Applying research to strengthen teaching practice and ensure students' success in mathematicsMore than seventy years of research point to the importance of teaching mathematics for understanding. Successful students actively construct understanding rather than passively receive knowledge. Implications of this fundamental lesson from research are explored in different ways in this book.More Lessons Learned from Research, Volume 2 rounds out More Lessons Learned from Research, Volume 1 (2015) by presenting twenty-four more chapters that share ideas for strengthening teaching and learning by applying accessible, relevant insights from research. As in the first volume, all the chapters have been adapted and updated from articles published in NCTM's Journal for Research in Mathematics Education between 2000 and 2010, and the authors have rewritten and revised their work to make it clear, understandable, and useful for classroom mathematics teachers.The chapters cover investigations of a wide range of topics, approaches, and settings, including:explorations related to teaching and learning with understanding, including how to use evidence of students' correct and incorrect thinking to guide instructionevaluations of reform efforts in mathematics education in schools serving high-poverty communities or students of colorexaminations of professional development to support teachers of mathematics to pre-K studentscase studies of theory-based approaches to teaching mathematics in the early elementary grades and an implementation of a mathematics curriculum based on social justice; andanalyses related to the teaching and learning of important topics in the school curriculum, including basic arithmetic operations; fractions and decimals; algebraic reasoning; probability, and calculusMathematics teachers at all levels will find examples of research that is relevant to the challenges they face. This book, together with its predecessor, enables researchers and teachers to meet on common ground to improve mathematics education for all students.