Secondary school students’ understanding of sampling variability

PID2019-105601GB-I00/AEI/10.13039/501100011033, Research group FQM-126

Institutional and personal meaning of order statistics

El objetivo de este trabajo es caracterizar el significado institucional de los estadísticos de orden en la Educación Secundaria (ESO y Bachillerato), identificando los objetos matemáticos elementales involucrados. Para ello presentamos un análisis semiótico de los estadísticos de orden, utilizando el Enfoque Ontosemiótico del Conocimiento y la Instrucción matemáticos (EOS), que muestra su complejidad, incluso limitándonos a la estadística descriptiva. También resumimos las dificultades descritas, respecto a cada uno de los tipos de objetos primarios identificados en el EOS, con el fin de caracterizar los posibles significados personales que los estudiantes pueden asignar a los mismos. Esta información puede ser útil para identificar estas dificultades en los estudiantes y ayudarles a superarlas.The aim of this work is to characterize the institutional meaning of order statistics in Secondary Education (ESO and High School), by identifying the elementary mathematical objects required in the work with the same. To achieve this goal, we present a semiotic approach using Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSA), which reveals the complexity of its meaning, even in descriptive analysis. We also summarize the main difficulties identified in previous research to characterize the personal meaning that students may assign to these statistics. This information is useful in order to identify these difficulties and help students to overcome them

Conhecimento didático-matemático sobre a distribuição da média amostral de professores bacharéis estagiários

[Objetivo] El objetivo del trabajo es evaluar el conocimiento didáctico-matemático de profesores españoles en formación sobre la distribución de la media muestral, específicamente, el conocimiento común del contenido, y las facetas epistémicas y cognitiva del conocimiento didáctico. [Metodología] Se pidió a una muestra de futuros profesores resolver un problema propuesto a los estudiantes en las pruebas de acceso a la universidad, además de resolverlo debían identificar los conceptos, propiedades y procedimientos requeridos para su resolución y los errores previsibles de los estudiantes en este proceso. [Resultados] Los resultados de la evaluación fueron muy buenos en lo que se refiere al conocimiento matemático común del tema, aunque se observaron algunos errores, como la confusión de la distribución de la variable analizada en la población con la distribución muestral del estadístico. Los participantes mostraron un desempeño razonable de análisis de los objetos matemáticos requeridos (conceptos, procedimientos y propiedades) para solucionar la tarea propuesta. Fue menor la competencia de análisis de los posibles errores que podrían cometer los estudiantes en la resolución de la tarea. [Conclusiones] El estudio revela puntos de mejora en la formación de los futuros profesores sobre la distribución de la media muestral, un contenido relevante para la posterior comprensión del resto de la inferencia. Dicha formación debiera enfatizar la diferencia entre las tres distribuciones de probabilidad que aparecen en el muestreo y la diferencia entre estadístico y parámetro, pues el futuro profesorado no reconoce la posibilidad de errores de este tipo en su alumnado.[Objective] The aim of this study is to evaluate the didactic-mathematical knowledge of prospective Spanish teachers about the sampling distribution of the mean – specifically, basic knowledge about content, as well as epistemic and cognitive aspects of didactic knowledge. [Methodology] A sample of prospective teachers were asked to solve a problem presented to students in the university’s entrance exams, to identify the concepts, properties and procedures required for its solution, and to describe the foreseeable errors of the students in this process. [Results] The results obtained showed very good levels of common mathematical knowledge, although some errors were observed, such as confusing population distributions with sampling distributions. The participants were reasonably competent in analyzing the mathematical objects (concepts, procedures and properties) required to solve the proposed task, but the level of competence in identifying possible student errors in solving the task was lower. [Conclusions] The study identifies areas for improvement in the training of prospective teachers about the sampling distribution of the mean, which should be well understood when making inferences. Such training should emphasize the difference between the three probability sampling distributions and the difference between statistics and parameters, since prospective teachers do not recognize the possibility of this type of error by their students.[Objetivo] O objetivo do trabalho é avaliar o conhecimento didático-matemático dos professores estagiários espanhóis sobre a distribuição da média amostral, especificamente, o conhecimento comum do conteúdo, e as facetas epistêmicas e cognitivas do conhecimento didático. [Metodologia] Foi solicitado a uma amostra de futuros professores resolver um problema proposto aos alunos nas provas de vestibular e, além de resolvê-lo, eles tiveram que identificar os conceitos, as propriedades e os procedimentos necessários para sua resolução e os erros previsíveis dos alunos neste processo.[Resultados] Os resultados da avaliação foram muito bons em termos do conhecimento matemático comum do assunto, embora alguns erros tenham sido observados, tais como a confusão da distribuição da variável analisada na população com a distribuição amostral da estatística. Os participantes mostraram um desempenho razoável na análise dos objetos matemáticos necessários (conceitos, procedimentos e propriedades) para resolver a tarefa proposta. Havia menos competência na análise dos possíveis erros que os estudantes poderiam cometer para resolver a tarefa. [Conclusões] O estudo revela pontos de melhoria na capacitação de futuros professores sobre a distribuição da média amostral, um conteúdo relevante para o entendimento subsequente do resto da inferência. Essa capacitação deve enfatizar a diferença entre as três distribuições de probabilidade que aparecem na amostragem e a diferença entre estatístico e parâmetro, pois os futuros professores não reconhecem a possibilidade de tais erros em seus alunos

