Proof in dynamic geometry environments

This article suggests that there is a range of evidence that working with dynamic geometry software affords students possibilities of access to theoretical mathematics, something that can be particularly elusive with other pedagogical tools. Yet the paper concludes that further research into the use dynamic geometry software to support the development of students’ mathematical thinking could usefully focus on the nature of the tasks students tackle, the form of teacher input, and the role of the classroom environment and culture

On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications

In a recent paper (J.R. Morris, Quant. Stud. Math. Found. 2 (2015) 359), an inhomogeneous compactification of the extra dimension of a five-dimensional Kaluza-Klein metric has been shown to generate a position-dependent mass (PDM) in the corresponding four-dimensional system. As an application of this dimensional reduction mechanism, a specific static dilatonic scalar field has been connected with a PDM Lagrangian describing a well-known nonlinear PDM oscillator. Here we present more instances of this construction that lead to PDM systems with radial symmetry, and the properties of their corresponding inhomogeneous extra dimensions are compared with the ones in the nonlinear oscillator model. Moreover, it is also shown how the compactification introduced in this type of models can alternatively be interpreted as a novel mechanism for the dynamical generation of curvature.Comment: 11 pages, 6 figures. New figures. Updated to match the published version in Physics Letters

Perspectiva de la Investigación en Didáctica de las Matemáticas

La investigación en Didáctica de las Matemáticas estudia los diferentes factores que influyen en la comprensión y el aprendizaje de las matemáticas por individuos de cualquier edad y nivel educativo. Esto supone un amplio campo de trabajo que incluye factores relacionados con los propios estudiantes, con los profesores, con el contexto de las aulas, y con el entorno social, cultural y político de los estudiantes. En este artículo se hace una descripción global de la actividad investigadora actual y una descripción más detallada de algunas áreas de investigación específicas.Research in Mathematics Education deals with the diversity of factors influencing the understanding and learning of mathematics by subjects of any age and educational level. This means that research in Mathematics Education embraces a wide work area including factors related to students themselves, to teachers, to the classroom context, and to students’ social, cultural and political environments. In this paper we make a global review of current research, and make more detailed reviews of some specific research areas

Introducción al seminario I sobre enseñanza y aprendizaje de la geometría

Entre las líneas más destacadas de la agenda de investigación en didáctica de la geometría se encuentran las que tienen que ver con el aprendizaje del razonamiento deductivo matemático, el aprendizaje de conceptos geométricos, y el uso de entornos tecnológicos para la enseñanza y el aprendizaje de la geometría. Estos son los temas de las tres ponencias que forman el seminario

Reflexiones sobre la enseñanza de la geometría en los niveles de primaria y secundaria

En este texto presento introducciones a los principales elementos didácticos centrales de la enseñanza de la geometría en los niveles educativos. El modelo de van Hiele es el marco más efectivo para organizar la enseñanza de la geometría en los diferentes niveles educativos. Me centraré en uno de sus componentes, las fases de aprendizaje, que sugiere cómo organizar los contenidos de las secuencias de enseñanza de las matemáticas escolares. A continuación, prestaré atención a una propuesta más específica, centrada en describir el aprendizaje de conceptos geométricos, basada en la distinción entre las imágenes conceptuales y las definiciones conceptuales, para mostrar el papel crítico que deben jugar los ejemplos. Por último, reflexionaré sobre la necesidad de que los profesores tengan en cuenta las representaciones gráficas, físicas y mentales, utilizadas en la enseñanza y el aprendizaje de la geometría. Describiré los principales elementos que forman parte de los procesos y destrezas de visualización presentes en el trabajo con elementos geométricos

Las representaciones planas de cuerpos 3-dimensionales en la enseñanza de la geometría espacial

En este artículo se presentan algunas reflexiones sobre la importancia de utilizar representaciones planas de cuerpos geométricos espaciales adecuadas a los estudiantes de diferentes edades. Se analizan diversas formas usuales de representación plana de objetos 3-dimensionales y, tomando como base los resultados de algunas investigaciones, se describen varias dificultades observadas cuando los estudiantes dibujan o interpretan representaciones planas de sólidos, incluyéndose algunos ejemplos de respuestas de los estudiantes. También se hacen sugerencias a los profesores acerca de la capacidad de los estudiantes de diversos grados para utilizar las distintas representaciones y se plantean algunos ejercicios que pueden proponerse para mejorar la habilidad de los estudiantes para dibujar y leer representaciones planas de cuerpos espaciales

Acerca del postmodernismo en la música académica y la obra del compositor cubano Leo Brouwer

