This document, the last volume of a four-part publication, describes the programs in basic skills in mathematics at the nine senior colleges and eight community colleges of the City University of New York (CUNY), updating surveys made in 1976. These programs are for students who do not meet CUNY's standard for minimum competency in mathematics, or…

Discusses what areas of ability are being assessed in timed, closed-book examinations and to what extent the procedure might foster possible educational objectives. Also describes a list of 10 "qualities" by which a mathematics question can be graded to see what skills are needed for its solution. (Author/JN)

The purpose of this paper is to offer a framework for categorizing and describing the different types of processes that undergraduates use to construct proofs. Based on 176 observations of undergraduates constructing proofs collected over several studies, I describe three qualitatively different ways that undergraduates use to construct proofs. In…

Discussed is the tendency of students to equate the concepts of continuity and connected graphs based on their lack of an understanding of such concepts as limit points, closed sets, and connected sets. Included is a theorem with three lemmas with their proofs. (KR)

Discussed is the problem of inscribing a rectangle of maximum area in a given right triangle. Answered is whether there is an advantageous orientation and whether a corner of the rectangle of maximum area can lie on the midpoint of a leg of the triangle. (KR)

There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (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)

Provides several problems and their solutions for a descriptive statistics course. Included are problems related to measurement, data collection, sample construction, applications, and computation. Discusses the misleading nature of statistics. (YP)

Provides a BASIC program to compute the number of shuffles required for packs containing even numbers of cards up to 100. Lists 4 further questions on the shuffling program. (YP)

Shows a series of Euclidean equations using the Euclidean algorithm to get the greatest common divisor of two integers. Describes the use of the equations to generate a series of circles. Discusses computer generation of Euclidean circles and provides a BASIC program. (YP)

Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)

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…

"The Price is Right" ("TPIR") is a rich source of examples of applied probability, combinatorics, and game theory. While some of the games played on stage by individual contestants stress a knowledge of pricing, many are also heavily based on probability. "TPIR" stage games are a treasury of interesting modules that can be effective learning tools…

In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and…