Theorem Justification and Acquisition in Dynamic Geometry: A Case of Proof by Contradiction

Theorem acquisition and deductive proof have always been core elements in the study and teaching of Euclidean geometry. The introduction of dynamic geometry environments,DGE (e.g., Cabri-Géomètre, Geometer's Sketchpad), into classrooms in the past decade has posed a challenge to this praxis. Student scan experiment through different dragging modalities on geometrical objects that they construct, and consequently infer properties(generalities, theorems) about the geometrical artefacts. Because of the inductive nature of the DGE, the experimental-theoretical gap that exists in the acquisition and justification of geometrical knowledge becomes an important pedagogical and epistemological concern. In this paper, we will describe and study a ‘Cabri proof by contradiction’ of a theorem on cyclic quadrilaterals given by a pair of 16 year-old students in a Hong Kong secondary school. We will discuss how their construction motivates a visual-cognitive scheme on `seeing' proof in DGE, and how this scheme could fit into the theoretical construct of cognitive unity of theorems proposed by Boero, Garuti and Mariotti(1996). The issue of a cognitive duality and its relation to visualization will be raised and discussed. Finally, we propose a possible perspective to bridge the experimental-theoretical gap in DGE by introducing the idea of a dynamic template as a visualizer to geometrical theorem justification and acquisition.postprin

Properties of tangential and cyclic polygons: an application of circulant matrices

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon Pn with n even is slippable (or conformable) and the sum of a set of non-adjacent sides (or interior angles) of Pn satisfies certain equalities. On the other hand, for a tangential (or cyclic) polygon Pn with n odd, it is rigid and the sum of a set of non-adjacent sides (or interior angles) of Pn satisfies certain inequalities. These inequalities give a definite answer to the question raised by Lopez-Real concerning the alternating sum of interior angles of a cyclic polygon.postprin

An Immersive Virtual Reality Curriculum for Pediatric Hematology Clinicians on Shared Decision-making for Hydroxyurea in Sickle Cell Anemia

Although hydroxyurea (HU) is an effective treatment for sickle cell anemia, uptake remains low. Shared decision-making (SDM) is a recommended strategy for HU initiation to elicit family preferences; however, clinicians lack SDM training. We implemented an immersive virtual reality (VR) curriculum at 8 pediatric institutions to train clinicians on SDM that included counseling virtual patients. Clinicians’ self-reported confidence significantly improved following the VR simulations on all communication skills assessed, including asking open-ended questions, eliciting specific concerns, and confirming understanding (Ps≤0.01 for all). VR may be an effective method for educating clinicians to engage in SDM for HU

Addressing Recruitment Challenges in the Engage-HU Trial in Young Children with Sickle Cell Disease

