1,360 research outputs found
Theoretical frameworks for the learning of geometrical reasoning
No full textWith the growth in interest in geometrical ideas it is important to be clear about the nature of geometrical reasoning and how it develops. This paper provides an overview of three theoretical frameworks for the learning of geometrical reasoning: the van Hiele model of thinking in geometry, Fischbein’s theory of figural concepts, and Duval’s cognitive model of geometrical reasoning. Each of these frameworks provides theoretical resources to support research into the development of geometrical reasoning in students and related aspects of visualisation and construction. This overview concludes that much research about the deep process of the development and the learning of visualisation and reasoning is still needed
The shaping of student knowledge: learning with dynamic geometry software
No full textThe focus of this paper is a software genre usually referred to as ‘dynamic geometry’ because of the ability of the user to dynamically manipulate geometrical figures created with the software tool. Using data from a longitudinal study of 12-13 students’ use of dynamic geometry software, the focus of the analysis is on the interpretations the students make of geometrical objects and relationships when using this form of software. The analysis suggests that the students’ mathematical reasoning is shaped by their interactions with the software in that their ability to explain geometrical facts and relationships evolves from imprecise, ‘everyday’ expressions, through reasoning that is overtly mediated by the software environment, to mathematical explanations of the geometric situation that transcend the particular tool being used. Such findings suggest that curriculum initiatives that encourage the use of dynamic geometry software are appropriate but that the incorporation of such software into classroom practices is unlikely to be straightforward
The mediation of mathematical learning through the use of pedagogical tools: a sociocultural analysis
No full textA sociocultural analysis suggests that pedagogical artifacts employed in the teaching and learning of mathematics both enable and constrain learning. This paper summarises three classroom studies of mathematics learning that have utilised a sociocultural approach. Each of the studies indicates how insight can be gained into the ways in which students attempt to make sense of the mathematics they encounter
The jingling Geordie: community arts and the regional culture of the North East of England
No full textIn the light of the massive economic and social changes which have affected the North East of England over the last 25 years, the author assesses the vitality of the indigenous culture and reflects upon current cultural trends and the North East’s future, particularly in relation to a regional Europe. He traces the folk-tradition of the region and looks at ways in which this can be drawn upon to develop a meaningful link between past and present. He looks closely at the changing nature of class-relationships in the North East and reflects upon how a valid local culture can survive in a multi-cultural society. He draws upon his own extensive experience in Community Arts, looking at definitions of the term in the new political climate and arguing for its positive contribution to the cultural debate. He dwells on the issue of regionalism and devolution in a new Europe, comparing the situation in the North East of England with political and cultural changes in Scotland and other parts of the United Kingdom
Using imagery to solve spatial problems
No full textThis report focuses on the use of imagery to solve a range of spatial problems. The research projects reviewed in this report offer some insight into the range of strategies used by solvers of spatial problems and point to relationships between spatial and verbal skills
The design features of forecasting support systems and their effectiveness
No full textForecasts play a key role in the management of the supply chain. In most organisations such forecasts form part of an information system on which other functions such as scheduling, resource planning and marketing depend. Forecast accuracy is, therefore, an important component in the delivery of an effective supply chain. Typically, the forecasts are produced by integrating managerial judgment with quantitative forecasts within a forecasting support system (FSS). However, there is much evidence that this integration is often carried out poorly with deleterious effects on accuracy. This study considers the role that a well-designed FSS might have in improving this situation. It integrates the literatures on forecasting and decision support to explain the causes of the problem and to identify design features of FSSs that might help to ameliorate it. An assessment is made of the extent to which currently available business forecasting packages, which are widely employed in supply chain management, possess these feature
Opportunities for the development of geometrical reasoning in current textbooks in the UK and Japan
No full textDeveloping a good model of the school geometry curriculum continues to be one of the most important tasks in curricular design in mathematics. This paper reports on an initial analysis of current best-selling textbooks used in lower secondary schools in Japan and the UK (specifically England and Scotland). The analysis indicates that, following the specification of the mathematics curriculum in these countries, Japanese textbooks set out to develop students’ deductive reasoning skills through the explicit teaching of proof in geometry, whereas comparative UK textbooks tend, at this level, to concentrate on finding angles, measurement, drawing, and so on, coupled with a modicum of opportunities for conjecturing and inductive reasoning. The available research suggests that each approach has its own strengths and weaknesses. Finding ways of capitalising on the strengths and mitigating the weaknesses could prove helpful in formulating new curricular models and designing new student textbooks
The process of re-designing the geometry curriculum: the case of the Mathematical Association in England in the early twentieth century
No full textThis paper examines a key period of change in geometry teaching in England. Our focus is the character and nature of the recommendations of the 1902 geometry report of the UK Mathematical Association. We analyse historical documents of the Mathematical Association using a theoretical framework informed by work in the sociology of education. Our analysis shows that the character and recommendations of the Mathematical Association report were influenced by various factors including: that Mathematical Association members at the time still respected the traditional Euclidean approach to geometry as a basis for school geometry; that the academic and ‘power’ resources available to the Mathematical Association at the time were not sufficient to enable a complete change from the traditional approach; that a lack of consensus between the various members of the Mathematical Association prevented a more radical proposal; and that the general climate in schools at that time was not prepared for far-reaching changes to the teaching of geometry. These findings accord with other research on educational reform which indicates that curriculum change processes are invariably complex and often subject to much politicking
The Baronage in the Reign of Richard II, 1377-1399
No full textThis thesis is a prosopographical study of the English baronage during the reign of Richard II. It considers the role of barons within the political community and attempts to characterise them, both in terms of their engagement with institutions and by exploring private power relations. In the tradition of the political culture framework within which the study is situated, it seeks ultimately to determine the group’s motives.
The first section explores structures, defining the baronage and tracing the historical development of the class. The stresses and concepts that moulded and distinguished the political culture are also set out. Three broad themes – politics, land and lordship - are then discussed in the second section. These endeavour to quantify and qualify the power and authority that were exercised by the 66 baronial families from the reign. In the political arena barons’ engagement with the apparatus of royal government, administration and justice are investigated, along with political favour and its rewards. The size and distribution of their landholding is then assessed and the strategies they employed for putting their estates together determined. The service they performed and received is afterwards discussed and the reasons for and benefits of it analysed. These broader themes are then enriched by a demonstration of the differences on the ground. In this third section two case studies, of the Gloucestershire and Sussex barons, revisit the same themes, but look in more detail at just the handful of resident barons in those counties. Finally, the different situations in the two sample localities are reconciled by deciphering the barons’ motives
Visualisation, imagery, and the development of geometrical reasoning
No full textThis report focuses on some aspects of the nature and role of visualisation and imagery in the teaching and learning of mathematics, particularly as a component in the development of geometrical reasoning. Issues briefly addressed include the relationship between imagery and perception, imagery and memory, the nature of dynamic images, and the interaction between imagery and concept development. The report concludes with a series of questions that may provide a suitable programme for research and lays the foundation for further work of the BSRLM geometry working group
- …
