research (Sarama et al., 2008). Each is a research-based curriculum that has been evaluated using randomized control-group designs, and both curricula have met the What Works Clearinghouse criteria for inclusion, demonstrating their effectiveness in meaningfully improving child outcomes in mathematics (What Works Clearinghouse, 2007).

The documentation provided to programs adopting Building Blocks details elements of the training and support offered to teachers using the TRIAD model (Clements and Sarama, 2008; Sarama et al., 2008). Building Blocks training and support, which has been demonstrated to be effective through research, consists of three elements over the course of one school year: (1) 34 hours of focused group training, (2) 16 hours of in-class coaching and mentoring, and (3) electronic communications, including the use of an interactive project website (Clements and Sarama, 2008).

Understanding mathematical learning trajectories (which are called teaching-learning paths in this book) is a particular focus of the training, as a part of helping teachers learn the “conceptual storyline” (Clements and Sarama, 2008). In addition, trained coaches provide teachers with regular coaching and mentoring as well as individualized feedback and address any concerns or problems with implementation. The Building Blocks Learning Trajectory web application provides best practice exemplars, video-based illustration of children’s mathematical thinking and development, and resources for lesson planning. Finally, teachers receive resources for documenting student progress. Thus, training is fairly extensive, ongoing, hands-on, specific, job-embedded, and tied to curriculum. Furthermore, training is provided by highly qualified trainers, and distance learning facilitates reaching participants in multiple locations. The documented gains in outcomes for teachers, classrooms, and children confirmed the efficacy of this approach to professional development (Clements and Sarama, 2008).

In sum, the research from these examples indicates that professional development in mathematics in early childhood settings is most successful when it is a component of an overall change process that is supported by all key players. They demonstrate that, although teachers can make highly significant improvements in children’s mathematics outcomes, learning the knowledge and skills needed to do so requires an ongoing effort with support to achieve this success. Frequently, the number of contact hours in professional development that produces success is substantially greater than typically offered by curriculum publishers, an issue that should be addressed. Mentoring or coaching also appears to play an important role in helping teachers to solve problems as they learn to apply new knowledge and skills, as well as helping to sustain the change process over time. Evidence also shows that providing teachers with knowledge of mathematics and children’s mathematical thinking and development, as well as how to apply this knowledge through the use of a particular curriculum, is highly

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