Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving

Although various studies support the multicomponent nature of visuospatial working memory, to date there is no general consensus on the distinction of its components. A difference is usually proposed between visual and spatial components of working memory, but the individual roles of these components in mathematical learning disabilities remains unclear. The present study aimed to examine the involvement of visual and spatial working memory in poor problem-solvers compared with children with normal level of achievement. Fourth-grade participants were presented with tasks measuring phonological loop, central executive, and visual versus spatial memory. In two separate experiments, both designed to distinguish visual and spatial component involvement, poor problem-solvers specifically failed on spatial—but not visual or phonological—working memory tasks. Results are discussed in the light of possible working memory models, and specifically demonstrate that problem-solving ability can benefit from analysis of spatial processes, which involves ability to manipulate and transform relevant information; instead, no benefit is gained from the analysis of visual pictorial detail.     

Insight versus analysis: Evidence for diverse methods in problem solving

Since the Gestalt psychologists made the distinction approximately 100 years ago, psychologists have differentiated between solving problems through analysis versus insight. The present paper presents evidence to support the idea that, rather than conceptualising insight versus analysis as distinct modes of solving problems, it is more useful to conceive of insight and analysis as two approaches within a set of possible solving methods. In the present research, 60 participants solved insight problems while thinking aloud, which provided evidence concerning the processes underlying problem solution. Comparison with performance of a nonverbalisation control group (n = 35) indicated no negative effects of thinking aloud on insight in problem solving. The results supported the idea that various methods are utilised in solving insight problems. The “classic” impasse–restructuring–insight sequence occurred in only a small minority of solutions. A number of other solution methods were found, ranging from relatively direct applications of knowledge, to various heuristic methods, to restructuring arising from new information gleaned from a failed solution. It is concluded that there is not a sharp distinction between solving a problem through analysis versus insight, and implications of that conclusion are discussed.     

Expert and “novice” problem solving strategies in chess: Sixty years of citing de Groot (1946)

In a famous study of expert problem solving, de Groot (1946 de Groot, A. D. 1946. Het denken van den schaker, Amsterdam: Noord Hollandsche.  [Google Scholar]/1978 de Groot, A. D. 1965. Thought and choice in chess, The Hague: Mouton Publishers.  [Google Scholar]) examined how chess players found the best move. He reported that there was little difference in the way that the best players (Grand Masters) and very good players (Candidate Masters) searched the board. Although this result has been regularly cited in studies of expertise, it is frequently misquoted. It is often claimed that de Groot found no difference in the way that experts and novices investigate a problem. Comparison of expert and novice chess players on de Groot's problem shows that there are clear differences in their search patterns. We discuss the troublesome theoretical and practical consequences of incorrectly reporting de Groot's findings.     

Human behaviour in the Euclidean Travelling Salesperson Problem: Computational modelling of heuristics and figural effects

The Travelling Salesperson Problem (TSP) describes a situation where an imaginary individual wishes to visit multiple cities once before returning to his/her own city. This type of problem is known as a nondeterministic polynomial (NP) hard problem, since the factorial number of solutions results in it being impractical to solve using exhaustive processing. Interestingly, when presented as a Euclidean graph (i.e., ETSP), humans identify near optimal solutions almost effortlessly, despite billions of possible tours. In this study, we consider human processing of the ETSP, and introduce the reader to a number of factors that literature proposes as impacting human performance. We hypothesise that: (i) human ETSP activity may be modelled by considering the quotient relationship between node-to-node and node-to-centroid distances; and (ii) consideration of figural effects can optimise automated TSP solution generation. In this paper human processing based heuristics are developed, i.e. replacing the cost function within the nearest neighbour algorithm, to guide node selection. Results showed that the quotient relationship between node-to-node and node-to-centroid distances can be used to closely model average human performance, across a range of ETSP graphs. Interestingly, however, additional consideration of graph figural effects (e.g. distance between boundary points in the convex hull, standard deviation of distances between nodes that make up the convex hull, and number of nodes in the convex hull) results in significantly improved tour costs.     

An Evaluation of Interventions to Facilitate Algebra Problem Solving

Three participants were trained on 6 target algebra skills and subsequently received a series of 5 instructional interventions (cumulative practice, tiered feedback, feedback plus solution sequence instruction, review practice, and transfer training) in a multiple baseline across skills design. The effects of the interventions on the performance of 5 problem-solving tasks that required novel combinations of 2 or more of the target skills were evaluated. Results showed that cumulative practice of the skills and a combination of feedback with solution sequence instruction led to limited performance increases on some of the problem-solving tasks, with one task meeting the mastery criterion following the solution sequence intervention. The introduction of the transfer training resulted in more consistent improvements across tasks such that participants achieved the performance criterion on all remaining problem-solving tasks during a final baseline condition. The findings suggest that a structured intervention designed to transfer stimulus control from previously established discriminative stimuli to more complex, novel stimuli can facilitate problem solving without extensive direct instruction on the higher-level skills. This research was funded in part by a contract with the Florida Department of Children and Families. The content and opinions expressed herein do not necessarily reflect the position or policy of the Department of Children and Families. We thank Tim Vollmer for suggestions made throughout this study and for helpful comments on an earlier draft of this paper. We also thank Linda Meckler for her assistance with data collection. Kristin H. Mayfield, now at iLearn, Inc., Marietta, GA, USA.     

