دانلود کتاب Making the connection : research and teaching in undergraduate mathematics education

The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.  Read more... On developing a rich conception of variable / Maria Trigueros and Sally Jacobs --Rethinking change / Bob Speiser and Chuck Walter --Foundational reasoning abilities that promote coherence in students' function understanding / Michael Oehrtman, Marilyn Carlson and Patrick Thompson --The concept of accumulation in calculus / Patrick Thompson and Jason Silverman --Developing notions of infinity / Michael A. McDonald and Anne Brown --Layers of abstraction : theory and design for the instruction of limit concepts / Michael Oehrtman --Divisibility and transparency of number representations / Rina Zazkis --Overcoming students' difficulties in learning to understand and construct proofs / Annie Selden and John Selden --Mathematical induction : cognitive and instructional considerations / Guershon Harel and Stacy Brown --Proving starting from informal notions of symmetry and transformations / Michelle Zandieh, Sean Larson, and Denise Nunley --Teaching and learning group theory / Keith Weber and Sean Larsen --Teaching for understanding : a case of students' learning to use the uniqueness theorem as a tool in differential equations / Chris Rasmussen and Wei Ruan --Meeting new teaching challenges : teaching strategies that mediate between all lecture and all student discovery / Karen Marrongelle and Chris Rasmussen --Examining interaction patterns in college-level mathematics classes : a case study / Susan Nickerson and Janet Bowers --Mathematics as a constructive activity : exploiting dimensions of possible variation / John Mason and Anne Watson --Supporting high achievement in introductory mathematics courses : what we have learned from 30 years of the emerging scholars program / Eric Hsu, Teri J. Murphy and Uri Treisman --The role of mathematical definitions in mathematics and in undergraduate mathematics courses / Barbara Edwards and Michael Ward --Computer-based technologies and plausible reasoning / Natalie Sinclair --Worked examples and concept example usage in understanding mathematical concepts and proofs / Keith Weber, Mary Porter and David Housman --From concept images to pedagogic structure for a mathematical topic / John Mason --Promoting effective mathematical practices in students : insights from problem solving research / Marilyn Carlson, Irene Bloom and Peggy Glick --When students don't apply the knowledge you think they have, rethink your assumptions about transfer / Joanne Lobato --How do mathematicians learn to teach? Implications from research on teachers and teaching for graduate student professional development / Natasha Speer and Ole Hald.