‘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

613 cases of splenic rupture without risk factors or previously diagnosed disease: a systematic review

Background Rupture of the spleen in the absence of trauma or previously diagnosed disease is largely ignored in the emergency literature and is often not documented as such in journals from other fields. We have conducted a systematic review of the literature to highlight the surprisingly frequent occurrence of this phenomenon and to document the diversity of diseases that can present in this fashion. Methods Systematic review of English and French language publications catalogued in Pubmed, Embase and CINAHL between 1950 and 2011. Results We found 613 cases of splenic rupture meeting the criteria above, 327 of which occurred as the presenting complaint of an underlying disease and 112 of which occurred following a medical procedure. Rupture appeared to occur spontaneously in histologically normal (but not necessarily normal size) spleens in 35 cases and after minor trauma in 23 cases. Medications were implicated in 47 cases, a splenic or adjacent anatomical abnormality in 31 cases and pregnancy or its complications in 38 cases. The most common associated diseases were infectious (n = 143), haematologic (n = 84) and non-haematologic neoplasms (n = 48). Amyloidosis (n = 24), internal trauma such as cough or vomiting (n = 17) and rheumatologic diseases (n = 10) are less frequently reported. Colonoscopy (n = 87) was the procedure reported most frequently as a cause of rupture. The anatomic abnormalities associated with rupture include splenic cysts (n = 6), infarction (n = 6) and hamartomata (n = 5). Medications associated with rupture include anticoagulants (n = 21), thrombolytics (n = 13) and recombinant G-CSF (n = 10). Other causes or associations reported very infrequently include other endoscopy, pulmonary, cardiac or abdominal surgery, hysterectomy, peliosis, empyema, remote pancreato-renal transplant, thrombosed splenic vein, hemangiomata, pancreatic pseudocysts, splenic artery aneurysm, cholesterol embolism, splenic granuloma, congenital diaphragmatic hernia, rib exostosis, pancreatitis, Gaucher's disease, Wilson's disease, pheochromocytoma, afibrinogenemia and ruptured ectopic pregnancy. Conclusions Emergency physicians should be attuned to the fact that rupture of the spleen can occur in the absence of major trauma or previously diagnosed splenic disease. The occurrence of such a rupture is likely to be the manifesting complaint of an underlying disease. Furthermore, colonoscopy should be more widely documented as a cause of splenic rupture

Ansvar för matematiklärande. Effekter av undervisningsansvar i det flerspråkiga klassrummet

The aim of the thesis is to contribute to knowledge about crucial conditions for students' mathematics learning, and more specifically what role mathematics teaching plays in that process. Also taken into account is the effect of group composition in terms of family background or language skills, and also the relation between group composition and teaching design. The study is based on the assumption that it is essential for students’ performances if the teacher in the multilingual classroom takes responsibility for key dimensions of mathematics teaching. The study is a secondary analysis of TIMSS data, produces by IEA, from 2003 focusing on mathematics for Swedish students in 8th grade. Based on theories of learning and teaching have important dimensions of mathematics teaching for which the teacher should take responsibility been identified. It has then been investigated how these dimensions of responsibility for students’ mathematics learning are related to achievement, and also how they are related to different group-compositions. Unlike traditional models of mathematics teaching, the model developed in this study simultaneously highlights three dimensions of teacher responsibility. The first dimension concerns teacher's responsibility to actively and openly support students in their mathematics learning by for example highlighting and explaining the mathematics content, questioning and conversing with students and organizing instruction so as to create conditions for interaction and various social activities. The second dimension concerns teacher's responsibility for handing over responsibility to the students for their own construction of knowledge by for example encouraging them to their own reflections and reasoning about mathematical problems. Finally, the third dimension concerns teacher’s responsibility for highlighting the content relevant to the grade as object of teaching. The results show that when teachers through actively teaching and guidance take responsibility for students' mathematics learning it will affect the performances positively. The results also indicate that this is of particularly importance for students with weak skills in the language of instruction. However, the results show that mathematics education in Sweden is characterized by pedagogical segregation. In groups where many students are likely to have needs for support, teachers take a less responsibility for students’ learning than is done in other groups. The thesis discusses that pedagogical segregation and the responsibility that in Sweden for a long time has been put on the students themselves for their mathematics learning may have contributed to the negative knowledge development in mathematic

Effects of Collaborative Group Composition and Inquiry Instruction on Reasoning Gains and Achievement in Undergraduate Biology

This study compared the effectiveness of collaborative group composition and instructional method on reasoning gains and achievement in college biology. Based on initial student reasoning ability (i.e., low, medium, or high), students were assigned to either homogeneous or heterogeneous collaborative groups within either inquiry or didactic instruction. Achievement and reasoning gains were assessed at the end of the semester. Inquiry instruction, as a whole, led to significantly greater gains in reasoning ability and achievement. Inquiry instruction also led to greater confidence and more positive attitudes toward collaboration. Low-reasoning students made significantly greater reasoning gains within inquiry instruction when grouped with other low reasoners than when grouped with either medium or high reasoners. Results are consistent with equilibration theory, supporting the idea that students benefit from the opportunity for self-regulation without the guidance or direction of a more capable peer