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Increasing students' exposure to mathematical reasoning (Lannin, Ellis, & Elliot, 2011) has been a constant call from mathematics education reform efforts. However, studies have raised concerns about whether teachers are prepared to teach reasoning. This paper explores one aspect of reasoning, refutations, by examining the geometric refutations of thirteen pre-service secondary teachers (PSTs). Findings suggest that the PSTs did struggle to create culturally accepted refutation, but their results were less concerning than previous studies suggest. Primary challenges include that the PSTs separate the work they do for the different subprocesses of reasoning, reason differently depending on the subprocess, and favor non-culturally accepted means of refutations. Additionally, when the PSTs created culturally accepted refutations, they often used specific counterexamples, which are less pedagogically powerful than general counterexamples (Zaslavsky & Peled, 1996). However, the PSTs in this study did provide general counterexamples more often than the participants of other studies (Potari, Zachariades, & Zaslavsky, 2009). Suggestions for ways to improve PSTs understanding of reasoning are provided.

Cognitively demanding tasks have been shown to support students' understanding of mathematics. How a task is launched, or introduced, determines how students engage with the task, as well as the type of work the teacher engages in during the task implementation. The authors designed a unit focused on launching a task where prospective teachers (PSTs) planned and enacted a task launch as part of their methods of teaching secondary mathematics courses. Participants in the study spanned three institutions. Using a curricular noticing framework, this paper describes how the prospective teachers (PSTs) "interpreted" their task by identifying key contextual features, mathematical relationships, and common language, and then focuses on how they "responded" to their "interpretations" as they planned to elicit and develop their students' understanding of those key aspects. This paper also describes how the PSTs "responded" to their "interpretations" in planning to maintain the cognitive demand of the task. Findings suggest that the prospective teachers valued student-centered approaches and used a range of pedagogical methods to launch cognitively demanding tasks. We also found the prospective teachers needed support identifying context in tasks and in determining how much to tell while maintaining the cognitive demand of the task. We conclude with implications and suggestions for methods courses on both launching a cognitively demanding task and on teaching practices more generally.

Cognitively demanding tasks provide important opportunities for students to develop an understanding of mathematics; however, they are challenging to launch and implement. The authors designed a secondary methods unit on launching tasks. Participants in the study were enrolled in five different methods courses. Using a noticing framework, findings suggest that by engaging in the unit, preservice teachers developed a greater understanding of the four aspects of an effective task launch. When viewing video examples, preservice teachers were able to talk about the four aspects of a task launch with increased specificity. Additionally, they began to identify ways of developing common language without reducing cognitive demand. We discuss implications of this work and offer suggestions for future teacher education research.

Three iterative, 18-episode design experiments were conducted after school with groups of 6-9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI emerged: proactively tailoring instruction to students' mathematical thinking while developing a cohesive classroom community. Analysis of 10 episodes across experiments yielded five teaching practices that facilitated DI: using research-based knowledge of students' mathematical thinking, providing purposeful choices and different pathways, inquiring responsively during group work, attending to small group functioning, and conducting whole class discussions across different thinkers. The latter three practices, at times, impeded DI. This study is a case of using second-order models of students' mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students' thinking are at the heart of differentiating mathematics instruction.

Background: In 2014, the Affordable Care Act Medicaid Expansion (ME) increased Medicaid eligibility for adults with an income level up to 138% of the federal poverty level. In this study, we examined the impact of ME on mortality and amputation in patients with peripheral artery disease (PAD). Methods: The 100% MedPAR and Part-B Carrier files from 2011 to 2018 were queried to identify all fee-for-service Medicare beneficiaries with PAD using International Classification of Diseases codes. Our primary exposure was whether a state had adopted the ME on January 1, 2014. Our primary outcomes were the change in all-cause 1-year mortality and leg amputation. We used a state-level difference-in-differences (DID) analysis to compare the rates of the primary outcomes among patients who were in states (including the District of Columbia) who adopted ME (n = 25) versus those who were in states that did not (n = 26). We performed a subanalysis stratifying by sex, race, region, and dual-eligibility status. Results: Over the 8-year period, we studied 37,743,929 patients. The average unadjusted 1-year mortality decreased from 2011 to 2018 in both non-ME (9.5% to 8.7%, p < 0.001) and ME (9.1% to 8.3%, p < 0.001) states. The average unadjusted 1-year amputation rate did not improve in either the non-ME (0.86% to 0.87%, p = 0.17) or ME (0.69% to 0.69%, p = 0.65) states. Across the entire cohort, the DID model revealed that ME did not lead to a significant change in mortality (p = 0.15) or amputation (p = 0.34). Conclusion: Medicaid Expansion was not associated with reduced mortality or leg amputation in Medicare beneficiaries with PAD. [ABSTRACT FROM AUTHOR]