Collective Effervescence, Self-Transcendence, and Gender Differences in Social Well-Being During 8 March Demonstrations

8 March (8M), now known as International Women’s Day, is a day for feminist claims where demonstrations are organized in over 150 countries, with the participation of millions of women all around the world. These demonstrations can be viewed as collective rituals and thus focus attention on the processes that facilitate different psychosocial effects. This work aims to explore the mechanisms (i.e., behavioral and attentional synchrony, perceived emotional synchrony, and positive and transcendent emotions) involved in participation in the demonstrations of 8 March 2020, collective and ritualized feminist actions, and their correlates associated with personal well-being (i.e., affective well-being and beliefs of personal growth) and collective well-being (i.e., social integration variables: situated identity, solidarity and fusion), collective efficacy and collective growth, and behavioral intention to support the fight for women’s rights. To this end, a cross-cultural study was conducted with the participation of 2,854 people (age 18–79; M = 30.55; SD = 11.66) from countries in Latin America (Mexico, Chile, Argentina, Brazil, Peru, Colombia, and Ecuador) and Europe (Spain and Portugal), with a retrospective correlational cross-sectional design and a convenience sample. Participants were divided between demonstration participants (n = 1,271; 94.0% female) and non-demonstrators or followers who monitored participants through the media and social networks (n = 1,583; 75.87% female). Compared with non-demonstrators and with males, female and non-binary gender respondents had greater scores in mechanisms and criterion variables. Further random-effects model meta-analyses revealed that the perceived emotional synchrony was consistently associated with more proximal mechanisms, as well as with criterion variables. Finally, sequential moderation analyses showed that proposed mechanisms successfully mediated the effects of participation on every criterion variable. These results indicate that participation in 8M marches and demonstrations can be analyzed through the literature on collective rituals. As such, collective participation implies positive outcomes both individually and collectively, which are further reinforced through key psychological mechanisms, in line with a Durkheimian approach to collective rituals.Fil: Zumeta, Larraitz N.. Universidad del País Vasco; EspañaFil: Castro Abril, Pablo. Universidad del País Vasco; EspañaFil: Méndez, Lander. Universidad del País Vasco; EspañaFil: Pizarro, José J.. Universidad del País Vasco; EspañaFil: Włodarczyk, Anna. Universidad Católica del Norte; ChileFil: Basabe, Nekane. Universidad del País Vasco; EspañaFil: Navarro Carrillo, Ginés. Universidad de Jaén; EspañaFil: Padoan De Luca, Sonia. Universidad del País Vasco; EspañaFil: da Costa, Silvia. Universidad del País Vasco; EspañaFil: Alonso Arbiol, Itziar. Universidad del País Vasco; EspañaFil: Torres Gómez, Bárbara. Universidad del País Vasco; EspañaFil: Cakal, Huseyin. Keele University; Reino UnidoFil: Delfino, Gisela Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires"; ArgentinaFil: Techio, Elza M.. Universidade Federal da Bahia; BrasilFil: Alzugaray, Carolina. Universidad de Santo Tomas; ChileFil: Bilbao, Marian. Universidad Alberto Hurtado; ChileFil: Villagrán, Loreto. Universidad de Concepción; ChileFil: López López, Wilson. Pontificia Universidad Javeriana; ColombiaFil: Ruiz Pérez, José Ignacio. Universidad Nacional de Colombia; ColombiaFil: Cedeño, Cynthia C.. Universidad Politécnica Salesiana; EcuadorFil: Reyes Valenzuela, Carlos. Universidad Andina Simon Bolivar - Sede Ecuador.; EcuadorFil: Alfaro Beracoechea, Laura. Universidad de Guadalajara; MéxicoFil: Contreras Ibáñez, Carlos César. Universidad Autónoma Metropolitana; MéxicoFil: Ibarra, Manuel Leonardo. Universidad Autónoma del Estado de México; MéxicoFil: Reyes Sosa, Hiram. Universidad Autonoma de Coahuila; MéxicoFil: Cueto, Rosa María. Pontificia Universidad Católica de Perú; PerúFil: Carvalho, Catarina L.. Universidad de Porto; PortugalFil: Pinto, Isabel R.. Universidad de Porto; Portuga

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to <90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], >300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase 1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age  6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score  652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc = 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N = 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in Asia and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701