Una indagación teórico-filosófica sobre el fenómeno del postmodernismo en la Música Académica Occidental. Un análisis del compositor cubano Leo Brouwer a partir de los elementos postmodernos presentes en su obra

Mutant Huntingtin toxicity modifiers revealed by a spatiotemporal proteomic profiling

Huntington's disease (HD) is a genetic hereditary disorder characterized by aggregation of polyQ-expanded mutant Huntingtin (mHTT) protein and progressive neurodegeneration within different brain regions, but specially in cortex and striatum. The pathology is associated with motor, cognitive and psychiatric symptoms. A hallmark of HD is the aggregation of polyglutamine-expanded (polyQ) huntingtin from soluble oligomers to inclusion bodies. Still nowadays, the character of these aggregates and the transition to the neuronal functional disorder, is poorly understood. In this thesis, the progression of the disease was assessed in a spatiotemporal manner in the R6/2 mice, a HD model, in order to find molecular signatures that could lead first, to a more detailed description of the disorder and second, to the elucidation of possible protein candidates that eventually have the ability of modify HD-related toxicity. Initially, it was approached by mass spectrometry-based quantitative proteomics to break down the spatiotemporal mechanisms of degeneration in HD. The formation of insoluble inclusion bodies throughout the disease progression correlated with the profound remodeling of the soluble proteome. The complexity in protein numbers of the aggregates was detailed through a quantitative characterization. This deep analysis unraveled the dependency of the aggregates' protein sequestration on specific biophysical features and sequence domains. Based on the proteomic data and applying different criteria, a follow-up study of some proteins was carried out. Overexpression of a selected group of the sequestered proteins improved the cellular viability in a cell line model of HD and reduced in most cases the inclusion body size. The effect of most of those proteins was specific to a mHTT-toxicity induced context. These results suggest that widespread loss of function contributes to aggregate-mediated toxicity. The strong effect of one of the protein candidates in the viability assays, Hepatome-derived grow factor (HDGF), lead to a closer examination. The effect of the protein was confirmed in primary neurons, in both transient transfection and in long-term viral transduction. Overexpression of HDGF in the striatum of R6/2 mice significantly rescued their exploratory behavior and ameliorated their clasping phenotype. In summary, the thesis represents a multi-disciplinary study in the R6/2 mouse model, spanning from proteomics to in vivo overexpression of a validated sequestered protein, which appears to be a potential therapeutic mHTT-toxicity modifier. Collectively, the study provides an integrative approach to solve HD molecular mechanisms and contributes to fill in the gap between identification of disease-associated pathways and their corresponding phenotypes

Quality evaluation of cheddar cheese containing Gamma-Oryzanol

Health benefits from consuming rice bran oil (RBO) have been extensively studied in humans. RBO has been shown to decrease cholesterol absorption by inhibiting the oxidation of the LDL-cholesterol. Gamma-Oryzanol is one of the RBO components that possess antioxidative properties; it is a polyphenolic compound resembling tocopherol (vitamin E), which is another component of RBO. There are evidences that oryzanol has potential applications for enhancing shelf-life of foods containing fats processed at a high temperature, decreasing the total cholesterol, LDL-cholesterol and triglyceride levels in plasma lipids, and healing ulcers. In order to take advantage of the health benefits of oryzanol, food products fortified with oryzanol should be developed and characterized. Cheddar cheese containing Gamma-Oryzanol was developed, and the effects of oryzanol on cheese quality during ripening process were studied. Cheese was stored for 5 months and drawn every month for quality evaluation of color, texture, microbial growth, aroma development, bacterial identification by polymerase chain reaction, oryzanol retention, moisture content and free fatty acid profile. The consumer acceptance was evaluated after 5 months of maturation. The results indicated that by adding Gamma-Oryzanol to cheddar cheese changes occurred in the quality, but, they were not significant when stored for up to 4 months, and the Gamma-Oryzanol was well retained. Consumers were able to differentiate the cheddar cheese containing Gamma-Oryzanol from the control containing no Gamma-Oryzanol. Overall appearance, texture, taste and hardness were the most discriminatory sensory attributes. There was a significant positive increase 0.13 to 0.30 times higher in the purchase intent of cheddar cheese containing Gamma-Oryzanol after consumers had been informed about the health benefits of oryzanol. Overall liking was the attribute critical to purchase intent and the most important attribute that changed the acceptability of the cheese. Consumers preferred the cheese with Gamma-Oryzanol less than the control but were willing to buy it and compromise the overall liking of cheese merely to get the health benefits of the product. Further studies need to be done to determine the direct effects of cheddar cheese containing Gamma-Oryzanol in human health, and to optimize the homogenization and fortification of Gamma-Oryzanol when incorporated in cheese products