1,388 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
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
Miridiba siamensis Keith 2004
No full text<i>Miridiba siamensis</i> Keith, 2004 <p> <i>Miridiba siamensis</i> Keith, 2004: 11, figs 2–3 (type loc.: Na Haeo, Loei, Thailand).</p> <p> <i>Miridiba siamensis</i> – Coca-Abia 2008: 682, 684 (in key).</p> Diagnosis <p>See Keith (2004).</p> Remarks <p> Keith (2004) described <i>Miridiba siamensis</i> from only one male specimen. Unfortunately, we were unable to study the holotype. However, according to the original description, this species shows features of the external morphology that characterize the genus <i>Miridiba</i>, such as labrum strongly depressed at middle, frons with developed carina, foretibia with a row of longitudinal pubescence and apices of first-four segments of fore- and mesotarsi with a tuft of setae ventrally. On the other hand, the author illustrated the male genitalia in lateral and dorsal views (Keith 2004: figs 2–3). According to the illustrations (Keith 2004: fig. 2), the parameres in lateral view could have the dorsal tubular complex characteristic of morphotype IX. The upper part shows divergent branches in dorsal view (Keith 2004: fig. 3), and the lower part shows short ventral branches pubescent with apical ends curved ventrally (Keith 2004: fig. 2). Besides, dorsal tubular complex forms a soft concavity, typical of this genital morphotype at distal end. Unfortunately, Keith (2004) did not illustrate the parameres in ventral view, and it is not possible to tell whether the ventral branches under the dorsal tubular complex are present, or not. In our opinion, the morphology of the parameres shows features that characterize the genital morphotype IX “ <i>Ciliatipennis</i> ”. Hence, we consider <i>Miridiba siamensis</i> should be included in this genital morphotype. Nevertheless, the holotype must be studied to confirm this consideration.</p> Distribution <p>Thailand.</p>Published as part of <i>Gao, Chuan-bu & Coca-Abia, María Milagro, 2021, Revision of the genus Miridiba Reitter, 1902 (Coleoptera, Scarabaeidae, Melolonthinae): genital morphotypes and new taxonomic data, pp. 1-94 in European Journal of Taxonomy 749</i> on pages 79-80, DOI: 10.5852/ejt.2021.749.1355, <a href="http://zenodo.org/record/4770293">http://zenodo.org/record/4770293</a>
The appraisal of three gas-fired small-scale CHP systems.
No full textThe research in this thesis has undertaken a technical. economic and environmeiital
appraisal of three gas-fired, small-scale Combined Heat-and-Power (CHP) systenlýý
together with a study of the UK's electricity supply industry (ESi) and CHP market.
The purpose of each system is to attempt to utilise more of the heat and/or electricitY
output from the CHP unit. Within the non-technical research area, t hree
scenarios for the evolution of the ES1 have been developed to help establish llow
changes to forces acting within the industry, might affect the development of the
UK CHP market. New applications of several strategic management, alialysis tools
were used to develop and select the following scenarios: (i) 'N-ewa nd reduced ('02
limits set by the Climate Control Conference + stricter environmental legislatioil,
(ii) Changes to the Pool mechanism for pricing electricity. (iii) Business as usual.
It was concluded that in isolation scenarios I and 3 would aid the expansion of the,
CHP market, whereas scenario 2 is likely to hinder it. The selection of the scenarios
and the implications for the ESi and CHP market are supported by the opinions of
'industry specialists', which were solicited in a survey specifically undertaken for
this study.
The investigation into the first of the three technical systems involves the substitution
of two separate CHP units in place of a single larger unit. The intention
is to operate the larger of the two CHP units at maximum output to satisfy the
base heat-load and to use the second unit for meeting peak loads. The results for
five test-cases were produced via a newlY-developed predictive model, and indicated
that it is possible, for one of the case studies considered, to achieve shorter
pay-back periods when using the double-unit - with a higher availability of 9.5% -
rather than the single-unit system. In the other two cases (where CHP is a viable
economic option), longer pay-back periods ensue by the installation of the twounit
rather than the single-unit system. The operation of the two-unit system call
potentially increase energy-utilisation from the CHP units at one of the other sites'.
