Comparing mathematics interventions: Does initial level of fluency predict intervention effectiveness?

A paucity of research has directly compared empirically supported interventions to examine their effectiveness among students with different mathematics fluency skills. The purpose of this study was to compare the effects of two empirically supported interventions and a control condition on the mathematics fluency of 98 second and third grade students. Specifically, effects of explicit timing and cover-copy-compare on subtraction fluency were examined each session, which occurred twice weekly for a total of six weeks. HLM was used to examine progress during the intervention sessions and determine the effect of initial fluency level on intervention effectiveness. Results suggested students' initial level of fluency impacted intervention effectiveness. That is, for students whose fluency levels fell within the frustrational range CCC and control conditions resulted in the best performance over time but for children whose fluency was in the instructional range explicit timing was the most effective treatment.     

Mathematical skill in individuals with Williams syndrome: evidence from a standardized mathematics battery

Williams syndrome (WS) is a developmental disorder associated with relatively spared verbal skills and severe visuospatial deficits. It has also been reported that individuals with WS are impaired at mathematics. We examined mathematical skills in persons with WS using the second edition of the Test of Early Mathematical Ability (TEMA-2), which measures a wide range of skills. We administered the TEMA-2 to 14 individuals with WS and 14 children matched individually for mental-age on the matrices subtest of the Kaufman Brief Intelligence Test. There were no differences between groups on the overall scores on the TEMA-2. However, an item-by-item analysis revealed group differences. Participants with WS performed more poorly than controls when reporting which of two numbers was closest to a target number, a task thought to utilize a mental number line subserved by the parietal lobe, consistent with previous evidence showing parietal abnormalities in people with WS. In contrast, people with WS performed better than the control group at reading numbers, suggesting that verbal math skills may be comparatively strong in WS. These findings add to evidence that components of mathematical knowledge may be differentially damaged in developmental disorders.     

Use of Self-perspectives and their Sources to Predict the Mathematics Enrollment Intentions of Girls and Boys

An understanding of the differences in the ways in which self-efficacy and interest influence boys’ and girls’ intentions to continue enrollment in mathematics courses may provide insight into how to encourage continued mathematics enrollment for all students. Two competing theoretical models of mathematics self-efficacy and interest in predicting students’ enrollment intentions and achievement were evaluated separately across samples of middle level boys and girls. One model was empirically supported for both groups and indicated the independent influence of self-efficacy and interest in predicting enrollment intentions. Multi-group analyses revealed that self-efficacy’s influence in enrollment intentions and achievement was significantly stronger for boys than for girls, and interest was significantly more important in the prediction of enrollment intentions for girls than for boys.     

归因、自我效能和社会容认度对心理求助行为的影响

在江光荣心理求助行为的“阶段-决策模型”框架下,探查处于第三阶段的被试的求助行为,侧重研究⑴对心理问题的归因、⑵作为心理咨询当事人的自我效能和⑶心理求助行为的社会容认度这三个变量对实际求助行为的影响,同时探讨变量之间的作用机制。结果表明,这三个变量对求助行为均有预测作用。其中心理求助行为的社会容认度除了对求助行为有直接作用外,还以作为心理咨询当事人的自我效能为中介变量间接影响求助行为。整个模型对求助行为解释的变异量达到26％     

The role of career adaptability in predicting entrepreneurial intentions: A moderated mediation model

Guided by the Career Construction Theory (Savickas, 2013), we view entrepreneurship as an adaptive vocational behavior driven by an individual's self-regulatory capacity to thrive in a complex entrepreneurial career context. Our research model posited that individuals rely on their adaptive resources and entrepreneurial self-efficacy as they form entrepreneurial intentions. Career adaptability, as self-regulatory competencies, is further strengthened by prior exposure to family business. We collected data over three measurement periods from Serbian business students (n = 380) and validated the Career Adapt-Abilities Scale (CAAS). The moderated mediation model was supported and as predicted: (a) career adaptability was positively associated with entrepreneurial intentions and (b) the mediated relationship between career adaptability and entrepreneurial intentions via entrepreneurial self-efficacy was stronger for individuals with prior exposure to family business. In addition, we provide evidence for the psychometric properties of CAAS by examining its internal consistency, test–retest reliability, and factor structure. Taken together, our study offers the groundwork for understanding successful adaptation in the entrepreneurial career context and supports the cross-national measurement equivalence and utility of CAAS in a developing economy.     

Brief non-symbolic,approximate number practice enhances subsequent exact symbolic arithmetic in children

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children’s performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children’s performance of symbolic mathematics.     

Productive Failure in Learning Math

When learning a new math concept, should learners be first taught the concept and its associated procedures and then solve problems, or solve problems first even if it leads to failure and then be taught the concept and the procedures? Two randomized‐controlled studies found that both methods lead to high levels of procedural knowledge. However, students who engaged in problem solving before being taught demonstrated significantly greater conceptual understanding and ability to transfer to novel problems than those who were taught first. The second study further showed that when given an opportunity to learn from the failed problem‐solving attempts of their peers, students outperformed those who were taught first, but not those who engaged in problem solving first. Process findings showed that the number of student‐generated solutions significantly predicted learning outcomes. These results challenge the conventional practice of direct instruction to teach new math concepts and procedures, and propose the possibility of learning from one's own failed problem‐solving attempts or those of others before receiving instruction as alternatives for better math learning.     

Empowering leadership,uncertainty avoidance,trust, and employee creativity: Interaction effects and a mediating mechanism

Taking an interactional approach, we hypothesized that (a) there is an interaction between empowering leadership, uncertainty avoidance, and trust that affects creativity, such that empowering leadership has the strongest positive relationship with creativity when the employees have high levels of uncertainty avoidance and trust their supervisors; and (b) creative self-efficacy mediates the effect that this three-way interaction between empowering leadership, uncertainty avoidance and trust has on creativity. In Study 1, we used a time-lagged research design, collecting multi-source data from 322 employees and their supervisors. The results of Study 1 supported our hypotheses. In Study 2, we used a more temporally rigorous research design in which data were collected in three stages, with a two-month time interval separating Stages 1 and 2, and Stages 2 and 3. On the basis of the time-lagged and multi-source data from 199 employees and their supervisors, Study 2 produced the same results as Study 1. We discuss the implications of these results for future research and practice.