Solving the Flagpole Problem

In this paper I demonstrate that the causal structure of flagpole-like systems can be determined by application of causal graph theory. Additional information about the ordering of events in time or about how parameters of the systems of interest can be manipulated is not needed.     

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.     

Promoting Insightful Problem Solving

This work assessed whether insightful problem solving could be trained. Specifically, we tested whether solutions to a heterogeneous set of verbal insight problems could be promoted. A training scheme was developed to promote the application of mechanisms that underlie the process of restructuring. Training across the five experiments consisted of different combinations of the following training techniques: advance strategic instructions, varying amounts of practice, practice with different types of feedback, and problem comparison. Results from all five experiments showed that training can promote solutions to verbal insight problems. Facilitation effects ranged from a 14%–24% gain in overall solution rates relative to no‐treatment controls. This work demonstrated that insightful problem solving could be trained at a relatively high level of generality.     

Solving the Caesar Problem Without Categorical Sortals

The neo-Fregean account of arithmetical knowledge is centered around the abstraction principle known as Hume’s Principle: for any concepts X and Y, the number of X’s is the same as the number of Y’s just in case there is a 1–1 correspondence between X and Y. The Caesar Problem, originally raised by Frege in §56 of Die Grundlagen der Arithmetik, emerges in the context of the neo-Fregean programme, because, though Hume’s Principle provides a criterion of identity for objects falling under the concept of Number–namely, 1–1 correspondence—the principle fails to deliver a criterion of application. That is, it fails to deliver a criterion that will tell us which objects fall under the concept Number, and so, leaves unanswered the question whether Caesar could be a number. Hale and Wright have recently offered a neo-Fregean solution to this problem. The solution appeals to the notion of a categorical sortal. This paper offers a reconstruction of their solution, which has the advantage over Hale and Wright’s original proposal of making clear what the structure of the background ontology is. In addition, it is shown that the Caesar Problem can be solved in a framework more minimal than that of Hale and Wright, viz. one that dispenses with categorical sortals. The paper ends by discussing an objection to the proposed neo-Fregean solutions, based on the idea that Leibniz’s Law gives a universal criterion of identity. This is an idea that Hale and Wright reject. However, it is shown that a solution very much in keeping with their own proposal is available, even if it is granted that Leibniz’s Law provides a universal criterion of identity.

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Problem Solving and Suicidal Behavior

Research on suicidal behavior falls into two main areas: studies that aim to identify demographic and social risk factors, and studies that aim to investigate the psychological processes mediating suicidal behavior. Within the latter approach, impaired problem-solving ability has been found to be an important variable. This paper reviews recent research focusing on problem-solving deficits and their relation to suicidal behavior and considers some of the methodological problems that arise. These findings are discussed in terms of active versus passive problem solving, state or trait factors, and the psychological processes underlying problem solving. Suggestions for further research are made, focusing on the links between suicidal behavior, problem solving, and autobiographical memory.     

Incubation in Insight Problem Solving

A break in the attentive activity devoted to a problem may eventually facilitate the solution process. This phenomenon is known by the name incubation. A new hypothesis regarding the incubation mechanism is suggested. It is based on analysis of the structure of insight problems and their solution process. According to this hypothesis, no activity takes place during the break. The break's only function is to divert the solver's attention from the problem, thus releasing her mind from the grip of a false organizing assumption. This enables the solver to apply a new organizing assumption to the problem's components upon returning to the problem. The numbers of experimental studies that confirm the existence of the incubation phenomenon, and those that do not support it, are roughly equal, thus the primary experimental aim of the study is to improve the methodology of manipulating the break. This was done by starting the break only after an impasse has been reached. The results indicate that the break improves performance in insight problem solving, but its length does not make a difference. This supports the suggested hypothesis and does not support hypotheses that postulate unconscious ongoing processes during the break.     

Gender and Mathematical Problem Solving

The relationship between gender and mathematical problem-solving among high ability students depends on the attributes of the problem solving questions. This was evident in the present study of 12-year-olds. The children were from predominately White families. Eighty-three males and 76 females were tested in both the fall and the spring on the Fennema-Sherman Mathematics Attitudes Scales and on the Canadian Test of Basic Skills (CTBS). In the Spring, students were also tested on the GAUSS. Both the CTBS and the GAUSS measure mathematical problem solving. Among high ability students, there were gender differences on the problem-solving scale of the CTBS but not on the GAUSS, even though the GAUSS was independently rated as the more abstract and difficult of the two tests. The present study describes the implications of this for the question of the origin of gender differences in mathematics, and also looked at the relationship between attitudes toward mathematics and mathematical problem-solving performance.     