Furthermore, the proposed system can offer, in some cases, significant secondarý'
benefits, which could encourage a potential investor in the technology. These benefits
include the increased heat- an d-elect ri city output, increased availability from
the system, back-up from the secondary unit if one unit fails.
The second system determines the viability of an integrated small-scale CHP and
TES system. Another predictive model was developed and tested on five test -case",.
It was found that there is insufficient potential for the system and that the pot(, iitial
is limited by the following factors (i) CHP-sizing methodology, (ii) the relat IvCIN,
high capital cost for TEs hardware and installation, (iii) the relatively low econwilic
value attributed to heat and (iv) the availability of IoN%-pricedo ff-peak electricitv.
An industrial case study provided a rare and useful operational exainple of tlic
proposed system and the findings indicated that the heat-store could reduce i he
energy and monetary expenditures by up to 2.8/7c of the site's annual gas usage.
displacing approximately 30 tones Of C02 emissions each year. Howe\-er, becauýw
of the high financial cost of the TES components and installation. the pay-back
period produced would rarely be acceptable to a prospecti\-e investor. except in
exceptional circumstances.
Finally, the viability of an integrated CHP/absorption chiller systeni was in\-(, stigated.
The effectiveness of these types of systems are dependent on several factors,
namely: the source-water temperature from the hot-engine CHP unit - for a high
cop - and the cooling load at the site, the cooling demand at the site and the
temperature of the cooling water. A first-stage predictive model was developed to
determine the initial appropriateness of the installation of the integrated system
at a local hospital for the first time. The indications were that the cooling demand
was too low and the surplus waste-heat from the CHP unit insufficient to make the
system viable at the site. A second working-system was studied with a full ('02
investigation undertaken. The intention was to compare the total C02 emissions
for the integrated CHP and absorption chiller system with those for a similarl. y
sized vapour-compression system. The results indicate that the installed systc1l)
will produce 0.30kgCO2/kWhcoolth compared with 0.27 kg and 0.32kg for two different
types of vapour compression systems at design conditions. If the CHP heat
output is increased - to supply all of the heat required by the absorption chiller -
then the proposed system can displace up to 0.06 kgC02 per kWhcoolth at design
conditions and 0.10 kgC02 per kWh of cooling delivered for lower cooling water
temperatures. This represents a reduction of 22% and 40% respectively, when
compared with the vap our- compressions system
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
Keith Johnstone
No full textKeith Johnstone entered the Royal Court Theatre as a new playwright in 1956: a decade later he emerged as a groundbreaking director and teacher of improvisation. His decisive book Impro (1979), described Johnstone’s unique system of training: weaving together theories and techniques to encourage spontaneous, collaborative creation using the intuition and imagination of the actors. Johnstone has since become world-renowned, inspiring theatre greats and beginners alike; and his work continues to influence practice within and beyond the traditional theatre.
Theresa Robbins Dudeck is the first author to rigorously examine Johnstone's life and career using a combination of archival documents – many from Johnstone's personal collection – participant observation, and interviews with Johnstone, his colleagues and former students.
Keith Johnstone: A Critical Biography is a fascinating journey through the physical spaces that have served as Johnstone's transformative classrooms, and into the conceptual spaces which inform his radical pedagogy and approach to artistic work.</JATS1:p
The place of experimental tasks in geometry teaching: learning from the textbook designs of the early 20th century
No full textThe dual nature of geometry, in that it is a theoretical domain and an area of practical experience, presents mathematics teachers with opportunities and dilemmas. Opportunities exist to link theory with the everyday knowledge of pupils but the dilemmas are that learners very often find the dual nature of geometry a chasm that is very difficult to bridge. With research continuing to focus on understanding the nature of this problem, with a view to developing better pedagogical techniques, this paper examines the place of experimental tasks in the process of learning geometry. In particular, the paper provides some results from an analysis of innovative geometry textbooks designed in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis suggests that experimental tasks have a vital role to play and that a potent tool for informing the design of such tasks, so that they build effectively on pupils’ geometrical intuition, is the notion of the geometrical eye, a term coined by Charles Godfrey in 1910 as “the power of seeing geometrical properties detach themselves from a figure"
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
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