The PD program delivered in this study focused entirely on rational number topics and was designed to develop teachers' capability to teach positive rational number topics effectively. For each rational number topic area, the PD program design emphasized using precise definitions and the properties and rationales underlying common procedures used with rational numbers. In addition, the PD emphasized developing teachers' ability to explain rational number concepts and procedures, identify and address persistent student misconceptions(often by presenting students with problems designed to reveal their thinking), and use representations of rational number concepts in teaching.
Two providers—America's Choice and Pearson Achievement Solutions—were selected through a competitive process to produce and deliver the PD.2 Both providers worked with a common set of guidelines regarding the structure of the PD program, the knowledge to be developed, and key aspects of the delivery of the PD while also building on their existing PD materials that addressed topics in rational numbers. Facilitator guides were refined through a yearlong pilot and review process. The study's external advisors reviewed both providers' facilitator guides, focusing on the accuracy, appropriateness, and coherence of the mathematics content presented to teachers.
As shown in Table ES-1, during each year of the study, the study-provided PD included a summer institute, a series of one-day follow-up seminars held during the school year, and in-school coaching visits conducted in association with the seminar days and delivered by the seminar facilitators. The specification of the PD program was guided by the literature, which is largely based on correlational research and practitioner experience.3
The PD program provided to teachers who participated in both years of the study was designed to deliver 114 contact hours (68 hours in the first year and 46 hours in the second year). For teachers who entered the study in the second year, the PD provided 58 contact hours, including the 46 hours offered to all teachers and a 12-hour "makeup" institute that provided a condensed version of the summer institute from the first year of the study. The amount of PD in mathematics offered annually by the study was more than most mathematics teachers typically receive in a single year.4
For the summer institutes and seminars, the planned PD activities included opportunities for teachers to solve mathematics problems individually and in groups, make short oral presentations to explain how they solved problems, receive feedback on how they solved and presented their solutions, engage in discussions about the most common student misconceptions associated with topics in rational numbers, and plan lessons that they would teach during the follow-up coaching visits. The coaching visits, which were scheduled to occur within a few days of each of the seminar days, employed both individual and group activities and were designed to help the teachers apply material covered in the institutes and seminars to their classroom instruction.
The PD was not presented to teachers as an opportunity to improve their understanding of rational number content, and the PD did not offer an opportunity for teachers to explicitly evaluate their own knowledge of rational numbers (by assigning a test of rational numbers, for example).5 Further, the PD did not generally require teachers to spend time outside the institutes and coaching activities studying rational number content or practicing pedagogical techniques.