Discussed are the difficulties that entering college freshmen seem to have with mathematics, particularly with fractional forms. A success-oriented program is suggested in which all students are successful. To obtain this goal, a number of alternative routes are discussed such as presenting decimals before fractional forms and the use of the…

Within the context of the developments in mathematics and computer science, this paper argues that the emergence of the microcomputer gives mathematics the opportunity to survive as a viable and healthy discipline. Section I traces the development of the computer and the position of established mathematics on the sidelines of this development.…

In this paper the notion of "procept" (in the sense of Gray & Tall, 1994) is extended to advanced mathematics by considering mathematical proof as "formal procept". The statement of a theorem as a symbol may theoretically evoke the proof deduction as a process that may contain sequential procedures and require the synthesis…

In July 1982, a conference was held at Williams College in Williamstown, Massachusetts, to discuss the need for more discrete mathematics in the first two years of the core undergraduate mathematics curriculum. This paper reviews the recommendations that were made during the conference, the progress that has been made in the implementation of…

This paper considers the nature of "understanding" in mathematics, and of instruction designed to foster it. The first part is theoretical, presenting an argument that there are (at least) three qualitatively different components to competent mathematical performance: (1) possession of the appropriate set of cognitive "resources," (2) the ability…

Preparing students for transfer to four-year colleges remains a significant part of the mission of most community college mathematicians. For some 30 years, calculus has been synonymous with entry-level college mathematics. Recent educational and technological changes, however, demand that the definition of college-level work in mathematics be…

Arguing that a major re-thinking of the mathematics curriculum is needed, this paper urges two-year colleges to take the lead in curriculum revision. Section I suggests that the pre-calculus orientation of high school mathematics may be inappropriate, viewing mathematics related to computers and dependent on computers for computation as more…

Statistics tend to become interesting to non-methodologists when taught in a research context that is relevant to them. Real data sets supplemented by sufficient background information can provide just such a context. Despite this, many textbook authors and instructors of applied statistics rely on artificial data sets to illustrate statistical…

For the remainder of the century, large numbers of students will transfer from two-year to four-year colleges. In light of this, two- and four-year mathematics faculty need to sharpen their understanding of each other and to plan improved interaction. The problem in communication between two- and four-year mathematics faculty comes from living in…

In light of substantial declines in enrollments in liberal arts mathematics courses in two-year colleges, this paper looks at some of the reasons for these declines and suggests ways of revitalizing the traditional "great ideas" mathematics course. First, a brief outline is presented of the history of liberal arts mathematics, focusing on the…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

The question of the advisability of incorporating discrete mathematics into the mathematics curriculum is addressed by examining the different types of courses typically offered in the first two years of college and the appropriateness of including discrete mathematics topics in these courses. The introductory section explains how the advent of…

A discussion is presented of the relationship between community college general education mathematics courses and the technical education curricula they support. Introductory remarks sketch the history and emphasis of community colleges; review President Truman's Commission on Higher Education's recommendations concerning the functions of…

Drawing from experience at Lansing Community College (LCC), this paper discusses how to best prepare students for success in a beginning algebra course. First, an overview is presented of LCC's developmental math sequence, which includes Basic Arithmetic (MTH 008), Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra (MTH…

Discusses the potential impact of the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics on teacher education programs. Considers an historical perspective on reform as well as teacher and student conceptions. (PK)