In this chapter, the authors present the design rationale for and empirical results from a predominantly synchronous three-part online model for the professional development of mathematics teachers in rural contexts. They describe how the design of the components are complementary and are intended to support teachers to develop challenging instructional practices, even when the teachers are geographically remote and dispersed. The three parts include an online course, online video coaching, and online demonstration lessons. They describe how they used conjecture mapping to enhance collaboration within the project team and to inform iterations of the model. They then present empirical results related to each of the components of the model and draw conclusions based upon what they have learned.

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Student-generated algorithms, despite being inelegant and cumbersome, can nevertheless highlight a Common Core standard on rational number subtraction to show flexibility and understanding.

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