Development of angle concepts by progressive abstraction and generalisation

This paper presents a new theory of the development of angle concepts. It is proposed that children progressively recognise deeper and deeper similarities between their physical angle experiences and classify them firstly into specific situations, then into more general contexts, and finally into abstract domains. An angle concept is abstracted from each class at each stage of development. We call the most general angle concept the standard angle concept. To investigate the role of the standard abstract angle concept in conceptual development, 192 children from Grades 2 to 8 were tested to find how they used it in modelling 9 physical angle situations and in expressing similarities between them. It was found that the standard angle concept first develops in situations where both arms of the angle are visible. Even at Grade 8, there are still significant proportions of students who do not use standard angles to represent turning and sloping situations. Implications for theory and practice are explored.This revised version was published online in September 2005 with corrections to the Cover Date.     

Developing Diversity Through Specialisation in Secondary Education: Comparing approaches in New Zealand and England

The paper compares approaches to curriculum specialisation in secondary education in New Zealand and England. In both countries there have been movements towards increased specialisation, though these have been quite different in form and scope. In both countries specialisation cannot be divorced from broader education policies designed to increase devolution and choice and the paper discusses these contexts before analysing the different approaches to specialisation and attempting an explanation. The authors draw on findings from research undertaken in New Zealand schools. The paper identifies three dimensions that have played a part in influencing curriculum specialisation in both countries. These are opportunity, source of impetus and support. It is argued that while local initiative is possible in New Zealand, central planning and guidance is inadequate. In England while central planning is strong and support is available, it is far from clear that real specialisation is encouraged by existing curriculum and assessment frameworks. In these circumstances in both countries it seems likely that vertical, rather than horizontal, diversity will continue to hold sway.     

Requisite Variety: The problem with generic guidelines for diverse genres of inquiry

In response to an invitation to explore the idea that potential guidelines be considered for qualitative inquiry in environmental education research, this article argues that prerequisite understanding of the nature and scope of qualitative inquiry required for such a task will reveal the problem inherent in it. Understanding the diverse complexities, the requisite variety, of qualitative inquiry not only challenges the methodological uniformity necessitated by this task philosophically; it unmasks the epistemological and ontological limits of such an endeavor, however well intentioned.     

Public Understanding of Climate Change: Certainty and willingness to act

During a 10-week period prior to the 1997 Kyoto conference on climate change, two parallel studies were conducted: Study 1 examined media portrayals of global warming and the certainty with which information was reported (percentage of 'hedging'); Study 2 was a telephone survey to assess public knowledge about key topics in global climate change, people's certainty about their information, trust in the media, and willingness to take action on global warming. Media reports were found to be scarce, and about half of the references to global warming were found to be hedged. More hedging was evident in the New York Times than in other print media and national television reports, and economic impacts of climate change were reported with the greatest certainty. The audience (N = 139 adults, average age 36–45, with at least a high school education) reported trusting their media sources more than 50% of the time. They were collectively fairly knowledgeable and certain about global warming information (9.1 on a scale of - 20 to + 20), and they appeared to be willing to adopt a range of responsible behaviors seen to be useful in countering global warming (average response 3.0 out of 4). The knowledge/certainty factor was described as 'attitude under uncertainty', and was significantly related to media trust (r = 0.325, p < 0.01) and willingness to act responsibly (r = 0.400, p < 0.01). Comparing Study 1 with Study 2, the research does not support a hypothesis that media hedging is related to uncertainty. Implications for environmental communicators are discussed.     

Making More of Faculty Culture: An Experiment in Building Intellectual Community

With the increase in academic specialty,scholars and leaders have sought new ways tostrengthen intellectual community. Their strategiesinclude experimenting with organisational structuresto bring about desired change. This qualitative casestudy examines the influences of such a structure. The Luce Seminars was a programme designed to supportsustained faculty conversation across disciplines atEmory University, a research university located in theUnited States. The analysis found that key functional and symbolic aspects of the program contributed to intenseparticipant involvement, resulting in broadened anddeepened intellectual discourse, enhanced disciplinaryorientation, and expanded possibilities for teachingand research. The authors conclude that structuredfaculty conversation across disciplines strengtheneddimensions of faculty culture related to interactionand scholarship at the university and suggest somebroad areas for future research.     

Promoting Mathematical Communication in the Classroom: Two Preservice Teachers' Conceptions and Practices

Recent reforms in mathematics education have encouraged teachers to engage their students in various forms of communication. Scholars have begun to consider questions such as: In what ways do teachers facilitate and guide classroom discourse? How does the quality of students' reflections impact the development of rich mathematical understanding? In order to address these and similar questions, the authors provide a framework of four constructs that can be used to analyze various forms of classroom communication: uni-directional communication, contributive communication, reflective communication, and instructive communication. Throughout the article,the authors both develop and use these constructs as they consider two preservice teachers concepts of communication and their corresponding classroom practices.     

A general approach for calculating the likelihood of dyadic interactions: Applications to sex preferences in rat pups and agonistic interactions in adults

We introduce a general approach for calculating the expected frequency of different types of dyadic interactions between animals and illustrate it with two applications. The first application determines whether there are sex contact biases between male and female Norway rat pups. We hypothesized that opposite-sex contact biases should be small, because it is likely that differences in contact based on the sex of animals would interfere with other biological functions, such as group temperature regulation. We found a small but significant bias of 3% in opposite-sex contacts. The second application reanalyzed J. B. Calhoun’s (1962) data on antagonistic encounters between rats for two factors (sex and birth location), each with two levels. The results of these two applications suggest that sex contact biases among pups are predictive of agonistic encounters among adults and that this approach has general application to the analysis of dyadic interactions among animals.