James J. Kaput (1942–2005) imagineer and futurologist of mathematics education

Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his ‘big ideas’ as he lived through the most amazing innovations in technology that have changed our lives more in a generation than in many centuries before. His vision continues as is exemplified by the collected papers in this tribute to his life and work

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

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

Climate forecasts in disaster management: Red Cross flood operations in West Africa, 2018

In 2008, the International Federation of Red Cross and Red Crescent Societies (IFRC) used a seasonal forecast for West Africa for the first time to implement an Early Warning, Early Action strategy for enhanced flood preparedness and response. Interviews with disaster managers suggest that this approach improved their capacity and response. Relief supplies reached flood victims within days, as opposed to weeks in previous years, thereby preventing further loss of life, illness, and setbacks to livelihoods, as well as augmenting the efficiency of resource use. This case demonstrates the potential benefits to be realised from the use of medium-to-long-range forecasts in disaster management, especially in the context of potential increases in extreme weather and climate-related events due to climate variability and change. However, harnessing the full potential of these forecasts will require continued effort and collaboration among disaster managers, climate service providers, and major humanitarian donors

Lymphatic vasculature mediates macrophage reverse cholesterol transport in mice

Reverse cholesterol transport (RCT) refers to the mobilization of cholesterol on HDL particles (HDL-C) from extravascular tissues to plasma, ultimately for fecal excretion. Little is known about how HDL-C leaves peripheral tissues to reach plasma. We first used 2 models of disrupted lymphatic drainage from skin — 1 surgical and the other genetic — to quantitatively track RCT following injection of [3H]-cholesterol–loaded macrophages upstream of blocked or absent lymphatic vessels. Macrophage RCT was markedly impaired in both models, even at sites with a leaky vasculature. Inhibited RCT was downstream of cholesterol efflux from macrophages, since macrophage efflux of a fluorescent cholesterol analog (BODIPY-cholesterol) was not altered by impaired lymphatic drainage. We next addressed whether RCT was mediated by lymphatic vessels from the aortic wall by loading the aortae of donor atherosclerotic Apoe-deficient mice with [2H]6-labeled cholesterol and surgically transplanting these aortae into recipient Apoe-deficient mice that were treated with anti-VEGFR3 antibody to block lymphatic regrowth or with control antibody to allow such regrowth. [2H]-Cholesterol was retained in aortae of anti–VEGFR3-treated mice. Thus, the lymphatic vessel route is critical for RCT from multiple tissues, including the aortic wall. These results suggest that supporting lymphatic transport function may facilitate cholesterol clearance in therapies aimed at reversing atherosclerosis

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

Estudio sobre las praxeologías que se proponen estudiaren un curso universitario de cálculo

En este trabajo se analizan las organizaciones que se proponen estudiar en un curso de cálculo universitario relativas a las nociones de límite y continuidad funcional. Desde la Teoría Antropológica de lo Didáctico se analizó el material editado por lo profesores destinado a estudiantes universitarios. Los principales resultados indican que se propone el estudio de tareas aisladas, que no conducen a la elaboración y validación de elementos tecnológicos. De esta manera, se evidencia la organización de los saberes en dos niveles: uno teórico y otro práctico, donde este último no tiene incidencia para la conformación del primero. Esto genera una inadecuada interpretación del conocimiento científico, reduciendo su estudio a organizaciones matemáticas desarticuladas

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer