Distinguishing schemes and tasks in children's development of multiplicative reasoning

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children’s thinking, and learning situations must be organized to (a) build on children’s available schemes, (b) promote the next scheme in the sequence, and (c) link to intended mathematical concepts

Characteristics of the upper-level outflow and its impact on the rapid intensification of Typhoon Roke (2011)

In this study, we investigate the structural characteristics of the upper-level outflow and its impact on the rapid intensification (RI) of Typhoon Roke (2011), which experienced an evident outflow transformation from equatorward to poleward during its RI period. The simulations by the Weather Research and Forecasting Model suggest that the upper-level outflow extends from 100 hPa to 150 hPa, with an upper-level warm core at around 150 hPa. The upper-level outflow is enhanced ahead of the typhoon intensification, which is closely related to the outflow-environment interaction. Further analyses indicate that at the early stage of Roke (2011) before the RI, the strong equatorward outflow and the updraft south of the typhoon center are enhanced, favoring the onset of RI. During the RI period, the strong divergent flow near the entrance of the southwesterly jet in front of the upper-level trough, induces the poleward outflow. The eddy flux convergence of angular momentum inward propagated to the typhoon center from a 1000-km radius further enhances the poleward outflow and leads to the development of the vertical motion north of the typhoon center. Then Roke (2011) intensifies rapidly. Simultaneously, the shallow weak positive potential vorticity (PV) anomaly south of the southwesterly jet increases the inner-core PV, favoring the sustained intensification of Roke (2011). After Roke (2011) reaches its peak intensity, its intensity decreases due to the increase of vertical wind shear and the approaching of the southwesterly jet. It is indicated that the interaction between the upper-level outflow and the upper-tropospheric trough has significant influence on the RI of TC

Distinción de esquemas y tareas en el desarrollo del razonamiento multiplicativo de los niños

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children’s thinking, and learning situations must be organized to (a) build on children’s available schemes, (b) promote the next scheme in the sequence, and (c) link to intended mathematical concepts.Presentamos una síntesis de hallazgos de experimentos de enseñanza constructivistas en relación con seis esquemas que los niños construyen para razonar multiplicativamente y tareas para promoverlos. Proveemos una plataforma de juego generadora de tareas, descripciones de cada esquema y tareas para apoyarlos. Las tareas deben distinguirse del pensamiento de los niños, y las situaciones de aprendizaje deben organizarse para que (a) se basen en los esquemas que los niños tienen disponibles, (b) promuevan el siguiente esquema en la secuencia y (c) se relacionen con los conceptos matemáticos pretendidos.This research was supported by the US National Science Foundation under grant DRL 0822296, which funded the activities of the Nurturing Multiplicative Reasoning in Students with Learning Disabilities in a Computerized Conceptual-Modeling Environment (NMRSD) project. The opinions expressed in this article do not necessarily reflect the views of the Foundation

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase 1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age  6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score  652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc = 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N = 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in Asia and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701

Chinese middle school mathematics teachers’ practices and perspectives viewed through a western lens