The Comet Interceptor Mission

Here we describe the novel, multi-point Comet Interceptor mission. It is dedicated to the exploration of a little-processed long-period comet, possibly entering the inner Solar System for the first time, or to encounter an interstellar object originating at another star. The objectives of the mission are to address the following questions: What are the surface composition, shape, morphology, and structure of the target object? What is the composition of the gas and dust in the coma, its connection to the nucleus, and the nature of its interaction with the solar wind? The mission was proposed to the European Space Agency in 2018, and formally adopted by the agency in June 2022, for launch in 2029 together with the Ariel mission. Comet Interceptor will take advantage of the opportunity presented by ESA’s F-Class call for fast, flexible, low-cost missions to which it was proposed. The call required a launch to a halo orbit around the Sun-Earth L2 point. The mission can take advantage of this placement to wait for the discovery of a suitable comet reachable with its minimum ΔV capability of 600 ms−1. Comet Interceptor will be unique in encountering and studying, at a nominal closest approach distance of 1000 km, a comet that represents a near-pristine sample of material from the formation of the Solar System. It will also add a capability that no previous cometary mission has had, which is to deploy two sub-probes – B1, provided by the Japanese space agency, JAXA, and B2 – that will follow different trajectories through the coma. While the main probe passes at a nominal 1000 km distance, probes B1 and B2 will follow different chords through the coma at distances of 850 km and 400 km, respectively. The result will be unique, simultaneous, spatially resolved information of the 3-dimensional properties of the target comet and its interaction with the space environment. We present the mission’s science background leading to these objectives, as well as an overview of the scientific instruments, mission design, and schedule

Prospective Mathematics Teachers Understanding of Classical and Frequentist Probability

Strengthening the teaching of probability requires an adequate training of prospective teachers, which should be based on the prior assessment of their knowledge. Consequently, the aim of this study was to analyse how 139 prospective Spanish mathematics teachers relate the classical and frequentist approaches to probability. To achieve this goal, content analysis was used to categorize the prospective teachers’ answers to a questionnaire with open-ended tasks in which they had to estimate and justify the composition of an urn, basing their answers on the results of 1000 extractions from the urn. Most of the sample proposed an urn model consistent with the data provided; however, the percentage that adequately justified the construction was lower. Although the majority of the sample correctly calculated the probability of an event in a new extraction and chose the urn giving the highest probability, a large proportion of the sample forgot the previously constructed urn model, using only the frequency data. Difficulties, such as equiprobability bias or not perceiving independence of trials in replacement sampling, were also observed for a small part of the sample. These results should be considered in the organisation of probabilistic training for prospective teachers.PID2019-105601GB-I00/AEI/10.13039/501100011033 (Ministerio de Ciencia e Innovación)FQM-126 (Junta de Andalucía, Spain

Collective effervescence, self-transcendence, and gender differences in social well-being during 8-M demonstrations

8 March (8M), now known as International Women’s Day, is a day for feminist claims where demonstrations are organized in over 150 countries, with the participation of millions of women all around the world. These demonstrations can be viewed as collective rituals and thus focus attention on the processes that facilitate different psychosocial effects. This work aims to explore the mechanisms (i.e., behavioral and attentional synchrony, perceived emotional synchrony, and positive and transcendent emotions) involved in participation in the demonstrations of 8 March 2020, collective and ritualized feminist actions, and their correlates associated with personal well-being (i.e., affective well-being and beliefs of personal growth) and collective well-being (i.e., social integration variables: situated identity, solidarity and fusion), collective efficacy and collective growth, and behavioral intention to support the fight for women’s rights. To this end, a cross-cultural study was conducted with the participation of 2,854 people (age 18–79; M = 30.55; SD = 11.66) from countries in Latin America (Mexico, Chile, Argentina, Brazil, Peru, Colombia, and Ecuador) and Europe (Spain and Portugal), with a retrospective correlational cross-sectional design and a convenience sample. Participants were divided between demonstration participants (n = 1,271; 94.0% female) and non-demonstrators or followers who monitored participants through the media and social networks (n = 1,583; 75.87% female). Compared with nondemonstrators and with males, female and non-binary gender respondents had greater scores in mechanisms and criterion variables. Further random-effects model metaanalyses revealed that the perceived emotional synchrony was consistently associated with more proximal mechanisms, as well as with criterion variables. Finally, sequentialmoderation analyses showed that proposed mechanisms successfully mediated the effects of participation on every criterion variable. These results indicate that participation in 8M marches and demonstrations can be analyzed through the literature on collectiverituals. As such, collective participation implies positive outcomes both individually and collectively, which are further reinforced through key psychological mechanisms, in line with a Durkheimian approach to collective rituals.The Spanish Ministry of the Economy supported this research (under Grants PSI2017-84145-P and Predoctoral Research Grant PRE2018-083265 to PC-A), as well as the Basque Government (under Grant IT-1187-19), the University of the Basque Country (under Grant IT-666-13, Postdoctoral Research Grant DOCREC20/23 to JP and ESPDOC18/33 to LZ), and FONDECYT Initiation 11190980 granted to AW