Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the…

The usual definition of the Riemann integral as a limit of Riemann sums can be strengthened to demand more of the function to be integrated. This super-Riemann integrability has interesting properties and provides an easy proof of a simple change of variables formula and a novel characterization of derivatives. This theory offers teachers and…

We present background and an activity meant to show both instructors and students that mere button pushing with technology is insufficient for success, but that additional thought and preparation will permit the technology to serve as an excellent tool in the understanding and learning of mathematics. (Contains 5 figures.)

Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

For many years, the author has been involving his students in classroom teaching of their own classes. The day-to-day practice is described, and the advantages and disadvantages for both the instructor and the students are discussed. Comparisons with the Moore Method of teaching are made.

This article shows how to use six parameters describing the International Space Station's orbit to predict when and in what part of the sky observers can look for the station as it passes over their location. The method requires only a good background in trigonometry and some familiarity with elementary vector and matrix operations. An included…

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

Teaching the art of counting can be quite difficult. Many undergraduate students have difficulty separating the ideas of permutation, combination, repetition, etc. This article develops some examples to help explain some of the underlying theory while looking carefully at the selection of various subsets of objects from a larger collection. The…

The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)

This textbook is one of a series of publications designed to provide information needed by Navy personnel whose duties require an elementary and general knowledge of the fundamental concepts of number systems, logic circuits, and Boolean algebra. Topic 1, Number Systems, describes the radix; the positional notation; the decimal, binary, octal, and…

The focus of this book is on a rationale and a set of strategies for problem generation in mathematics. Six chapters attempt to involve readers in the process of posing problems and in understanding why that process is important. Chapter 1 discusses two problem posing perspectives, while chapter 2 looks at the first phase of problem posing. The…

Discussed are the results of a study which suggests that people remember more mathematics and other high school material when learning occurs spaced out over several years and when each subsequent session involves broader applications of previously learned information. Highlights of this study and related studies are presented. (CW)