IMPACT OF EXPLICIT PRESENTATION OF SLOPES IN THREE DIMENSIONS ON STUDENTS’ UNDERSTANDING OF DERIVATIVES IN MULTIVARIABLE CALCULUS

In two dimensions (2D), representations associated with slopes are seen in numerous forms before representations associated with derivatives are presented. These include the slope between two points and the constant slope of a linear function of a single variable. In almost all multivariable calculus textbooks, however, the first discussion of slopes in three dimensions (3D) is seen with the introduction of partial derivatives. The nature of the discussions indicates that authors seem to assume that students are able to naturally extend the concept of a 2D slope to 3D and correspondingly it is not necessary to explicitly present slopes in 3D. This article presents results comparing students that do not explicitly discuss slopes in 3D with students that explicitly discuss slopes in 3D as a precursor to discussing derivatives in 3D. The results indicate that students may, in fact, have significant difficulty extending the concept of a 2D slope to a 3D slope. And that the explicit presentation of slopes in 3D as a precursor to the presentation of derivatives in 3D may significantly improve student comprehension of topics of differentiation in multivariable calculus.

     

Smithsonian Folkways Recordings: The Role of Music in Breaching the Barriers of the Box

Smithsonian Folkways Recordings is the nonprofit record label of the Smithsonian Institution, the United States national museum. Folkways pairs with the Smithsonian's annual Folklife Festival in honoring and bringing to public attention the keepers of intangible cultural heritage traditions from many parts of the world. At the Folklife Festival, which takes place on the National Mall in Washington, D.C. each summer, the culture bearers speak for themselves in a presentational environment designed to promote interaction among the participants and audience members. In 2011, Folkways recordings of regional music from Colombia sparked an entire Folklife Festival program.     

Two decades and little change: British Asians,football and calls for action

Only ten British Asian professional footballers are competing in England out of approximately 4000 despite there being a population of 3.6 million in England and Wales. Just six British Asian footballers between the ages of 16 to 18 years old were attached to the 72 Football League academies in 2009 out of over 1300 players. There is only one British Asian coach out of the 522 senior football coaches in England. These figures speak volumes and are the reason why academics, campaign groups and key stakeholders have investigated, and attempted to combat, the British Asian football exclusion. This work will offer a detailed academic review of over 20 years of research in this field before adding new empirical data. It critically analyses several reform strategies that have been created by key stakeholders. Finally, I will present various recommendations for reform which are borne out of a decade of primary research.     

You’ll never watch alone: media and community in the sports bar

This paper positions itself within the ongoing debate about the impact of media on community generated by Robert Putnam’s research. Accordingly, the increasing availability of sophisticated means of communication has led the progressive substitution of indirect interactions for direct interactions in shared space, thereby eroding an essential basis of community. In contrast, other theoretical perspectives have presented communication technologies as either enhancing community by altering the field of possible social interactions or incapable of replacing direct interactions. This debate is addressed through an ethnography of fans who gathered at a sports bar to watch the World Cup. Observations revealed that while televised broadcasts served as a primary motivation for attendance and a centrepiece of subsequent interactions, patrons did not watch alone; they watched with each other.     

One step antibody-mediated isolation and patterning of multiple cell types in microfluidic devices

Cell-cell interactions play a key role in regeneration, differentiation, and basic tissue function taking place under physiological shear forces. However, current solutions to mimic such interactions by micro-patterning cells within microfluidic devices have low resolution, high fabrication complexity, and are limited to one or two cell types. Here, we present a microfluidic platform capable of laminar patterning of any biotin-labeled peptide using streptavidin-based surface chemistry. The design permits the generation of arbitrary cell patterns from heterogeneous mixtures in microfluidic devices. We demonstrate the robust co-patterning of α-CD24, α-ASGPR-1, and α-Tie2 antibodies for rapid isolation and co-patterning of mixtures of hepatocytes and endothelial cells. In addition to one-step isolation and patterning, our design permits step-wise patterning of multiple cell types and empty spaces to create complex cellular geometries in vitro. In conclusion, we developed a microfluidic device that permits the generation of perfusable tissue-like patterns in microfluidic devices by directly injecting complex cell mixtures such as differentiated stem cells or tissue digests with minimal sample preparation.