Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus has two major goals: to improve mathematics education at two-year colleges and at the lower division of four-year colleges and universities and to encourage more students to study mathematics. The document presents standards that are intended to revitalize the mathematics curriculum preceding calculus and to stimulate changes in instructional methods so that students will be engaged as active learners in worthwhile mathematical tasks. In addition, the implications of these changes in such areas as faculty development and student assessment are discussed. Preparation of these standards has been guided by the principle that faculty must help their students think critically, learn how to learn, and find motivation for the study of mathematics in appreciation of its power and usefulness.
This document represents a major effort of the American Mathematical Association of Two-Year Colleges (AMATYC), assisted by representatives of many other national mathematics education organizations. AMATYC's previous efforts to improve mathematics education at the two-year college level have taken the form of development of policy statements and guidelines. The most notable recent efforts have been Guidelines for the Academic Preparation of Mathematics Faculty at Two-Year Colleges (AMATYC, 1992) and Guidelines for Mathematics Departments at Two-Year Colleges (AMATYC, 1993). AMATYC was inspired toward additional efforts in education reform when in August 1991 the Mathematical Sciences Education Board (MSEB) convened a small planning group at the National Academy of Sciences to discuss two-year college mathematics education. Several members of the AMATYC leadership met with representatives from MSEB and others interested in two-year college mathematics education. This meeting and the subsequent efforts of the representatives of MSEB served to focus and launch the initiative.
The work of the Planning Group led to the development of a multiple-phase proposal designed to address curriculum and pedagogy reform initiatives at two-year colleges. The Exxon Education Foundation provided funds to assist with the initiative. AMATYC also committed funds while at the same time seeking additional support from other sources. Subsequently, the focus of the initiative was broadened to include all lower-division mathematics education below calculus, and substantial funding was received from the National Science Foundation (NSF). Marilyn Mays was designated Principal Investigator, with Karen Sharp and Dale Ewen as Co-Principal Investigators. A steering committee was formed with representatives from AMATYC, the American Mathematical Society (AMS), the Mathematical Association of America (MAA), MSEB, the National Association for Developmental Education (NADE), and the National Council of Teachers of Mathematics (NCTM). This group met in February 1993, in Washington, D.C., to plan the process for the development of a standards document.
The Steering Committee determined that the following principles should guide the deliberations of the Task Force:
- Fundamental changes are occurring in mathematics education as a result of the impact of several national documents, calculus reform efforts, technological advances, and research into how students learn.
- Colleges and universities must prepare an increasingly diverse group of students for further study and the world of work.
- While two-year college and lower-division mathematics students are preparing for a multitude of future occupations, there exists a common core of mathematical experiences, viewpoints, concepts, and skills that should be learned by all students.
- The manner in which students learn is inseparable from the content.
- Research regarding how students learn mandates development of new pedagogical methods and implementation of proven teaching techniques.
- The impact of technology both as a mode of instructional delivery and as a mathematical tool requires a redefinition of the mathematics curriculum.
- The demands of the workplace require that all students become empowered citizens capable of critical thinking.
The Steering Committee appointed a Task Force to develop a standards document. The Task Force was asked to formulate recommendations for a foundation program that would serve all students lacking preparation for college level mathematics courses and to examine the special needs of students in technical, mathematics-intensive, liberal arts, and teacher preparation programs.
Before meeting, members of the Task Force reviewed a large collection of documents and articles on mathematics education reform and wrote position statements detailing their visions of the curricular and pedagogical reforms needed. These statements were distributed to the Task Force prior to the meeting.
The Task Force shaped a common vision for its work at its June 1993 meeting at State Technical Institute at Memphis. They also developed sections of the first draft of this document, originally titled Standards for Curriculum and Pedagogical Reform in Two-Year College and Lower Division Mathematics. Those sections were refined in subsequent weeks by the participants. Editor Don Cohen compiled them into a common format and produced a noncirculating draft which went back to the Task Force, to the National Steering Committee, and to a few reviewers and leaders of the mathematics education community. Then the document was further refined and published as a circulating draft. This draft was mailed to all AMATYC members and has been widely distributed outside of the two-year college community. Hearings were held at several national, regional, and state conferences. Reviews were solicited.
A writing team selected from the Task Force met in Dallas, February 24-27, 1994, to consider all of the comments made on the first circulating draft and to start the revision process. A second circulating draft was prepared and sent to the Task Force and other selected reviewers on July 15, 1994. A preliminary final draft was published in October 1994. It was distributed and discussed at several regional and national conferences including the November 1994 AMATYC conference in Tulsa, the January 1995 AMS-MAA joint mathematics meetings in San Francisco, the February 1995 NADE conference in Chicago, and the April 1995 NCTM conference in Boston. Crossroads in Mathematics is based on the many comments and reviews that were received.
The members of the Task Force, along with the names of members of the Writing Team, Planning Group, Steering Committee, and Advisory Panel are listed in the front matter.
We are grateful to the National Science Foundation, the Exxon Education Foundation, and Texas Instruments Incorporated as well as to all who contributed to the development and publication of this document.
