Domain Coloring and the Argument Principle

Abstract

The domain-coloring algorithm allows us to visualize complex-valued functions on the plane in a single image—an alternative to before-and-after mapping diagrams. It helps us see when a function is analytic and aids in understanding contour integrals. The culmination of this article is a visual discovery and subsequent proof of the Argument Principle, which relates the count of poles and zeros of a meromorphic function inside a contour to the accumulated change in argument of the function around the contour. Throughout, I offer connections to standard learning goals of courses in complex variables.     

Infusing moral education into English language teaching: an ontogenetic analysis of social values in EFL textbooks in Hong Kong

ABSTRACT

This paper investigates the representation of social values and their ontogenetic development in English as a foreign language textbooks in Hong Kong. Adopting a social semiotic approach, it considers social values in textbooks as semantic categories which are constructed by complex semiotic discursive resources, and develops an explicit framework to model what values are selected and how the values are constructed. Analysis of 19 textbooks from Primary 1 to Secondary 4–6 shows that the social values change from the personal domain (e.g. good hygiene and healthy lifestyle), through the interpersonal domain (e.g. politeness and respect), to the altruistic concern for all mankind. The result also suggests that the textbooks are more concerned with the didactic education of good citizens than with cultivating children’s critical thinking. The analytical framework and the findings can be used for the explicit instruction and critical analysis of social values in English language teaching.     

The construction of teacher identities in educational policy documents: A critical discourse analysis

Abstract

Critical Discourse Analysis (CDA) is a complex eclectic method that has potential to be a valuable tool for critical policy analysis. This article highlights this potential by demonstrating how CDA can be applied to policy texts. That is, it focuses on the processes involved in ‘doing’ critical discourse analysis. In particular, it examines the framework identified by Chouliaraki & Fairclough (1999) as the means by which CDA can be ‘operationalised’ in order to produce ‘theoretically grounded analyses in a wide range of cases’. The framework is outlined and discussed in relation to the construction of teacher identities in educational policies. The article then applies CDA to an analysis of one education policy document to illustrate the framework in operation. In so doing, it addresses the problem of teacher quality, which is analysed in terms of the discursive constructions of teachers’ professional identities. The analysis demonstrates how CDA may be used both as a tool for critical policy analysis and for the analysis of the construction of identities in educational, and other, documents.     

For whom does “what works” work? The political economy of evidence-based education

ABSTRACT

What role does scientific evidence play in educational practice? Supporters of evidence-based education (EBE) see it as a powerful way of improving the quality of public services which is readily applicable to the education sector. Academic scholarship, however, points out important limits to this applicability. I offer an account inspired by Tullock’s theory of bureaucracy that helps explain EBE’s influence despite these limits. Recent configurations of EBE are an imperfect solution to 2 imperatives where policymakers are at an informational disadvantage: (a) guiding professionals working in the field and (b) evaluating evidence from academic researchers. EBE, especially in the form of RCTs and systematic reviews, offers a way of filtering a complex range of research to produce a determinate result that is transparent to policymakers. However, this impression of research transparency is misleading as it omits theoretical background that is critical for successfully interpreting the results of particular interventions. This comes at a cost of relevance to the frontline professionals whom this research evidence is supposed to inform and help.     

Teacher students’ dilemmas when teaching science through inquiry

Background: Inquiry-based science education (IBSE) is suitable to teach scientific contents as well as to foster scientific skills. Similar conclusions are drawn by studies with respect to scientific literacy, motivational aspects, vocabulary knowledge, conceptual understandings, critical thinking, and attitudes toward science. Nevertheless, IBSE is rarely adopted in schools. Often barriers for teachers account for this lack, with the result that even good teachers struggle to teach science as inquiry. More importantly, studies indicate that several barriers and constraints could be ascribed to problems teacher students have at the university stage.

Purpose: The purpose of this explorative investigation is to examine the problems teacher students have when teaching science through inquiry. In order to draw a holistic picture of these problems, we identified problems from three different points of view leading to the research question: What problems regarding IBSE do teacher students have from an objective, a subjective, and a self-reflective perspective?

Design &; method: Using video analysis and observation tools as well as qualitative content analysis and open questionnaires we identified problems from each perspective.

Results: The objectively stated problems comprise the lack of essential features of IBSE especially concerning ‘Supporting pupils’ own investigations’ and ‘Guiding analysis and conclusions.’ The subjectively perceived problems comprise concerns about ‘Teachers’ abilities’ and ‘Pupils’ abilities,’ ‘Differentiated instruction’ and institutional frame ‘Conditions’ while the self-reflectively noticed problems mainly comprise concerns about ‘Allowing inquiry,’ ‘Instructional Aspects,’ and ‘Pupils’ behavior.’

