Deep intuition as a level in the development of the concept image

To explicate certain phenomena, e.g., the possibility of deduction without definition, we hypothesize that an individual is able to understand and appreciate reasoning with a due feeling of its necessity when the concept image of each concept involved in the reasoning has reached a certain level of development; we then speak of deep intuition. This conception is presented (with a variety of examples) in the framework of D. Tall’s theory of three worlds of mathematics (‘conceptual-embodied’, ‘proceptual-symbolic’, and ‘formal-axiomatic’).

From the Didactic to the Dialectic—Intercultural Exchanges in Contemporary Counsellor Education

Within the context of the growing development of intercultural counsellor education, the question of how different cultures reconceptualize and transform Western counselling theories for their own context is an important one. In this intercultural exchange in education, concepts such as ‘globalization’, ‘indigenization’ and ‘universalization’ have an impact on the education process. This paper briefly explores these terms and movements and then highlights findings from a research project that took place with a group of counselling graduates in Hong Kong examining how they undertook the processes of reconceptualization and transformation. The dialogical process involved in that enabled participants and researcher to co-explore the process of knowledge development within the counselling education field. Implications for counsellor education are highlighted.

Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks

This study examined how selected school mathematics textbooks in China, Singapore, and USA at the lower secondary grade level represent problem-solving procedures. The analysis of problem-solving procedures was carried out in two layers – general strategies, which adopted Pólya’s four-stage problem-solving model, and specific strategies, which consisted of 17 different problem-solving heuristics such as ‘acting it out,’ ‘looking for a pattern,’ ‘working backwards,’ etc. Both similarities and differences in the representation of problem-solving procedures in the textbooks across the three countries were revealed and compared. The possible reasons for the similarities and especially for the differences were explored. Suggestions about how to improve the representation of problem-solving in mathematics textbooks were provided at the end of the study.

Participation,financial support and the marginal student

This paper examines differences between the decision-making of marginal and nonmarginal students about participation in higher education (HE). We distinguish between two kinds of marginality: being ‘borderline’ on account of prior achievements in school and being ‘unsure’ after taking prior achievement into account. We identify a significant minority of students in their final year of schooling who are unsure about participation in higher education even though they have prior school achievements typical of entrants to HE. Being ‘unsure’ is found to be unrelated to socioeconomic background, but it is associated with significantly different attitudes towards the potential benefits and risks of participation, different levels of knowledge about financial support that is available and different approaches to information search about participation in HE.

Gender, Learning and Social Practice

The aim of this paper is to analyse the relationship between learning and gender at the workplace, by means of an empirical study. It is argued that gendered participation is learnt at the workplace and does not constitute a ‘natural’ division. The empirical part of the paper is based on a qualitative study of a bakery in which gender and learning in vocational training are the key focus. For centuries, bakeries have been masculine workplaces. However, in recent years, the percentage of female apprentices has increased. This paper takes a situated perspective on learning and gender, by focusing on how everyday work practices influence the discourses in workplace practice, and how this affects participant perceptions of themselves. Furthermore, Holzkamp’s distinction between expansive and restrictive perspective on learning is central to understanding the role of gendered discourses. In the first part of the paper, gender is situated in the bakeries, emphasizing the historical circumstances, physical environment and economic aspects that create a specific gendered discourse. In the second part of the paper, the focus is on how various ways of learning are situated in the bakeries.

The role of principal empowerment within a site-based management environment: empirical testing of a structural model

A model examining psychological empowerment, transformational leadership and innovation for school principals is proposed and tested within a Site (School)-Based Management environment. Developed from management literature, the model was adapted for state school principals experiencing increased decision-making powers and accountability. Empirical results provide a level of support for the model. ‘Role clarity’ and ‘access to resources’ were found to exert a positive influence on principals’ feelings of empowerment, though the value placed by principals on strategic information was found to have a slightly negative influence. The influence of empowerment on transformational leadership was not found to be as strong as anticipated. The paper includes a discussion of the implications of these findings for theory and policy development.

Committed for life? Variations in teachers’ work, lives and effectiveness

This paper is based upon a unique mixed methods 4-year research project which focused upon the variations in teachers’ work, lives, and effectiveness of 300 elementary and secondary school teachers in a range of 100 schools across seven regions of England. Its findings challenge linear conceptions of teacher development and expertise and provide new understandings of the effects of personal, school and broader policy contexts upon professional life phase trajectories and teachers’ emotional identities. It finds connections between these and teachers’ commitment, resilience, and effectiveness. This paper discusses these in relation to the school standards and teacher retention agendas.

