Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

Discusses how to express an n factorial as a product of powers of primes. Provides two examples and answers. Presents four related suggestions. (YP)

The purpose of this study was to identify common problems students that experience in proof writing. Toward this end, the authors videotaped groups of students in a bridge course as they worked to construct mathematical proofs. They report on their observations and offer suggestions as to how teachers of transition courses might enhance the…

We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

Literature suggests that the type of context wherein a task is placed relates to students' performance and solution strategies. In the particular domain of logical thinking, there is the belief that students have less difficulty reasoning in verbal than in logically equivalent symbolic tasks. Thus far, this belief has remained relatively…

This paper reports a study in which eighteen structural and linguistic variables were identified, defined and used in an attempt to determine which variables accounted for a significant amount of the observed variance in the difficulty level of items on two different conditional reasoning tests administered to high school and college students. The…

Researches in Mathematics Education about proof by contradiction revealed some difficulties of the students but also that this kind of argumentation comes spontaneously in certain situations. In this paper we shall show some processes that might lead the student to produce a proof by contradiction. In particular, we shall point out a deep link…

This study extends research of college students' comprehension of implication into the area of conjunction and disjunction. The results indicated that the majority of the students did not comprehend conjunction and disjunction well enough to correctly respond to most subtest components. (MP)

The concept and use of proof in mathematics are examined. Uses and purposes of proofs are listed and described. (MP)

Describes Newton's method to locate roots of an equation using the Newton-Raphson iteration formula. Develops an adaptive method overcoming limitations of the iteration method. Provides the algorithm and computer program of the adaptive Newton-Raphson method. (YP)

Numerous research studies over the past five years indicate that a high percentage of college students have severe deficiencies in their ability to use mathematics as a language for representing simple quantitative relationships. In the United States these problems are nearly as common among students with strong computational skills in algebra and…

In this paper we describe a number of types of errors and underlying misconceptions that arise in mathematical reasoning. Other types of mathematical reasoning errors, not associated with specific misconceptions, are also discussed. We hope the characterization and cataloging of common reasoning errors will be useful in studying the teaching of…

Contrasted are engineering statistics with statistics for students of mathematics and social science. Topics considered are level of abstraction, amount of technical detail, and choice of subject. The nature of exercises suitable for various courses is described. (KR)

The four-color theorem stating that any map in a plane can be colored using no more than four colors represents a problem suitable for the liberal arts student. Presented is an algorithm for coloring familiar maps through the temporary removal of states bordering three or fewer states. (MDH)

Discusses a new computer mathematics curriculum introduced at the Department of Information and Network at Tokai University, Takanawa Campus, Japan. Outlines the reform project consisting of sections on mathematical literacy and computer mathematics as well as the use of personal computers. (KS)