Some comments on the ``Role of proof in comprehending and teaching elementary linear algebra' by F.Uhlig

In a recent issue of this journal (ESM 50.3) Frank D. Uhlig published in a recent issue of this journal (ESM 50.3) a very interesting article about the question of proof in linear algebra. We have been doing research in the field of mathematics education about the teaching of linear algebra since the 1980s. In this paper, we want to underline the common points in Uhlig's approach and some of our work. We also want to bring a new light of some of his ideas and give perspective for a further didactical development of Uhlig's first experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

Improving calculus I in community colleges: It takes a [multidisciplinary] village

In 2010, the Mathematical Association of America began a 5-year study of Calculus I, a critical gatekeeper for students interested in science, technology, engineering, and mathematics careers. The study, titled Characteristics of Successful Programs in College Calculus, included case studies of successful Calculus I programs conducted by multidisciplinary research teams. The purpose of this article is to present the community college case study findings and to highlight the benefit of the multidisciplinary research teams. Using multiple lenses and analytical frameworks, the study identified factors that jointly contributed to Calculus I program success, including high-quality instruction, academic and social support for students, loose course coordination, a culture of faculty autonomy and trust, and attention to course placement and transfer policies. The findings suggest areas of focus for faculty, administrators, and other stakeholders working collectively to improve Calculus I in community colleges. These include faculty professional development to improve interactive lecture, strategic use of outcomes assessment, and attention to institutional placement and transfer policies.     

The complex development of student-teachers' thinking

Studies of student-teacher development have tended to suggest a three-stage model of development in which the novices' concerns shift outwards from an initial preoccupation with self, to a focus on tasks and teaching situations, and finally to consideration of pupil learning. This paper, based on sequence of post-lesson interviews conducted with 25 student teachers following 1-year postgraduate courses within school-based partnership schemes of initial teacher education, questions the adequacy of such a model. Analysis of the reasons that the student-teachers offered for their teaching decisions, and of their lesson evaluations suggests a high level of concern for pupils' learning and an awareness of the complexity of teaching from very early in their training. The implications of these findings are explored; in particular, the challenges that they pose to teacher educators in terms of course structure and curricula, and the need to be responsive to individual learners.     

Strengthening and sustaining professional learning in the second year of teaching

The data discussed in this paper derive from post‐lesson and end‐of‐year interviews with 17 teachers in their second year of teaching. They form part of a longitudinal study which first tracked these teachers through their initial postgraduate teacher education programme and induction year. In the light of earlier analysis, which had highlighted both the enduring importance of individuals’ dispositions towards their own learning and the profound sense of professional isolation that some teachers experience once the support of their induction year is withdrawn, this paper focuses specifically on the interplay between teachers’ orientations towards their own professional learning and the nature of the learning environments in which they are working. The complex interrelationships between these two dimensions are illuminated by six case studies, which offer strong support to those who have challenged exclusive conceptualisations of ‘learning’ as either ‘construction’ or ‘participation’. The findings have important implications for all those responsible for the professional education of beginning and early career teachers, especially as they respond to the government launch in England of a new ‘national framework’ intended (eventually) to offer opportunities for Masters level professional learning to all newly qualified teachers.     

Watching Learning Happen: Results of a Longitudinal Study of Journalism Students

The results from a five-year study of the information skills of journalism students provide insights into what students use and how that usage evolves, and have implications for information literacy instruction. Using a simple tool, the author watched learning happen in response to classes, work, and the changing information environment.     

Deconstructing the Carter Review: competing conceptions of quality in England’s ‘school-led’ system of initial teacher education

The commitment to establish a ‘school-led’ system of teacher education in England, announced by the Coalition Government in 2011 and relentlessly pursued thereafter, represented a radical departure from previous kinds of initial teacher education partnership. While it is entirely consistent with a neoliberal agenda, with its strong regulatory framework and appeal to market mechanisms, it is also underpinned by a particular conception of teaching as a craft – ‘best learnt as an apprentice observing a master craftsman or woman’. In 2014, the government established a Review of Initial Teacher Training, led by a primary school head teacher, Sir Andrew Carter. This signalled the recognition of teacher education as a ‘policy problem’, adopting Cochran-Smith’s term. The ensuing report, published in early 2015, was more nuanced than might have been anticipated, although a number of profound tensions emerge from a closer analytical reading; four of these tensions are similar to those previously defined by Cochran-Smith and two are newly emergent. This paper identifies and discusses these tensions as they appear in the Carter Review and relates them to wider debates about the links between teaching, teacher education, evidence and research and to policy-making processes in education.     

Access to higher education in the Federal Republic of Germany and the United States

Despite some important differences between the higher education systems of the Federal Republic of Germany and the United States, they share a number of comparable problems, especially in the field of access. The competitiveness of admission in certain faculties and disciplines in both countries and at the more prestigious and selective institutions in the U.S. raise serious questions about the proper balance between meritocratic and egalitarian policies. It is emphasized that access policies cannot be determined in a vacuum because of their close relationship to other factors in higher education institutions and systems.

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Zusammenfassung Trotz einiger wichtiger Unterschiede in den höheren Bildungssystemen der Bundesrepublik Deutschland und den Vereinigten Staaten teilen sie einige vergleichbare Probleme, insbesondere auf dem Gebiet des Zugangs. Die Konkurrenz bei der Zulassung zu gewissen Fakultäten und Institutionen in beiden Ländern, und zu prestigeträchtigen und selektiven Institutionen in den U.S.A. wirft ernste Fragen auf über das richtige Gleichgewicht zwischen bildungspolitischen Entscheidungen nach dem Prinzip des Verdiensts und solchen nach dem Prinzip der Chàncengleichheit. Es wird betont, dass Zulassungsfragen wegen ihres engen Zusammenhangs mit anderen Faktoren in höheren Bildungsinstitutionen nicht im luftleeren Raum entschieden werden können.

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Résumé Malgré certaines différences importantes entre les systèmes d'éducation supérieure de la République fédérale d'Allemagne et des Etats-Unis, ces deux pays présentent un certain nombre de problèmes comparables, surtout en ce qui concerne l'admission. Le caractère compétitif de l'admission dans certaines facultés et disciplines des deux pays susmentionnés, et dans les institutions plus célèbres et plus sélectives des Etats-Unis, soulèvent d'importantes questions sur l'équilibre approprié entre les politiques méritocratiques et égalitaires. On souligne que les politiques d'admission ne peuvent pas être déterminées dans le vide, à cause de leurs rapports étroits avec d'autres facteurs dans les institutions et systèmes d'enseignement supérieur.

     

English history teachers’ views on what substantive content young people should be taught

Public and policy discourse about the content of history curricula is frequently contested, but the voice of history teachers is often absent from such debate. Drawing on a large-scale online survey of history teachers in England, this paper explores their responses to major curriculum reforms proposed by the Coalition government in February 2013. In particular, it examines teachers’ responses to government plans to prescribe a list of topics, events and individuals to be taught chronologically that all students would be expected to study. Nearly 550 teachers responded to the survey, and more than two-thirds of them provided additional written comments on the curriculum proposals. This paper examines these comments, with reference to a range of curriculum models. The study reveals a deep antagonism towards the proposals for various reasons, including concerns about the extent and nature of the substantive content proposed and the way in which it should be sequenced. Analysis of these reactions provides an illuminating insight into history teachers’ perspectives. Whilst the rationales that underpin their thinking seem to have connections to a variety of different theoretical models, the analysis suggests that more attention could usefully be devoted to the idea of developing frameworks of reference.