论数学问题解决中情境模型与问题模型的关系

情境模型与问题模型是数学问题解决研究中的两个重要概念,前者是对问题所述情境的日常化的定性表征,后者是基于图式知识对问题关键变量的数量关系表征。本文介绍了两种模型的发展历史以及目前存在的争议,并提出了未来研究需要解决的问题。     

Thinking Inside the Tool Box: Creativity,Constraints, and the Colossal Portraits of Chuck Close

This article presents a problem‐solving model to examine the often problematic relationship between expertise and creativity. The model has two premises, each the opposite of a common cliché. The first cliché asserts that creativity requires thinking outside‐the‐box. The first premise argues that experts can only think and problem solve inside the tool boxes of their expertise. The second cliché, that creativity requires freedom from constraints, points to the problem with expertise. Free to do anything, experts repeat what has worked best in the past. A solution is suggested by the second premise: to circumvent the liabilities of expertise, creativity requires constraints of a particular paired kind. The model is introduced as an expansion of prior process models focused on problem identification and construction. Problem‐finding is reanalyzed as constraint‐finding. A case study shows how one recognized creator, painter Chuck Close, uses constraints as a tool to solve the expertise‐creativity problem.     

小学生应用题表征的类型和特点

以124名小学六年级学生为被试。采用应用题解决问卷考查了我国小学生应用题表征的类型和特点。结果表明小学生应用题的表征方式有复述内容、图式表征、图片表征、直译表征、语义结构分析等;成功解题者和不成功解题者对各种表征方式的使用次数上没有显着差异;成功解题者和不成功解题者在各种表征方式下的解题成绩有显着差异,成功解题者在图式表征、直译表征和语义结构分析表征下的成绩显着优于不成功解题者。     

心理表征对正投影问题解决及轴测投影图再认水平的影响

借鉴内隐记忆的研究范式,采用平面、分离的正投影问题解决及其相应轴测投影图的再认任务,探讨问题表征的结构特征性对空间问题解决和再认水平的影响。实验结果表明,一般在正投影问题获得正确解决时,对其相应的、先前从未见到过的轴测投影图往往也可获得正确再认,而且基于正投影问题获得正确解决条件下的再认水平（PCC）显著地高于那些问题未得获得解决下的再认水平（PCI）。在结合被试口语记录的基础上,研究结果证明：基于正投影图上的问题解决过程是受到一个具有三维结构特性而非正投影图中二维特性心理表征的调节;并且,正是这一具有三维结构特性心理表征的建构,使得对具有相同结构特性的轴测投影图获得了更为有效的再认。     

Adolescent problem behavior: The effect of peers and the moderating role of father absence and the mother-child relationship

Examined the effect of peer problem behavior, the absence of a father or equivalent in the home, and the mother-adolescent relationship as predictors of adolescent problem behavior in a sample of 112 African American adolescents. Statistical analyses compared a moderator model to a mediational model and a cumulative risk model. As predicted, the moderator model was superior to the alternative models. Specifically, whereas the mediational model predicted that the effect of father absence and the mother-child relationship upon adolescent problem behavior would be mediated by peer problem behavior, neither effected peer problem behavior or adolescent problem behavior. Similarly, a cumulative risk index did not predict either child or parent reports of problem behavior and was not sensitive to specific contingencies that existed between the predictor variables. In contrast, an interactive, moderator model described the data quite well. This model suggested that father or equivalent absence magnifies the negative impact of peer problem behavior, while a positive mother-adolescent relationship attenuates this risk. A strong mother-adolescent relationship also served to protect adolescents in father-absent homes from the risk of peer problem behavior. This research was supported by a grant (NICHHD: HD24056) awarded to A. M. Cauce. The authors thank Nydia Ordonez, Tanya Aguilar, and Laurie Deppman for their assistance on the project, and Cliff Lunneberg for suggestions regarding resampling procedures. Portions of this paper were presented at the meetings of the Western Psychological Association, April 1992.     

Creative Thinking Strategies for Life: A Course for Professional Adults Using Art

To thrive in today's economy and the workforce of the future, individuals need creativity and problem-solving skills. Emotion skills have been increasingly discussed as well, with companies listing emotional intelligence as one of the top skills needed for professional success. The present paper describes a course designed to teach professional adults two sets of creativity skills (problem finding and idea generation) and two sets of emotional intelligence skills (using emotions to facilitate thinking and understanding emotions) using visual art as a medium. The course consisted of eight, 60-min sessions in which professional adults participated in art observation and art engagement activities. Fifty-six professional adults completed measures of creative abilities and emotional intelligence skills in a pretest, posttest, and 2-month follow-up design. Participants who engaged in the course showed significant gains in the originality of their ideas on divergent thinking and problem construction tasks, as well as their self-reported creative behavior compared with controls. No significant changes in emotion understanding were detected. We discuss the course's distinct value to creativity and emotion skills training research.     