The aim of this updated statement is to provide comprehensive and timely evidence-based recommendations on the prevention of stroke among individuals who have not previously experienced a stroke or transient ischemic attack. Evidence-based recommendations are included for the control of risk factors, interventional approaches to atherosclerotic disease of the cervicocephalic circulation, and antithrombotic treatments for preventing thrombotic and thromboembolic stroke. Further recommendations are provided for genetic and pharmacogenetic testing and for the prevention of stroke in a variety of other specific circumstances, including sickle cell disease and patent foramen ovale.

ObjectiveFactors responsible for the variability in outcomes after lower extremity vein bypass grafting (LEVBG) are poorly understood. Recent evidence has suggested that a single nucleotide polymorphism (SNP) in the promoter region of the p27(Kip1) gene, a cell-cycle regulator, is associated with coronary in-stent restenosis. We hypothesized an association with vein graft patency.MethodsThis was a retrospective genetic association study nested within a prospective cohort of 204 patients from three referral centers undergoing LEVBG for claudication or critical ischemia. The main outcome measure was primary vein graft patency.ResultsAll patients were followed up for a minimum of 1 year with duplex graft surveillance (median follow-up, 893 days; interquartile range, 539-1315). Genomic DNA was isolated and SNP analysis for the p27(Kip1)-838C>A variants was performed. Allele frequencies were correlated with graft outcome using survival analysis and Cox proportional hazards modeling. The p27(Kip1)-838C>A allele frequencies observed were CA, 53%; CC, 30%; and AA, 17%, satisfying Hardy-Weinberg equilibrium. Race (P = .025) and history of coronary artery disease (P = .027) were different across the genotypes; all other baseline variables were similar. Primary graft patency was greater among patients with the -838AA genotype (75% AA vs 55% CA/CC at 3 years; P = .029). In a Cox proportional hazards model including age, sex, race, diabetes, critical limb ischemia, redo (vs primary) bypass, vein type, and baseline C-reactive protein level, the p27(Kip1)-838AA genotype was significantly associated with higher graft patency (hazard ratio for failure, 0.4; 95% confidence interval, 0.17-0.93). Genotype was also associated with early (0-1 month) changes in graft lumen diameter by ultrasound imaging.ConclusionsThese data suggest that the p27(Kip1)-838C>A SNP is associated with LEVBG patency and, together with previous reports, underscore a central role for p27(Kip1) in the generic response to vascular injury.

ObjectiveSuccessful adaptation of a vein graft to an arterial environment is incompletely understood. We sought to investigate whether early vein graft remodeling is predictive of subsequent patency.MethodsA prospective longitudinal study was conducted of 67 patients undergoing lower extremity bypass with autogenous vein between February 2004 and April 2008. Preoperative blood samples were drawn for biomarkers. During the bypass operation, a 5-cm index segment of the graft was registered for serial lumen diameter measurements at 0, 1, 3, 6, 9, and 12 months using duplex ultrasound imaging. The imaging substudy analysis included patients with at least two ultrasound assessments.ResultsPatients (55% male) were a median age of 70 years (interquartile range [IQR], 59-76 years), 40% had diabetes mellitus, 49% had critical limb ischemia, 75% were taking a statin, and 91% were taking an antiplatelet medication. Median follow-up was 32 months (IQR, 15-47 months). The median baseline high-sensitivity C-reactive protein level (hsCRP) was 3.2 mg/L (IQR, 1.4-9.7 mg/L). The average intraoperative, postimplantation vein lumen diameter was 3.9±1.0 mm, increasing to 4.7±1.1 mm at 1 month, an average 24%±27% change per patient. By 3 months, the average lumen diameter was 5.1±1.6 mm, with little subsequent change observed to 12 months. Nonwhite race, baseline hsCRP ≥5 mg/L, statin use, and initial lumen diameter were significantly associated with early (0- to 1-month) vein remodeling in a multivariable regression model. The primary patency rate for the cohort was 60%±6.3% at 2 years. Initial lumen diameter of the index segment was not associated with primary patency, whereas larger lumen diameter achieved at 1 month (≥5.1 mm) was positively associated with primary patency (log-rank, P=.03). Early (30-day) remodeling behavior was used to divide patients into "poor remodelers" (+25% change, n=30). Early remodeling category was significantly associated with primary patency rate at 2 years (log-rank, P=.02). A multivariable Cox proportional hazards model showed that modest remodelers (hazard ratio, 3.9; 95% confidence interval, 1.02-15; P=.04) and poor remodelers (hazard ratio, 13; 95% confidence interval; P=.008) had significantly higher hazard ratios for graft failure than robust early remodelers.ConclusionsEarly remodeling of the arterialized vein appears to predict midterm bypass graft patency. In addition to baseline diameter, race, inflammation, hsCRP, and statin use are associated with early adaptive remodeling, but the mechanisms for these observations are not understood.

