Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an algebraic structure to get a sense of those properties which form the basis of the fundamental definitions. We will explain the transition from examples to abstract algebra as a series of shifts of attention and in this paper we will use a case study to examine the initial shift, which we will call apprehending a structure, and examine how one student came to apprehend the structure of the commutative ring Z99

Educational Design Research in Mozambique: Starting Mathematics from Authentic Resources

This article describes a research on learner-centred instruction in Mozambique, Africa. A starting point was the use of real-life resources, such as traditional art craft objects and authentic newspaper clippings. The study used a method which is termed 'design research'. This method aligns theory with practice and is geared towards improving educational practice. In two sub-studies, On geometry and on statistics, learner-centred instruction was facilitated through the use of worksheets with open-ended questions tailored for group work. The designs were tested in cyclic interventions and formatively evaluated through observation reports, interviews and assessment of learners' work. A decentralised, student-centred learning ecology proved to be feasible in overcrowded classrooms, typical in African education

DIFFERENT MEDIA, DIFFERENT TYPES OF COLLECTIVE WORK IN ONLINE CONTINUING TEACHER EDUCATION: WOULD YOU PASS THE PEN, PLEASE?

This paper presents some findings regarding the interaction between different computer interfaces and different types of collective work. We want to claim that design in online learning environments has a paramount role in the type of collaboration that happens among participants. In this paper, we report on data that illustrate how teachers can collaborate online in order to learn how to use geometry software in teaching activities. A virtual environment which allows that construction to be carried out collectively, even if the participants are not sharing a classroom, is the setting for the research presented in this paper

Recent sediment dynamics in hadal trenches:evidence for the influence of higher-frequency (tidal, near-inertial) fluid dynamics

In addition to high hydrostatic pressure, scarcity of food is viewed as a factor that limits the abundance and activity of heterotrophic organisms at great ocean depths, including hadal trenches. Supply of nutritious food largely relies on the flux of organic-rich particulate matter from the surface ocean. It has been speculated that the shape of hadal trenches helps to 'funnel' particulate matter into the deeper parts of the trench, leading to sediment 'focussing' and improved benthic food supply. Here we investigate for five Northwest Pacific trenches the efficiency of sediment focussing by evaluating ratios of measured (sediment-derived) and expected (water-column-derived) sedimentary inventories of the naturally occurring and radioactive particulate-matter tracer Pb-210(xs). The sites comprise a broad range of surface-ocean productivity and physical-oceanographic regimes. Across the five trench-axis settings the inventory ratio varies between 0.5 and 4.1, with four trench-axis settings having ratios > 1 (sediment focussing) and one trench-axis setting a ratio < 1 (sediment winnowing). Although the fluid- and sediment-dynamical forcing behind sediment focussing remains unclear, this study finds evidence for another mechanism that is superimposed on, and counteracts, the focussing mechanism. This superimposed mechanism is related to higher-frequency (tidal, near-inertial) fluid dynamics. In particular, there is evidence for a strong and negative relation between the intensity of propagating internal tides and the extent of sediment focussing in the trench-axis. The relation can be approximated by a power function and the most intense drop in sediment focussing already occurs at moderate internal-tide intensities. This suggests that propagating internal tides may have a subtle but significant influence on particulate-matter dynamics and food supply in hadal trenches in particular, but possibly also in the deep seas in general. A mechanism for the influence of internal tides on sediment dynamics is proposed. (C) 2014 Elsevier Ltd. All rights reserved

Inhibition of radiographic progression with combination etanercept and methotrexate in patients with moderately active rheumatoid arthritis previously treated with monotherapy

OBJECTIVE: To determine the effect of changing from etanercept or methotrexate monotherapy to etanercept plus methotrexate combination therapy on radiographic progression in rheumatoid arthritis (RA) patients. METHODS: Patients enrolled in this 1-year open-label study previously completed a 3-year blinded study in which they received methotrexate or etanercept monotherapy or the combination of both. All patients received the combination of etanercept 25 mg subcutaneously twice weekly plus oral methotrexate up to 20 mg/week. The primary radiographic endpoint was a change in modified total Sharp score (TSS), as assessed by blinded readers. RESULTS: At baseline, patients previously receiving methotrexate monotherapy (etanercept-added, n = 52) or etanercept monotherapy (methotrexate-added, n = 68) had moderate disease activity levels (mean disease activity score (DAS) of 2.6 and 2.5, respectively), whereas patients previously receiving combination therapy (n = 90) had a low disease activity level (mean DAS of 2.0). The addition of etanercept to methotrexate monotherapy resulted in a significant reduction in radiographic progression (p<0.05). Mean TSS changes in the previous year versus the current year were +1.79 versus +0.25 for the etanercept-added group (p<0.05); +0.51 versus -0.18 for the methotrexate-added group (NS) and +0.42 versus +0.24 for the combination group (NS). CONCLUSION: In these RA patients with on average moderate disease activity despite previous methotrexate monotherapy, combination treatment with etanercept and methotrexate inhibited radiographic progression and improved radiographic outcomes. These data, in conjunction with the previously published clinical data, support the use of combination therapy in RA patients with moderate disease activity

Pilot study to assess reagent and instrument quality for reproducible diagnosis of chronic lymphocytic leukemia: an ESCCA and ERIC harmonisation project

Pilot study to assess reagent and instrument quality for reproducible diagnosis of chronic lymphocytic leukemia: an escca and eric harmonisation proje