Solving the (Real) Other Minds Problem

People care about others’ thoughts, feelings, and intentions but can have considerable difficulty reading others’ minds accurately. Recent advances in understanding how people make such inferences provide significant insight into when people are likely to be reasonably accurate mind readers and when they are not. People tend to reason about others’ mental states by starting with their own and only subsequently adjusting that egocentric default to accommodate differences between themselves and others. Such adjustments tend to be insufficient, rendering final estimates egocentrically biased. When more information about others is available, people tend to rely on existing stereotypes or other expectations to intuit others’ mental states. Systematic errors resulting either from excessive egocentrism or inaccurate expectations can lead to miscommunication, misunderstanding, and social conflict, but these biases also suggest useful strategies for improving mind reading in everyday life.     

Internal Models in Physics Problem Solving

In this paper, we discuss the relations among internal mental models, attentional cues, and knowledge structure in solving elementary physics problems. The notion of semantic sensitivity is introduced as a qualitative measure of problem-solver receptivity to cues for generating, or making a shift to, a new internal model that may lead to the correct answer. Using three physics problems and their variations, the following results were obtained. First, think-aloud protocol data of two experts and one novice, working on those problems, were analyzed to provide empirical examples of internal models, and also to show that generation and shift of internal models generally results from the interplay of two kinds of processes, model construction and model development. Second, protocol data from 15 novices and seven professionals were used to present a more extensive empirical taxonomy of internal models for those problems. Third, seven experiments were used, along with the results from the protocol data, to suggest the following conditions on semantic sensitivity. (1) If the problem solver's present internal model is independent of his knowledge of physics principles underlying the given problem, but if attentional cues are related directly to the knowledge, then his present model is semantically sensitive to the cues, that is, it can be shifted easily to another model that is based on the knowledge. (2) His present model is semantically insensitive, if given cues are encoded based on the same knowledge as used for generating the model. (3) The relevance of cues to knowledge structure is critical for semantic sensitivity of the presently encoded model: Which cues to attend to is guided by the problem solver's knowledge, and if he can focus on those most relevant to the physics principles underlying the problem, then his present model is semantically sensitive to those cues, that is, he is more able to shift the present model to another that would lead to the correct answer.     

Suicide Ideation and Creative Problem Solving

This investigation utilized the recent technology for the assessment of creativity to examine the association between problem solving and suicide ideation. Three kinds of problem-finding and -solving tasks were administered to 81 (nonclinical) college students. One of these tasks assesses “problem generation” and was expected to be particularly informative, given that individuals considering suicide may perceive many problems but find few solutions. Results supported this expectation: Problem generation scores were significantly correlated with suicide ideation, even after stress was statistically controlled. A secondary analysis suggested that the originality and flexibility of solutions may be influenced by the particular problem an individual faces.     

社会性问题解决研究述评

社会性问题解决是指个体在真实的社会情境中,有效地识别日常生活中遇到的特定问题或生活境遇,积极地面对问题,分析问题,发现有效解决方案的自我导向的认知、情感和行为过程。首先分析了社会性问题解决的概念,介绍了相应的测量工具,然后着重分析了社会性问题解决的影响因素(如个性特点),最后总结了社会性问题解决的影响效果。今后的研究需进一步探讨:社会性影响因素、相关研究的拓展和社会性问题解决疗法的应用等问题。     

问题解决的表征态理论

问题解决的表征态理论(简称RST)认为问题解决就是问题的表征态连续、非线性的变化的过程,其中存在数据驱动和概念驱动两种方式。在问题表征态变化的过程中,问题解决者所掌握的专业知识起着重要的作用,它是问题解决者对问题情境信息进行同化的基础,也是对问题结构进行心理建构的基础。RST的假设及其推论在中学生物理问题解决过程中得到检验。     

On Runco's Problem Finding,Problem Solving,and Creativity

The relative significance of the "golden section" (? 0.618) and other notable proportions was investigated using a new unobtrusive methodology, a modified Fechnerian method of production. Fourteen professional painters each sketched under controlled conditions--"veridically, accurately, and realistically" (but without there being any mention of proportions)--27 complex stimuli presented as slides, thus producing a total of 378 sketches. The stimuli in the slides were (a) vase cutouts of various proportions placed in a mantelpiece context and (b) paintings by Kodama, Mondrian, and Whistler. The golden section and other significant and control proportions (a total of 120 occurrences) were identified beforehand by the researcher in the 27 stimuli. The 378 painters' sketches were subsequently measured by the researcher and two assistants to determine the accuracy with which the various proportions had been reproduced by the painters (a grand total of 1680--14 x 120--possible occurrences). The overall accuracy of rendering the proportions was found to be low for the vases and Kodama's paintings, but increased considerably for the Whistlers and Mondrians. As predicted, the accuracy of rendering the golden section increased from the vases to the Kodamas to the Whistlers and Mondrians. For the latter two, the golden section was in fact the most accurately rendered proportion, followed by 1.00 (found, for example, in the square and circle). The golden section is clearly important in art and to artists, but both its use and detection are subtle and must be pursued with great analytic care. The use of professional artists as informants and research participants may be of considerable help.