The discovery of the endothelium as a crucial organ for the regulation of the vasculature to physiological needs and the recognition of endothelial dysfunction as a key pathological condition - which is associated with most if not all cardiovascular risk factors - led to a tremendous boost of endothelial research in the past 3 decades. Despite the possibility to measure endothelial function in the individual and its widespread use in research, its use as a clinical tool in daily medicine is not established yet. We review the most common methods to assess vascular function in humans and discuss their advantages and disadvantages. Furthermore we give an overview about clinical settings were endothelial function measurements may be valuable in individual patients. Specifically, we provide information why endothelial function is not only a risk marker for cardiovascular risk but may also provides prognostic information beyond commonly used risk scores in primary prevention, and in patients with already established coronary disease. We conclude, that non-invasive endothelial function measurements provide valuable additional information, however, to ascertain its use for daily clinical practice, future research should determine whether endothelial function can be used to guide treatment in the individual and if this translates into better outcomes.

ObjectiveThis study was conducted to determine if there are sex-based differences in the inflammatory phenotype of patients undergoing lower extremity bypass (LEB) and if they correlate with clinical outcomes.MethodsThis was a retrospective analysis of a prospective cohort of 225 patients (161 men and 64 women) who underwent autogenous vein LEB between February 2004 and May 2008. Fasting baseline blood samples were obtained before LEB, and the inflammatory biomarkers high-sensitivity C-reactive protein (CRP) and fibrinogen were assessed. All patients underwent ultrasound graft surveillance. CRP levels were dichotomized at 5 mg/L and fibrinogen levels at 600 mg/dL.ResultsThere were no significant differences in age, race, history of hypertension or diabetes mellitus, body mass index, or coronary artery disease between men and women. Men were more likely to be current smokers (P = .02), have a history of hypercholesterolemia (P = .02), and be taking statins (P = .02). Women were more likely to present with critical limb ischemia (P = .03) and had higher median baseline CRP levels (5.15 mg/L; interquartile range [IQR], 1.51-18.62 mg/L) than men (2.70; IQR, 1.24-6.98 mg/L; P = .02). Median follow-up was 893 days (IQR, 539-1315 days). A multivariable Cox proportional hazards model for primary vein graft patency showed a significant interaction between sex and CRP (P = .03) and fibrinogen (P = .02). After adjustment for key covariates, primary vein graft patency was significantly less in women with CRP >5 mg/L compared with women with CRP 600 mg/dL vs women with fibrinogen

Mathematical knowledge for teaching (MKT) is often thought of as a transformed, mutually-influencing mixture of content and pedagogy. However when individuals' MKT does not integrate content and pedagogy, one type of knowledge can supersede the other, sometimes unconsciously. We exemplify this with Emma, a prospective elementary teacher, whose views on students' learning needs overshadowed her content knowledge. Specifically, Emma answered mathematical questions incorrectly, despite being aware of the correct answers, because she inadvertently gave more weight to pedagogical than to mathematical concerns. Implications for research and teacher education are discussed.