The Suuji Approach to Multi-Digit Addition: Using Length to Deepen Students’ Understanding of the Base 10 Number System

We describe the Suuji representation of numbers which aims to deepen elementary students’ understanding of the base 10 system. (“Suuji” means “number” in Japanese.) This representation takes a two pronged approach of (1) making the place value more explicit and (2) using length to represent numbers, thus allowing students to reason spatially. We taught multi-digit addition using the Suuji representation to 20 second and third grade students. The article uses lesson descriptions and student work to illustrate the Suuji approach, as well as its impact on student learning

Mathematical Habits of Mind for Teaching: Using Language in Algebra Classrooms

The notion of mathematical knowledge for teaching has been studied by many researchers, especially at the elementary grades. Our understandings of this notion parallel much of what we have read in the literature, but are based on our particular experiences over the past 20 years, as mathematicians engaged in doing mathematics with secondary teachers. As part of the work of Focus on Mathematics, Phase II MSP, we are developing, in collaboration with others in the field, a research program with the ultimate goal of understanding the connections between secondary teachers’ mathematical knowledge for teaching and secondary students’ mathematical understanding and achievement. We are in the early stages of a focused research study investigating the research question: What are the mathematical habits of mind that high school teachers use in their professional lives and how can we measure them? The main focus of this paper is the discussion of the habit of using mathematical language, and particularly how this habit plays out in a classroom setting

“I Got You”: Centering Identities and Humanness in Collaborations Between Mathematics Educators and Mathematicians

Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations – one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration – and a look at how collaborations built with that intentionality and acknowledgment can be impactful for students and institutions and be personally and professionally rewarding for the collaborators

Description, Utilisation and Results from a Telehealth Primary Care Weight Management Intervention for Adults with Obesity in South Carolina

Introduction: In the US, obesity rates are higher in rural areas than in urban areas. Rural access to treatment of obesity is limited by a lack of qualified clinicians and by transportation and financial barriers. We describe a telemedicine weight management programme, Wellness Connect, developed through a partnership of academic clinicians and rural primary care providers in South Carolina, and present utilisation and weight outcomes from seven patient cohorts. Methods: Eight bi-weekly sessions were provided via telemedicine videoconferencing for groups of patients at these rural primary care clinics. Protocol-based sessions were led by registered dietitians, exercise physiologists and clinical psychologists at a central urban location. Results: Of 138 patients who started the programme, 62% (N ¼ 86) of patients met the criteria for completion. Completers lost an average of 3.5% (standard deviation (SD) ¼ 3.9%) body weight, which was statistically significant (p \u3c.001) and corresponded with an average loss of 3.8 kg (SD ¼ 4.5 kg). There were no differences in weight change among clinics (p ¼.972). Overall, patients and providers reported satisfaction with the programme and identified several challenges to sustainability. Discussion: The use of innovative telemedicine interventions continues to be necessary to alleviate barriers to accessing evidence-based services to reduce chronic diseases and decrease obesity rates among rural populations

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

Baseline factors associated with early and late death in intracerebral haemorrhage survivors

Background and purpose: The aim of this study was to determine whether early and late death are associated with different baseline factors in intracerebral haemorrhage (ICH) survivors. Methods: This was a secondary analysis of the multicentre prospective observational CROMIS‐2 ICH study. Death was defined as ‘early’ if occurring within 6 months of study entry and ‘late’ if occurring after this time point. Results: In our cohort (n = 1094), there were 306 deaths (per 100 patient‐years: absolute event rate, 11.7; 95% confidence intervals, 10.5–13.1); 156 were ‘early’ and 150 ‘late’. In multivariable analyses, early death was independently associated with age [per year increase; hazard ratio (HR), 1.05, P = 0.003], history of hypertension (HR, 1.89, P = 0.038), pre‐event modified Rankin scale score (per point increase; HR, 1.41, P < 0.0001), admission National Institutes of Health Stroke Scale score (per point increase; HR, 1.11, P < 0.0001) and haemorrhage volume >60 mL (HR, 4.08, P < 0.0001). Late death showed independent associations with age (per year increase; HR, 1.04, P = 0.003), pre‐event modified Rankin scale score (per point increase; HR, 1.42, P = 0.001), prior anticoagulant use (HR, 2.13, P = 0.028) and the presence of intraventricular extension (HR, 1.73, P = 0.033) in multivariable analyses. In further analyses where time was treated as continuous (rather than dichotomized), the HR of previous cerebral ischaemic events increased with time, whereas HRs for Glasgow Coma Scale score, National Institutes of Health Stroke Scale score and ICH volume decreased over time. Conclusions: We provide new evidence that not all baseline factors associated with early mortality after ICH are associated with mortality after 6 months and that the effects of baseline variables change over time. Our findings could help design better prognostic scores for later death after ICH

