You’ll see what you mean: Students encode equations based on their knowledge of arithmetic

This study investigated the roles of problem structure and strategy use in problem encoding. Fourth-grade students solved and explained a set of typical addition problems (e.g., ) and mathematical equivalence problems (e.g., or ). Next, they completed an encoding task in which they reconstructed addition and equivalence problems after viewing each for 5 s. Equivalence problems of the form overlap with a perceptual pattern found in traditional arithmetic problems (i.e., answer blank in final position), and students’ encoding was poorest on problems of this type. Individual differences in encoding the equivalence problems were related to variations in strategy use. Some students solved blank-final equivalence problems using the standard arithmetic strategy of performing all given operations on all given numbers. These students made more errors in encoding problem structure, but fewer errors in encoding the numbers, than did students who solved the problems using correct or other incorrect strategies. Moreover, students who expressed many strategies for solving the blank-final equivalence problems made fewer errors in encoding problem structure, but more errors in encoding the numbers, than did students who expressed only a single strategy. Results highlight that encoding is intended to guide action and that prior experience can simultaneously facilitate and interfere with accurate encoding.     

“We want the world and we want it now”: Materialism,time perspectives and problem spending tendency of Chinese

Chinese consumers' spending has been expanding rapidly in the past decade, and along with it household and credit card debt. The present research collected evidence to triangulate the contention that materialism is positively related with Chinese's problem spending tendency (PST), and that present‐time‐perspective (PTP) and future‐time perspectives (FTP) interact systematically with materialism to affect PST. A survey of the general population in Macao, China (Study 1; N = 239) confirmed that materialism was positively correlated with PST. An interaction between materialism and PTP intensified the relationship, whereas an interaction with FTP weakened the relationship. Another survey with a sample of university students (Study 2; N = 223) again found positive relationships among PST, materialism, and PTP, as measured by temporal discount rate. But further exploration showed that PST was only related with temporal discounting among high materialists, but not among low materialists. Study 3 experimentally examined the causal effects of materialism and FTP on PST. When being primed of an orientation towards materialism (n = 33), the participants' planned consumption doubled that of the control group (n = 31). A FTP prime interacted with materialism prime and put a “damper” on participants' planned spending (n = 29), compared to their counterparts who were not primed of such a time perspective.     

Perfectionism: The good,the bad,and the creative

The influence of adaptive and maladaptive perfectionism on creativity was examined. Initially, six measures of creativity were administered, including creative self-perceptions, behavior, and performance measures. Adaptive perfectionism was weakly positively related to creativity, whereas maladaptive perfectionism was unrelated to creativity across five of the six measures. A follow-up study assessed whether initial findings could be generalized to an everyday problem-solving task. Results indicated that adaptive perfectionism was related to higher quality but not originality of solutions. Further, a curvilinear relationship in the shape of an inverted “U” occurred between adaptive perfectionism and four of eight creativity measures. Overall, adaptive perfectionism was consistently, albeit weakly, related to creativity across various types of measures, whereas maladaptive perfectionism was not related to creativity.     

Dissociable stages of problem solving (II): first evidence for process-contingent temporal order of activation in dorsolateral prefrontal cortex

In a companion study, eye-movement analyses in the Tower of London task (TOL) revealed independent indicators of functionally separable cognitive processes during problem solving, with processes of building up an internal representation of the problem preceding actual planning processes. These results imply that processes of internalization and planning should also be distinguishable in time and space with respect to concomitant brain activation patterns. To investigate this possibility, here we conducted analyses of fMRI data for left and right dorsolateral prefrontal cortex (dlPFC) during problem solving in the TOL task by accounting for the trial-by-trial variability of onsets and durations of the different cognitive processing stages. Comparisons between stimulus-locked and response-locked modeling approaches affirmed that activation in left dlPFC was elicited particularly during early processes of internalization, comprising the extraction of goal information and the generation of an internal problem representation, whereas activation in right dlPFC was predominantly attributable to later processes of mental transformations on this representation, that is planning proper. Thus, present data corroborate the proposal that often observed bilateral dlPFC activation patterns during complex cognitive tasks such as problem solving may reflect functionally and, to some extent, even temporally separable processes with opposing lateralizations.     

Dissociable stages of problem solving (I): temporal characteristics revealed by eye-movement analyses

Understanding the functional neuroanatomy of planning and problem solving may substantially benefit from better insight into the chronology of the cognitive processes involved. Based on the assumption that regularities in cognitive processing are reflected in overtly observable eye-movement patterns, here we recorded eye movements while participants worked on Tower of London (TOL) problems that comprised an experimental manipulation of different task demands. Single-trial saccade-locked analyses revealed that higher demands on forming an internal problem representation were associated with an increased number of gaze alternations between start state and goal state, but did not show any effect on the durations of these inspections of the states. In contrast, higher demands on actual planning in terms of mental manipulations of working memory contents coincided with a prolonged duration of the very last inspection of the start state (i.e., immediately preceding movement execution) but did not show any effect on the number of gaze alterations. Differential task demands on internalization and planning processes during problem solving hence selectively affect different eye-movement parameters. Moreover, these findings complement previous neuroimaging data on dissociable contributions of left and right dorsolateral prefrontal cortex in problem solving with novel evidence for a corresponding dissociation in the eye-movement patterns reflecting the associated cognitive processes.     

A Test of the Testing Effect: Acquiring Problem‐Solving Skills From Worked Examples

The “testing effect” refers to the finding that after an initial study opportunity, testing is more effective for long‐term retention than restudying. The testing effect seems robust and is a finding from the field of cognitive science that has important implications for education. However, it is unclear whether this effect also applies to the acquisition of problem‐solving skills, which is important to establish given the key role problem solving plays in, for instance, math and science education. Worked examples are an effective and efficient way of acquiring problem‐solving skills. Forty students either only studied worked examples (SSSS) or engaged in testing after studying an example by solving an isomorphic problem (STST). Surprisingly, results showed equal performance in both conditions on an immediate retention test after 5 min, but the SSSS condition outperformed the STST condition on a delayed retention test after 1 week. These findings suggest the testing effect might not apply to acquiring problem‐solving skills from worked examples.     

Working memory components as predictors of children's mathematical word problem solving

This study determined the working memory (WM) components (executive, phonological loop, and visual–spatial sketchpad) that best predicted mathematical word problem-solving accuracy of elementary school children in Grades 2, 3, and 4 (N = 310). A battery of tests was administered to assess problem-solving accuracy, problem-solving processes, WM, reading, and math calculation. Structural equation modeling analyses indicated that (a) all three WM components significantly predicted problem-solving accuracy, (b) reading skills and calculation proficiency mediated the predictive effects of the central executive system and the phonological loop on solution accuracy, and (c) academic mediators failed to moderate the relationship between the visual–spatial sketchpad and solution accuracy. The results support the notion that all components of WM play a major role in predicting problem-solving accuracy, but basic skills acquired in specific academic domains (reading and math) can compensate for some of the influence of WM on children’s mathematical word problem solving.     

Longitudinal Modeling of Adolescents' Activity Involvement, Problem Peer Associations, and Youth Smoking

Longitudinal associations among different types of organized activity involvement, problem peer associations, and cigarette smoking were examined in a sample of 1040 adolescents (mean age = 15.62 at baseline, 16.89 at 15-month assessment, 17.59 at 24 months) enriched for smoking experimentation (83% had tried smoking). A structural equation model tested longitudinal paths between three categories of involvement (team sports, school clubs and activities, and religious activities, measured at baseline and 15 months), problem peer associations (baseline and 15 months), and cigarette smoking behavior (baseline and 24 months). Multi-group analyses indicated pathways differed by type of activity and adolescent gender. Boys' baseline team sports and religious involvement predicted lower levels of smoking at 24 months via continued activity involvement at 15 months. Girls' involvement in school clubs and activities and religious activities indirectly predicted lower levels of smoking at 24 months via reduced exposure to problem peers at 15 months.     

试析高校创新氛围的营造路径

21世纪是一个充满了激烈竞争的世纪,是一个由“创新”引领时代潮流的世纪。国家富强,社会发展,教育进步离不开这一主旋律,更离不开具有创新思维的人才。本文通过探讨营造校园创新氛围的路径,来阐释校园创新氛围对大学生创新思维的养成有着至关重要的作用。     

The Impact of Analogies on Creative Concept Generation: Lessons From an In Vivo Study in Engineering Design

Research on innovation often highlights analogies from sources outside the current problem domain as a major source of novel concepts; however, the mechanisms underlying this relationship are not well understood. We analyzed the temporal interplay between far analogy use and creative concept generation in a professional design team's brainstorming conversations, investigating the hypothesis that far analogies lead directly to very novel concepts via large steps in conceptual spaces (jumps). Surprisingly, we found that concepts were more similar to their preceding concepts after far analogy use compared to baseline situations (i.e., without far analogy use). Yet far analogies increased the team's concept generation rate compared to baseline conditions. Overall, these results challenge the view that far analogies primarily lead to novel concepts via jumps in conceptual spaces and suggest alternative pathways from far analogies to novel concepts (e.g., iterative, deep exploration within a functional space).