Meanings of “mastery” in mathematics education: creation of concourse for a research study

This article outlines the rationale for and methodological choices made in designing an online Q study. Pre-service and experienced secondary mathematics teachers in the UK use the word “mastery” to describe a specific development programme, a curriculum or a set of teacher or student behaviours; these multiple meanings inspired a Q methodological study to identify types of views held by mathematics teachers. The article details the study’s design process, from generation of research question, through concourse and Q sample creation and pilot studies, to the final research design and Q sample. In the UK, changes to teacher practice are often quickly dismissed as fads and fashions, so greater use of Q to evaluate teachers’ views on educational initiatives would be a useful tool to uncover and explain that which is valued by teachers

Flexible autonomy: an online approach to developing mathematics subject knowledge for teachers

This paper uses an adaptation of Brookfield’s (2017) lenses to critically reflect upon a Subject Knowledge Enhancement Course designed and taught by the authors. Learning occurs through a synthesis of asynchronous engagement with online e-learning modules, weekly synchronous tutorials and self-reflection following formative and summative assessment opportunities. Interrogating the course design, learner feedback and observation, and tutor pedagogic choices through connectivist and social constructivist learning theory, the paper concludes that the common perceived learning gains occur through the flexibility in learning, and the supported autonomy that learners are given. Further developments in our offer should therefore aim to improve these opportunities for learners where possible

Heat and salt balances over the New England continental shelf, August 1996 to June 1997

Author Posting. © American Geophysical Union, 2010. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 115 (2010): C07017, doi:10.1029/2009JC006073.Heat and salt balances over the New England shelf are examined using 10 month time series of currents, temperature, and salinity from a four element moored array and surface heat and freshwater fluxes from a meteorological buoy. A principal result is closure of the heat budget to 10 W m−2. The seasonal variation in depth-average temperature, from 14°C in September to 5°C in March, was primarily due to the seasonal variation in surface heat flux and a heat loss in winter caused by along-shelf advection of colder water from the northeast. Conductivity sensor drifts precluded closing the salt balance on time scales of months or longer. For time scales of days to weeks, depth-average temperature and salinity variability were primarily due to advection. Advective heat and salt flux divergences were strongest and most complex in winter, when there were large cross-shelf temperature and salinity gradients at the site due to the shelf-slope front that separates cooler, fresher shelf water from warmer, saltier slope water. Onshore flow of warm, salty slope water near the bottom and offshore flow of cooler, fresher shelf water due to persistent eastward (upwelling-favorable) winds caused a temperature increase of nearly 3°C and a salinity increase of 0.8 in winter. Along-shelf barotropic tidal currents caused a temperature decrease of 1.5°C and a salinity decrease of 0.7. Wave-driven Stokes drift caused a temperature increase of 0.5°C and a salinity increase of 0.4 from mid December to January when there were large waves and large near-surface cross-shelf temperature and salinity gradients.The field program was funded by the Office of Naval Research, Code 322, under grant N00014‐95‐1‐0339. Analysis was also partially supported by the National Science Foundation Physical Oceanography program under grants OCE‐0647050 and OCE‐0548961

On estimating tropical forest carbon dynamics in Papua New Guinea

One of the few initiatives to address ongoing global warming that did not completely stall at the UNFCCC climate change negotiations was the reduction emissions from deforestation and forest degradation (REDD). REDD has a focus on the forests of the tropics. Unfortunately forest mensuration in most tropical countries has been inadequate to accurately determine forest carbon stocks, much less the effects of land use and changes in land use on them (Houghton et al. 2009; Bryan et al. 2010a). Whilst tropical logging is known to be widespread, the exact areas of tropical forest subject to logging have not been accurately mapped (Asner et al. 2009) or mapped with sufficient regularity to provide adequate data on the areas subject to this activity. Biomass losses due to logging have usually been derived from limited plot data, or derived via various models from estimates of regional biomass and timber extraction volumes (Houghton et al. 2009) and thus encapsulate considerable uncertainty. For these reasons the carbon impact of tropical logging remains an open question, and one that needs to be closed before any international institutional arrangement considers promoting forms of timber extraction as a tool for controlling carbon emissions. Here, we examine the current state of forest carbon research in Papua New Guinea (PNG) to illustrate the problems that can arise by developing forest management policy prematurely from incomplete forest research

The effect of epidural anaesthesia on peripheral resistance and graft flow following femorodistal reconstruction

