Counting,Recounting and Matching

Although we start our mathematical education by learning to count, it is this very thing which is one of the most difficult things to carry out in practice. In this article, we discuss a very simple method which is available in a very general form under the name of Fubini’s principle (see Box 1). In its simplest form, it is the obvious observation that counting in two different ways produces the same sum. However, the various examples we discuss will hopefully convince the reader that the principle is surprisingly effective.     

On identity, diversity, and educational change

In this article, I discuss two areas of Andy Hargreaves’ scholarship, teachers’ identity and biography and the three periods of educational change spanning the 1960s to 1990s, that have influenced my work as a teacher educator and researcher. I describe research projects, including self-studies, in which I have examined the influence of teachers’ identities and biographies on their beliefs and practices of responding to student diversity. I also explore how the topic of teachers’ identity and biography are integrated into the courses I teach. Additionally, I describe how I have related the three periods of educational change—a period of optimism and innovation, a period of complexity and contradiction, and a period of marketization and standardization, along with the monocultural restoration—to corresponding policies and practices of responding to student diversity in the US and Ontario, Canada. Finally, I discuss a current project in which Andy and I are exploring core issues related to educational leadership and diversity.     

Supporting Professionalism,Diversity, and Context Within a Collaborative Approach to Gifted Education

Educators concerned about gifted learners are moving toward an evidence-based perspective focusing on children with exceptionally advanced learning needs who require flexibly responsive educational attention. This article describes two system-wide implementation experiences, one in a mixed urban/rural public school board and the other in an urban board of affiliated parochial schools, designed to meet the educational needs of diversely competent students. The authors discuss the intersecting roles of consultants, teachers, administrators, and parents, and some creative applications they have implemented that illustrate a respect for (a) teachers' professionalism, (b) individual developmental diversity, and (c) context-specific opportunities and constraints. The authors discuss ways that this flexible collaborative approach to integrating consultative processes into board-wide practices addresses the diverse educational needs of gifted learners, and also encourages high-level outcomes in learners not formally identified as gifted.     

School ethos and personal,social, health education

This paper will discuss research undertaken within a London borough in 2009 that aimed to examine how Personal, Social, Health and Economic education (PSHE) was perceived and delivered. The ethos of schools was incorporated into the enquiry as a key determinate of both perception and delivery of PSHE. The findings are presented with particular reference to three areas: school ethos, participation and evaluation. The overall conclusion of the study is that staff value PSHE, but with some reservations. Staff believe that PSHE has a positive impact on pupil behaviour. The value placed by schools on PSHE, and how it interrelates with the existing ethos of schools, remains a crucial factor in its provision.     

Dewey,Interest, and Well-Being: Prospects for Improving the Educational Value of Physical Education

Despite the current policy prominence of physical education, there is still unease about the subject's educational contribution. In this respect, we are surprised by how seldom John Dewey's writings inform contemporary reviews of aims and values. We outline how his writings on connecting the child and the curriculum and schools with society are relevant to deliberations on how students could derive enhanced meaning from physical education. We address criticisms by Richard Peters of Dewey and discuss related issues on: interest and engagement, problem solving and criteria for personal growth. We discuss how the thinking of Dewey and Valerie Tiberius might inform the development of physical education curricular that are more deeply connected with the lives of students and which promote well-being. In particular, we argue there is a need for future curriculum to be designed in ways that invite students to cultivate informed and stable physical activity habits and values.     

Feeling Heard: Inclusive Education,Transformative Learning,and Productive Struggle

Developments in international inclusive education policy, including in prominent UN documents, often refer to the aim of a quality education for all. Yet, it remains unclear: What exactly is meant by quality education? And, under what conditions are quality educational experiences possible for all learners? In this essay, Diana Murdoch, Andrea English, Allison Hintz, and Kersti Tyson bring together research on inclusive education with philosophy of transformative learning, in particular John Dewey and phenomenology, to further the discussion on these two questions. The authors argue that teacher–learner relationships, of a particular kind, are necessary for fostering environments wherein all learners have access to quality educational experiences associated with productive struggle as an indispensable aspect of transformative learning processes. They define such relationships as “educational relationships that support students to feel heard.” In developing their argument, the authors first analyze the concept of productive struggle, an aspect of learning increasingly recognized in research and policy as an indicator of quality education. Second, they discuss three necessary, though not sufficient, conditions for the teacher to cultivate educational relationships that support students to feel heard. Third, they draw out connections between environments that support feeling heard and those that support productive struggle, and they discuss teachers' challenges and risk-taking in creating such environments. The authors close with a discussion of implications for international policy, practice, and research.     

