Understanding teachers’ noticing of children’s mathematical thinking in written work from different sources

Expertise in teacher noticing of children's thinking is central to a vision of responsive teaching in which teachers regularly elicit and build on children’s thinking during instruction (Richards & Robertson, 2016). In mathematics classrooms, this core instructional practice of noticing children’s mathematical thinking repeatedly occurs during instruction and involves attending to and making sense of children's mathematical thinking (Sherin, Jacobs, & Philipp, 2011). Teachers daily have opportunities to notice children’s mathematical thinking during their conversations with students and in students’ written work. However, expertise in noticing children’s mathematical thinking does not develop automatically or through years of teaching, and teachers need support developing noticing expertise. To help teachers develop noticing expertise, professional developers often employ artifacts of practice (e.g., video clips and student written work) from teachers’ own classrooms as well as strategically selected artifacts from classrooms taught by teachers unfamiliar to the PD participants. This study explored the potential differences in teachers’ noticing with written work from these two sources—teachers’ own classrooms and classrooms unfamiliar to the teachers. Drawing on the construct of framing (Goffman, 1974), particular attention was paid to the various frames (or lenses) teachers used during noticing. Using a context of professional development focused on children's mathematical thinking in the domain of fractions, this three-phase study explored teachers’ noticing and their use of frames by investigating the relationship between teachers' noticing of children's mathematical thinking in written work from their own classrooms versus unfamiliar classrooms. In the first phase, this study identified the frames individual teachers used when noticing children’s thinking in written work from their own classrooms. The second phase explored the frames that small groups of teachers used when collectively noticing children’s thinking in written work from unfamiliar classrooms during professional development. The third phase used in-depth interviews to investigate the relationship between the quality of teacher noticing and the use of frames of six teachers who were asked to notice children’s thinking in written work on the same problem from their own classrooms and from unfamiliar classrooms. Findings identified six frames teachers used while noticing children's mathematical thinking in written work from the two sources, and they fell into three broad categories: (a) noticing focused on the child’s current mathematical performance, (b) noticing focused on the child’s non-mathematical performance, and (c) noticing that compared the child’s performance to the expected performance based on the child’s past performance, the performance of the rest of the class, or curricular or testing guidelines. Confirmation of these frames in three data sets highlighted the variety of ways teachers reason during noticing, suggesting that frames are a useful construct for understanding the complexity of teachers’ noticing because frames capture the multiple and sometimes competing ideas that teachers need to coordinate. When comparing teachers’ noticing of children’s thinking in written work from their own classrooms versus unfamiliar classrooms, a lack of substantial evidence was found to distinguish the sources in terms of the use of particular frames, the prevalence of particular frames, or the quality of teachers’ noticing of children’s thinking. Further, there was evidence that teachers “imagined” insider knowledge of children from unfamiliar classrooms to assist with their noticing, which might explain why engaging with written work from either source did not seem to change the quality of teachers’ noticing. On the other hand, comparative analyses identified a distinction between teachers’ use of frames when they were considering one child’s strategy versus several children’s strategies regardless of whether the written work came from the teachers’ classrooms or unfamiliar classrooms. Specifically, when teachers’ noticing focused on more than one child, more frames and a greater variety of frames were invoked. Implications for professional development focus on the need to appreciate and address teachers’ coordination of multiple frames and the idea that the use of these frames depends less on the source of the written work and more on the number of children involved in the task

Closing the Loop: Modelling of Heart Failure Progression from Health to End-Stage Using a Meta-Analysis of Left Ventricular Pressure-Volume Loops

Introduction The American Heart Association (AHA)/American College of Cardiology (ACC) guidelines for the classification of heart failure (HF) are descriptive but lack precise and objective measures which would assist in categorising such patients. Our aim was two fold, firstly to demonstrate quantitatively the progression of HF through each stage using a meta-analysis of existing left ventricular (LV) pressure-volume (PV) loop data and secondly use the LV PV loop data to create stage specific HF models. Methods and Results A literature search yielded 31 papers with PV data, representing over 200 patients in different stages of HF. The raw pressure and volume data were extracted from the papers using a digitising software package and the means were calculated. The data demonstrated that, as HF progressed, stroke volume (SV), ejection fraction (EF%) decreased while LV volumes increased. A 2-element lumped parameter model was employed to model the mean loops and the error was calculated between the loops, demonstrating close fit between the loops. The only parameter that was consistently and statistically different across all the stages was the elastance (Emax). Conclusions For the first time, the authors have created a visual and quantitative representation of the AHA/ACC stages of LVSD-HF, from normal to end-stage. The study demonstrates that robust, load-independent and reproducible parameters, such as elastance, can be used to categorise and model HF, complementing the existing classification. The modelled PV loops establish previously unknown physiological parameters for each AHA/ACC stage of LVSD-HF, such as LV elastance and highlight that it this parameter alone, in lumped parameter models, that determines the severity of HF. Such information will enable cardiovascular modellers with an interest in HF, to create more accurate models of the heart as it fails

Early Check: Pathways of Awareness

The Early Check study offers free expanded newborn screening for Fragile X syndrome and spinal muscular atrophy to all pregnant women in North Carolina that sign up between 13 weeks gestation and four weeks postpartum. Disseminating information to the public about the Early Check program is imperative to its success in identifying affected children and connecting them with the resources needed for early intervention. This project was undertaken with the goal of increasing the knowledge of OB/GYN providers and their ancillary staff regarding Early Check to enable them to answer patient questions about the program. OB/GYN practices in nine counties of North Carolina were contacted via phone and email for participation in brief education sessions about Early Check. Of 42 practices contacted, ten responses were received with seven practices participating in education sessions and eight practices agreeing to disseminate flyers to their patients. Outreach to OB/GYN practices was minimally successful, but the effects of collaboration with the small number of participants were significant. This intervention alone has the potential to reach more than 8,000 women each year. Collaborating with OB/GYN practices shows promise for current and future health initiative information dissemination targeted to pregnant and newly postpartum women

Analyse de fractions organiques de sols argileux, modifiees par humidification d'un compost petrolier

SIGLEINIST RP 185 (2428) / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc