Professional Development Publications

Clements, D. H., & Sarama, J. (2021). Sustainable, scalable professional development in early mathematics: Strategies, evaluation, and tools. In Y. Li, R. E. Howe, W. J. Lewis, & J. J. Madden (Eds.), Developing mathematical proficiency for­ elementary instruction (pp. 221-238). Springer. https://doi.org/10.1007/978-3-030-68956-8

The third edition of this significant and groundbreaking book summarizes current research into how young children learn mathematics and how best to develop foundational knowledge to realize more effective teaching. Using straightforward, practical language, early math experts Douglas Clements and Julia Sarama show how learning trajectories help teachers understand children’s level of mathematical understanding and lead to better teaching. By focusing on the inherent delight and curiosity behind young children’s mathematical reasoning, learning trajectories ultimately make teaching more joyous: helping teachers understand the varying levels of knowledge exhibited by individual students, it allows them to better meet the learning needs of all children. This thoroughly revised and contemporary third edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics and become confident, credible professionals. The new edition draws on numerous new research studies, offers expanded international examples, and includes updated illustrations throughout. This new edition is closely linked with Learning and Teaching with Learnings Trajectories-[LT]2-an open-access, web-based tool for early childhood educators to learn about how children think and learn about mathematics. Head to LearningTrajectories.org for ongoing updates, interactive games, and practical tools that support classroom learning.

• Clements, D.H., & Sarama, J. (2020). Learning and Teaching Early Math: The Learning Trajectories Approach (3rd ed.). Routledge. https://doi.org/10.4324/9781003083528

Germeroth, C., & Sarama, J. (2017). Coaching in early mathematics. Advances in Child Development and Behavior, 53, 127-168.

Sarama, J., Clements, D. H., Wolfe, C. B., & Spitler, M. E. (2016).Professional development in early mathematics: Effects of an intervention based on learning trajectories on teachers’ practices. Nordic Studies in Mathematics Education, 21(4), 29–55.

Clements, D.H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14(2), 113-148.