As extended by Ginsberg, Midi's theorem says that if the repeated section of a decimal expansion of a prime is split into appropriate blocks and these are added, the result is a string of nines. We show that if the expansion of 1/p[superscript n+1] is treated the same way, instead of being a string of nines, the sum is related to the period of…

Howard Eves captured people's imagination by proposing a hinged table whose top could swing around to be either an equilateral triangle or a square. But is Eves's mathematically motivated design actually good furniture design? This paper identifies potential design flaws in that hinged table and proposes an intriguing new design. Both the original…

In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

This article looks at some of the conceptual difficulties that students have in a linear algebra course. An overview of previous research in this area is given, and the various theories that have been espoused regarding the reasons that students find linear algebra so difficult are discussed. Student responses to two questions testing the ability…

In this article, I present some "axioms" that relate to undergraduate mathematics education. When I first heard the word axiom, it was defined as a "self-evident truth"; but an axiom is not a truth, it is a subjective assumption on which an argument or proof can be based. My purpose in presenting these axioms is to stimulate debate about…

Arithmetic tests for divisibility of an integer by another integer are well known. This article states and proves conditions for divisibility in binary form.

In this article, a systematic approach is given for solving a magic star puzzle that usually is accomplished by trial and error or "brute force." A connection is made to the symmetries of a cube, thus the name Magic Hexahedron.

Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with…

In my Calculus classes I encourage my students to actively reflect on course material, to work collaboratively, and to generate diverse solutions to questions. To facilitate this I use peer instruction (PI), a structured questioning process, and i-clickers, a radio frequency classroom response system enabling students to vote anonymously. This…

The fact that students have difficulties in constructing proofs is well documented. However, some of these difficulties may be lessened if instructors and students have access to a common evaluation framework. Operating in the theoretical tradition of heuristic inquiry, a proof error evaluation tool (PEET) is constructed that may be used by…

The purpose of this study is to determine whether educators believe mathematics should be taught to liberal arts students, what topics are taught in liberal arts mathematics courses, and what the motivation is for teaching such topics. The study consists of two parts, a review of the opinions of educators regarding liberal arts mathematics, and a…

This paper reports findings of a post test experimental control group design conducted to investigate the role of modified Moore learning approach on improving students' mathematical understanding and proving abilities. Subjects of study were 56 undergraduate students of one state university in Bandung, who took advanced abstract algebra course.…

The National Council of Teachers of Mathematics has set ambitious goals for the teaching and learning of mathematics that include preparing students for both the workplace and higher education. While this suggests that it is important for students to develop strong mathematical competencies by the end of high school, there is evidence to indicate…

A problem given in the Australian Mathematics Competition for the Westpac Awards was stated as follows: With how many zeros does 2008! end? In this article, the author solves this problem, and provides further discussion on the related problems. These problems form a good model that helps students develop a logical thinking process toward problem…

The purpose of this article is to investigate the mathematical practice of proof validation--that is, the act of determining whether an argument constitutes a valid proof. The results of a study with 8 mathematicians are reported. The mathematicians were observed as they read purported mathematical proofs and made judgments about their validity;…