Evolving social networks, attitudes and beliefs and counter terrorism

'The Princeton Companion to Applied Mathematics' is an introduction to applied mathematics for students, teachers, and professionals. This article is for the "Application Areas" part of the book, which comprises articles on connections between applied mathematics and other disciplines.

Social networks and occupational choice: the endogenous formation of attitudes and beliefs about tax compliance

The paper analyses the emergence of group-specific attitudes and beliefs about tax compliance when individuals interact in a social network. It develops a model in which taxpayers possess a range of individual characteristics – including attitude to risk, potential for success in self-employment, and the weight attached to the social custom for honesty – and make an occupational choice based on these characteristics. Occupations differ in the possibility for evading tax. The social network determines which taxpayers are linked, and information about auditing and compliance is transmitted at meetings between linked taxpayers. Using agent-based simulations, the analysis demonstrates how attitudes and beliefs endogenously emerge that differ across sub-groups of the population. Compliance behaviour is different across occupational groups, and this is reinforced by the development of group-specific attitudes and beliefs. Taxpayers self-select into occupations according to the degree of risk aversion, the subjective probability of audit is sustained above the objective probability, and the weight attached to the social custom differs across occupations. These factors combine to lead to compliance levels that differ across occupations.

Enterprise pedagogy in music: an exploration of multiple pedagogies

This article investigates the nature of enterprise pedagogy in music. It presents the results of a research project that applied the practices of enterprise learning developed in the post-compulsory music curriculum in England to the teaching of the National Curriculum for music for 11-to-14-year-olds. In doing so, the article explores the nature of enterprise learning and the nature of pedagogy, in order to consider whether enterprise pedagogy offers an effective way to teach the National Curriculum. Enterprise pedagogy was found to have a positive effect on the motivation of students and on the potential to match learning to the needs of students of different abilities. Crucially, it was found that, to be effective, not only did the teacher’s practice need to be congruent with the beliefs and theories on which it rests, but that the students also needed to share in these underlying assumptions through their learning. The study has implications for the way in which teachers work multiple pedagogies in the process of developing their pedagogical identity.

Nuclear Mentalities? Strategies and Beliefs in Britain, France and the FRG

This is volume II of my two-volume study of the nuclear strategies/strategy preferences of Britain, France and West Germany in the Cold War. It shows that the great variable is the mentalities, culture, and particular interpretations of particular historical experiences of these three countries. These mental frameworks are reconstructed, in the tradition of the French Annales/Mentalite schools (that in turn is rooted in anthropology) by looking at a very large nunber of public texts in the context of the public discourse about nuclear strategy in each country.

Beliefs, cultures, proliferation and use of nuclear weapons

This article demonstrates the centrality of mentality, culture, beliefs and historical lessons for nuclear prolifertion. Using the historical casestudies of Britain, France, and West Germany, it encourages researchers to look at the mentality/culture of potential proliferators rather than apply a culture-less "Realist" IR theory approach that assumes that desicion-makers the world over think like Bismarck.

The earth, the sky and the water's edge: changing beliefs in the earlier prehistory of Northern Europe

There have been two kinds of study of ancient beliefs in the earlier prehistory of Scandinavia. One considers the impact of ideas which originated further to the south and east. It considers a cosmology based on the movements of the sun. A second tradition develops out of the ethnography of the circumpolar region and combines archaeological evidence with the beliefs of hunter-gatherers. It postulates the existence of a three-tier cosmology in which people could communicate between different worlds. This paper argues that certain elements that are thought to epitomize the ‘Southern’ system might have been suggested by existing ideas within Scandinavia itself. Both sets of beliefs came to influence one another, but they became increasingly distinct towards the end of the Bronze Age. This paper reconsiders the rock carvings, metalwork and mortuary cairns of that period and the Iron Age in relation to the process of religious change.

Aspect selection in adult L2 Spanish and the competing systems hypothesis: when pedagogical and linguistic rules conflict.

Native-like use of preterit and imperfect morphology in all contexts by English learners of L2 Spanish is the exception rather than the rule, even for successful learners. Nevertheless, recent research has demonstrated that advanced English learners of L2 Spanish attain a native-like morphosyntactic competence for the preterit/imperfect contrast, as evidenced by their native-like knowledge of associated semantic entailments (Goodin-Mayeda and Rothman 2007, Montrul and Slabakova 2003, Slabakova and Montrul 2003, Rothman and Iverson 2007). In addition to an L2 disassociation of morphology and syntax (e.g., Bruhn de Garavito 2003, Lardiere 1998, 2000, 2005, Prévost and White 1999, 2000, Schwartz 2003), I hypothesize that a system of learned pedagogical rules contributes to target-deviant L2 performance in this domain through the most advanced stages of L2 acquisition via its competition with the generative system. I call this hypothesis the Competing Systems Hypothesis. To test its predictions, I compare and contrast the use of the preterit and imperfect in two production tasks by native, tutored (classroom), and naturalistic learners of L2 Spanish.

Relationship between classroom authority and epistemological beliefs as espoused by primary school mathematics teachers from the very high and very low socio-economic regions in Thailand

This article presents findings of a larger single-country comparative study which set out to better understand primary school teachers’ mathematics education-related beliefs in Thailand. By combining the interview and observation data collected in the initial stage of this study with data gathered from the relevant literature, the 8-belief / 22-item ‘Thai Teachers’ Mathematics Education-related Beliefs’ (TTMEB) Scale was developed. The results of the Mann-Whitney U Test showed that Thai teachers in the two examined socio-economic regions espouse statistically different beliefs concerning the source and stability of mathematical knowledge, as well as classroom authority. Further, these three beliefs are found to be significantly and positively correlated.

The relationship between parent and child dysfunctional beliefs about sleep and child sleep

Cognitive theories emphasise the role of dysfunctional beliefs about sleep in the development and maintenance of sleep-related problems (SRPs). The present research examines how parents' dysfunctional beliefs about children's sleep and child dysfunctional beliefs about sleep are related to each other and to children's subjective and objective sleep. Participants were 45 children aged 11 -12 years and their parents. Self-report measures of dysfunctional beliefs about sleep and child sleep were completed by children, mothers and fathers. Objective measures of child sleep were taken using actigraphy. The results showed that child dysfunctional beliefs about sleep were correlated with father (r=.43, p<.05) and mother (r=.43, p<.05) reported child SRPs, and with Sleep Onset Latency (r=.34, p<.05). Maternal dysfunctional beliefs about child sleep were related to child SRPs as reported by mothers (r=.44, p<.05), and to child dysfunctional beliefs about sleep (r=.37, p<.05). Some initial evidence was found for a mediation pathway in which child dyfunctional beliefs mediate the relationship between parent dysfunctional beliefs and child sleep. The results support the cognitive model of SRPs and contribute to the literature by providing the first evidence of familial aggregation of dysfunctional beliefs about sleep.

Teacher beliefs about listening in a foreign language

This study investigated, through a questionnaire, the stated beliefs and stated practices of 115 foreign language teachers in England regarding listening pedagogy: whether such beliefs and practices reflect the literature on listening, whether beliefs and stated practices converged, and what factors might underpin them. Responses indicated a mismatch between teachers’ stated belief in the importance of teaching learners how to listen more effectively, and the lack of evidence in their stated practice of such teaching, with a focus instead on task completion. Findings are discussed against the accountability agenda of the study’s context, and its implications for teacher development highlighted.