372 research outputs found

    The process of re-designing the geometry curriculum: the case of the Mathematical Association in England in the early twentieth century

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    This 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 We analyse historical documents of the Mathematical Association using a theoretical framework informed by work in the sociology of education.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

    Opportunities for the development of geometrical reasoning in current textbooks in the UK and Japan

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    Developing 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 place of experimental tasks in geometry teaching: learning from the textbook designs of the early 20th century

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    The 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"

    The making of a montane taro garden

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    Taro (Colocasia esculenta) is an essential crop in Papua New Guinea, especially in the highlands where taro grows at high altitudes (above 2,000 m) and sweet potato is absent. Taro and its cultivation are part of the collective memory of the Oksapmin society, in Sandaun province. The creation, maintenance, and harvest of a taro garden follow elaborate techniques and rules, the knowledge of which is not universal among villagers. This article describes the making of a taro garden by Oksapmin cultivators. The process is divided into two parts: activities related to the “mother garden”, where cuttings for the garden-to-be must be harvested, along with activities and techniques involved in preparing the new taro garden. The author discusses the significance of taro gardens in Oksapmin society

    The process of re-designing the geometry curriculum: the case of the Mathematical Association in England in the early 20th Century

    No full text
    This paper examines a key period of change in geometry teaching in England. Our focus is the character and nature of the recommendations of the geometry report of the UK Mathematical Association in 1902. We analyse historical documents of the Mathematical Association using a theoretical framework developed from Cooper’s model. Our analysis shows that the character and recommendations of the Mathematical Association report was influenced by various factors including: that the Mathematical Association members 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 for a complete change from the traditional approach; that conflicts between the various members of the Mathematical Association prevented a complete consensus; and that the climate outside the teaching committee of the Mathematical Association was not ready for radical reform at that time

    Genome Sequence Resource of a Taro Bacterial Soft Rot Pathogen, Dickeya fangzhongdai ZXC1

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    Dickeya fangzhongdai ZXC1 is a newly identified highly virulent causal agent of taro bacterial soft rot disease isolated from a taro sample showing typical soft rot symptoms in Shaoguan, Guangdong Province, China. The pathogen produces plant cell wall–degrading enzymes that macerate the taro tube tissues. In this study, we report the whole-genome sequencing analysis of strain ZXC1. The results showed that strain ZXC1 has one circular DNA chromosome of 5,129,951 bp with a 56.59% G+C content. In addition to sharing a conserved zms gene cluster that encodes the genes for biosynthesis of phytotoxin zeamines and 11 copies of predicted pectate lyase genes, the strain ZXC1 genome contains more prophage loci and a higher number of type IV secretion system and type IV secretion system gene clusters than the D. fangzhongdai strains isolated from pears or phalaenopsis, which may account for its strong virulence phenotype. The data from this study present a valuable resource for elucidation of the pathogenic mechanisms of D. fangzhongdai and may aid in developing new disease control approaches to safeguard taro production. [Figure: see text] Copyright © 2024 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license

    Proof and proving in current classroom materials

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    Research across many countries reports that teaching the key ideas of proof and proving to all students is not an easy task. This paper reports on the session of the BSRLM Geometry Working Group which examined current classroom material from the UK with the intention of uncovering the ‘opportunities for proof’ in geometry that are provided by such material. To carry out such an analysis three analytical frameworks are compared. Two of the analytical frameworks, while placing proof and proving in a wider context of learners’ mathematics, may not fully uncover the detail of proof and proving. The third analytical framework, while permitting a detailed analysis of explicit proof and proving, may not fully account for textbooks that devote most space to discussions of proof and proving and/or contain problems that implicitly provoke proof. This comparison reveals some of the complexity of textbook analysis and suggests that further work is needed on a suitable analytical framework

    NieR: <i>Automata</i> Yoko Taro. Egzystencjalna podróż przez absurd

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    The focus of this article is Yoko Taro’s NieR: Automata in general and its four main characters—androids 2B and 9S as well as machines Adam and Eve—in particular. Following their evolution in the game, I intend to show that they serve its author as a tool with which to propose that the sense of absurd, and the sense of life’s meaninglessness around which their world is created, can be fought with selflessness.Głównym tematem artykułu jest gra NieR: Automata Yoko Taro, w szczególności jej cztery główne postaci—androidy 2B i 9S, a także maszyny Adam i Eve. Śledząc ich ewolucję w grze, tekst pokazuje, że służą one jako narzędzie, dzięki któremu autor gry może zaproponować tezę, że walka z poczuciem absurdu i bezsensowności życia, wokół którego powstaje ich świat, jest możliwa i że da się je pokonać za pomocą bezinteresowności

    Boundary conditions of Weyl semimetals

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    We find that generic boundary conditions of theWeyl semimetal are dictated by only a single real parameter in the continuum limit. We determine how the energy dispersions (the Fermi arcs) and the wave functions of edge states depend on this parameter. Lattice models are found to be consistent with our generic observation. Furthermore, the enhanced parameter space of the boundary condition is shown to support a novel topological number. © The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan2211Nsciescopu
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