New Directions in Two-Year College Mathematics : Proceedings of the Sloan Foundation Conference on Two-Year College Mathematics, Held July 11–14 at Menlo College in Atherton, California

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. Front Matter....Pages i-xx Front Matter....Pages xxi-xxi Mathematics in Today’s Community College....Pages 1-19 Let’s Keep the “College” in our Community Colleges: Mathematics for College Transfer....Pages 21-29 A New Start for Mathematics Curriculum....Pages 30-39 Mathematics as a Course of Study in Problem Solving—Then and Now....Pages 41-52 Front Matter....Pages 81-81 Technical Mathematics: A Dilemma....Pages 83-100 Occupational Education and Mathematics: Ownership Makes the Difference....Pages 101-117 Technical Mathematics Two-Year College Programs....Pages 119-130 Front Matter....Pages 140-140 Reflections on Basic Mathematics Programs in the Two-Year College....Pages 141-158 Liberal Arts Mathematics— Cornerstone or Dinosaur ?....Pages 159-172 Statistics in the Two-Year College Curriculum....Pages 173-184 Front Matter....Pages 203-203 It’s Going to Happen Anyway......Pages 205-223 Discrete Topics in the Undergraduate Mathematics Curriculum: How Big A Step Should We Take ?....Pages 225-241 Calculators Do More Than Compute....Pages 243-254 The Lessons of Williamstown....Pages 255-270 Style Versus Content: Forces Shaping the Evolution of Textbooks....Pages 271-287 Front Matter....Pages 310-310 Research in the Learning of Mathematics: Some Genuinely New Directions....Pages 311-340 Knowledge Transmission and Acquisition: Cognitive and Affective Considerations....Pages 341-365 Front Matter....Pages 379-379 Relevancy and Revitalization: Retaining Quality and Vitality in Two-Year College Mathematics Faculty....Pages 381-392 The Academic Training of Two-Year College Mathematics Faculty....Pages 393-403 Current Continuing Education Needs of Two-Year College Faculty Must Be Met !....Pages 405-422 Front Matter....Pages 437-437 Coordinating Curriculum in Two-Year Colleges with Baccalaureate Institutions....Pages 439-453 Some Reflections on the Interaction of Mathematics Programs at Two-and Four-Year Colleges....Pages 455-466 Mathematics Programs in High Schools and Two-Year Colleges....Pages 467-479 Back Matter....Pages 489-491 This book records the Proceedings of a working conference on mathematics education in two-year colleges held on July 11-14, 1984, at Menlo College in Atherton, California. Over the last quarter century, the objectives of two-year colleges have shifted from primarily serving the needs of students who wish to transfer to four-year colleges to serving students who desire technical and job-related training. Rapidly advancing technology has made calculators and computers accessible to students and faculty and impacted the teaching of mathematics. Conference participants came from secondary schools, two- and four-year colleges, and vocational and professional organizations, and after discussing the papers, formulated a list of general recommendations. These focused on curriculum, new technologies, faculty development and renewal, and collaborative efforts from and for all levels of mathematics education