Mathematics and the Internet: A Source of Enormous Confusion and Great Potential

Graph theory models the Internet mathematically, and a number of plausible mathematically intersecting network models for the Internet have been developed and studied. Simultaneously, Internet researchers have developed methodology to use real data to validate, or invalidate, proposed Internet models. The authors look at these parallel developments, particularly as they apply to scale-free network models of the preferential attachment type

Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better

Joel Cohen offers a historical and prospective analysis of the relationship between mathematics and biolog

The Centrality Of Culture And Community To Participant Learning At And With The Math Forum

In this chapter, the terms culture and community are problematized, and their centrality to participant learning at and with The Math Forum (mathforum.org) is discussed. Culture, as it is used here, refers to the rituals and norms that come to be associated with a site and its functioning. Community describes recognition of connections to and identification with other participants. The Math Forum is an interactive and inquiry-informed digital library, or virtual resource center, for mathematics education. Previous chapters have addressed the ways in which The Math Forum has leveraged the concept of community in order to become a dynamic and resource-rich educational site (Renninger & Shumar, 2002; Shumar & Renninger, 2002). In the present chapter, this analysis is taken a step further. The culture of The Math Forum is described as providing its participants with a unique set of opportunities for learning and for making the relationship between the individual and the community one in which individual and community needs can both be met. Site culture enables contributions from individuals that by definition help to build out and sustain this community. Math Forum participants include Math Forum staff members and a mix of teachers, students, and other individuals such as parents, software developers, mathematicians, math educators, professionals, and tradespeople, many of whom also volunteer their time as mentors for the site. Participants differ not only in terms of their roles, but in their experience, level of expertise, and interest for mathematics (Renninger & Shumar, 2002)

STEMteach: Preparing the Next Generation of Mathematics and Science Teachers

With an increasing demand for individuals prepared in Science, Technology, Engineering, and Mathematics (STEM), one university responded to this call by changing its teacher preparation program. Better-prepared mathematics and science teachers have the opportunity to engage and excite students, thereby preparing and promoting more of them to enter the STEM professions. The described program is a replication of the national UTeach model that recruits content majors in mathematics and science to explore the teaching profession during a first-semester course that includes an early field experience in the elementary grades. This field experience is designed to be engaging for both the teacher education candidates and the elementary students in an effort to demonstrate the joy of teaching and to retain the candidates in the program. The ultimate goal of the program is to increase the production of quality secondary mathematics and science teachers who can transfer their own deep understanding of their content to students so that these students will be career and college ready in the STEM disciplines

Helping Change of Career Individuals to Prepare to Become Secondary Mathematics Teachers

This article describes the development and content of a special introductory course developed and offered at New York University for change of career individuals entering the field of mathematics and science teaching at the graduate rather than the undergraduate level. With a critical shortage of qualified mathematics and science teachers at the secondary level being exacerbated in urban public schools, such as those in New York City, by high attrition rates during the first few years of teaching, it is important to find and encourage new populations of potential teachers. One such population is that of career changers, and the course described in this article is an attempt to help such individuals make their career change more smoothly and successfully. The focus of this course, and the illustrations provided in this article, are on the three major themes: What Does It Mean To Be An Effective Mathematics Teacher ; Technology and the Internet ; and, A Model of Effective Mathematics Teaching

The domination number of on-line social networks and random geometric graphs

We consider the domination number for on-line social networks, both in a stochastic network model, and for real-world, networked data. Asymptotic sublinear bounds are rigorously derived for the domination number of graphs generated by the memoryless geometric protean random graph model. We establish sublinear bounds for the domination number of graphs in the Facebook 100 data set, and these bounds are well-correlated with those predicted by the stochastic model. In addition, we derive the asymptotic value of the domination number in classical random geometric graphs

Community College Perspectives on Teacher Preparation in Virginia

The need for future teachers who are well versed in mathematics and science will not be provided by Virginia’s four-year institutions alone. A large portion of those students who complete their K-8 teacher preparation programs at Virginia’s four-year institutions have studied a significant portion, if not all, of their mathematics and science at community colleges. Therefore, if future teachers are to have completed appropriate mathematics and science courses these must be provided by the community colleges. In addition, community colleges can play a critical role in attracting people with a high potential for becoming excellent teachers. Two-year colleges are located in urban and rural areas, enroll a large portion of Virginia’s minority students, and welcome returning adults. We need to attract students from this source if we are to produce sufficient numbers of well prepared teachers in Virginia. A recent National Science Foundation workshop developed detailed recommendations conceming the role of two-year colleges. This paper will focus on these recommendations

Student experiences of technology integration in school subjects: A comparison across four middle schools

This research examined student perspectives on their in-school, subject specific, technology use in four U.S. public schools. Considering students’ perspectives may provide a significant reframing of adult-created rhetoric of the utopian power of digital technologies for changing teaching and learning. A survey and focus group interviews were administered to 6th and 7th students (n=1,544) in four public middle schools, with varying demographics, that rely on local funding. These four schools revealed moderate use of many well-established digital technologies, such as word processing, presentation software, and quiz games. Students voiced outright hatred for teacher-directed PowerPoint-supported lectures, the most prominent technology activity students experienced, yet reported enjoying creation activities. The students in the rural school with a Hispanic-majority and high economically disadvantaged population reported much lower technology use. Discussion frame the digital inequities in the four schools and emphasizes the need for awareness and inclusion of students’ digital experiences to form any trajectory toward establishing digital equity and learning in schools

Superprocesses as models for information dissemination in the Future Internet

Future Internet will be composed by a tremendous number of potentially interconnected people and devices, offering a variety of services, applications and communication opportunities. In particular, short-range wireless communications, which are available on almost all portable devices, will enable the formation of the largest cloud of interconnected, smart computing devices mankind has ever dreamed about: the Proximate Internet. In this paper, we consider superprocesses, more specifically super Brownian motion, as a suitable mathematical model to analyse a basic problem of information dissemination arising in the context of Proximate Internet. The proposed model provides a promising analytical framework to both study theoretical properties related to the information dissemination process and to devise efficient and reliable simulation schemes for very large systems