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

Background: Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events. Methods: The REstart or STop Antithrombotics Randomised Trial (RESTART) was a prospective, randomised, open-label, blinded endpoint, parallel-group trial at 122 hospitals in the UK. We recruited adults (≥18 years) who were taking antithrombotic (antiplatelet or anticoagulant) therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage, discontinued antithrombotic therapy, and survived for 24 h. Computerised randomisation incorporating minimisation allocated participants (1:1) to start or avoid antiplatelet therapy. We followed participants for the primary outcome (recurrent symptomatic intracerebral haemorrhage) for up to 5 years. We analysed data from all randomised participants using Cox proportional hazards regression, adjusted for minimisation covariates. This trial is registered with ISRCTN (number ISRCTN71907627). Findings: Between May 22, 2013, and May 31, 2018, 537 participants were recruited a median of 76 days (IQR 29–146) after intracerebral haemorrhage onset: 268 were assigned to start and 269 (one withdrew) to avoid antiplatelet therapy. Participants were followed for a median of 2·0 years (IQR [1·0– 3·0]; completeness 99·3%). 12 (4%) of 268 participants allocated to antiplatelet therapy had recurrence of intracerebral haemorrhage compared with 23 (9%) of 268 participants allocated to avoid antiplatelet therapy (adjusted hazard ratio 0·51 [95% CI 0·25–1·03]; p=0·060). 18 (7%) participants allocated to antiplatelet therapy experienced major haemorrhagic events compared with 25 (9%) participants allocated to avoid antiplatelet therapy (0·71 [0·39–1·30]; p=0·27), and 39 [15%] participants allocated to antiplatelet therapy had major occlusive vascular events compared with 38 [14%] allocated to avoid antiplatelet therapy (1·02 [0·65–1·60]; p=0·92). Interpretation: These results exclude all but a very modest increase in the risk of recurrent intracerebral haemorrhage with antiplatelet therapy for patients on antithrombotic therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage. The risk of recurrent intracerebral haemorrhage is probably too small to exceed the established benefits of antiplatelet therapy for secondary prevention

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

Background: Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events. Methods: The REstart or STop Antithrombotics Randomised Trial (RESTART) was a prospective, randomised, open-label, blinded endpoint, parallel-group trial at 122 hospitals in the UK. We recruited adults (≥18 years) who were taking antithrombotic (antiplatelet or anticoagulant) therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage, discontinued antithrombotic therapy, and survived for 24 h. Computerised randomisation incorporating minimisation allocated participants (1:1) to start or avoid antiplatelet therapy. We followed participants for the primary outcome (recurrent symptomatic intracerebral haemorrhage) for up to 5 years. We analysed data from all randomised participants using Cox proportional hazards regression, adjusted for minimisation covariates. This trial is registered with ISRCTN (number ISRCTN71907627). Findings: Between May 22, 2013, and May 31, 2018, 537 participants were recruited a median of 76 days (IQR 29–146) after intracerebral haemorrhage onset: 268 were assigned to start and 269 (one withdrew) to avoid antiplatelet therapy. Participants were followed for a median of 2·0 years (IQR [1·0– 3·0]; completeness 99·3%). 12 (4%) of 268 participants allocated to antiplatelet therapy had recurrence of intracerebral haemorrhage compared with 23 (9%) of 268 participants allocated to avoid antiplatelet therapy (adjusted hazard ratio 0·51 [95% CI 0·25–1·03]; p=0·060). 18 (7%) participants allocated to antiplatelet therapy experienced major haemorrhagic events compared with 25 (9%) participants allocated to avoid antiplatelet therapy (0·71 [0·39–1·30]; p=0·27), and 39 [15%] participants allocated to antiplatelet therapy had major occlusive vascular events compared with 38 [14%] allocated to avoid antiplatelet therapy (1·02 [0·65–1·60]; p=0·92). Interpretation: These results exclude all but a very modest increase in the risk of recurrent intracerebral haemorrhage with antiplatelet therapy for patients on antithrombotic therapy for the prevention of occlusive vascular disease when they developed intracerebral haemorrhage. The risk of recurrent intracerebral haemorrhage is probably too small to exceed the established benefits of antiplatelet therapy for secondary prevention

