Possible number systems

Number systems—such as the natural numbers, integers, rationals, reals, or complex numbers—play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people’s concept of a number system by asking them whether “number lines” of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms’ ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).     

A National Survey of Trauma Training in Psychology Internships

Directors from psychology internship programs across the United States were asked to participate in a survey regarding their sites’ provision of services to traumatized populations and didactic and supervisory training offered to interns. All totaled, 259 training directors completed the survey. Using a point system, an impact score of training saturation was determined based on the content and frequency of training offered in didactic, supervision, or combined formats. Of these, all reported at least one trauma training opportunity in either didactic or supervision format. More than half indicated that they offered at least 1 to 3 hours of didactics on trauma per week (62.2%) and slightly less offered supervision-specific training opportunities (54.5%). However, only 30.8% identified training opportunities in trauma/posttraumatic stress disorder that reached a high level of saturation in training, meaning they offered training activities above the median impact score. The most commonly reported barrier to offering trauma training was related to being busy meeting other specialty or program requirements. Findings provide a preliminary overview of current training practices that can be useful to students seeking trauma internship placements and administrators and faculty who are looking to revise their curriculum.     

The contribution of executive control to semantic cognition: Convergent evidence from semantic aphasia and executive dysfunction

Semantic cognition, as described by the controlled semantic cognition (CSC) framework (Rogers et al., 2015 , Neuropsychologia, 76, 220), involves two key components: activation of coherent, generalizable concepts within a heteromodal ‘hub’ in combination with modality‐specific features (spokes), and a constraining mechanism that manipulates and gates this knowledge to generate time‐ and task‐appropriate behaviour. Executive–semantic goal representations, largely supported by executive regions such as frontal and parietal cortex, are thought to allow the generation of non‐dominant aspects of knowledge when these are appropriate for the task or context. Semantic aphasia (SA) patients have executive–semantic deficits, and these are correlated with general executive impairment. If the CSC proposal is correct, patients with executive impairment should not only exhibit impaired semantic cognition, but should also show characteristics that align with those observed in SA. This possibility remains largely untested, as patients selected on the basis that they show executive impairment (i.e., with ‘dysexecutive syndrome’) have not been extensively tested on tasks tapping semantic control and have not been previously compared with SA cases. We explored conceptual processing in 12 patients showing symptoms consistent with dysexecutive syndrome (DYS) and 24 SA patients, using a range of multimodal semantic assessments which manipulated control demands. Patients with executive impairments, despite not being selected to show semantic impairments, nevertheless showed parallel patterns to SA cases. They showed strong effects of distractor strength, cues and miscues, and probe–target distance, plus minimal effects of word frequency on comprehension (unlike semantic dementia patients with degradation of conceptual knowledge). This supports a component process account of semantic cognition in which retrieval is shaped by control processes, and confirms that deficits in SA patients reflect difficulty controlling semantic retrieval.     

Follower Jealousy at Work: A Test of Vecchio's Model of Antecedents and Consequences of Jealousy

The present study tests the validity of Robert P. Vecchio's seminal work on antecedents and consequences of jealousy. Specifically, we examine whether antecedents such as in-group status, supervisory considerateness, and supervisory differentiation of subordinates are associated with jealousy. In addition, we examine whether jealousy is associated with the outcome variable of social loafing. Leaders (n = 73) and their followers (n = 303) working in business organizations in Norway contributed data. Multilevel analyses showed that a high-quality working relationship with one's supervisor was inversely related to reports of jealousy. In addition, supervisors who displayed high levels of considerateness, for example, by providing followers with positive emotional support, were better able to reduce subordinate jealousy. This is a novel observation since previous research failed to demonstrate such a relationship. Finally, jealousy was positively associated with social loafing, suggesting that jealous followers engaged in an active counterproductive resistance response. The present study contributes to the extant literature by identifying unexamined antecedents of jealousy and a dysfunctional behavioral response to jealousy in the form of social loafing in the workplace.     

The everyday dynamics of rumination and worry: precipitant events and affective consequences

ABSTRACT

Rumination and worry are two perseverative, negatively valenced thought processes that characterise depressive and anxiety disorders. Despite significant research interest, little is known about the everyday precipitants and consequences of rumination and worry. Using an experience sampling methodology, we examined and compared rumination and worry with respect to their relations to daily events and affective experience. Participants diagnosed with Major Depressive Disorder (MDD), Generalized Anxiety Disorder (GAD), co-occurring MDD–GAD, or no diagnosis carried an electronic device for one week and reported on rumination, worry, significant events, positive affect (PA), and negative affect (NA). Across the clinical groups, occurrences of everyday events predicted subsequent increases in rumination, but not worry. Further, higher momentary levels of rumination, but not worry, predicted subsequent decreases in PA and increases in NA. Thus, in these clinical groups, rumination was more susceptible to daily events and produced stronger affective changes over time. We discuss implications for theory and clinical intervention.     

Political Skill and Work Outcomes: A Theoretical Extension,Meta‐Analytic Investigation,and Agenda for the Future

This quantitative review explored the political skill construct and its predictive ability across a number of organizational outcomes. First, we extended the Ferris et al. meta‐theoretical framework of political skill. Next, incorporating meta‐analysis, we found political skill is positively related to self‐efficacy, job satisfaction, organizational commitment, work productivity, organizational citizenship behavior (OCB), career success, and personal reputation, and negatively related to physiological strain. Political skill was not significantly related to psychological strain or perceptions of organizational politics. Using meta‐regression and dominance analyses, political skill predicted task performance after controlling for the Big Five personality characteristics and general mental ability. In a test of indirect relationships, our results suggest that personal reputation and self‐efficacy partially mediate the political skill–task performance relationship. Finally, in a post hoc test of political skill dimensions, we found that networking ability, interpersonal influence, and apparent sincerity (but not social astuteness) predicted task performance. Our findings provide a comprehensive assessment of theory and research to date on political skill and extend theoretical foundations to stimulate new inquiry into the operation of this important construct.     

Underlying Spatial Skills to Support Navigation Through Large,Unconstrained Environments

Studies of spatial navigation in real‐world settings have been limited to neighborhoods, campuses, and buildings. These locations have structural components, such as roads or hallways, which may direct navigation. The current study assessed navigational skills within a large‐scale forested environment that contained few pre‐established paths. Participants were asked to find flags using only a map and compass; dependent variables included target‐finding accuracy and efficiency. In addition, measurements of sense of direction, strategy, and working memory were taken to identify how these cognitive abilities influence performance. The results demonstrate the expected correlations between sense of direction and navigational success. An unexpected correlation between spatial working memory and navigational success was also found, which was the only significant predictor of performance when all measures were regressed together. These results suggest that studies should not forget basic cognitive abilities, which may predict success more than measures of sense of direction. Copyright © 2015 John Wiley & Sons, Ltd.