Background: Sickle cell disease (SCD) is a genetic disorder that causes significant medical and neurologic morbidity in children. Hydroxyurea (HU) is the primary medication used to prevent these complications. National Heart, Lung, and Blood Institute (NHLBI) guidelines recommend offering HU to children as young as 9 months of age with SCD (HbSS or HbSB0 thalassemia) using a shared decision-making approach. Although HU has proven efficacious it remains underutilized and caregivers report that they are not always actively involved in the decision to initiate this therapy. Reasons for limited HU uptake likely include lack of clinician knowledge and training and negative caregiver perceptions. Thus, we developed the Engage-HU trial as a novel approach to address HU utilization barriers. A critical consideration for this trial was that SCD primarily affects individuals of African and Hispanic/Latino descent. In these minority populations, intervention trials are sometimes terminated early because of recruitment difficulties related to mistrust of research, caregiver burden, and transportation issues. As such, the Engage-HU trial design included best-practice strategies for recruiting people of color in research. This study describes these strategies, the initial recruitment plan, preliminary recruitment outcomes and strategies, and our procedural adaptations. Study Design and Methods: Engage-HU is a randomized control trial (NCT03442114) to assess how clinicians can engage caregivers in a shared discussion that considers their values and preferences and includes evidence that supports HU. Engage-HU compares two dissemination methods for clinicians to facilitate shared decision-making with caregivers of young children with SCD: 1) the American Society of Hematology Pocket Guide, and 2) the HU Shared-Decision Making (H-SDM) Toolkit. The study aims to recruit 174 caregivers and evaluate the effectiveness of the dissemination methods on patient-centered outcomes (caregiver confidence in decision-making and perceptions of experiencing shared decision-making) as well as HU uptake and child health outcomes. Eligible children are aged 0 to 5 years, candidates for HU, and their caregiver has not made a decision about HU in the past 3 months. The trial is being conducted at 9 sites in the United States and uses a stepped-wedge design. Data will be analyzed based on the intent-to-treat principle. All participants will remain in the arm of the study to which they were randomized, regardless of whether or not they receive the assigned dissemination method. The primary endpoints are caregiver decisional uncertainty and caregiver perception of shared decision-making measured using validated tools. Data will be analyzed using a linear mixed effects regression model with a robust variance estimator and maximum likelihood estimation with observations clustered within site. The Engage-HU trial includes adaptations to increase recruitment such as tailored messaging, a relational recruitment approach, streamlined data collection, and a Stakeholder Advisory Committee. However, even with these adaptations, the first 6-months of the trial yielded lower than anticipated recruitment. Rather than terminate the trial or accept low enrollment, the research team implemented a series of recruitment strategies to address barriers including helping to improve research coordinator knowledge of the study purpose and adjusting no-show and follow-up procedures (e.g., calls to families after missed appointments and reminder calls before appointments). Site clinicians and clinic staff were provided with additional training so they could give more context about Engage-HU to caregivers and the study principal investigator led monthly "all coordinator" calls to provide support by sharing updates and experiences about successful recruitment. Implementation of these strategies resulted in triple the number of enrollments over the next 7-months compared to the previous 6-months (Table 1). Our goal in sharing this information is to provide lessons learned that can be implemented in future trials with the systematically underserved SCD population. It is also anticipated that methods described here may also inform clinical approaches to better engage caregivers of young children around critical clinical conversations, such as initiating medications like HU. Disclosures King: Magenta Therapeutics: Membership on an entity's Board of Directors or advisory committees; Bioline: Consultancy; RiverVest: Consultancy; Novimmune: Research Funding; Celgene: Consultancy; Tioma Therapuetics: Consultancy; Amphivena Therapeutics: Research Funding; WUGEN: Current equity holder in private company; Cell Works: Consultancy; Incyte: Consultancy. Smith-Whitley:Prime: Other: Education material; Celgene: Membership on an entity's Board of Directors or advisory committees; Global Blood Therapeutics: Membership on an entity's Board of Directors or advisory committees; Novartis: Membership on an entity's Board of Directors or advisory committees. Neumayr:Emmaus: Consultancy; Bayer: Consultancy; CTD Holdings: Consultancy; Pfizer: Consultancy; ApoPharma: Consultancy, Membership on an entity's Board of Directors or advisory committees; Micelle: Other: Site principal investigator; GBT: Other: Site principal investigator; PCORI: Other: site principal investigator; Novartis: Other: co-investigator; Bluebird Bio: Other: co-investigator; Sangamo Therapeutics: Other; Silarus: Other; Celgene: Other; La Jolla Pharmaceuticals: Other; Forma: Other; Imara: Other; National Heart, Lung, and Blood Institute: Other; Health Resources and Services Administration: Other; Centers for Disease Control and Prevention: Other; Seattle Children's Research: Other. Yates:Novartis: Research Funding. Thompson:Novartis: Consultancy, Honoraria, Research Funding; CRISPR/Vertex: Research Funding; BMS: Consultancy, Research Funding; Baxalta: Research Funding; Biomarin: Research Funding; bluebird bio, Inc.: Consultancy, Research Funding. </jats:sec

A colorectal cancer susceptibility new variant at 4q26 in the Spanish population identified by genome-wide association analysis

This work was partially supported by the CENIT program from the Centro Tecnológico Industrial (CEN-20091016), grants from the Spanish Institute of Health Carlos III (ADE10/00026, PI09/02444, PI12/00511, Acción Transversal de Cáncer) grants from the Fondo de Investigacion Sanitaria/FEDER (08/1276, 08/0024, PS09/02368, 11/00219, 11/00681), and by COST office through COST action BM1206. SCB is supported by contracts from the Fondo de Investigación Sanitaria (CP 03-0070). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Centro Tecnológico IndustrialInstituto de Salud Carlos IIIFondo de Investigación Sanitaria / FEDE

Engaging Caregivers and Providers of Children With Sickle Cell Anemia in Shared Decision Making for Hydroxyurea: Protocol for a Multicenter Randomized Controlled Trial