Reducing the Risk for Preschool Expulsion: Mental Health Consultation for Young Children with Challenging Behaviors

Increasing numbers of young children are being expelled from child care settings because of their problem behavior. Access to mental health consultation is related to lower rates of expulsion, but additional data are needed to document the pathways through which mental health consultation reduces the risk of expulsion. We report on outcomes from a 4-year project designed to reduce the number of children expelled for problem behavior in a large suburban county in Maryland. Two master’s-level professionals provided behavioral consultation to child care providers who identified nearly 200 children at imminent risk for expulsion. Child care providers rated children’s social skills and problem behaviors at referral and discharge using the Preschool Kindergarten Behavior Scales and the Brief Infant Toddler Social Emotional Assessment. Statistically significant increases in social skills and reductions in problem behaviors were seen for children who received individualized consultation. More than three-quarters of the children who were at risk for expulsion were able to be maintained in their current child care placement; of those that changed placements, only half (n = 13) were removed involuntarily. These findings provide additional support for mental health consultation as a promising strategy to reduce the risk for expulsion for young children with problem behaviors.     

课程嵌入型表现性评定对数学问题解决影响的实验研究

课程嵌入型表现性评定是当前基础教育新课程改革倡导的重要的学生学业评价方式。以335名初中一年级学生为被试,采用为期一学年的追踪实验研究方式,探索课程嵌入型表现性评定对数学问题解决的影响效果。研究结果表明,此方式对学生的数学问题解决能力发展具有显著促进作用,且促进作用随实验进程不断增加并受到学生原有学业水平的影响。对口语报告资料的分析进一步表明,此评定方式对数学问题解决的促进作用主要体现在理解问题、元认知与问题解决策略等方面。     

Theodicy: The Solution to the Problem of Evil,or Part of the Problem?

Theodicy, the enterprise of searching for greater goods that might plausibly justify God’s permission of evil, is often criticized on the grounds that the project has systematically failed to unearth any such goods. But theodicists also face a deeper challenge, one that places under question the very attempt to look for any morally sufficient reasons God might have for creating a world littered with evil. This ‘anti-theodical’ view argues that theists (and non-theists) ought to reject, primarily for moral reasons, the project of ‘justifying the ways of God to men’. Unfortunately, this view has not received the serious attention it deserves, particularly in analytic philosophy of religion. Taking my cues from such anti-theodicists as Kenneth Surin, D.Z. Phillips and Dostoyevsky’s Ivan Karamazov, I defend several reasons for holding that the way of thinking about God and evil enshrined in theodical discourse can only add to the world’s evils, not remove or illuminate them.

On the spontaneous discovery of a mathematical relation during problem solving

People spontaneously discover new representations during problem solving. Discovery of a mathematical representation is of special interest, because it shows that the underlying structure of the problem has been extracted. In the current study, participants solved gear-system problems as part of a game. Although none of the participants initially used a mathematical representation, many discovered a parity-based, mathematical strategy during problem solving. Two accounts of the spontaneous discovery of mathematical strategies were tested. According to the automatic schema abstraction hypothesis, experience with multiple, unique problem exemplars facilitates extraction of the parity relation. According to the comparison-based abstraction hypothesis, explicitly comparing gear pathways that have different number, but the same parity, should result in extraction of parity. An event history analysis showed that accumulation of experiences with different-number, same-parity comparisons predicted discovery of parity; accumulation of unique exemplars did not. Results suggest that comparison-based abstraction processes can lead to the discovery of a mathematical relation.     

分析哲学的兴趣:在哲学与生活之间--从批判理论和生活世界的视角对罗素和维特根斯坦的一个批评解读

分析哲学是有其人文和社会的兴趣与关怀的。本文试图从批判理论的视角．运用哲学与生活世界相关联的解释学方法,分别解读了分析哲学创始人之一的罗素的逻辑分析哲学与他作为一个哲学家的社会批判兴趣之间的关系,以及前期维特根斯坦的逻辑语言分析哲学和后期的日常语言分析哲学与维特根斯坦所属的生活世界的关系。指出分析哲学由于没有建立在对现代性的科学一形而上学思维方式和生活方式的足够反思基础上,所以它对形而上学的批判兴趣最终仍然导致了一种非批判的形而上学。