Mathematics Capstone Course Resources: Preparing Secondary School Mathematics Teachers
The preparation of the highest quality teachers and learners of mathematics is a national imperative. As undergraduates, future secondary school teachers take many courses from professors with advanced degrees in mathematics. However, university faculty members often do not possess deep knowledge of the kinds of teaching demands faced by new school teachers. There is a notable need for instructional materials that deliberately and explicitly connect undergraduate mathematics content to the knowledge needed for teaching secondary mathematics. This project will leverage the existence of Capstone Courses for future teachers found in many universities, which bring together ideas from across the college mathematics experience, as well as recent developments in policy and school accountability, to create and refine activities for use by university faculty in mathematics pre-service teachers Capstone Courses. This project will develop Capstone Course modules which provide access to advanced mathematical ideas along with opportunities to unpack mathematics in ways helpful for teaching it in middle and high school settings. The proof-of-concept work of the project has two parts. One is the development and refinement of two full modules, each designed to take about a week of instructional time in a Capstone Course. The second aspect is refining the module development process itself.
This project is significant in that it intends to strengthen the pre-service preparation of teachers while it will also contribute to educational research on the improvement of pre-service teacher learning experiences in mathematics. The design for each module will use assessments linked to state mathematics standards as anchors for discussion, sites for development of mathematical knowledge, and foundations for other mathematics-specific knowledge used in teaching. Modules will include mathematical task exploration, analysis of middle and high school student thinking illustrated in video-recorded clinical interviews, and examination of sample formative and summative assessment items. The project brings together WestEd with San Francisco State University and the University of Maine to: (1) develop and pilot multi-media instructional modules for advanced pre-service secondary mathematics teacher learning; (2) create guidance for college mathematics faculty for effective use of the modules with target audiences; and (3) gather information from instructors and the pre-service teachers in their courses to inform future module development work. Design-based implementation research (DBIR) strategies will be employed, using an iterative process to examine a persistent problem of college instructional practice, to develop theory and tools for systematic inquiry into feasibility and fidelity of implementation of the modules. Intellectual Merit of the project resides in the expertise of the PI team, the materials that will be developed, and a research agenda that will examine feasibility (accessibility and usability by mathematics faculty), promise (pre-service teacher learning based on the modules), and scalability (identification of challenges to effective implementation). The Broader Impacts are present in the intention to have faculty members at other institutions pilot test materials during the project and in the potential for faculty, nationwide, to use the modules to replace parts of, or enrich, current capstone course designs. Also contributing to the Broader Impacts is that knowledge gained from project research will provide a foundation for future research-based development efforts to increase tools available for preparing mathematics teachers.