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Mathematics education research in undergraduate mathematics has increased significantly in the last decade and shows no signs of abating in the near future. Thus far, this research has often been associated with innovations in curriculum such as calculus reform, statistics education, and the use of computational and graphing technology in instruction. Carefully conducted mathematics education research is something far more fundamental and widely useful than might be implied by its use by the advocates of innovation in undergraduate mathematics education. Most simply, mathematics education research is inquiry by carefully developed research methods aimed at providing evidence about the nature and relationships of many mathematics learning and teaching phenomena. It seeks to clarify the phenomena, illuminate them, explain how they are related to other phenomena, and explain how this may be related to undergraduate mathematics course organization and teaching.This book - the collaborative effort of a research mathematician, mathematics education researchers who work in a research mathematics department and a professional librarian - introduces research mathematicians to education research. The work presents a non-jargon introduction for educational research, surveys the more commonly used research methods, along with their rationales and assumptions, and provides background and careful discussions to help research mathematicians read or listen to education research more critically.This guide is of practical interest to university-based research mathematicians. It introduces the methodology of quantitative and qualitative research in education, provides critical guidelines for assessing the reliability and validity of mathematics education research, and explains how to use online database resources to locate education research. The book will also be valuable to graduate students in mathematics who are planning academic careers, and to mathematics department chairs and their deans.