Prototypes,metaphors, metonymies and imaginative rationality in high school mathematics

The growing recognition that imagination, far from being a peripheral adjunct plays a central role in reasoning has important implications for the teaching and learning of mathematics. This paper has two main parts. In the first part, examples from high school case studies are used to illustrate prototypical mathematical images and the use of imagery in metaphoric and metonymic ways in mathematics. In the second part, pattern imagery and other types of imagery are discussed as central components in a model of mathematical reasoning. It is suggested that different forms of imagery may be used in ways that make abstraction and generalization possible in mathematics. The more abstract forms are idiosyncratically constructed by individuals. However, it is suggested that the activity of the imagination in the model presented here is central to meaning-making, and that the process makes shared meanings possible. Some social consequences for mathematics classrooms are explored briefly.This paper is a modified version of a presentation at the Fifth International Conference on Theory of Mathematics Education, Paderno del Grappa, Italy, June 20–27, 1991. The research described was undertaken for a PhD at the University of Cambridge, England, and was supported in part by grants from The Ernest Oppenheimer Memorial Trust, the Human Sciences Research Council, Pretoria, and the Overseas Research Student Fund of the United Kingdom. The author wishes to thank several anonymous reviewers for their helpful comments on an earlier draft.     

THE INFLUENCE OF HIGHER EDUCATION ON THE ASSESSMENT OF STUDENTS OF PHYSIOTHERAPY

The majority of physiotherapists are trained in hospital‐based schools outside the mainstream of further and higher education. It has been assumed that professional standards of competence are maintained through central control of the syllabus, nationally set examinations and centrally appointed examiners.

During the last decade, a small number of schools have transferred to polytechnics and begun to develop internally examined courses. It is essential that students who are successful in these examinations are automatically eligible for Membership of the Chartered Society of Physiotherapy.

This paper describes the planning of an internally examined course which is acceptable to the professional bodies as well as to the Sheffield City Polytechnic. It explores some of the conflicts which have arisen concerning the extent to which control of the profession should extend to control of the curriculum in any and every institution. It concludes that the Chartered Society's need to control right of entry to the profession and to monitor standards of competence is reconcilable with lecturers’ desire to design a course and appropriate methods of assessment which reflect their overall rationale.     

Narratives of ‘doing,knowing, being and becoming’: examining the impact of an attachment-informed approach within initial teacher education

The Scottish Government’s vision of improving outcomes for children prioritises attachment theory and research in promoting children’s well-being across children’s services. This theme is also noted as increasing international relevance. Our narrative research springs from the experience of designing and delivering the first course within initial teacher education in Scotland to focus on the application of attachment theory to the role and identity of the teacher – particularly, in supporting children vulnerable through experiences of trauma and adversity. We capture students’ ‘real time’ learning moments through reflective journaling during school experience within the analytic ‘Doing, knowing, being and becoming’. Emergent themes include: looking behind and responding to behaviours, making links with ‘lived lives’, understanding teachers’ potential as attachment figures and ‘secure base’, understanding the relevance of adult attachment theory and resilience/self-care to teachers’ emotions and their own attachment experiences.     

对高师《世界地理》课程的看法

《世界地理》是研究某一地理区域地理环境综合特征的一门课程,是最能体现地理学综合性特征的课程之一。在研究区域地理环境综合特征时,需要运用各部门地理学的研究成果,对相互作用相互影响的各地理要素进行综合研究。《世界地理》与各部门地理学纵横交织,共同构建起地理科学的知识体系。目前,《世界地理》的教材建设还没有引起有关方面足够的重视。2004年出版的《世界地理》教材还需要不断补充完善,一些印刷性错误尤其应当及时更正。这对促进《世界地理》教学水平的不断提高是很有必要的。     

TEACHING MATHEMATICS IN TWO LANGUAGES: A TEACHING DILEMMA OF MALAYSIAN CHINESE PRIMARY SCHOOLS

This paper discusses a teaching dilemma faced by mathematics teachers in the Malaysian Chinese primary schools in coping with the latest changes in language policy. In 2003, Malaysia launched a new language policy of teaching mathematics using English as the language of instruction in all schools. However, due to the complex sociocultural demands of the Malaysian Chinese community, mathematics is taught in both Mandarin and English in the Malaysian Chinese primary schools. Teachers faced the dilemma of code-switching between English and Mandarin particularly in low-performing classes. A substantial amount of class time was spent in translating, especially the mathematical terminologies. Findings of this study imply that further research studies are needed to examine the effectiveness of teaching mathematics bilingually versus monolingually in a Malaysian context.     

Opportunities for a democratic pedagogy: a comparative study of South African and Swedish teachers' attitudes to inclusive education

This paper is based upon the collaboration between two research groups from Stockholm University and the University of South Africa. The main objective is to compare attitudes between South African (SA) and Swedish teachers regarding inclusive education (IE). IE in this paper is examined as a distinct part of the Swedish welfare system. The method used can be characterised as a combined, quantitative and qualitative research design with a purposive sampling. A similar adapted questionnaire was distributed in the two countries. The Swedish teachers in our data are more pro‐inclusion and more hesitating to accommodate learners with barriers in special schools. However, both the Swedish and the SA teachers in the study are hesitating towards the feasibility to implement IE practically. A team approach is concluded to be an adequate pedagogy for supporting IE both in South Africa and Sweden.     

Conditioned inhibition training of the competing cue after compound conditioning does not reduce cue competition

In each of two experiments, we studied Pavlovian fear conditioning (as assessed by barpress conditioned suppression) in 32 albino rats. Following a two-stage cue-competition procedure (A+ then AX+), we subjected the competing cue (A) to conditioned inhibition training (B+, BA?) before testing the target cue (X). Conditioned inhibition training was designed to weaken the putative A-unconditioned stimulus (US) association, perhaps changing it to an A-no-US association. Performance-deficit theories of cue competition, such as comparator theory and retrieval-interference theory, predict that such procedures should weaken cue competition, causing Conditioned Stimulus X (CS X) to evoke strong responding. The same prediction can be deduced from recent acquisition-focused models (Dickinson &; Burke, 1996; Van Hamme &; Wasserman, 1994). In opposition to this prediction, however, we found in both experiments that conditioned inhibition training had no detectable effect on cue competition even though it successfully abolished conditioned responding to CS A. In Experiment 2, moreover, we found evidence against the hypothesis that the weak response to CS X was due to generalization decrement rather than to cue competition. Results favor early learning-deficit theories of cue competition over performance-deficit theories and over the recent acquisition-focused models.     

Privileged learning

Students often attain memorable experiences from cadaver dissections through reflective writing. For many, facing a dissection for the first time elicits a wide range of emotions. These may include thoughts of their own mortality to the sheer admiration of knowing that someone cared enough to help others learn about the body, even in death. Poems or stories from medical students are often moving and heartfelt, and warrant being shared. Anat Sci Ed 2:47–48, 2009. © 2009 American Association of Anatomists.