Objective:To determine the extent to which epidural anaesthesia influences peripheral resistance and graft blood flow following femorocrural reconstruction.Design:Prospective, controlled study measuring blood flow, arterial pressure and peripheral resistance in femorocrural bypass grafts for 20 min following onset of epidural anaesthesia with 15ml of 0.25% bupivacaine.Patients:Twenty patients undergoing femorocrural reconstruction for critical lower-limb ischaemia with in situ long saphenous vein, under general anaesthesia. Ten patients had epidural cannulae inserted preoperatively and injected with bupivacaine after completion of the graft.Results:Peripheral resistance fell in all 10 patients receiving epidural anaesthesia from a mean (range) of 1.07 PRU (0.32–2.2) to 0.49 PRU (0.19–0.72), compared to control values of 0.95 PRU (0.39–2.0) to 0.91 PRU (0.41–1.51; P < 0.01, Wilcoxon). There was a tendency for blood pressure to fall in the study patients (not significant) but graft blood flow still increased from 98 ml min−1 (41–221) to 160 ml min−1 (101–250), compared to flow in the control patients of 101 ml min−1 (45–176) at baseline to 104 ml min−1 (56–168; p < 0.01) at 20 min.Conclusions:Epidural anaesthesia significantly decreases peripheral resistance and increases graft blood flow in femorocrural grafts and would appear, therefore, to be of benefit for patients undergoing femorodistal reconstruction

Measurement of cardiorespiratory fitness in children from two commonly used field tests after accounting for body fatness and maturity

Body fat and maturation both influence cardiorespiratory fitness, however few studies have taken these variables into account when using field tests to predict children's fitness levels. The purpose of this study was to determine the relationship between two field tests of cardiorespiratory fitness (20 m Maximal Multistage Shuttle Run [20-MST], 550 m distance run [550-m]) and direct measurement of VO2max after adjustment for body fatness and maturity levels. Fifty-three participants (25 boys, 28 girls, age 10.6 ± 1.2 y, mean ± SD) had their body fat levels estimated using bioelectrical impedance (16.6% ± 6.0% and 20.0% ± 5.8% for boys and girls, respectively). Participants performed in random order, the 20-MST and 550-m run followed by a progressive treadmill test to exhaustion during which gas exchange measures were taken. Pearson correlation coefficient analysis revealed that the participants' performance in the 20-MST and 550-m run were highly correlated to VO2 max obtained during the treadmill test to exhaustion (r = 0.70 and 0.59 for 20-MST and 550-m run, respectively). Adjusting for body fatness and maturity levels in a multivariate regression analysis increased the associations between the field tests and VO2max (r = 0.73 for 20-MST and 0.65 for 550-m). We may conclude that both the 20-MST and the 550-m distance run are valid field tests of cardiorespiratory fitness in New Zealand 8-13 year old children and incorporating body fatness and maturity levels explains an additional 5-7% of the variance. © Editorial Committee of Journal of Human Kinetics

Supporting engagement or engaging support?

The need for learning support in first year mathematics subjects in universities in Australia is increasing as student diversity increases. We studied the use of two modes of learning support in a first year mathematics subject for which there is no assumed mathematics knowledge. Many students in this subject have a poor mathematics background, noticeably worse than five years previously. Students were offered both online support and face-to-face workshops. Student use of support was tracked for a semester, along with some measures of engagement: tutorial attendance and use of the learning management system. The interplay between learning support and engagement was found to be significant and the use of support can be used as a measure of engagement. The success of support is intertwined with the success of engagement, making it difficult to measure the success of learning support. Hence, if we want to measure the success of support we somehow have to disentangle the effect of learning support from that of student engagement. However, student outcomes appear to be substantially improved through engagement with any learning activities. Engagement with both online support and face-to-face support was generally very poor, however the groups that utilised each mode were largely distinct. This indicates that a variety of support mechanisms, both face-to-face and online, are necessary to maximise the engagement with support. The poor engagement with learning support presents us with a huge challenge for the future, a challenge seen by many others: getting more students engaged in learning support. Though support is generally seen to be successful, few students engage with the support available and so many students are performing far worse than they could be. This has a serious effect on pass rates and can be detrimental to mathematics departments as mathematics academics could be seen poor teachers who are unable to motivate their students

β-Glucan is a major growth substrate for human gut bacteria related to Coprococcus eutactus

A clone encoding carboxymethyl cellulase activity was isolated during functional screening of a human gut metagenomic library using Lactococcus lactis MG1363 as heterologous host. The insert carried a glycoside hydrolase family 9 (GH9) catalytic domain with sequence similarity to a gene from Coprococcus eutactus ART55/1. Genome surveys indicated a limited distribution of GH9 domains among dominant human colonic anaerobes. Genomes of C. eutactus-related strains harboured two GH9-encoding and four GH5-encoding genes, but the strains did not appear to degrade cellulose. Instead, they grew well on β-glucans and one of the strains also grew on galactomannan, galactan, glucomannan and starch. Coprococcus comes and Coprococcus catus strains did not harbour GH9 genes and were not able to grow on β-glucans. Gene expression and proteomic analysis of C. eutactus ART55/1 grown on cellobiose, β-glucan and lichenan revealed similar changes in expression in comparison to glucose. On β-glucan and lichenan only, one of the four GH5 genes was strongly upregulated. Growth on glucomannan led to a transcriptional response of many genes, in particular a strong upregulation of glycoside hydrolases involved in mannan degradation. Thus, β-glucans are a major growth substrate for species related to C. eutactus, with glucomannan and galactans alternative substrates for some strains