Conclusions: Each of the three different perspectives provides plenty of problems, partially overlapping, partially complementing one another, and partially revealing completely new problems. Consequently, teacher educators have to consider these three perspectives.     

Tackling early school leaving and the governing of educational transitions in Italy

ABSTRACT

This article presents a critical policy historiography of how Early School Leaving has been understood as a social problem and what policy responses have been enacted to tackle it in the Italian context, devoting a specific attention to the analysis of the translation of EU policy ideas, tools and recipes to reduce ESL. It shows how the formulation of a global and integrated national strategy to tackle ESL in Italy in 2018 can be interpreted as the result of a troubled process of re-culturing. Such a reculturing is the effect of the complex interplay between the legacies of the Italian welfare regime in education and the co-option of the ESL issue within a EU political frame that struggles to combine economic rationalism and social justice. Such a struggle is interpreted as contributing to a profound rethinking of education and its mission.     

Criticality's affective entanglements: rethinking emotion and critical thinking in higher education

ABSTRACT

Critical thinking is often understood as a set of tangible, transferrable and measurable skills and competencies. Yet, it is also an intensely affective experience that is complex, contingent and contextualised. Using interview, focus group and observation data conducted with 15 first-year undergraduate social science students at a UK research-intensive university, this paper explores how students negotiate the complex knowledge practices that constitute critical thinking, particularly the affects of being and becoming critical. The theoretical tools offered by Karen Barad and Sara Ahmed allow a conceptualisation of critical thinking as a complex phenomenon of socio-material and affective practices. This paper turns to Barad and Ahmed to explore the potential of their clashing theorisations for thinking through the affective territories of critical thinking. It will argue that acknowledging the way(s) critical thinking feels (as well as what it is and what it is for) opens up new imaginaries for feminist scholarship about criticality.     

多项式零点的分布及其应用

文章主要研究一般复系数多项式零点的分布性质,讨论实系数多项式零点分布的某些性质．首先利用复变函数理论证明多项式零点存在定理;然后利用矩阵特征多项式、特征值的估计理论系统地讨论一般多项式零点的分布情况,并给出一些结果;最后给出多项式零点分布在线性控制系统中的应用,具体展示它的实用价值．     

Visual culture and critical pedagogy: from theory to practice

ABSTRACT

This article presents an educational approach that merges ideas of critical pedagogy with those of visual culture. According to this approach – termed visual critical pedagogy – art is an integral part of the textures of society and culture and their manifold and complex visual expressions, including the more controversial and subversive among them. It objects to locking art and visual culture in art departments, and to restricting art history to a formalist analysis of ‘masterpieces’ – which represent primarily the Western art market and its underlying politics. It likewise rejects the conception of art history as the history of artists and art movements – a conservative approach still prevalent in many academic institutions. Integrating critical pedagogy with visual culture provides fertile ground for an educational practice within art classes and beyond them. Visual critical pedagogy is formulated using the concepts exposure, deciphering, representation and visibility, shared by both critical pedagogy and visual culture. These are discussed in the context of educational projects and activities planned and implemented by Jewish and Arab students enrolled in an education-through-art program in an academic college in northern Israel.     

具有多项式系数的二阶线性微分方程解的零点分布

本文研究具有多项式系数的二阶线性微分方程解的零点分布,细化了Bank和Laine的结果。证明当n为偶数时,对任意正整数k,总可取系数A(z)为n次多项式,使得方程∫ A(z)f=0存在非平凡解f有k个零点(按重数计)。进一步.我们还给出了该方程存在无零点解的条件。特别地.当系数A(z)=z~(2m)时.我们证明该方程非平凡解的零点序列的收敛级都等于其增长级。     

关于单边四元数多项式系数的一个注记(英文)

只考虑单边四元数多项式,对于二次的四元数多项式,我们给出了一个判别准则(定理2.3),该准则利用其系数来判断该二次多项式的零点全体是否都只在一个球面上.而对于零点全体只在一个球面上的n次多项式,我们给出了这些多项式的系数必须要满足的一个条件.作为这些结论的应用,当四元数多项式(二次或者是n次)的系数不满足我们所给的条件时,那么该四元数多项式必须至少有两个互不同余的零点.     

The development of an efficient technique for collecting and analyzing qualitative data: The analysis of critical incidents

Traditionally, methods for collecting qualitative data have created practical difficulties in that they often require long-term engagement and, as a result, produce a great volume of data. This paper proposes and demonstrates a speedy technique for gathering and analyzing such data. It is argued that an analysis of critical incidents can be used by researchers interested in collecting qualitative data quickly as a method for doing a case study, but also, at the same time, in a participatory way that contributes to understandings that can be useful for the purpose of school improvement.     

Early childhood literacy: Creating a better world

Abstract

Problem‐posing teaching using multicultural children's literature nourishes an integrated literacy curriculum that supports young children's meaningful learning. This method encourages integrated learning that is both developmentally and culturally meaningful through interacting with story, reading literature, and participating in related learning activities. The problem‐posing method was developed by Paulo Freire [Education for Critical Consciousness, Seabury, New York] and critical pedagogists. The method leads students of any age, experience or ability level to base new learning on personal experience in a way that encourages critical reflection. This method has not been widely used with younger learners, but lends itself well to integrated early childhood literacy development.

This article shows selected qualitative data samples from case studies of early childhood teacher education students as they experience the method in a literacy course and as they use the method with young children. A critical analysis of the students’ work draws out key points regarding literacy development in a rapidly changing world. The teacher education students’ work provides an arena for developing the theory further as they implement theoretically‐based pedagogy with young learners. Data reveal issues regarding critical literacies and postmodern approaches to early childhood education.     

Life skills for ‘real life’: How critical thinking is contextualised across vocational programmes

Background: This article presents an analysis of how critical thinking is contextualised in everyday teaching in three vocational education and training (VET) programmes: Vehicle and transport, Restaurant and management, and Health and social care.

Purpose: The main question addressed is: What knowledge discourses permeate different VET-contexts, and hence what kinds of opportunities for critical thinking do they offer students?

Method: The qualitative analysis draws on data from a four-year ethnographic project exploring learning processes that can be characterised as civic education in Swedish vocational education. The analysis presented here used data collected during 85 days of observations of teaching in six VET classes, interviews with 81 students and 10 teachers, and collected teaching material. To explore why some contextualisations provided more opportunities and encouragement for critical thinking than others, we applied Bernsteinian concepts of ‘horizontal and vertical knowledge discourses’ and ‘discursive gaps’.

Findings and conclusions: Overall, teaching that was observed focused primarily on ‘doing’. However, in all three programmes, the analysis identified that there were also situations that touched upon critical thinking. Three major themes were identified: critical thinking related to ‘Personal experiences’, ‘The other(s)’ and ‘Wider perspectives’. It appeared that the frequency and nature of such situations varied with the knowledge discourses permeating the programme. Furthermore, we discuss the manifestations of critical thinking in relation to the wider context of what Bernstein refers to as pedagogic rights; individual enhancement, social inclusion and development of the competence and confidence to participate in political processes.     

Unfinished Agenda: a Comment on the Special JME Issue on the Relationship of ME and RE

Abstract

This article takes a critical look at the contents of the previous edition of The Journal of Moral Education, noting the points of agreement and the divergencies in the six essays it contains. Unresolved issues in the debate about the relationship of moral education and religious education are identified and matters which require further investigation and discussion are tabulated.     

Critical ethnography and a Vygotskian pedagogy of hope: The empowerment of Mexican immigrant children

This article, via the use of ethnographic research methods, suggests that critical theory and critical pedagogy can fruitfully redirect the attention from the predominant rhetoric on oppression to the developmental, cognitive, and academic needs of immigrant, low-income, and culturally different children. The Vygotskian approach is advocated to stress the need for the creation of linguistically and culturally appropriate learning environments that link the social and cognitive processes which constitute the basis for genuine empowerment in schoolchildren. The use of concrete examples will illustrate the major points of the article.     

Quadrature formulas for Fourier-Chebyshev coefficients

The aim of this work is to construct a new quadrature formula for Fourier-Chebyshev coef-ficients based on the divided differences of the integrand at points-1, 1 and the zeros of the nth Chebyshev polynomial of the second kind. The interesting thing is that this quadrature rule is closely related to the well-known Gauss-Turn quadrature formula and similar to a recent result of Micchelli and Sharma, extending a particular case due to Micchelli and Rivlin.     

A critical policy analysis of local religious education in England

ABSTRACT

This critical policy analysis investigates the opinions and activities of Standing Advisory Councils on Religious Education (SACREs) in England. It uses a critical approach to educational policy to examine the diffuse power structure of SACREs and give voice to those local councils. Using data gathered in an online survey of SACREs, conducted between January and May 2017, it critiques the activities of SACREs and, in identifying what they see as their future role, questions whether the complex, producer-based governance structure of religious education is preferable to a simple, neo-liberal centralised legal settlement. It suggests that those individuals and groups which are successful in surviving in the increasingly competitive, marketised, local RE policy landscape become intrinsic parts of the national neo-liberal solution.