with inaccessible grain delivery (under two conditions of keylight intensity) to determine if autoshaping would occur in the absence of primary reinforcement. In Experiment II, the procedure was repeated with accessible grain, for comparison. In Experiment III, the procedures were repeated with explicitly unpaired presentations of keylight and either inaccessible or accessible grain. The results indicated that key pecking occurred as quickly in the presence of keylight pairings with inaccessible grain as with accessible grain, though (except for one bird) key pecking was not maintained with inaccessible grain. Furthermore, compared to the dim keylight, the bright keylight greatly suppressed key pecking when paired with inaccessible grain, and reduced the rate of key pecking when paired with accessible grain. Little key pecking occurred in groups exposed to explicitly unpaired presentations of keylight (whether bright or dim) and grain (whether accessible or inaccessible). When the birds in Experiment III were retested with explicitly paired presentations of keylight and grain, little key pecking was observed, suggesting suppressive effects of prior explicitly unpaired presentations. It is suggested that the effects of key-brightness manipulation were produced by the association of grain with cues other than the response key, or by distraction produced by partial illumination of the grain hopper.     

Levels of number knowledge during early childhood

Researchers have long disagreed about whether number concepts are essentially continuous (unchanging) or discontinuous over development. Among those who take the discontinuity position, there is disagreement about how development proceeds. The current study addressed these questions with new quantitative analyses of children’s incorrect responses on the Give-N task. Using data from 280 children, ages 2 to 4 years, this study showed that most wrong answers were simply guesses, not counting or estimation errors. Their mean was unrelated to the target number, and they were lower-bounded by the numbers children actually knew. In addition, children learned the number-word meanings one at a time and in order; they treated the number words as mutually exclusive; and once they figured out the cardinal principle of counting, they generalized this principle to the rest of their count list. Findings support the ‘discontinuity’ account of number development in general and the ‘knower-levels’ account in particular.     

为“金规则”辨

学界近年在对“己所不欲,勿施于人”这个中国式的“金规则”的议论中,存在不少误读、误解。择要言之,一是将“金规则”之“金”理解为“道德价值最高”;二是用“知道做不到”质疑、贬低“金规则”;三是以“不同”的存在否证“金规则”：四是认为“金规则”不适合现代社会。然而经过仔细辨析可以发现,这些其实都是不确之语。     

The Rule of Opposites: A Paradigm for Counseling Native Americans

The Rule of Opposites offers a cultural lesson in perspective that is useful for counselors working with Native American clients. The Rule of Opposites, based on the concept of the Circle of Life, is presented as a worldview that allows individuals to move beyond their current frame of reference toward an understanding of universal truths and underlying meanings. Use of the Rule's 7 lessons helps both the counselor and the client to recognize and resolve conflict, to ask more effective questions, to seek harmony and balance in life for greater purpose and direction, and to explore personal decision making and choices.     

Rahner's Rule: An Emperor without Clothes?

Abstract:  Karl Rahner's famous Rule, 'The "economic" Trinity is the "immanent" Trinity, and the "immanent" Trinity is the "economic" Trinity', has had an enormous impact on trinitarian theology. Yet it is extraordinarily difficult to identify a reading of the Rule that meets two essential criteria: (1) it is interesting (that is, not trivial), and (2) it is possibly true. In this paper I consider three possible readings: strict realist, loose realist, and finally antirealist. Unfortunately, each reading leaves the Rule either trivial or obviously false and so fails to meet both criteria, thus calling into question the theological value of the Rule.     

Resources and the Rule of Rescue1

abstract The central issue that I consider in this paper is the use of the so‐called ‘Rule of Rescue’ in the context of resource allocation. This ‘Rule’ has played an important role in resource allocation decisions in various parts of the world. It was invoked in Ontario to overturn a decision not to fund treatment for Gaucher's Disease and it has also been used to justify resource decisions in Israel concerning the same condition. In the paper I consider the nature of the Rule of Rescue and its moral justification. The latter involves consideration of the distinction between agent‐relative and agent‐neutral obligations. If the Rule of Rescue is to be justified, it is plausible to think that it will be in the context of agent‐relative obligations. Two problems with this suggestion are considered: the role of identifiability in the Rule of Rescue and the extent to which policy makers in a health care system can be taken to have such obligations. It is argued that in both cases these problems can be overcome and hence that there is a prima facie obligation to follow the Rule of Rescue.     

A Topological Model of Epistemic Intentionality

Beyond their linguistic and rhetorical uses, the mental epistemic verbs to knowand to believe reveal a basic conceptual system for human intentionality and the theory of representational mind. Numerous studies, particularly in the field of child development, have been devoted to the conditions under which knowledge and belief are acquired. Upstream of this empirical approach, this paper proposes a topological model of the conceptual structure underlying the linguistic use of to know and to believe. A cusp model of catastrophe theory is chosen to model the formation of epistemic states. Its main characteristic is considering to believe as an intermediate state which lacks stability and presents the delayed effect of hysteresis. The attribution of mental states to the other (viewpoint of the third person) is obtained by the crossing of first and third person knowledge and belief, which gives rise to new categories (to know if and to falsely believe) and closes the system. Another merging of the beliefs of persons A and B, using the butterfly catastrophe, provides a model of interpersonal belief appreciated by an independent observer along a potential evolving from agreement to disagreement. This revised version was published online in August 2006 with corrections to the Cover Date.     

Rule Consequentialism and the Problem of Partial Acceptance

Most plausible moral theories must address problems of partial acceptance or partial compliance. The aim of this paper is to examine some proposed ways of dealing with partial acceptance problems as well as to introduce a new Rule Utilitarian suggestion. Here I survey three forms of Rule Utilitarianism, each of which represents a distinct approach to solving partial acceptance issues. I examine Fixed Rate, Variable Rate, and Optimum Rate Rule Utilitarianism, and argue that a new approach, Maximizing Expectation Rate Rule Utilitarianism, better solves partial acceptance problems.