What teachers know and believe is central to what they can do in classrooms. This study takes an innovative approach to documenting how teacher knowledge can be enhanced by incorporating a design experience into pre-service mathematics education. The study's participating prospective teachers will use digital and fabrication technologies (e.g., 3D printers and laser cutters) to design and use manipulatives for K-6 mathematics learning. The goals of the project include describing how this experience influences the prospective teachers' knowledge and identities while creating curriculum for teacher education. Also, because more schools and students have access to 3D fabrication capabilities, teacher education can utilize these capabilities to prepare teachers to take advantage of these resources. Prior research by the team demonstrated how the process of making a manipulative can support prospective teachers in learning about mathematics and how to teach elementary mathematics concepts. The project will generate resources for other elementary teacher education programs and research about how prospective elementary teachers learn mathematics for teaching. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.The project includes three research questions. First, what forms of knowledge are brought to bear as prospective elementary teachers make new manipulatives and write corresponding tasks to support the teaching and learning of mathematics? Second, how does prospective elementary teachers' knowledge for teaching mathematics develop as they make new manipulatives and write tasks to support the teaching and learning of mathematics? Third, as prospective elementary teachers make new manipulatives and write tasks to support the teaching and learning of mathematics, how do they see themselves in relation to the making, the mathematics, and the mathematics teaching? The project will employ a design-based research methodology with cycles of design, enactment, analysis and redesign to create curriculum modules for teacher education focused on making mathematics manipulatives. Data collection will include video recording of class sessions, participant observation, field notes, artifacts from the participants' design of manipulatives, and assessments of mathematical knowledge for teaching. A qualitative analysis will use multiple frameworks from prior research on mathematics teacher knowledge and identity development.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
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