Profiling Teacher/Teaching Using Descriptors Derived from Qualitative Feedback: Formative and Summative Applications

Considerable work has been done on student evaluation of teaching/teachers, but reservations remain about its use for summative purposes. Student ratings are not universally accepted as being reliable, nor can they provide really meaningful information. Qualitative comments can provide a better understanding but they tend not to be user-friendly from lack of structure and connectedness. This study attempts to devise a method for ‘quantifying’ students’ comments to increase their usefulness in complementing/confirming ratings. The quantified results enable the profile construction of what students regard as an effective/ineffective teacher, and enable identification of strengths and weaknesses. Our findings counter some commonly held assumptions, including those which held that high ratings are dependent on small class size and ‘dumbing down’ of courses and the consequent expectation of high grades. The findings also indicate that students value teaching quality more than teacher characteristics, suggesting their ability to make valid judgments about teaching effectiveness.

Teaching for creativity: towards sustainable and replicable pedagogical practice

This article explores the pedagogical significance of recent shifts in scholarly attention away from first generation and towards second generation understandings of creativity. First generation or big ‘C’ creativity locates the creative enterprise as a complex set of behaviours and ideas exhibited by an individual, while second generation or small ‘c’ creativity locates the creative enterprise in the processes and products of collaborative and purposeful activity. Second generation creativity is gaining importance for a number of reasons: its acknowledged significance as a driver in the new or digital economy; recent clarification of the notion of ‘creative capital’; the stated commitment of a growing number of universities to ‘more creativity’ as part of their declared vision for their staff and students; and, the recognition that the creative arts does not have a monopoly on creative capability. We argue that this shift allows more space for engaging with creativity as an outcome of pedagogical work in higher education. The article builds on the project of connecting ‘creative capital’ and university pedagogy that is already underway, assembling a number of principles from a wide range of scholarship, from computer modelling to social and cultural theorising. In doing so, it provides a framework for systematically orchestrating a ‘creativity-enhancing’ learning environment in higher education.

James J. Kaput (1942–2005) imagineer and futurologist of mathematics education

Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his ‘big ideas’ as he lived through the most amazing innovations in technology that have changed our lives more in a generation than in many centuries before. His vision continues as is exemplified by the collected papers in this tribute to his life and work.

Culture, food, and language: Perspectives from immigrant mothers in school science

The article explores the role of immigrant parents in middle school science as both teachers and learners as part of an urban middle school curriculum, the Linking in Food and the Environment (LiFE) program. The curriculum engaged parents as partners with science teachers to teach science through food. Over a 2-year period, parents attended a series of bilingual workshops, collaborated with classroom teachers, managed activities, guided student inquiry, and assisted in classroom management. The following study analyzes the role of culture, language, and identity as four mothers navigated their position as ‘insiders’ in a science classroom.

Ecofutures in Africa: Jenny Robson’s Savannah 2116 AD

Jenny Robson’s Savannah 2216 AD, a dark, futuristic novel for young adults, provides a strong critique on much of the world’s predilection for saving Africa’s animals at the expense of those human communities who are perceived to be in the way of the preservation of the continent’s remaining wild spaces. Using Robson’s novel as template, this article examines a few of those discourses regarding wilderness and conservation that have attached to Africa. Savannah 2116 AD strongly yet indirectly hints that literary educators should revisit the often unquestioned adoption of ‘greening’ agendas in school curricula which persist in re-colonising geo-political spaces by ignoring the fact that erecting fences between perceived conservators and destroyers, between spaces for wild animals and humans, merely condemns Africa’s animal riches to eventual death.

Crossover Literature and Abjection: Geraldine McCaughrean’s <Emphasis Type="Italic">The White Darkness</Emphasis>

This article provides a close reading of Geraldine McCaughrean’s award-winning novel, The White Darkness. It argues that this is a key text in the increasing debate about ‘crossover’ literature. Whereas, traditionally, adolescent books were seen to offer compensatory fantasies to the adolescent reader, McCaughrean’s text goes beyond this, exploring adolescence in deeper terms: not simply as an age-defined period but as a time when the traditional coordinates of the self are thrown into crisis, or become destabilized (as an ‘open psychic structure’, as Kristeva puts it). Adopting such a psychoanalytical approach, it is argued, we can begin to understand this book’s appeal (and others like it) to adolescent and adult alike; that is, it stages a shift from an imaginary identification with a stable self to a more realistic, albeit less secure recognition of the flimsiness of identity. The white wastes of Antarctica provide the perfect backdrop for this confrontation with the ungraspable Real.

