Dynamic geometry software: the teacher's role in facilitating instrumental genesis

In the UK, teachers’ use of dynamic geometry software (DGS) has remained limited. The importance of the teacher’s role is often stated in dynamic geometry research but has been seldom elaborated. This study aims to address the apparent deficiency in research. The author conducted the research in the role of a practitioner-researcher with a high ability year 8 class. By analysing teacher/pupil interactions in a DGS context, elements of instrumental genesis are distinguished in pupils’ dialogue and written work which suggest strategies that teachers can employ to facilitate this process. Whilst these strategies are specific to a DGS context, they highlight general principles of mathematics teaching. This paper argues that the focus of research needs to shift away from the context, towards teachers and the strategies they employ

Mathematical Knowledge for Teaching Using Technology: a Case Study

This paper analyses data from a PhD pilot study to explore the nature of mathematical knowledge for teaching using technology, as represented by the central construct of the TPACK framework. The case study of teacher Alice is used as an illustrative example to suggest that the central TPACK construct may be better understood as a transformation and deepening of existing mathematical knowledge rather than as a new category of knowledge representing the integration of technology, pedagogical and mathematical knowledge

The SAT Protein of the Minute Virus of Mice Induces the Lysis of the Cell through the Formation of Viroporin-like Structures

The prototype minute virus of mice (MVMp) and the H-1 virus belong to the family of Parvoviridae and can be used as oncolytic agents that infect, replicate in and kill human cancer cells. In preclinical trials the viruses were shown to be very successful to eradicate tumors in mice and rats. A phase I/IIa clinical trial with patients suffering from recurrent glioblastoma multiforme showed that parvovirus is safe to use in humans and that the therapy induces an infiltration of immune cells into the tumor tissue. Many aspects of the parvoviral life cycle have been studied over the last decades. The entry, replication, transcription and packaging mechanisms of the virus are well understood. However, the process of the virally-induced lysis of the cell is still unknown. The viral non structural protein 1 (NS1) was suggested to have cytotoxic features but a direct lytic mechanism could not be shown. Recently, the porcine parvovirus (PPV) was found to express the short transmembrane protein SAT. Mészáros and coworkers showed that a knockout of SAT led to a reduced lytic capacity of the virus (Mészáros et al., 2017). In the current study we show that the SAT protein of MVMp is also important for the lysis of the cell. A knockout of SAT in the genome of MVMp reduced the lytic capacity of the virus and SAT-ko viruses were also found to be less infectious than the wild type virus. The sole expression of SAT induced lysis and it exceeded the lytic capacity of NS1 by multiple times. Mészáros and coworkers suspected SAT to induce an irreversible stress in the endoplasmic reticulum which eventually led to the death of the cell. However, a direct mechanism of this process could not be shown. We suspect SAT to function as a viroporin - a class of virally-encoded transmembrane proteins that oligomerise to form pores through membranes. We could show that SAT is transported to the plasma membrane where it oligomerises in multimers and makes the plasma membrane permeable to the small molecule Hygromycin B. A computer simulation of the protein confirmed that SAT oligomerises in symmetrical complexes. However, pore-like structures were not observed. Furthermore, an increase in the permeability of ions such as calcium and sodium, which is often seen for other viroporins, was not found. In an attempt to increase the lytic capacity of MVMp we created the SUPER virus. The position of SAT was altered in the genome of SUPER in order to increase its translation. We could show that the translation of SAT was indeed increased for the SUPER virus which led to an accelerated lysis of the cells. However, the production of the SUPER virus was not very efficient. In order to increase the production of SUPER, we constructed shRNA constructs to knockdown SAT. Although the production of SAT was decreased, this approach did not increase the production of the virus. Nevertheless, the SUPER virus could be a promising candidate for the therapy with oncolytic parvoviruses. We suspect its increased lytic potential to release tumor antigens more efficiently compared to the lytic potential of the wild type virus. The released tumor antigens are suspected to stimulate cells of the immune system such as dendritic cells and cytotoxic T-cells in order to recognise and attack non-infected tumor cells

