Model RB is a model of random constraint satisfaction problems, which exhibits exact satisfiability phase transition and many hard instances, both experimentally and theoretically. Benchmarks based on Model RB have been successfully used by various international algorithm competitions and many research papers. In a previous work, Xu and Li defined two notions called i-constraint assignment tuple and flawed i-constraint assignment tuple to show an exponential resolution complexity of Model RB. These two notions are similar to some kind of consistency in (...) constraint satisfaction problems, but seem different from all kinds of consistency so far known in literatures. In this paper, we explicitly define this kind of consistency, called variable-centered consistency, and show an upper bound on a parameter in Model RB, such that up to this bound the typical instances of Model RB are variable-centered consistent. (shrink)

Moral hypocrisy (MH) occurs when people fail to practice what they preach. Despite the prevalence of the effect of social identity on an individual’s MH, few empirical studies have explored contextual factors that may help reduce MH. By conducting two experiments based on the research paradigm of real stranger presence, we examined how in-group and out-group strangers’ presence and moral behavior may contribute to reducing MH. The results of experiment 1 demonstrated that compared with the presence of out-group strangers, the (...) presence of in-group stranger could effectively inhibit MH (no significant difference between participants reported and actual donation proportions was obtained). The results of experiment 2 replicated and extended the results of experiment 1, first by showing that the presence of in-group strangers could effectively inhibit MH and then by revealing the influence of present strangers’ behavior (moral or hypocritical) on MH. The results indicated that strangers’ moral behavior could effectively eliminate participants’ MH, especially in the presence of in-group strangers. However, when present strangers exhibited hypocritical behavior, they exhibited no effect on participants’ MH, irrespective of the condition of in-group and out-group strangers. The current study provides empirical support for theories related to MH and moral decision making and contributes to the literature on in-group and out-group effects on MH and decision making. (shrink)

There has been a major international focus on the education and care of toddlers. To date, empirical studies on adults’ interactions in play with toddlers have focussed on the proximity of teachers, teachers’ affective responses, and joint attention between adults and children in play. However, less attention has been given to the role of two teachers working together in supporting children’s exploration of concepts in joint play. This paper takes a cultural-historical perspective and draws upon the concepts of play and (...) subjective positioning to investigate how co-teaching promotes toddlers’ joint play and exploration of mathematical concepts. Visual data of a group of toddlers playing with two teachers is analysed to explore how the teachers applied co-teaching pedagogy to support children’s exploration of mathematical concept. The study argues that co-teaching provides potential to support collective play as two teachers can work collaboratively to address the toddlers’ challenges and needs and support their exploration of the rules and mathematical concepts in play. Co-teaching by paired teachers enables toddlers’ joint play to become more complex, helping the children to explore mathematical concepts and, in turn, further enhancing their play. (shrink)