BACKGROUND: Sickle cell anemia (SCA) is a genetic blood disorder that puts children at a risk of serious medical complications, early morbidity and mortality, and high health care utilization. Until recently, hydroxyurea was the only disease-modifying treatment for this life-threatening disease and has remained the only option for children younger than 5 years. Evidence-based guidelines recommend using a shared decision-making (SDM) approach for offering hydroxyurea to children with SCA (HbSS or HbS/β0 thalassemia) aged as early as 9 months. However, the uptake remains suboptimal, likely because caregivers lack information about hydroxyurea and have concerns about its safety and potential long-term side effects. Moreover, clinicians do not routinely receive training or tools, especially those that provide medical evidence and consider caregivers' preferences and values, to facilitate a shared discussion with caregivers. OBJECTIVE: The aim of this study is to understand how best to help parents of young children with sickle cell disease and their clinicians have a shared discussion about hydroxyurea (one that considers medical evidence and parent values and preferences). METHODS: We designed our study to compare the effectiveness of two methods for disseminating hydroxyurea guidelines to facilitate SDM: a clinician pocket guide (ie, usual care) and a clinician hydroxyurea SDM toolkit (H-SDM toolkit). Our primary outcomes are caregiver reports of decisional uncertainty and knowledge of hydroxyurea. The study also assesses the number of children (aged 0-5 years) who were offered and prescribed hydroxyurea and the resultant health outcomes. RESULTS: The Ethics Committee of the Cincinnati Children's Hospital Medical Center approved this study in November 2017. As of February 2021, we have enrolled 120 caregiver participants. CONCLUSIONS: The long-term objective of this study is to improve the quality of care for children with SCA. Using multicomponent dissemination methods developed in partnership with key stakeholders and designed to address barriers to high-quality care, caregivers of patients with SCA can make informed and shared decisions about their health. TRIAL REGISTRATION: ClinicalTrials.gov NCT03442114; https://clinicaltrials.gov/ct2/show/NCT03442114. INTERNATIONAL REGISTERED REPORT IDENTIFIER (IRRID): DERR1-10.2196/27650

The membrane-spanning 4-domains, subfamily A (MS4A) gene cluster contains a common variant associated with Alzheimer's disease

Background\ud In order to identify novel loci associated with Alzheimer's disease (AD), we conducted a genome-wide association study (GWAS) in the Spanish population.\ud \ud Methods\ud We genotyped 1,128 individuals using the Affymetrix Nsp I 250K chip. A sample of 327 sporadic AD patients and 801 controls with unknown cognitive status from the Spanish general population were included in our initial study. To increase the power of the study, we combined our results with those of four other public GWAS datasets by applying identical quality control filters and the same imputation methods, which were then analyzed with a global meta-GWAS. A replication sample with 2,200 sporadic AD patients and 2,301 controls was genotyped to confirm our GWAS findings.\ud \ud Results\ud Meta-analysis of our data and independent replication datasets allowed us to confirm a novel genome-wide significant association of AD with the membrane-spanning 4-domains subfamily A (MS4A) gene cluster (rs1562990, P = 4.40E-11, odds ratio = 0.88, 95% confidence interval 0.85 to 0.91, n = 10,181 cases and 14,341 controls).\ud \ud Conclusions\ud Our results underscore the importance of international efforts combining GWAS datasets to isolate genetic loci for complex diseases

International Comparative Studies In Mathematics: Lessons For Improving students’ Learning

Comparing is one of the most basic intellectual activities. We consciously make comparisons to understand where we stand, both in relation to others as well as to our own past experiences. There has been a long history of international comparative studies in education (Alexander 2000). Especially in the past several decades, many international comparative studies of mathematics have been conducted, either to examine differences in mathematical proficiency and dispositions among students from various countries or to understand the possible influence on the observed differences of various factors such as curriculum, teacher preparation, quality of classroom instruction, and parental involvement. Some of these studies are large-scale, and others are small-scale in-depth analyses from cognitive or social perspectives. These international comparative studies in mathematics are valuable because they provide a large body of knowledge showing how students do mathematics in the context of the world’s varied educational institutions. In addition, they examine the cultural and educational factors that influence the learning of mathematics.published_or_final_versio

Deletion of iRhom2 protects against diet-induced obesity by increasing thermogenesis

Objective: Obesity is the result of positive energy balance. It can be caused by excessive energy consumption but also by decreased energy dissipation, which occurs under several conditions including when the development or activation of brown adipose tissue (BAT) is impaired. Here we evaluated whether iRhom2, the essential cofactor for the Tumour Necrosis Factor (TNF) sheddase ADAM17/TACE, plays a role in the pathophysiology of metabolic syndrome.Methods: We challenged WT versus iRhom2 KO mice to positive energy balance by chronic exposure to a high fat diet and then compared their metabolic phenotypes. We also carried out ex vivo assays with primary and immortalized mouse brown adipocytes to establish the autonomy of the effect of loss of iRhom2 on thermogenesis and respiration.Results: Deletion of iRhom2 protected mice from weight gain, dyslipidemia, adipose tissue inflammation, and hepatic steatosis and improved insulin sensitivity when challenged by a high fat diet. Crucially, the loss of iRhom2 promotes thermogenesis via BAT activation and beige adipocyte recruitment, enabling iRhom2 KO mice to dissipate excess energy more efficiently than WT animals. This effect on enhanced thermogenesis is cell-autonomous in brown adipocytes as iRhom2 KOs exhibit elevated UCP1 levels and increased mitochondrial proton leak.Conclusion: Our data suggest that iRhom2 is a negative regulator of thermogenesis and plays a role in the control of adipose tissue homeostasis during metabolic disease. (C) 2019 The Authors. Published by Elsevier GmbH