Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis

The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students’ responses, we describe students’ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis

Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space

In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher

A small erythropoietin derived non-hematopoietic peptide reduces cardiac inflammation, attenuates age associated declines in heart function and prolongs healthspan

BackgroundAging is associated with increased levels of reactive oxygen species and inflammation that disrupt proteostasis and mitochondrial function and leads to organism-wide frailty later in life. ARA290 (cibinetide), an 11-aa non-hematopoietic peptide sequence within the cardioprotective domain of erythropoietin, mediates tissue protection by reducing inflammation and fibrosis. Age-associated cardiac inflammation is linked to structural and functional changes in the heart, including mitochondrial dysfunction, impaired proteostasis, hypertrophic cardiac remodeling, and contractile dysfunction. Can ARA290 ameliorate these age-associated cardiac changes and the severity of frailty in advanced age?MethodsWe conducted an integrated longitudinal (n = 48) and cross-sectional (n = 144) 15 months randomized controlled trial in which 18-month-old Fischer 344 x Brown Norway rats were randomly assigned to either receive chronic ARA290 treatment or saline. Serial echocardiography, tail blood pressure and body weight were evaluated repeatedly at 4-month intervals. A frailty index was calculated at the final timepoint (33 months of age). Tissues were harvested at 4-month intervals to define inflammatory markers and left ventricular tissue remodeling. Mitochondrial and myocardial cell health was assessed in isolated left ventricular myocytes. Kaplan–Meier survival curves were established. Mixed ANOVA tests and linear mixed regression analysis were employed to determine the effects of age, treatment, and age-treatment interactions.ResultsChronic ARA290 treatment mitigated age-related increases in the cardiac non-myocyte to myocyte ratio, infiltrating leukocytes and monocytes, pro-inflammatory cytokines, total NF-κB, and p-NF-κB. Additionally, ARA290 treatment enhanced cardiomyocyte autophagy flux and reduced cellular accumulation of lipofuscin. The cardiomyocyte mitochondrial permeability transition pore response to oxidant stress was desensitized following chronic ARA290 treatment. Concurrently, ARA290 significantly blunted the age-associated elevation in blood pressure and preserved the LV ejection fraction. Finally, ARA290 preserved body weight and significantly reduced other markers of organism-wide frailty at the end of life.ConclusionAdministration of ARA290 reduces cell and tissue inflammation, mitigates structural and functional changes within the cardiovascular system leading to amelioration of frailty and preserved healthspan

Estudio basal de prevalencia de sífilis y VIH y comportamientos asociados en población privada de libertad, Perú 1999

Objetivos: Estimar la prevalencia de sífilis y VIH e identificar los comportamientos de riesgo asociados en personas privadas de libertad (PPL). Materiales y métodos: Estudio transversal realizado durante el año 1999 en 22 establecimientos penitenciarios peruanos. Se realizó RPR para la detección de sífilis (datos ligados) y ELISA para tamizaje de VIH (datos no ligados), confirmándose con IFI o Western Blot. Se realizó una encuesta estructurada y se analizaron los datos mediante los programas SPSS 9,0 y AMOS 4. Resultados: Participaron 6 963 PPL. La prevalencia de VIH fue 1,1% y de sífilis 4,1%. Los comportamientos de riesgo asociados a VIH más significativos fueron: consumo de drogas (OR:2,7), infecciones de transmisión sexual (OR: 2,3), relaciones sexuales entre hombres (OR: 2,2), uso de cocaína (OR: 2,1), úlcera genital (OR: 2,1), haber sido encarcelado previamente (OR: 2) y tener tatuajes (OR: 1,99). Mientras los asociados a sífilis fueron: tener relaciones sexuales entre hombres OR: (2,8), infecciones de transmisión sexual (OR: 2,4), úlcera genital (OR: 1,8), haber tenido relaciones sexuales con trabajadora sexual (OR: 1,5) y tener más de dos parejas sexuales (OR: 1,5). Utilizando un modelo de ecuaciones estructurales se asoció VIH con el reporte de tener tatuaje, más de dos parejas sexuales, más de un encarcelamiento previo y úlcera genital. Conclusiones: Se encontraron importantes valores de prevalencia de VIH y sífilis en este grupo de personas, siendo necesario continuar realizando estudios similares que nos permitan cononocer las tendencias (vigilancia de segunda generación) y conocer el impacto de posibles intervenciones