The project is an important study that builds prior research to bring a comprehensive implementation of reform mathematics instruction focused on mathematical argumentation to an urban school district. The objective of this full research and development project is to develop resources, models, and tools (RMTs) that help inservice middle grades mathematics teachers support mathematical argumentation throughout the school year. Mathematical argumentation, the construction and critique of mathematical conjectures and justifications, is a fundamental disciplinary practice in mathematics that students often never master. Building on a proof of concept of the project's approach in short curriculum units from two prior NSF-funded studies, this project expands the model to help teachers support mathematical argumentation all year. A coherent, portable, yearlong professional development program on mathematical argumentation has the potential to increase access to mathematical argumentation for students nationwide and, in particular, to address the needs of teachers and students in urban areas. Demonstrating this program in the nation's capital likely attracts broad interest and produces important knowledge about how to implement mathematical practices in urban settings. Increasing mathematical argumentation in schools has the potential for dramatic contributions to students' achievement and participation in 21st century workplaces.
Mathematical argumentation is rich discussion in which students take on mathematical authority and co-construct conjectures and justifications. For many teachers, supporting such discourse is challenging; many are most comfortable with Initiate-Respond-Evaluate types of practices and/or have insufficient content understanding. The professional development trains teachers to be disciplined improvisers -- professionals with a toolkit of tools, knowledge, and practices to be deployed creatively and responsively as mathematical argumentation unfolds. This discipline includes establishing classroom norms and planning lessons for argumentation. The model's theory of action has four design principles: provide the toolkit, use simulations of the classroom to practice improvising, support learning of key content, and provide job-embedded, technology-enabled supports for using new practices all year. Three yearlong studies will address design, feasibility, and promise. In Study 1 the team co-designs the RMTs with District of Columbia Public Schools staff. Study 2 is a feasibility study to examine program implementation, identify barriers and facilitators, and inform improvements. Study 3 is a quasi-experimental pilot to test the promise for achieving intended outcomes: expanding teachers' content knowledge and support of mathematical argumentation, and increasing students' mathematical argumentation in the classroom and spoken argumentation proficiency. The studies will result in a yearlong professional development program with documentation of the theory of action, design decisions, pilot data, and instrument technical qualities.