Cerebral microbleeds and intracranial haemorrhage risk in patients anticoagulated for atrial fibrillation after acute ischaemic stroke or transient ischaemic attack (CROMIS-2):a multicentre observational cohort study

Background: Cerebral microbleeds are a potential neuroimaging biomarker of cerebral small vessel diseases that are prone to intracranial bleeding. We aimed to determine whether presence of cerebral microbleeds can identify patients at high risk of symptomatic intracranial haemorrhage when anticoagulated for atrial fibrillation after recent ischaemic stroke or transient ischaemic attack. Methods: Our observational, multicentre, prospective inception cohort study recruited adults aged 18 years or older from 79 hospitals in the UK and one in the Netherlands with atrial fibrillation and recent acute ischaemic stroke or transient ischaemic attack, treated with a vitamin K antagonist or direct oral anticoagulant, and followed up for 24 months using general practitioner and patient postal questionnaires, telephone interviews, hospital visits, and National Health Service digital data on hospital admissions or death. We excluded patients if they could not undergo MRI, had a definite contraindication to anticoagulation, or had previously received therapeutic anticoagulation. The primary outcome was symptomatic intracranial haemorrhage occurring at any time before the final follow-up at 24 months. The log-rank test was used to compare rates of intracranial haemorrhage between those with and without cerebral microbleeds. We developed two prediction models using Cox regression: first, including all predictors associated with intracranial haemorrhage at the 20% level in univariable analysis; and second, including cerebral microbleed presence and HAS-BLED score. We then compared these with the HAS-BLED score alone. This study is registered with ClinicalTrials.gov, number NCT02513316. Findings: Between Aug 4, 2011, and July 31, 2015, we recruited 1490 participants of whom follow-up data were available for 1447 (97%), over a mean period of 850 days (SD 373; 3366 patient-years). The symptomatic intracranial haemorrhage rate in patients with cerebral microbleeds was 9·8 per 1000 patient-years (95% CI 4·0–20·3) compared with 2·6 per 1000 patient-years (95% CI 1·1–5·4) in those without cerebral microbleeds (adjusted hazard ratio 3·67, 95% CI 1·27–10·60). Compared with the HAS-BLED score alone (C-index 0·41, 95% CI 0·29–0·53), models including cerebral microbleeds and HAS-BLED (0·66, 0·53–0·80) and cerebral microbleeds, diabetes, anticoagulant type, and HAS-BLED (0·74, 0·60–0·88) predicted symptomatic intracranial haemorrhage significantly better (difference in C-index 0·25, 95% CI 0·07–0·43, p=0·0065; and 0·33, 0·14–0·51, p=0·00059, respectively). Interpretation: In patients with atrial fibrillation anticoagulated after recent ischaemic stroke or transient ischaemic attack, cerebral microbleed presence is independently associated with symptomatic intracranial haemorrhage risk and could be used to inform anticoagulation decisions. Large-scale collaborative observational cohort analyses are needed to refine and validate intracranial haemorrhage risk scores incorporating cerebral microbleeds to identify patients at risk of net harm from oral anticoagulation. Funding: The Stroke Association and the British Heart Foundation