Formulation of stable difference schemes for systems of initial-value partial differential equations

A general system of initial-value partial differential equations is classified into four categories based on the partial differential operators which define the equations. Specific combinations of the operators are termed “invariants” since they are common to all finite difference approximations to the system of equations. The “invariants” are used to a priori determine if one may formulate a stable difference approximation to a system of partial differential equations. This is in essence a numerical existence theory.     

Four dialogues and metalogues about the nature of science

We analyse and explore, in the form of dialogues and metalogues questions about the dialogic nature of beliefs and students belief talk about the nature of science and scientific knowledge. Following recent advances in discursive psychology, this study focuses not on students' claims but on the discursive resources and dialogical practices that support the particular claims they make. We argue that students' discourse is better understood as a textual bricolage that is sensitive to conversational context, common sense, interpretive repertoires, and textual resources available in the conversational situation. Our text is reflexive as it embodies the discursive construction of knowledge and undercuts any claims to authoritative knowledge. The very conception of “belief” is itself an expression or construction from within the mundane idiom.... We learn to use “belief” in conditions when the “objective facts” are unknown or problematic and we want to indicate the tenuous character of our claim.... The notion of “real world” or “objective reality” is embedded in an extensive, pervasive language game which includes as an intelligible move or possibility the use of the very concept of “belief” itself. (Pollner, 1987, p. 21)     

Jurisprudential and Ethical Perspectives on "The Best Interests of Children"

Justifications of policies must be clearly warranted if educational leaders are to continue to maintain integrity and to sustain the trust of those served. Educators are called upon to mediate many private and public interests, including those pertaining to personal, organizational, professional, and societal values. This work of mediating conflicting values often relates to guarding and/or advocating the interests of children. Leaders must understand what they mean when evoking the potent phrase in the best interests of children. More importantly, they must avoid the temptations of sophistic misuses of the best interests of children notion. What is meant when we say we are deciding in the best interests of children? Each of the political, psychological, pedagogical, philosophical, jurisprudential, and ethical grounds undergirding the concept of the best interests of the child contributes content and meaning to the phrase. While each of these perspectives merits consideration, this article is delimited to an exploration of three interpretations from the field of jurisprudence and four interpretations from the field of ethics.     

Relations between teachers' approaches to teaching and students' approaches to learning

This paper reports on an empirical study which shows that qualitatively different approaches to teaching are associated with qualitatively different approaches to learning. More specifically, the results indicate that in the classes where teachers describe their approach to teaching as having a focus on what they do and on transmitting knowledge, students are more likely to report that they adopt a surface approach to the learning of that subject. Conversely, but less strongly, in the classes where students report adopting significantly deeper approaches to learning, teaching staff report adopting approaches to teaching that are more oriented towards students and to changing the students conceptions. The study made use of a teaching approach inventory derived from interviews with academic staff, and a modified approach to learning questionnaire. These conclusions are derived from a factor and cluster analysis of 48 classes (involving 46 science teachers and 3956 science students) in Australian universities. The results complete a chain of relations from teacher thinking to the outcomes of student learning. Previous studies have shown relations between teachers' conceptions of teaching and learning and their approaches to teaching. Numerous studies have shown correlations between students' deeper approaches to learning and higher quality learning outcomes. The results reported here link these two sets of studies. They also highlight the importance, in attempts to improve the quality of student learning, of discouraging teacher-focused transmission teaching and encouraging higher quality, conceptual change/student-focused approaches to teaching.     

The costs of secondary schooling in developing countries; patterns and prospects

This research is concerned with the problems that may arise in paying for the costs of secondary school places in developing countries, which have experienced a rapid increase in primary school enrolments since the World Conference on Education for All at Jomtien. Many, but not all, of these countries are in sub-Saharan Africa. Case studies are being conducted six African and Asian countries. The basic argument is that cost structures, which may have been appropriate for systems that had low gross enrolment ratios and modest transition rates from primary to secondary are unlikely to be sustainable as enrolments become universalised. The challenge is to identify opportunities to expand quality secondary schooling to meet new needs while reducing costs to levels which can be afforded. Access to and quality of secondary schooling is likely to dominate the educational planning agenda in many developing countries in the early part of the twenty-first century.     

Teacher learning and policy intention: selected findings from an evaluation of a large‐scale programme of professional development in the Republic of Ireland

The study reported on in this paper is set in the context of a national programme of professional development for primary teachers in the Republic of Ireland which has been in operation since 1999 and finished in 2008. The paper explores the acquisition and interpretation by teachers of the elements of the reform. The authors consider the extent to which the professional development experiences facilitated change in teachers’ knowledge and if the teachers interpreted this in the way expected by policy‐makers. The theoretical basis to the study draws on previous research that conceptualises teacher learning/knowledge acquisition and the change process as being dependant on an interwoven mix of factors, including teacher, school and policy‐level contexts and characteristics. To a large degree the findings of this study do not deviate wildly from this prior work, which suggests that policy‐makers and planners of CPD programmes, despite their best intentions, still need to be cognisant of such factors.     

Cognitive biases in the interpretation of autonomic arousal: A test of the construal bias hypothesis

According to Bandura’s construal bias hypothesis, derived from social cognitive theory, persons with the same heightened state of autonomic arousal may experience either pleasant or deleterious emotions depending on the strength of perceived self-efficacy. The current study tested this hypothesis by proposing that college students’ preexisting efficacy beliefs may affect how physiological arousal during exams is construed as a valence of positive emotion. Survey data were collected from 172 students in a statistics course at a large research university in the Midwest. Students provided self-reported intensity of autonomic arousal during previous exams, statistics self-efficacy, and positive affect toward a proximal final exam. The construal bias hypothesis was supported by a significant interaction between autonomic arousal and self-efficacy on the dependent variable positive affect. Results revealed that as autonomic arousal increased, so did the moderating effect of self-efficacy. Specifically, as physiological arousal intensified, students with high or low self-efficacy reported divergent levels of positive emotion. Implications for theory, research, and practice are discussed.