This book attempts to clarify the nature of principles that govern the effective use of merging new research designs in mathematics and science education. A primary goal is to describe several of the most important types of research design that have been pioneered recently by mathematics and science educators, have distinctive characteristics when they are used in projects that focus on mathematics and science education, and have proven to be especially productive for investigating the kinds of complex, interacting, and adapting systems that underlie the development of mathematics or science students and teachers or for the development, dissemination, and implementation of innovative programs of mathematics or science instruction. A second goal is to begin discussions regarding the nature of appropriate and productive criteria for assessing the quality of research proposals, projects, or publications that are based on the preceding kinds of research designs. The final objective is to describe such guidelines in formats that will be used to educate students and others who are novices to the fields of mathematics or science education research. Chapters include: (1) "Purposes and Assumptions of This Book" (Richard Lesh, Barbara Lovitts, and Anthony E. Kelly); (2) "Trends and Shifts in Research Methods" (Anthony E. Kelly and Richard Lesh); (3) "Research Agendas: Identifying Priority Problems and Developing Useful Theoretical Perspectives" (Richard Lesh and Barbara Lovitts); (4) "The Impact of Standards-Based Reform on Methods of Research in Schools" (Thomas A. Romberg and Angelo Collins); (5) "Improving Research and Systemic Reform toward Equity and Quality" (Jere Confrey); (6) "Formulating Operational Definitions of Desired Outcomes of Instruction in Mathematics and Science Education" (Richard Lesh and David Clarke); (7) "Progress in Research: The Interplay among Theory, Research Questions, and Measurement Techniques" (Jose P. Mestre); (8) "The Corruption of a Research Design: A Case Study of a Curriculum Innovation Project" (Hugh F. Cline and Ellen B. Mandinach); (9) "Multitiered Teaching Experiments" (Richard Lesh and Anthony Kelly); (10) "Transformative Teaching Experiments through Conjecture-Driven Research Design" (Jere Confrey and Andrea Lachance); (11) "Teaching Experiment Methodology: Underlying Principles and Essential Elements" (Leslie P. Steffe and Patrick W. Thompson); (12) "Conducting Teaching Experiments in Collaboration with Teachers" (Paul Cobb); (13) "Research on the Development of Mathematics Teachers: The Teacher Development Experiment" (Martin A. Simon); (14) "Working on the Inside: Using OneOs Own Practice as a Site for Studying Teaching and Learning" (Deborah Loewenberg Ball); (15) "Paradigms for Teacher- Centered Classroom-Based Research" (Helen M. Doerr and Patricia P. Tinto); (16) "Action Research as a Research Methodology for the Study of the Teaching and Learning of Science" (Allan Feldman and Jim Minstrell); (17) "Integrating a Naturalistic Paradigm into Research on Mathematics and Science Cognition and Learning" (Judit N. Moschkovich and Mary E. Brenner); (18) "Interpretive Research in Science Education" (Kenneth Tobin); (19) "A Scientific Perspective on Structured, Task-Based Interviews in Mathematics Education Research" (Gerald A. Goldin); (20) "Analysis of Clinical Interviews: Foundations and Model Viability" (John Clement); (21) "Principles for Developing Thought--Revealing Activities for Students and Teachers" (Richard Lesh, Mark Hoover, Bonnie Hole, Anthony Kelly, and Thomas Post); (22) "Videorecording as Theory" (Rogers Hall); (23) "Iterative Refinement Cycles for Videotape Analyses of Conceptual Change" (Richard Lesh and Richard Lehrer); (24) "Choosing and Using Video Equipment for Data Collection" (Jeremy Roschelle); (25) "Mathematics Curriculum Development as a Scientific Endeavor" (Michael T. Battista and Douglas H. Clements); (26) "Designing Effective Software" (Douglas H. Clements and Michael T. Battista); (27) "Technology Design as Educational Research: Interweaving Imagination, Inquiry, and Impact" (Jeremy Roschelle and Nicholas Jackiw); (28) "The Role of Historical Studies in Mathematics and Science Educational Research" (David Dennis); (29) "Subgroup Differences on the GRE Quantitative Test Based on the Underlying Cognitive Processes and Knowledge" (Kikumi K. Tatsuoka and Gwyneth M. Boodoo); (30) "Cautions and Considerations: Thoughts on the Implementation and Evaluation of Innovation in Science Education" (S. Marie A. Cooper); (31) "Assessing Learning as Emergent Phenomena: Moving Constructivist Statistics Beyond the Bell Curve" (Walter M. Stroup and Uriel Wilensky); and (32) "When Using the Mean Is Meaningless: Examples from Probability Theory and Cardiology" (Larry Liebovitch, Angelo Todorov, Mark Wood, and Kenneth Ellenbogen). (KHR)