Each year, over 1,000,000 students take college-level courses below calculus such as precalculus, college algebra and others that fulfill general education requirements. Most college algebra courses, and certainly all precalculus courses, were originally intended to prepare students for calculus. Most are still offered in this spirit, even though only a small percentage of students have any intention of taking calculus. This volume examines how the courses below calculus might be refocused to provide better mathematical experiences for all students. This initiative involves a greater emphasis on conceptual understanding with a de-emphasizing on rote manipulation. It encourages the use of realistic applications, math modeling and data analysis that reflect the ways mathematics is used in other disciplines. It promotes the use of active learning approaches, including group work, exploratory activities and projects. It emphasizes communication skills: reading, writing, presenting and listening. It endorses the appropriate use of technology to enhance conceptual understanding, visualization, and to enable students to tackle real-world problems.The 49 papers in this volume seek to focus attention on the problems and needs of the courses and to provide guidance to the mathematics community. Major themes include: new visions for introductory collegiate mathematics, transition from high school to college, needs of other disciplines, research on student learning, implementation issues, and ideas and projects that work.
Readings in Innovative Ideas in Teaching Collegiate Mathematics is a collection of papers contributed by professional mathematicians in the United States and Great Britain. The topics in this volume represent the pros and cons of implementing creative instructional styles such as cooperative learning and educational technology in classrooms. The main objective of this book is to share the implementation and outcomes of these experiments with the teachers of mathematics at all educational levels and help them to learn about different teaching strategies and how they might incorporate them in their classrooms.
Volume III of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem solving - included here are three different articles analyzing aspects of Schoenfeld's undergraduate problem-solving instruction. The articles provide new detail and insight on a well-known and widely discussed course taught by Schoenfeld for many years. Understanding concepts - these articles feature a variety of methods used to examine students' understanding of the concept of a function and selected concepts from calculus. The conclusions presented offer unique and interesting perspectives on how students learn concepts.Understanding proofs - this section provides insight from a distinctly psychological framework. Researchers examine how existing practices can foster certain weaknesses. They offer ways to recognize and interpret students' proof behaviors and suggest alternative practices and curricula to build more powerful schemes. The section concludes with a focused look at using diagrams in the course of proving a statement.
The field of research in collegiate mathematics education has grown rapidly over the past twenty-five years. Many people are convinced that improvement in mathematics education can only come with a greater understanding of what is involved when a student tries to learn mathematics and how pedagogy can be more directly related to the learning process. Today there is a substantial body of work and a growing group of researchers addressing both basic and applied issues of mathematics education at the collegiate level.This second volume in ""Research in Collegiate Mathematics Education"" begins with a paper that attends to methodology and closes with a list of questions. The lead-off paper describes a distinctive approach to research on key concepts in the undergraduate mathematics curriculum. This approach is distinguished from others in several ways, especially its integration of research and instruction. The papers in this volume exhibit a large diversity in methods and purposes, ranging from historical studies, to theoretical examinations of the role of gender in mathematics education, to practical evaluations of particular practices and circumstances. As in RCME I, this volume poses a list of questions to the reader related to undergraduate mathematics education. The eighteen questions were raised at the first Oberwolfach Conference in Undergraduate Mathematics Education, which was held in the fall of 1995, and are related to both research and curriculum.
"This book focuses on an in-depth assessment on strategies and instructional design practices appropriate for the flipped classroom model, highlighting the benefits, shortcoming, perceptions, and academic results of the flipped classroom model"--Provided by publisher.