Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

Newly qualified physical education teachers’ experiences of developing subject knowledge prior to, during and after a Postgraduate Certificate in Education course

Office for Standards in Education (OFSTED) inspections of secondary Postgraduate Certificate in Education (PGCE) physical education courses in England between 1996 and 1998 (OFSTED, 1999) were critical of student teachers' subject knowledge. The purpose of this study was to investigate the development of subject knowledge and influences on the development of that subject knowledge in a sample of three newly qualified teachers (NQTs) who had completed a PGCE physical education course in England. The research comprised semi-structured interviews and analysis of documentation. Among these three NQTs there were some similarities, but more differences in terms of the development of subject knowledge as well as different influences on the development of subject knowledge. These results suggest that teacher educators may need to be flexible in how they approach and support the development of student teachers' subject knowledge. Results also suggest that teacher educators should work more closely with colleagues teaching sports-related undergraduate degree courses to support the development of subject knowledge for those students who wish to progress to a PGCE physical education course

‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal

Discipline-Specific Compared to Generic Training of Teachers in Higher Education

A recurrent theme arising in the higher education sector is the suitability and effectiveness of generic versus discipline-specific training of university teachers, who are often recruited based on their disciplinary specialties to become teachers in higher education. We compared two groups of participants who had undergone training using a generic post-graduate certificate in higher education (PGCertGeneric) versus a discipline-specific course in veterinary education (PGCertVetEd). The study was conducted using a survey that allowed comparison of participants who completed PGCertGeneric (n=21) with PGCertVetEd (n=22). Results indicated that participants from both PGCertGeneric and PGCertVetEd considered teaching to be satisfying and important to their careers, valued the teaching observation component of the course, and identified similar training needs. However, the participants of the PGCertVetEd felt that the course made them better teachers, valued the relevance of the components taught, understood course design better, were encouraged to do further courses/reading in teaching and learning, changed their teaching as a result of the course, and were less stressed about teaching as compared to the PGCertGeneric participants (p<.05). It is likely that the PGCertVetEd, which was designed and developed by veterinarians with a wider understanding of the veterinary sector, helped the participants perceive the training course as suited to their needs

Expanding student teachers’ implicit theories about explanations for the science classrooms

This study explored student teachers’ implicit theories about explaining for the science classroom in three courses at diverse universities. Based on microteaching situations, the participants simulated explanations and discussed the elements they considered relevant for giving peer feedback. This led to the design of rubrics for peer assessment, which expressed their implicit theories about what a good explanation for the science classroom would look like. The three rubrics are presented and discussed in the light of the connections between teachers’ thinking and practice. Shulman’s ideas about professional teaching knowledge development, as well as negotiation of meaning, provide theoretical under-pinning for understanding and expanding student teachers’ thinking about explanations for the science classrooms.</p

Malaria and Fetal Growth Alterations in the 3(rd) Trimester of Pregnancy: A Longitudinal Ultrasound Study.

Pregnancy associated malaria is associated with decreased birth weight, but in-utero evaluation of fetal growth alterations is rarely performed. The objective of this study was to investigate malaria induced changes in fetal growth during the 3(rd) trimester using trans-abdominal ultrasound. An observational study of 876 pregnant women (398 primi- and secundigravidae and 478 multigravidae) was conducted in Tanzania. Fetal growth was monitored with ultrasound and screening for malaria was performed regularly. Birth weight and fetal weight were converted to z-scores, and fetal growth evaluated as fetal weight gain from the 26th week of pregnancy. Malaria infection only affected birth weight and fetal growth among primi- and secundigravid women. Forty-eight of the 398 primi- and secundigravid women had malaria during pregnancy causing a reduction in the newborns z-score of -0.50 (95% CI: -0.86, -0.13, P = 0.008, multiple linear regression). Fifty-eight percent (28/48) of the primi- and secundigravidae had malaria in the first half of pregnancy, but an effect on fetal growth was observed in the 3(rd) trimester with an OR of 4.89 for the fetal growth rate belonging to the lowest 25% in the population (95%CI: 2.03-11.79, P<0.001, multiple logistic regression). At an individual level, among the primi- and secundigravidae, 27% experienced alterations of fetal growth immediately after exposure but only for a short interval, 27% only late in pregnancy, 16.2% persistently from exposure until the end of pregnancy, and 29.7% had no alterations of fetal growth. The effect of malaria infections was observed during the 3(rd) trimester, despite infections occurring much earlier in pregnancy, and different mechanisms might operate leading to different patterns of growth alterations. This study highlights the need for protection against malaria throughout pregnancy and the recognition that observed changes in fetal growth might be a consequence of an infection much earlier in pregnancy.\u

The History You Don’t Know, and the History You Do: The Promise of Signature Pedagogies in History Education

The persistent separation of subject-matter content and pedagogical training in traditional teacher education programs has made it difficult for many beginning teachers to establish a base of knowledge they can use to develop pedagogical content knowledge as their careers unfold. While existing efforts to bridge this gap have focused on intensive collaborations between education faculty and their colleagues in disciplinary fields, or on the integration of disciplinary knowledge into teacher education coursework, work still can be done to address the problem of providing beginning teachers with the balance of deep and flexible content knowledge complemented by practical teaching maneuvers that so many of them crave. This chapter explores the possibility of addressing this gap via the development of signature pedagogies, following the lead established in many other professional fields, paying special attention to Lee Shulman’s conceptualization of the idea and its potential impact on teacher education in history

Subject specific demands of teaching: Implications for out-of-field teachers

This chapter provides a framework for thinking about the subject-specific nature of teaching in terms of the knowledge, modes of inquiry and discursive practices that delineate one subject from another in the traditional school curriculum. The chapter will explore how these disciplinary traits are translated into teaching as curriculum, knowledge and pedagogy, and how this subject-specificity of teaching is juxtaposed against the more generic aspects of teaching. The chapter explores the idea that if a teacher’s expertise can be situated within a field, then they can also be positioned out-of-field. Implications for teaching out-of-field are discussed in terms of the subject-specific knowledge, processes and skills, and the difficulties associated with teacher practice. English and Australian illustrations of teacher practices from in-field and out-of-field situations are provided, in particular highlighting the demands of moving across subject boundaries. Cross-fertilisation is especially evident when subjects are integrated, therefore, the issues associated with integrated curriculum are discussed where the traditional subject boundaries are being challenged as schools are reorganised to integrate subjects through, for example, STEM teaching, or holistic curriculum designs

The neural substrate of positive bias in spontaneous emotional processing

Even in the presence of negative information, healthy human beings display an optimistic tendency when thinking of past success and future chances, giving a positive bias to everyday's cognition. The tendency to actively select positive thoughts suggests the existence of a mechanism to exclude negative content, raising the issue of its dependence on mechanisms like those of effortful control. Using perfusion imaging, we examined how brain activations differed according to whether participants were left to prefer positive thoughts spontaneously, or followed an explicit instruction to the same effect, finding a widespread dissociation of brain perfusion patterns. Under spontaneous processing of emotional material, recruitment of areas associated with effortful attention, such as the dorsolateral prefrontal cortex, was reduced relative to instructed avoidance of negative material (F(1,58) = 26.24, p = 0.047, corrected). Under spontaneous avoidance perfusion increments were observed in several areas that were deactivated by the task, including the perigenual medial prefrontal cortex. Furthermore, individual differences in executive capacity were not associated with positive bias. These findings suggest that spontaneous positive cognitive emotion regulation in health may result from processes that, while actively suppressing emotionally salient information, differ from those associated with effortful and directed control