Developing mathematical fluency: comparing exercises and rich tasks

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 quasi experimental 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 "mathematical 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

Exploring the relative lack of impact of research on ‘ability grouping’ in England: a discourse analytic account

Grouping students by ‘ability’ is a topic of long-standing contention in English education policy, research and practice. While policy-makers have frequently advocated the practice as reflecting educational ‘standards’, research has consistently failed to find significant benefits of ‘ability’ grouping; and indeed has identified disadvantages for some (low-attaining) pupil groups. However, this research evidence has apparently failed to impact on practice in England. This article, contextualised by the authors’ interests in education and social inequality, seeks to do two things. First, it provides a brief analysis of the existing research evidence on the impact of ‘ability’ grouping, with particular reference to socio-economic inequality, identifying seven different explanations for the poorer progress of pupils in low sets that emerge from the literature. Second, it applies Foucaultian ‘analysis of discourse’ to propose potential explanations for the apparent lack of traction of existing research with policy and practice, arguing that practices of ‘ability grouping’ reflect cultural investments in discourses of ‘natural order’ and hierarchy, with particular resonance for the discursive and political habitus of middle-class parents. The authors postulate that investing in a powerful counter-discourse of enlightenment science, illustrated via their current randomised control trial of different approaches to pupil grouping, may offer a means to challenge hegemonic discourses that underpin current classroom practice

Opportunities to Learn Mathematics Pedagogy and Connect Classroom Learning to Practice: A Study of Future Teachers in the United States and Singapore

In this study, we conducted secondary analyses using the TEDS-M database to explore future mathematics specialists teachers’ opportunities to learn (OTL) how to teach mathematics. We applied latent class analysis techniques to differentiate among groups of prospective mathematics specialists with potentially different OTL mathematics pedagogy within the United States and Singapore. Within the United States, three subgroups were identified: (a) Comprehensive OTL, (b) Limited OTL, and (c) OTL Mathematics Pedagogy. Within Singapore, four subgroups were identified: (a) Comprehensive OTL, (b) Limited Opportunities to Connect Classroom Learning with Practice, (c) OTL Mathematics Pedagogy, and (d) Basic OTL. Understanding the opportunities different prospective teachers had to learn from and their experiences with different components of instructional practice in university and practicum settings has implications for teacher preparation programs

Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome

Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome