BACKGROUND: The efficacy of polyclonal high titer convalescent plasma to prevent serious complications of COVID-19 in outpatients with recent onset of illness is uncertain. METHODS: This multicenter, double-blind randomized controlled trial compared the efficacy and safety of SARS-CoV-2 high titer convalescent plasma to placebo control plasma in symptomatic adults >18 years positive for SARS-CoV-2 regardless of risk factors for disease progression or vaccine status. Participants with symptom onset within 8 days were enrolled, then transfused within the subsequent day. The measured primary outcome was COVID-19-related hospitalization within 28 days of plasma transfusion. The enrollment period was June 3, 2020 to October 1, 2021. RESULTS: A total of 1225 participants were randomized and 1181 transfused. In the pre-specified modified intention-to-treat analysis that excluded those not transfused, the primary endpoint occurred in 37 of 589 (6.3%) who received placebo control plasma and in 17 of 592 (2.9%) participants who received convalescent plasma (relative risk, 0.46; one-sided 95% upper bound confidence interval 0.733; P=0.004) corresponding to a 54% risk reduction. Examination with a model adjusting for covariates related to the outcome did not change the conclusions. CONCLUSION: Early administration of high titer SARS-CoV-2 convalescent plasma reduced outpatient hospitalizations by more than 50%. High titer convalescent plasma is an effective early outpatient COVID-19 treatment with the advantages of low cost, wide availability, and rapid resilience to variant emergence from viral genetic drift in the face of a changing pandemic.

Mathematics educators have been publishing their work in international research journals for nearly 5 decades. How has the field developed over this period? We analyzed the full text of all articles published in Educational Studies in Mathematics and the Journal for Research in Mathematics Education since their foundation. Using Lakatos's (1978) notion of a research programme, we focus on the field's changing theoretical orientations and pay particular attention to the relative prominence of the experimental psychology, constructivist, and sociocultural programmes. We quantitatively assess the extent of the “social turn,” observe that the field is currently experiencing a period of theoretical diversity, and identify and discuss the “experimental cliff,” a period during which experimental investigations migrated away from mathematics education journals.

This article analyses lesson study as a mode of professional learning, focused on the development of mathematical problem solving processes, using the lens of culturalhistorical activity theory. In particular, we draw attention to two activity systems, the classroom system and the lesson-study system, and the importance of making artefacts instrumental in both. We conceptualise the lesson plan as a boundary object and use this to illustrate how professional learning takes place through the introduction of carefully designed artefacts that draw on teachers' professional knowledge of potential student approaches, and to the nature of progression in problem-solving processes. We identify the roles of instrumentalisation and instrumentation in supporting professional learning as these artefacts are prepared for use before a lesson and as they are again used as catalysts for reflection in post-lesson discussions. These artefacts are seen to effectively facilitate the socially situated learning of all participants. We conclude that the design of artefacts as boundary objects that support teaching and professional learning in their respective activity systems may be fundamental to the success of lesson study as a collaborative venture.

Confidence assessment (CA), in which students state alongside each of their answers a confidence level expressing how certain they are, has been employed successfully within higher education. However, it has not been widely explored with school pupils. This study examined how school mathematics pupils (N=345) in five different secondary schools in England responded to the use of a CA instrument designed to incentivise the eliciting of truthful confidence ratings in the topic of directed (positive and negative) numbers. Pupils readily understood the negative marking aspect of the CA process and their facility correlated with their mean confidence with r=.546, N=336, p<.001, indicating that pupils were generally well calibrated. Pupils' comments indicated that the vast majority were positive about the CA approach, despite its dramatic differences from more usual assessment practices in UK schools. Some pupils felt that CA promoted deeper thinking, increased their confidence and had a potential role to play in classroom formative assessment.

Achieving fluency in important mathematical procedures is fundamental to students' mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way? This paper reports three quasiexperimental studies carried out in a total of 11 secondary schools involving altogether 528 students aged 12-15. In each study, parallel classes were taught the same mathematical procedure before one class undertook traditional exercises while the other worked on a Bmathematical etude^(Foster International Journal of Mathematical Education in Science and Technology, 44(5), 765-774, 2013b), designed to be a richer task involving extensive opportunities for practice of the relevant procedure. Bayesian t tests on the gain scores between pre-and post-tests in each study provided evidence of no difference between the two conditions. A Bayesian meta-analysis of the three studies gave a combined Bayes factor of 5.83, constituting Bsubstantial^evidence (Jeffreys, 1961) in favour of the null hypothesis that etudes and exercises were equally effective, relative to the alternative hypothesis that they were not. These data support the conclusion that the mathematical etudes trialled are comparable to traditional exercises in their effects on procedural fluency. This could make etudes a viable alternative to exercises, since they offer the possibility of richer, more creative problem-solving activity, with comparable effectiveness in developing procedural fluency.

No abstract

Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on bite‐sized learning objectives and a tendency for mathematics teachers to path‐smooth their students’ learning. I argue that a reductionist mathematics pedagogy severely restricts students’ opportunities to engage in authentic mathematical thinking and deprives them of the enjoyment of solving richer, more worthwhile problems, which would forge connections across diverse areas of the subject. I attribute the rise of a reductionist mathematics pedagogy partly to an assessment‐dominated curriculum and partly to a systemic de‐professionalisation of teachers through a performative accountability culture in which they are constantly required to prove to non‐specialist managers that they are effective. I argue that pedagogical reductionism in mathematics must be resisted in favour of a more holistic approach, in which students are able to bring a variety of mathematical knowledge and skills to bear on rich, challenging and non‐routine mathematical tasks. Some principles for achieving this are outlined and some examples are given.

In this paper, we analyse a grade 8 (age 13–14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in which he shifted the focus from individual mathematical solutions to generalised properties. By comparing the teacher’s detailed prior planning of the board work (bansho) with that which he produced during the lesson, we distinguish between aspects of the lesson that he considered essential and those he treated as contingent. Our analysis reveals how the careful planning of the board work enabled the teacher to be free to explore with the students the multiple alternative solution methods that they had produced, while at the same time having a clear overall purpose relating to how angle properties can be used to find additional solution methods. We outline how these findings from within the strong tradition of the Japanese problem-solving lesson might inform research and teaching practice outside of Japan, where a deep heritage of bansho and neriage is not present. In particular, we highlight three prominent features of this teacher’s practice: the detailed lesson planning in which particular solutions were prioritised for discussion; the considerable amount of time given over to student generation and comparison of alternative solutions; and the ways in which the teacher’s use of the board was seen to support the richness of the mathematical discussions.