Hybridity in a Guidance Curriculum in Hong Kong

This paper presents findings on a hybrid guidance curriculum in Hong Kong, a place where East meets West in education and in many other spheres. A qualitative case study method is applied that uses questions for understanding the ‘self’ in guidance but incorporates Confucian cardinal human relationships of parent–child, brother–sister, husband–wife, superior–subordinate, teacher–pupil and friend–friend in understanding the ‘other’ relationships. The study of ‘self–other relationship’ is combined with Lawton’s (Social change, educational theory and curriculum planning, Hodder, London, 1973) model of curriculum development in Western traditions. Data obtained from stakeholders in schools include traditional Chinese ideas as well as modern Western ideas. Implications of this framework to the study of other societies with a mix of Western and traditional cultures are discussed.

Student and early career mobility patterns among highly educated people in Germany,Finland, Italy,and the United Kingdom

This article addresses the question of how great are higher education students’ incentives to change study programs or institutions to improve one’s personal employability in the course of the higher education-to-work transition process. The posed question is addressed at a system level. Students’ mobility between programs and institutions is referred to as ‘student mobility’ and graduates’ mobility between jobs is referred to as ‘early career mobility.’ The relationship between these two separate components of mobility is discussed in three different institutional frames: German/Finnish, Italian, and British. When depicting the relationship between the two components of mobility, the article also considers parallel phenomena such as prolongation of the degree-earning process and participation in work-life with student status. Indicator level analysis concerning graduates of the year 2000 reveals important differences between the three institutional frames: in Germany and Finland, there is a high level of student mobility at the basic degree level combined with a low level of career mobility after graduation; in the UK the opposite transition logic than that of Germany and Finland occurs, and in Italy students demonstrate prolonged transitions with little student mobility and early career mobility.

Powering Up, Philanthropically

Faculty members have an important role to play in helping to fund programs and direct donor dollars at colleges and universities. This paper outlines the ‘golden age of philanthropy’ that the United States has currently entered, explaining the combination of material resources and spiritual inclinations that have led to increased giving. It then outlines several principles that faculty members should keep in mind in approaching prospective donors, including the reasons for giving, donors’ interest in ideas, and the importance of persistence, local focus, and collaboration. Finally it offers several practical steps that faculty members can take to marshal philanthropic support for their visions.

Building a Common Platform on Students’ Participation

This article sets out to examine how school science activities can encourage students’ participation while supporting a specific science content. One ordinary class with 12-year-old students was chosen and their regular classroom work was studied without intervention and with a minimum of interference. Lessons were video filmed, transcribed and analyzed focussing on the participants’ speech acts. It was found that students’ initiatives and experiences were important parts of their participation. The results show how students’ participation was orchestrated with a science content by means of four different kinds of activities. The activities are called ‘individual inventory of experiences’, ‘building a common platform of experiences’, ‘sharing new experiences’ and ‘concluding a common platform’. The activities form a foundation for participation in human biology topics. For example, to ‘build a common platform of experiences’ seems to level out students’ different prerequisites for participating in subsequent tasks. Furthermore, to ‘conclude a common platform’ implied a checkpoint of the shared new experiences. The activities support students’ tentative use of scientific words as well as their learning of what counts as knowledge in the school science setting. However, it can be questioned if the time spent on each separate activity is necessary or if similar achievements could be made even if some activities were integrated. The question is open for further research.

School mathematics and its everyday other? Revisiting Lave’s ‘Cognition in Practice’

In the last three decades there have been a variety of studies of what is often referred to as ‘everyday’ or ‘street’ mathematics. These studies have documented a rich variety of arithmetic practices involved in activities such as tailoring, carpet laying, dieting, or grocery shopping. More importantly, these studies have helped to rectify outmoded models of rationality, cognition, and (school) instruction. Despite these important achievements, doubts can be raised about the ways in which theoretical conclusions have been drawn from empirical materials. Furthermore, while these studies rightly criticised prevalent theories of rationality and cognition as too simplistic to account for everyday activities, it seems that some of the proposed alternatives suffer from similar flaws (i.e., are straightforward inversions of the to-be-opposed theories, rather than more nuanced views on complicated issues). In this article we illustrate our sceptical view by discussing four case studies in Jean Lave’s pioneering and influential ‘Cognition in Practice’ (1988). By looking at the case studies in detail, we investigate how Lave’s conclusions relate to the empirical materials and offer alternative characterisations. In particular, we question whether the empirical studies demonstrate the existence of two different kinds of mathematics (‘everyday’ and ‘school,’ or ‘formal’ and ‘informal’) and whether school instruction tries to replace the former with the latter.

Gender and physics: feminist philosophy and science education

Physics education reform movements should pay attention to feminist analyses of gender in the culture of physics for two reasons. One reason is that feminist analyses contribute to an understanding of a ‘chilly climate’ women encounter in many physics university departments. Another reason is that feminist analyses reveal that certain styles of doing science are predominant in the culture of physics. I introduce recent philosophical work in social epistemology to argue that the predominance of certain styles of doing science is not good for science. Scientific communities would benefit from greater diversity in styles of doing science.