This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five sections that address research about (1) foundations, (2) methods, (3) mathematical processes and content, (4) students, teachers, and learning environments, and (5) futuristic issues. Each chapter offers a synthesis of research with an eye to the historical development of a research topic and, in particular, historical milestones of the research about the topic. Section 1, Foundations, contains: (1) Research: To Inform, Deform, or Reform? (Jere Confrey); (2) Linking Research and Practice in Mathematics Education: Perspectives and Pathways (Edward A. Silver and Crystal Lunsford); (3) Education Reform, Research, and Policy: Interwoven Influences on Mathematics Education in the United States (Joan Ferrini-Mundy); (4) A Taxonomy of Approaches to Learning Trajectories and Progressions (Joanne Lobato and C. David Walters); (5) The Role of Theory Development in Increasing the Subject Specificity of Research on Mathematics Teaching.(Patricio Herbst and Daniel Chazan); and (6) Exploring Different Theoretical Frontiers for Different (and Uncertain) Possibilities in Mathematics Education Research (David W. Stinson and Margaret Walshaw). Section 2, Methods, contains: (7) Qualitative Methods (Elizabeth de Freitas, Stephen Lerman, and Amy Noelle Parks); (8) Aligning Statistical Modeling With Theories of Learning in Mathematics Education Research (Finbarr C. Sloane and Jesse L. M. Wilkins); and (9) Conducting Design Studies to Investigate and Support Mathematics Students' and Teachers' Learning (Paul Cobb, Kara Jackson, and Charlotte Dunlap Sharpe). Section 3, Mathematical Processes and Content, contains: (10) Research on the Teaching and Learning of Proof: Taking Stock and Moving Forward (Gabriel J. Stylianides, Andreas J. Stylianides, and Keith Weber); (11) The Teaching and Learning of Mathematical Modeling (Gabriele Kaiser); (12) Providing Support for Student Learning: Recommendations from Cognitive Science for the Teaching of Mathematics (Jon R. Star and Lieven Verschaffel); (13) Early Number and Operations: Whole Numbers (Arthur J. Baroody with David J. Purpura); (14) Learning and Teaching Measurement: Coordinating Quantity and Number (John P. Smith III and Jeffrey E. Barrett); (15) Algebraic Thinking in the Elementary and Middle Grades (Ana C. Stephens, Amy B. Ellis, Maria Blanton, and Bárbara M. Brizuela); (16) Variation, Covariation, and Functions: Foundational Ways of Thinking Mathematically (Patrick W. Thompson and Marilyn P. Carlson); (17) The Learning and Teaching of Geometry (Nathalie Sinclair, Michelle Cirillo, and Michael de Villiers; (18) Teaching and Learning Probability and Statistics: An Integrated Perspective (Cynthia W. Langrall, Katie Makar, Per Nilsson, and J. Michael Shaughnessy); (19) Understanding the Concepts of Calculus: Frameworks and Roadmaps Emerging From Educational Research (Sean Larsen, Karen Marrongelle, David Bressoud, and Karen Graham); and (20) Post-Calculus Research in Undergraduate Mathematics Education (Chris Rasmussen and Megan Wawro). Section 4, Students, Teachers, and Learning Environments, contains: (21) Language Diversity and Mathematics: Second Language, Bilingual, and Multilingual Learners (Richard Barwell, Judit N. Moschkovich, and Mamokgethi Setati Phakeng); (22) Race and Mathematics Education (Danny Bernard Martin, Celia Rousseau Anderson, and Niral Shah); (23) Identity in Research on Mathematics Education (Jennifer M. Langer-Osuna and Indigo Esmonde); (24) Research on Gender and Mathematics (Sarah Theule Lubienski and Colleen M. Ganley); (25) The Complexities of Mathematical Engagement: Motivation, Affect, and Social Interactions (James Middleton, Amanda Jansen, and Gerald A. Goldin); (26) The Multimodal Material Mind: Embodiment in Mathematics Education (Luis Radford, Ferdinando Arzarello, Laurie Edwards, and Cristina Sabena); (27) Highlighting Heritages and Building Tasks: A Critical Analysis of Mathematics Classroom Discourse Literature (Beth Herbel-Eisenmann, Tamsin Meaney, Jessica Pierson Bishop, and Einat Heyd-Metzuyanim); (28) Research on Core Practices in K--12 Mathematics Teaching (Victoria R. Jacobs and Denise A. Spangler); (29) Research on Mathematics Professional Development (Paola Sztajn, Hilda Borko, and Thomas M. Smith); (30) Issues in Curriculum Studies: Evidence-Based Insights and Future Directions (Gwendolyn M. Lloyd, Jinfa Cai, and James E. Tarr); and (31) Technology for Learning Mathematics (Jeremy Roschelle, Richard Noss, Paulo Blikstein, and Nicholas Jackiw). Section 5, Futuristic Issues, contains: (32) Mathematics Educational Neuroscience: Promises and Challenges (Anderson Norton and Martha Ann Bell); (33) Instruction That Meets the Needs of Students With Mathematics Disabilities and Difficulties (Anne Foegen and Barbara Dougherty); (34) Creativity and Giftedness in Mathematics Education: A Pragmatic View (Bharath Sriraman and Per Haavold); (35) Assessment in the Era of Teacher Accountability (Peter Kloosterman and Hugh Burkhardt); (36) Doctorates in Mathematics Education: How They Have Evolved, What Constitutes a High-Quality Program, and What Might Lie Ahead (Robert E. Reys); (37) Mathematics Education at U.S. Public Two-Year Colleges (Vilma Mesa); and (38) Toward a Vibrant and Socially Significant Informal Mathematics Education (Ricardo Nemirovsky, Molly L. Kelton, and Marta Civil).