This study was designed to investigate Chinese middle school mathematics teachers’ practices and perspectives on knowing and learning that may underlie their observed practices. In particular, this study addressed the following research questions: (a) What pedagogical activities and strategies can be identified in Chinese middle school mathematics teachers’ practices? (b) What teacher perspectives of mathematics knowing and learning may underlie these teachers’ practices? To address these questions, the researcher, a native Chinese who moved to Australia and became an Australian citizen, used a constructivist (western) conceptual framework as a lens. This framework combined two lines of previous work, Ernest’s (1989b) characterisation of mathematics teaching and Simon and Tzur et al.’s (Heinz et al., 2000b; Simon et al., 2000; Tzur et al., 2001) distinction of perspectives that seem to underlie reform-oriented teaching practices. Eleven year-7 middle school mathematics teachers from two different schools located in a Southeast province in Mainland China volunteered to participate in this study. For each of these 11 teachers, a set of data was collected, consisting of two video recorded classroom observations (consecutive lessons) interspersed with three video recorded interviews with the teacher about those observed lessons (before, between, and after each classroom observations). Transcripts of the interviews and classroom observations were translated into English. Six teachers were then selected as case studies and their practices and perspectives were analysed using the constant comparison method proposed by Glaser and Strauss (1967) as part of the Grounded Theory methodology. Findings of this study indicate that, typically, the participating Chinese teachers used a five-component cyclic teaching practice—Reviewing, Bridging, Variation, Summarising, and Reflection/Planning. The first four components constituted their implemented lesson structure. Data are presented to depict the nature of these first four components along with the participating teachers’ rationale for using each component the way they did. The significance of these findings is discussed in terms of a perspective about knowing and learning that seem to underlie the participating teachers’ five-component practice. This perspective appears to differ from perspectives that were identified previously. Coupled with the four-component lesson structure this perspective is discussed in terms of how it may inform mathematics teachers’ development of effective pedagogical practices, as well as future research and theory development

Chinese middle school mathematics teachers’ practices and perspectives viewed through a western lens

This study was designed to investigate Chinese middle school mathematics teachers’ practices and perspectives on knowing and learning that may underlie their observed practices. In particular, this study addressed the following research questions: (a) What pedagogical activities and strategies can be identified in Chinese middle school mathematics teachers’ practices? (b) What teacher perspectives of mathematics knowing and learning may underlie these teachers’ practices? To address these questions, the researcher, a native Chinese who moved to Australia and became an Australian citizen, used a constructivist (western) conceptual framework as a lens. This framework combined two lines of previous work, Ernest’s (1989b) characterisation of mathematics teaching and Simon and Tzur et al.’s (Heinz et al., 2000b; Simon et al., 2000; Tzur et al., 2001) distinction of perspectives that seem to underlie reform-oriented teaching practices. Eleven year-7 middle school mathematics teachers from two different schools located in a Southeast province in Mainland China volunteered to participate in this study. For each of these 11 teachers, a set of data was collected, consisting of two video recorded classroom observations (consecutive lessons) interspersed with three video recorded interviews with the teacher about those observed lessons (before, between, and after each classroom observations). Transcripts of the interviews and classroom observations were translated into English. Six teachers were then selected as case studies and their practices and perspectives were analysed using the constant comparison method proposed by Glaser and Strauss (1967) as part of the Grounded Theory methodology. Findings of this study indicate that, typically, the participating Chinese teachers used a five-component cyclic teaching practice—Reviewing, Bridging, Variation, Summarising, and Reflection/Planning. The first four components constituted their implemented lesson structure. Data are presented to depict the nature of these first four components along with the participating teachers’ rationale for using each component the way they did. The significance of these findings is discussed in terms of a perspective about knowing and learning that seem to underlie the participating teachers’ five-component practice. This perspective appears to differ from perspectives that were identified previously. Coupled with the four-component lesson structure this perspective is discussed in terms of how it may inform mathematics teachers’ development of effective pedagogical practices, as well as future research and theory development

The impact of latitude and altitude on the extent of permafrost during the Last Permafrost Maximum (LPM) in North China

This paper examines the relationship between the extent of permafrost during the Last Permafrost Maximum (LPM, largely between 22 and 17 ka BP) and the altitudinal and latitudinal temperature gradients that controlled its extent. The region chosen, namely, the Qinghai-Tibet Plateau and the transition to the northern adjacent plains in the North China Plain, is of relatively limited extent in order to avoid regional effects. This area extends over 15 degrees of latitude while altitudes vary from 1000 to 1500 m above sealevel (asl) in the northern plains to more than 4000 m asl in the central-to-south part of the Qinghai-Tibet Plateau. The respective lowest southernmost permafrost occurrences at a northern and a southern position are used for reconstruction of the latitudinal and altitudinal gradients. As a first approximation, we conclude that the elevation compensation during the LPM for a 1° latitude change was between 309 m and 385 m. This is considerably higher than the value calculated for existing permafrost in the region that uses thermal data at a depth of zero amplitude change (139–198 m altitudinal compensation for 1° latitude)

The extent of permafrost during the Last Permafrost Maximum (LPM)on the Ordos Plateau, north China

This paper presents new field observations that assist in further defining the extent of Last Permafrost Maximum (LPM)permafrost and frozen ground in north China. In that respect, this region is specific by its arid environment and continental position. Bedrock exposures and sand and gravel pits were examined along a south-north transect from southern Ordos as far as the vicinity of Dongsheng District, Ordos City on the Ordos Plateau (North China). Attention focussed upon the recognition of sand-wedge remains and possible cryoturbations. Two types of wedge structures were recognized: type A wedges extend to depths in excess of 3.0 m and are thought to have formed under conditions of continuous permafrost. Type B wedges are restricted to the upper 1.5 m and are thought to reflect discontinuous permafrost and/or deep seasonal frost. OSL dating of wedge infills indicates that type A wedges formed between 23–19 ka and younger type B wedges formed until the early Holocene. It is now possible to delineate a more exact position of the boundary between continuous permafrost and discontinuous permafrost and/or deep seasonal frost on the Ordos Plateau during the LPM. This boundaries occur between Dongsheng and Jinbian at 37°-39°N

Timing of river capture in major Yangtze River tributaries: Insights from sediment provenance and morphometric indices

The eastern margin of the Tibetan Plateau represents one of the morphologically most active regions on Earth, where the interplay of recent crustal deformation and subsequent fluvial landscape adjustment has affected the course of continental-scale rivers by river piracy events. Based solely on field observations, such an event has been hypothesised for two of the largest tributaries of the Yangtze River: the Jialing and Hanjiang Rivers. To test this hypothesis, we employ a novel combination of independent methods including a provenance study based on age distributions of detrital zircons from both modern riverbeds and river terraces and a morphometric analysis of river channels and drainage divides. We supported the morphometric analysis with a time-dependent numerical model describing the evolution of river channel long profiles and drainage divides in a succession of river capture events. Analysed zircon ages show clearly distinguishable distributions for the modern Jialing and Hanjiang Rivers, but similar distributions for the recent Hanjiang River up to its topmost terraces. This suggests that the capture of the Hanjiang headwaters by the Jialing River is unlikely to have taken place during the last 1.2 million years. However, several knickpoints in the main stem and the tributaries of the Jialing River cluster at an elevation of about 900 m and separate steeper (downstream) from less steep channel segments (upstream), which is consistent with the morphological expression of a major capture event. chi mapping indicates drainage divide asymmetry at catchment scale with on average steeper rivers on the Jialing side, whereas Gilbert metrics show a symmetric divide at hillslope scale. This numerical model explains this apparent contradiction by the travel time of capture-related knickpoints from the capture point towards the watershed, where chi mapping indicates divide asymmetry immediately after the river capture, while Gilbert metrics are only affected as soon as the knickpoints reach the channel heads and the divide effectively starts moving. Based on knickpoint travel distances and constraints on regional incision / uplift rates, we estimate the possible date of river capture to be the Pliocene. This is earlier than the formation of the terraces investigated in the provenance study but recent enough that most of the drainage divides are still unaffected and currently almost stable. Only the wind gap located in the almost dry valley connecting the two competing drainage systems is likely to have shifted towards the Hanjiang side. We suggest that this resulted in the capture of another important tributary of the Hanjiang River (the Heishui River) by the Jialing drainage system. Our results illustrate the complex evolution of drainage networks along the eastern margin of the Tibetan Plateau, and highlight the importance for combining provenance and morphometric analyses in regions of active landscape rejuvenation where river captures are likely to occur. (c) 2021 Elsevier B.V. All rights reserved