Designed to strengthen the teaching of mathematics in the elementary grades, this book focuses on helping teachers engage in instruction based on learning trajectories (LTs). The authors bring together the experiences and key research-based findings of four different groups of teacher educators that created effective professional development around LTs. Beginning with a brief introduction to the key principles of LTs, the text then examines four exemplary projects with details on professional development design, teacher learning, and project implementation. The book features contributions from renowned scholars, including a final discussion and commentary chapter by professional development researcher Hilda Borko. The book features: (1) A brief introduction to learning trajectories--what they are and their potential to improve instruction; (2) Key takeaways from professional development designers; (3) The practices of professional development designers and facilitators with years of experience helping teachers learn about trajectories; and (4) Exclusive details about professional development design not found in other resources. Chapters in the book include: (1) Learning Trajectories and Professional Development (Paola Sztajn and P. Holt Wilson); (2) The Learning Trajectories Based Instruction Project (Paola Sztajn, Cyndi Edgington, P. Holt Wilson, Jared Webb, and Marrielle Myers); (3) Children's Measurement Project: Sharing Trajectories with Teachers (Jeffrey E. Barrett, Megan H. Wickstrom, Jennifer M. Tobias, Craig J. Cullen, Amanda L. Cullen, and Jae M. Baek); (4) The Responsive Teaching in Elementary Mathematics (RTEM) Project (Victoria R. Jacobs, Susan B. Empson, D'Anna Pynes, Amy Hewitt, Naomi Jessup, and Gladys Krause); (5) The Building Blocks and TRIAD Projects (Julie Sarama and Douglas H. Clements); (6) Design Considerations for Professional Development Involving Learning Trajectories (P. Holt Wilson and Paola Sztajn); and (7) Learning Trajectories in Mathematics Professional Development: A Commentary (Hilda Borko).