Presented is the theorem proposed by Volterra based on the idea that there is no function continuous at each rational point and discontinuous at each irrational point. Discussed are the two conclusions that were drawn by Volterra based on his solution to this problem. (KR)

Illustrated is the use of computer algebra software to assist in both a computational and theoretical way to develop the underlying theory of polynomials and the partial fraction decomposition of a rational function. Background information and a discussion of theoretical considerations are provided. (KR)

We describe two classes of sequences that give rise to accessible problems for undergraduate research. These problems may be understood with virtually no prerequisites and are well suited for computer-aided investigation. The first sequence is a variation of one introduced by Stephen Wolfram in connection with his study of cellular automata. The…

Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.

Within the context of traditional quality management principles, a program designed to enhance soft skills of College Algebra students was piloted in fall 2001. Results of the pilot project include increased retention, persistence, note-taking ability, and positive responses concerning course expectations. Quality enhancement efforts in this…

A deliberate attempt is made in Business Mathematics oriented text books as well as in some reform calculus oriented text books to interpret the derivative f[prime](a) of a function y = f(x) at the value x = a as the change in the y-value of the function per "unit" of change in the x-value. This note questions the above interpretation and suggests…

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

Studies of methods of teaching statistics are reported. Three brief texts were written for the investigations; they varied in degree of explanation of basic concepts of elementary probability. Subjects were undergraduate students at the University of Massachusetts, Amherst. None of the subjects had had previous formal exposure to probability or…

Vector analysis is viewed to play a key role in many branches of engineering and the physical sciences. This unit is geared towards deriving identities and establishing "machinery" to make derivations a routine task. It is noted that the module is not an applications unit, but has as its primary objective the goal of providing science,…

Thirty-six prospective elementary education teachers were randomly assigned to three instructional moves: a characterization-exemplification with declarative statements (CED), a characterization-exemplification with interrogative statements (CEI), and an exemplification (E). The purposes of the study were to: (1) examine the efforts of the three…

Considers the problem of constructing Venn diagrams for more than three sets. Presents an unusual geometric display of a Venn diagram for five sets. (PK)

Computing pi efficiently has been of great interest to mathematicians for centuries. This article presents an algorithm to solve this problem through skillful computer use. (PK)

Presents ideas that are intended to convey new insights on familiar topics and to enhance pedagogy. The mathematical topics addressed are applications of transformations to numerical integration, the golden ratio, Cramer's rule, a counting problem, and the general form of the arithmetic-geometric mean inequality. (PK)

In this paper, we discuss the (potentially positive) pedagogical role of intrinsic limitations of computational descriptions for mathematical concepts, with special focus on the concept of derivative. Our claim is that, in a suitable approach, those limitations can act for the enrichment of learners' concept images. We report a case study with a…

This document consists of the two issues of the "AMATYC Review" published during volume year 1997-1998. Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regularly…