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.
Table of Contents
Part 1. Student Thinking
1a. Foundations for Beginning Calculus
1b. Infinity, Limit and Divisibility
1c. Proving Theorems
Part 2. Cross-Cutting Themes
2a. Interacting with Students
2b. Using Definitions, Examples and Technology
2c. Knowledge, Assumptions, and Problem Solving Behaviors for Teaching
About the Editors
About the Editors
Marilyn Carlson was awarded her PhD (in mathematics education) from The University of Kansas. Dr. Carlson joined the ASU faculty in 1995. She has served first as interim director and the director of CRESMET since 2003. Her teaching and research career began as a lecturer of mathematics on the Haskell Indian Nations in 1978, and she has also taught high school mathematics and served on the mathematics and computer science faculty at the University of Kansas. At both Kansas and ASU she has been Director of First-Year Mathematics, and at ASU she led the development of a PhD concentration in mathematics education. Dr. Carlson is a frequent invited speaker and the author of more than 60 published and presented research papers. She received a National Science Foundation CAREER award, was a member of the Eisenhower Advisory Board for the State of Arizona, served as coordinator of the Special Interest Group for Research in Undergraduate Mathematics Education, served on a National Research Council panel investigating advanced mathematics and science programs in U.S. high schools, and has participated in policy deliberations at state and national levels. Dr. Carlson has been an investigator on a dozen projects funded by NSF. Currently, she is the principal investigator and co-principal investigator on two NSF grants of nearly $20 million that are funding research-based professional development to support teachers of math and science in Arizona secondary schools (Math and Science Partnership and Teacher Professional Continuum). The projects are conducting intensive research into coursework and professional learning communities for secondary mathematics and science teachers, seeking the structures and practices that help teachers to deepen their knowledge and improve their classroom practice. Dr. Carlson is currently leading an effort to reform the ASU program of college algebra. Dr. Carlson has been an invited speaker at numerous international conferences, is a consultant to peer universities seeking to improve undergraduate programs in mathematics, has traveled to study school mathematics as practiced in China, Japan, and Singapore, and is engage in national efforts to improve U.S. programs that educate and support teachers, including the Teachers for a New Era project led by the Carnegie Corporation of New York. Under her leadership CRESMET has increased its supported research projects from less than $5 million to more than $30 million.
Chris Rasmussen earned a BS (in mechanical engineering) from the University of Maryland in 1985. He was awarded an MA in mathematics (1993) and then a PhD in mathematics education (1997) from the same institution. In 2006 Dr. Rasmussen was honored by the University of Maryland with their Distinguished Alumni Award: Outstanding New Scholar and also by San Diego State University with their Most Influential Teacher Award. He received the 2006 (inaugural) Annie and John Selden Award for Research in Undergraduate Mathematics Education. In 2002 Dr. Rasmussen won the Outstanding Faculty Scholar Award from Purdue University Calumet. He is active in the mathematics education community and is a member of the American Educational Research Association (AERA) and the AERA Special Interest Group for Research in Mathematics Education, the Association of Mathematics Teacher Educators, the Mathematical Association of America (MAA) and the Special Interest Group of the MAA on Research in Undergraduate Mathematics Education, the National Council of Teachers of Mathematics (NCTM), the International Group for the Psychology of Mathematics Education (PME), and the North American Chapter of the International group for the PME.