New Directions in Two-Year College Mathematics

by Donald J. Albers ix INTRODUCTION In July of 1984 the first national conference on mathematics education in two-year colleges was held at Menlo College. The conference was funded by the Alfred P. Sloan Foundation. Two-year colleges account for more than one-third of all undergraduate enrollments in mathematics, and more than one-half of all college freshmen are enrolled in two-year colleges. These two facts alone suggest the importance of mathematics education in two-year colleges, particularly to secondary schools, four-year colleges, and universities. For a variety of reasons, four-year colleges and universities are relatively unaware of two-year colleges. Arthur Cohen, who was a participant at the "New Directions" conference warns: "Four-year colleges and universities ignore two-year colleges at their own peril." Ross Taylor, another conference participant, encouraged two-year college faculty to be ever mindful of their main source of students--secondary schools- and to work hard to strengthen their ties with them. There are many other reasons why it was important to examine two-year college mathematics from a national perspective: 1. Over the last quarter century, rio other sector of higher education has grown so rapidly as have two-year colleges. Their enrollments tripled in the 60's, doubled in the 70's, and continue to increase rapidly in the 80's. x 2. Twenty-five years ago, two-year colleges accounted for only one-seventh of all undergraduate mathematics enrollments; today the fraction is more than one-third.

1. A Case for Curriculum Change.- Mathematics In Today's Community College.- Let's Keep the "College" In Our Community Colleges: Mathematics for College Transfer.- A New Start for Mathematics Curriculum.- Mathematics as a Course of Problem Solving- Then and Now.- 2. Technical Mathematics.- Technical Mathematics: A Dilemma.- Occupational Education and Mathematics: Ownership Makes the Difference.- Technical Mathematics in Two-Year College Programs.- 3. Endangered Curriculum Elements.- Reflections on Basic Mathematics Programs in the Two-Year College.- Liberal Arts Mathematics-Cornerstone or Dinosaur?.- Statistics in the Two-Year College Curriculum.- 4. New Curricula and New Tools.- It's Going to Happen Anyway....- Discrete Topics in the Undergraduate Curriculum: How Big a Step Should We Take?.- Calculators Do More than Compute.- The Lessons of Williamstown.- Style Versus Content: Forces Shaping the Evolution of Textbooks.- 5. The Learning of Mathematics.- Research in the Learning of Mathematics: Some Genuinely New Directions.- Knowledge Transmission and Acquisition: Cognitive and Affective Considerations.- 6. Faculty Renewal and Professionalism.- Relevancy and Revitalization: Retaining Quality and Vitality in Two-Year College Mathematics Faculty.- The Academic Training of Two-Year College Mathematics Faculty.- Current Continuing Education Needs of Two-Year College Faculty Must be Met!.- 7. Coordinating Curriculum Change.- Coordinating Curriculum in Two-Year Colleges with Baccalaureate Institutions.- Some Reflections on the Interaction of Mathematics Programs at Two- and Four-Year Colleges.- Mathematics Programs in High Schools and Two-Year Colleges.