Conceptualising TPACK Within Mathematics Education: Teachers’ Strategies for Capitalising on Transitions Within and Beyond Dynamic Geometry Software

This article investigates the knowledge arising in mathematics teachers’ planning of how to manage transitions within and beyond dynamic geometry environments in the topic of circle theorems. The notion of situated abstraction is used to elaborate the central TPACK construct within mathematics education and address previous criticisms of the framework, specifically to clarify the distinction between the central construct and the dyadic constructs. Four case-study teachers each participated in a semi-structured interview based upon a pre-configured GeoGebra file. The teachers were asked to demonstrate how they would use the GeoGebra file to introduce students to the circle theorem that the angle at the centre of the circle, subtended by an arc, is double the angle at the circumference subtended by the same arc. The visual and audio aspects of the GeoGebra interviews were recorded and the TPACK framework used to analyse teachers’ knowledge arising in the four interviews. The central TPACK construct is illustrated with examples of teachers’ strategies for capitalising on transitions within and beyond dynamic geometry environments for the purposes of teaching circle theorems and contrasted with the dyadic construct of TCK. The utility of the theoretical elaboration of the TPACK construct within mathematics education is demonstrated and implications discussed

Using the Knowledge Quartet to analyse interviews with teachers manipulating dynamic geometry software

International audienceThis paper reports the use of the Knowledge Quartet as a tool for analysing mathematical knowledge in teaching arising in interviews with four secondary mathematics teachers based around a pre-configured GeoGebra file involving circle theorems. This research was part of larger doctoral study, where the Knowledge Quartet was chosen as a means of providing a fine-grained analysis focusing on mathematical knowledge in teaching. The sub-codes of the Knowledge Quartet were originally grounded in classroom observation and have been rarely exemplified through situations involving teachers use of technology. A tension is identified in applying the Knowledge Quartet to an interview situation involving technology centring around the sub-code ‘adherence to textbook’, with wider implications for how the framework is applied to situations involving teachers’ use of (technological) tools

Matthew\u27s Concept of the Son of God in the Context of Jesus\u27 Baptism and First Temptation

Like Cullmann, Fuller sees a close conceptual relationship between the language of sonship and that of the Servant in Deutero- Isniah. It is to this kind of inquiry that the present study hopes to make a contribution. We shall not attempt, as others have done, to construct a total Christology, or even to trace our single term through the whole of the New Testament. We shall concentrate on one Book, the Gospel of Matthew, and within that book on one moment, the baptism of Jesus and His first (wilderness) temptation. Resources which contribute to this limited area of study we shall tap, of course. We shall leave many questions still to be answered. Nevertheless, what we lose in breadth we shall hope to gain in depth, and thereby to suggest a course for further inquiry

Challenging assumptions about relationships between mathematics pedagogy and ICT integration: surveying teachers in English secondary schools

This study investigates associations between mathematics pedagogy and teachers’ integration of Information Communication Technologies (ICT). As an early adopter of presentation-oriented hardware and software in mathematics classrooms, England represents a critical case for investigating associations between mathematics pedagogy and teachers’ integration of ICT into classroom practice. This paper reports the results of a survey of English secondary mathematics teachers’ use of ICT (n = 183). Using Rasch analysis to construct a measure of mathematics pedagogy, a consistent trend is found between frequent use of “teacher-centred” software and a more “student-centred” orientation. The analysis also suggests that some “teacher-centred” practices involving ICT may instead be construed as “dominant” practices. Taken together with case-study evidence of teachers’ ICT integration from research on technology in education, these findings challenge assumptions about relationships between mathematics pedagogy and ICT integration prevalent in the mathematics education literature

Galois coverings of weakly shod algebras

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence, we show that a weakly shod algebra is simply connected if and only if its first Hochschild cohomology group vanishes.Comment: Some references were added. The proof of Lemma 6.5 was modifie

Theological Observer

Theological Observe

Theological Observer. - Kirchlich-Zeitgeschichtliches

Theological Observer. – Klrchllch Zeitgeschichtliches (Theological Observer. – Of course contemporary history