Introducing the concept of infinite series: Preliminary analyses of curriculum content and pedagogical practice

Introducing the concept of infinite series: preliminary analyses of curriculum content and pedagogical practice

Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests

Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions

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 gut microbiome in konzo.

Konzo, a distinct upper motor neuron disease associated with a cyanogenic diet and chronic malnutrition, predominately affects children and women of childbearing age in sub-Saharan Africa. While the exact biological mechanisms that cause this disease have largely remained elusive, host-genetics and environmental components such as the gut microbiome have been implicated. Using a large study population of 180 individuals from the Democratic Republic of the Congo, where konzo is most frequent, we investigate how the structure of the gut microbiome varied across geographical contexts, as well as provide the first insight into the gut flora of children affected with this debilitating disease using shotgun metagenomic sequencing. Our findings indicate that the gut microbiome structure is highly variable depending on region of sampling, but most interestingly, we identify unique enrichments of bacterial species and functional pathways that potentially modulate the susceptibility of konzo in prone regions of the Congo

Investigating the secondary–tertiary transition

International audienceThe secondary–tertiary transition has been studied in a great amount of research in mathematics education, adopting different focuses and theoretical approaches. I present here how these focuses led the authors to identify and study different students' difficulties and to develop different means of didactical action. Individual, social, but also institutional phenomena are considered with different perspectives. Each perspective yields a particular view of transition. The association and comparison of these views makes it possible to build an organized outline of this complex object, combining several kinds of ruptures and long-term evolutions