Loss of Dimension in the History of Calculus and in Student Reasoning

Research indicates that calculus students often imagine objects losing a dimension entirely when a limit is taken, and that this image serves as an obstacle to their understanding of the fundamental theorem of calculus. Similar imagery, in the form of “indivisibles”, was similarly unsupportive of the development of the fundamental theorem in the mid-1600s, unlike the more powerful subsequent imagery of infinitesimals. This parallel between student issues and historical issues suggests several implications for how to provide students with imagery that is more productive for understanding the fundamental theorem, such as the imagery of infinitesimals or the more modern quantitative limits approach, which relies heavily on quantitative reasoning

Creating a creative university

The research focuses on an auto-ethnographic case study of the creation of a new university specialising in creativity in Singapore between 2003 and 2005. The author is the President and CEO of that institution and the Vice Chancellor designate of the University of the Arts Singapore (UARTS@). Through the personal application of knowledge and documentary research, the context for the study is explored, together with the conceptual framework within which it will operate. Some of the social, economic and political issues are described, as they relate to the Singapore Education System, drawing direct comparison with the two systems from which that system originated: the United Kingdom and to some degree, Australia. The case study is centred on the evolution of a private institution, but one that is in receipt of public funding, operating directly under the supervision of the Ministry of Education in Singapore. During the period of the study, the institution transits from a polytechnic towards a full university status and the study observes the extent to which the development impacts on the Singapore Higher Education System and how it responds to two major Singapore government objectives: • The Global Schoolhouse Initiative • The Creative Industries Development The case study illustrates a number of specific challenges facing many existing universities as they attempt to reposition themselves in response to mission convergence

DC to DC Power Conversion

We present results from a capacitor charge pump DC-DC converter prototype using 0.35um HV-CMOS technology fabricated in April 2006. The purpose of this prototype is to test the switch technology both for achievable efficiency and for radiation tolerance. The IC of this test device contains only switches, with all clocks being externally supplied and driven and the capacitors also external. The configuration used is a 4 capacitor stack producing a nominal x4 input current multiplication factor. The goal for this type of device is to be of low enough mass and high enough radiation tolerance to be placed on individual modules in the innermost layers of the Atlas collider detector. Irradiation results will be presented if available. A prototype test card for use with a silicon strip stave prototype is under development

A Glimpse into Secondary Students’ Understanding of Functions

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students’ intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able to do so. Instead, these students tend to represent the physical characteristics of the situation. In addition, we discovered that middleschool students had sophisticated ideas of dependency and covariance. All the students were able to use their models of the situation to generalize and make predictions. These findings suggest that secondary students have the ability to describe covariant and dependent relations and that their models of functions tend to be more intuitive than mathematical-even for the students in algebra II and calculus. Our work suggests a possible framework that begins describing a way of analyzing students’ understanding of functions