Implications and refinements of the establishing operation concept

In this paper I discuss (a) three steps in the development of establishing operation (EO) terminology, (b) my early neglect of its possible relevance to applied behavior analysis, (c) the importance of functional analysis methodology for increasing awareness of EO issues, and (d) three comprehensive reviews that clarify the role of EOs in applied work. I then review and further analyze seven topics that require further clarification or that have been raised since my 1982 and 1993 articles: the EO evocative effect, deprivation and satiation, problem behavior maintained by attention, decreasing behavior evoked by a transitive conditioned establishing operation, EOs in the context of escape and avoidance, academic demand, and decreasing behavior evoked by a reflexive conditioned establishing operation.     

关于问题难度的实验研究

利用一种新型的人工问题,探讨了一些影响问题难度的因素。结果表明：未知参数越多,问题难度越大;中间未知参数不予提示时问题难度显著提高;参数排列方式越乱,问题难度越大;供选择的操作数越多,问题难度越大;供选择的操作的相似性越强,问题难度就越大;对过去题目中某些特征的意识水平越高,经验就越容易迁移,从而影响难度。     

问题解决:涵义、过程与教学模式

提高学生解决问题能力已经成为现代教育的一个重要目标。问题解决就是由一定情境引起的,按照一定的目标,应用各种认知活动、技能等,经过一系列思维操作,使问题得以解决的过程。本文界定了问题和问题解决的概念内涵,构建了问题解决的过程模型,进而提出了问题解决的教学模式和教学策略。     

数学解题过程的眼动研究

数学解题过程的眼动研究可划分为3个阶段：第一阶段是对数字运算过程的眼动研究,第二阶段是对数学应用题解题过程的眼动研究,第三阶段是对几何题解题过程的眼动研究。在我国,对数学解题过程的眼动研究尚为空白。加强这一领域的研究,可以深化对数学问题表征的认识,对数学学科的教与学具有重要意义。     

Problem Solving Therapy

This paper describes how problem solving therapy (PST) would be applied to the treatment of Sylvia (I. Caro, 2001), a 27-year-old depressed wife and mother of three. PST involves training individuals in five major processes: problem orientation, problem definition and formulation, generation of alternatives, decision making, and solution implementation and verification. We briefly describe a problem solving model of depression that highlights the moderating nature of problem solving ability regarding the stress–depression relationship. Based on this model, we then delineate how PST can be specifically applied to Sylvia. This is followed by a brief overview of the research base supporting the efficacy of PST for depression.     

From Walls to Windows: Using Barriers as Pathways to Insightful Solutions

The purpose of this study was to explore and develop a conceptual model for how individuals unlock insight. The concept of insight — the ‘out of the box’ or ‘aha!’ solution to a problem — offers a framework for exploring and understanding how best to enhance problem solving skills due to the cognitive shift insight requires. Creative problem solving (CPS) is inherent to a variety of performance realms including effective decision making, innovation, and organizational development; however, related processes of insight, innovation and creativity remain intangible. The model, based on a review of the problem solving literature, proposes that insight involves a five stage, cyclical process emerging as: primary appraisal of the problem, secondary appraisal based on prior knowledge, initial focus, problem representation, and solution generation when, if no solution is found, the cycle begins again. The research has implications for individual, team and organizational settings suggesting that performance on a wide variety of problems may be improved by utilizing an integrated focus rather than a barrier or goal focus alone.     

问题发现研究述评

问题发现的重要性很早就引起了学者们的关注,但有关这方面的研究成果并不丰富。文章概述了在艺术、生活、教育以及相关研究等领域有关问题发现的实验研究成果,分析了现有研究存在的不足并就未来的研究方向提出了自己的观点。     

顿悟与问题表征的转变

阐述了解决残缺棋盘问题的顿悟过程。该实验的结果证明,顿悟过程中需要发现一种正确的问题表征,即对等性问题空间,为了发现这一表征,被试必须使问题表征从“铺试问题空间”转变为“元水平的问题空间”．被试在这两个空间中进行搜索时,必须有很强的限制,使搜索成为有高度选择性的搜索,才能最终在元水平问题空间中发现正确的表征。本研究还发现,被试的搜索并不总是知觉驱动的,有时是概念驱动的,而且后者的迁移性更高。     

THOG问题的演译结构及其非Wason-Brooks判定方法

本文探讨THOG问题的演绎结构及其非Wason-Brooks判断方法,据于Wason-Brooks判断程序和THOG问题逻辑结构的分析导致如下结论：1．Wason-BrooksTHOG判定方法并非判定THOG的唯一方法;2、被试选择那一种演绎判定模式取决于被试如何对原问题进行等效表征转换;3．判断失败可能意味着被试存在短时记忆容量障碍或者等效表征转换障碍。     

Eight-dimensional methodology for innovative thinking about the case and ethics of the mount graham,large binocular telescope project

This paper introduces the Eight Dimensional Methodology for Innovative Thinking (the Eight Dimensional Methodology), for innovative problem solving, as a unified approach to case analysis that builds on comprehensive problem solving knowledge from industry, business, marketing, math, science, engineering, technology, arts, and daily life. It is designed to stimulate innovation by quickly generating unique “out of the box” unexpected and high quality solutions. It gives new insights and thinking strategies to solve everyday problems faced in the workplace, by helping decision makers to see otherwise obscure alternatives and solutions. Daniel Raviv, the engineer who developed the Eight Dimensional Methodology, and paper co-author, technology ethicist Rosalyn Berne, suggest that this tool can be especially useful in identifying solutions and alternatives for particular problems of engineering, and for the ethical challenges which arise with them. First, the Eight Dimensional Methodology helps to elucidate how what may appear to be a basic engineering problem also has ethical dimensions. In addition, it offers to the engineer a methodology for penetrating and seeing new dimensions of those problems. To demonstrate the effectiveness of the Eight Dimensional Methodology as an analytical tool for thinking about ethical challenges to engineering, the paper presents the case of the construction of the Large Binocular Telescope (LBT) on Mount Graham in Arizona. Analysis of the case offers to decision makers the use of the Eight Dimensional Methodology in considering alternative solutions for how they can proceed in their goals of exploring space. It then follows that same process through the second stage of exploring the ethics of each of those different solutions. The LBT project pools resources from an international partnership of universities and research institutes for the construction and maintenance of a highly sophisticated, powerful new telescope. It will soon mark the erection of the world’s largest and most powerful optical telescope, designed to see fine detail otherwise visible only from space. It also represents a controversial engineering project that is being undertaken on land considered to be sacred by the local, native Apache people. As presented, the case features the University of Virginia, and its challenges in consideration of whether and how to join the LBT project consortium. Earlier versions of this paper were presented at the “Ethics and Social Responsibility in Engineering and Technology” meeting, New Orlenas, 2003 and at the American Society of Engineering Education (ASEE) annual Meeting, 2003.     

布朗芬布伦纳从襁褓走向成熟的人类发展观

布朗芬布伦纳的思想在人类发展理论中占有着举足轻重的地位,这个一直处于演进之中的理论实现了人类发展观从静到动的转变,开创性的提出了一个全新的视角与理论框架.文章沿着历史的轨迹,完整记述了布朗芬布伦纳思想的起源与演进,重点关注了生态学视角中全新的人与环境关系、发展中人的概念和环境的概念,以及生物生态学模型中过程、人、环境、时间概念和相关应用中存在的问题.     

Applying the principles and techniques of solution-focused therapy to career counselling

Career counselling aims to help clients become more effective agents in solving problems in their vocational aspects of life. To achieve this goal, theorists and practitioners are called upon to form useful helping approaches that can help clients in a more efficient and effective manner. This article proposes an alternative model toward this end by considering and adopting principles and techniques from the solution-focused therapy in career counselling practice. After a very brief introduction of the basic features of the solution-focused counselling, the paper reviews some key theoretical principles of the solution-focused therapy, and connects these principles to career counselling context. It then illustrates several solution-focused counselling techniques that are particularly applicable to career counselling intervention.     

On ugliness

Ugliness results from the emergence into consciousness of certain fantasies that alter the person's aesthetic sense in such a way that the formal qualities of the experience, the shape, texture, and color, appear to become the sources of our most disturbing and repulsive feelings. This paper reviews the psychoanalytic writings concerning the problem of ugliness and offers a psychoanalytic model of this universal phenomenon. Clinical vignettes illustrate key points. The paper closes with a discussion of how ugliness can be an opportunity for both the analyst and the artist--he or she confronts ugliness, and through the analytic and creative process, brings form and perfection to disintegration and disorder.