COVID-19, mathematics education,and the evaluation of expert knowledge

Maturity and citizenship in a democracy require that laypersons are able to critically evaluate experts’ use of mathematics. Learning to critically reflect on the use of mathematics, including the acquisition of the mathematical knowledge and skills required to that end, has been repeatedly postulated as an indispensable goal of compulsory education in mathematics. However, it remained unclear in how far such reflection is possible, even for the well-educated layperson in mathematics. We use different discussions in German mass media on the pandemic policy in the SARS-CoV-2 crisis in 2020 as examples with far-reaching individual and social consequences. The selected discussions build heavily on mathematical concepts such as mortality rates, casualty numbers, reproduction numbers, and exponential growth. We identify the concepts and discuss how far they can be understood by laypersons. On the one hand, we found that some mathematical models are inappropriate, which can also be determined by laypersons. On the other hand, we found uses of mathematics where ideal concepts are intermingled with complex statistical concepts. While only the ideal concepts can be understood by laypersons, only the statistical concepts lead to actual data. The identification of both types of concepts leads to a situation where the use of mathematics evades social control and opens spaces for misconceptions and manipulation. We conclude that the evaluation of experts’ use of mathematics by laypersons is not possible in all relevant cases, and we discuss possible implications of this result.

     

Scaling,Linking, and Reporting in a Periodic Assessment System

A new entry in the testing lexicon is through‐course summative assessment, a system consisting of components administered periodically during the academic year. As defined in the Race to the Top program, these assessments are intended to yield a yearly summative score for accountability purposes. They must provide for both individual and group proficiency estimates and allow for the measurement of growth. They must accommodate students who vary in their patterns of curricular exposure. Because they are meant to provide actionable information to teachers they must be instructionally sensitive, so item‐operating characteristics can be expected to change relative to one another as a function of patterns of curricular exposure. This paper discusses methodology one can draw upon to tackle this ambitious collection of inferences. We consider a modeling framework that consists of an item response theory component and a population component, as in the National Assessment of Educational Progress, and show how performance and growth could be expressed in terms of expected performance on a market basket of tasks. We discuss conditions under which modeling simplifications might be possible and discuss studies that would be needed to fit models, estimate parameters, and evaluate data requirements.     

Early School-leaving in Spain: evolution,intensity and determinants

Spain has one of the highest levels of early school leaving and educational failure of the European Union. The purpose of this paper is to analyse the anatomy of early school leaving in Spain and its characteristics. In order to do so, in the first part we discuss the measurement problems related with this concept and the evolution of drop-out rates in Spain. We argue that the published figures of early school leaving slightly underestimate the phenomenon, and discuss the impact of the increase in immigration rates on the level of educational failure and its very unequal distribution in terms of gender. In a second part, using data from the Labour Force Surveys of 2000 and 2007, we explore the factors behind educational failure by means of a logistic regression. The results of this model confirm the explanatory power of social reproduction hypotheses, but also show that there are important aspects of the patterns and recent evolution of early school leaving which cannot be explained by a single theoretical approach.     

Learning,Testing, and the Evaluation of Learning Environments in Medicine: Global Performance Assessment in Medical Education

Changes in the profession of medicine are creating the demand for a substantive reexamination of current practices in medical education. Many of the major issues in addressing this challenge are structural and political rather than scientific; here we address one critical scientific issue that will be important to (though not by itself adequate for) guiding such changes. The factor we address is the development of a global performance assessment: a standardized mechanism to assess individual skills and abilities that can be used to evaluate alternative educational interventions. We discuss the issues involved in developing such a system, and describe a set of principles for defining desired outcomes and developing assessment tools, including (a) wide clinical scope, (b) direct relationship to actual clinical performance, (c) reliability and repeatability, and (d) non-longitudinal measurement. We discuss the role of simulation, reflective practice, and portfolios of work in developing such a system, and argue that whatever form such metrics take, a system of global performance assessment will develop from close collaboration between clinicians and educators with innovative ways of thinking about performance and expertise.     

Leading higher education professionals: local,connected, and artful

In this paper, we explore the work life of a scholar new to academia in her methods of leading informally. We discuss five vignettes that offer moments of learning and reflection, including reducing performance anxiety, privileging financial accountability, the rise of the virtual world, the impact of silence, and the potential for confrontation to strengthen working relationships. We offer suggestions as to how contemporary leaders may adapt to the freedom that artful action offers.     

Vocational teachers' gendered reflections on education,teaching and care

In this article, we discuss teachers' reflections on the relation between teaching and care in the two most gender-segregated sectors of vocational upper secondary education in Finland, namely Health and Social services and Transport and Technology. We first discuss the concepts around education, teaching, taking care for and caring about students, using theoretisations of care and feminist pedagogies. Using teacher interviews and field notes, we then analyse teachers' ambivalence about care work in the context of teaching, placing special emphasis on care as a gendered task, and then discuss the ‘moral panic’ or ‘worry speech’ about young people in vocational education from the perspective of caring about. The findings are reflected through earlier studies in lower secondary schools. We argue that even if teachers in vocational education, especially male teachers, tend to feel awkward about caring work, they cannot avoid it, and they do care about their students and regard care as a general responsibility.     

From expectancy-value theory to situated expectancy-value theory: A developmental,social cognitive,and sociocultural perspective on motivation

Eccles and colleagues’ expectancy-value theory of achievement choice has guided much research over the last 40+ years. In this article, we discuss five “macro” level issues concerning the theory. Our broad purposes in taking this approach are to clarify some issues regarding the current status of the theory, make suggestions for next steps for research based in the theory, and justify our decision to call the theory Situated Expectancy-Value Theory (SEVT). First, we note how visual representations of the model make it appear static, linear, and monolithic, something that was not intended from its inception. Second, we discuss definitions of the major psychological constructs in the model, focusing on our and others’ elaboration of the task value component, particularly the “cost” component. In this section we also discuss research on the development of expectancies and values. Third, we discuss the often-neglected middle part of the model focused on how individuals understand and interpret their own performance as well as the many messages they receive from different socializers regarding their activity participation and performance. In the fourth section we discuss the situative and culturally-focused aspects of the model, stressing the impact of the situation and cultural background on children’s developing expectancy and value hierarchies. The fifth issue (one that we mention in several of the previous sections) concerns the importance of understanding the development of individuals’ hierarchies of expectancies of success and subjective task values and how they relate to performance, choice, and engagement.     

Mental deficiency,a challenge to education

The purpose of this article is to expose the politics that arise in the research and evaluation of school reform efforts. We draw on qualitative data gathered in a study of comprehensive school reform to elucidate methodological issues in several areas. We discuss how we were perceived as researchers, how participants used our research and our presence in political ways, and how we questioned our own role in the research process. We discuss challenges in the data-gathering process, including the selection of interviewees for the study. Finally, we discuss challenges in the interpretation of data, including the representation of multiple perspectives and how to portray data on schools where reform appears to be a nonevent.     

ITEM BANKS: WHAT, WHY, HOW

In this paper, we discuss curricular implications of item banking and its practical value to teachers and students, and list a variety of working banks with their sources. We also review the psychometric basis of item banking, outline a family of computer programs for accomplishing banking, and give the equations necessary to build a bank. We conclude with a discussion of item quality control and examples of items that misfit because of miskeying, guessing, or carelessness.     

Transnational academic mobility,knowledge, and identity capital

This article begins with the contemporary context of transnational academic mobility, and sketches a typology of mobile academics according to their self-identification. UK examples are offered as the main case study here. The article will then explore the relations of mobile academics and their embodied and encultured knowledge. It employs a concept of ‘transnational identity capital’ to discuss the position of transnational mobile academic intellectuals as a ‘stranger’ as inspired by Simmel's sociology of space.     

The building of knowledge,language, and decision-making about climate change science: a cross-national program for secondary students

The United Nations’ declaration on climate change education in December 2014 has sparked a renewal of policies and programs initiated during the ‘Decade of Education for Sustainable Development’ (DESD, 2005–2014), aimed at promoting awareness, understanding, and civic action for environmental sustainability within learning communities all around the world. We present findings from a dialogic, multimodal, and literacies-based educational project designed to provide secondary students (N?=?141) from four countries with the resources to read about and discuss evidence regarding climate change from seminal studies with peers and a core group of scientists (N?=?7). Post-program interviews revealed a significant increase in language use related to evidence-based reasoning. Students also demonstrated an increased propensity to recycle. These findings support the hypothesis that providing opportunities for students to read and discuss seminal scientific sources incites positive changes in beliefs, attitudes, and behaviors related to climate change and climate science, and understandings of the nature of scientific evidence and argumentation.     

Creating next generation blended learning environments using mixed reality,Video Games and Simulations

Summary The goal of this article has been to discuss next generation learning environments and next generation training technologies as well as the learning and design challenges faced in using these. Specifically, we discuss theoretical and design principles of constructivist learning environments and how advanced technologies can potentially support meeting these principles as well as the challenges they may pose to various types of designers, instructional, game, graphic and programming. To address methods for designing complex environments, we also address the use of methodologies and authoring systems with various tools to support the design process. In this context, to illustrate how tools can be used to help instructional design teams manage the complexities of developing for these environments. As an example, we discuss one tool,IIPI CREATE, that supports this process and organizes the development process