G. Donald Allen

A Survey of Online Mathematics Course Basics

G. Donald Allen (dallen @math.tamu.edu) is a professor of mathematics at Texas A&M University. He has done research in functional analysis, numerical analysis, and mathematical modeling of political processes. His main * A f interest in the past few years has been Internet application of mathematics instruction and distance learning. He has been instrumental in developing a fully online masters of _ -_^^j B ~mathematics degree. This program, now in its third year, has more than thirty graduate students.

Constructing and Role-Playing Student Avatars in a Simulation of Teaching Algebra for Diverse Learners

From the perspectives of Graduate Research Assistants (GRAs), this study examines the design and implementation of a simulated teaching environment in Second Life (SL) for prospective teachers to teach algebra for diverse learners. Drawing upon the Learning-for-Use framework, the analyses provide evidence on the development of student avatars in construction and role-playing activities. The study reveals challenges, procedures, and suggestions for future simulations. This study also calls for research efforts toward preparing mathematics teachers for cultural diversity.

When It Comes To Math, What Exactly are We Testing For?

So many platitudes; so many directives; so many hopes; so much preparation; so much criticism; so much condemnation; so much money. All this applies to modern high-stakes testing, and particularly because the US performs poorly in international competitions, and not that well here at home.

A bridge to engineering: A personalized precalculus (bridge) program

Mathematics continues to be a major hurdle for engineering students. The authors presented results of a pilot precalculus summer program at FIE 2014. In the current paper, we examined longitudinally the results of the institutionalized version of the precalculus summer program over four years. Students who scored less than 22 on the Mathematics Placement Exam could either a) participate in the personalized precalculus program (PPP) or b) take the fall precalculus course. The research question for this study was: How well did the students who took the PPP perform in the precalculus and engineering calculus course sequence compared with the students who did not participate in the PPP? The PPP included an online study plan with practice problems in common areas of difficulty in algebra and trigonometry and required online tutoring sessions for 30 hours over a six-week period for the first three years and the same number of hours over a three-week period for the fourth year. For this paper, we analyzed the trends over four years of the program to determine whether participants are progressing successfully through the engineering calculus sequence.

Smoothness and Superconvergence for Approximate Solutions to the One Dimensional Monoenergetic Transport Equation

Over the past several years, numerous papers proposing a variety of projection methods for the solution of the linear one-dimensional monoenergetic transport have been published. For the characteristic form, many of these method reduce to standard methods for the solution of linear integral equations of the second kind. In this paper we propose a general framework for several projection methods based on function approximation of specified orders of approximation and/or smoothness. In addition, we illustrate how superconvergence (of the moment type) arises and how to obtain a desired order of superconvergence while maintaining other desired properties, such as smoothness.