Developing Technological Pedagogical Content Knowledge of Pre-Service Math Teachers by Enhancement of a Methods Course Using Instrumental Orchestration and Lesson Study Strategies

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With support from the NSF Improving Undergraduate STEM Education Program: Education and Human Resources (IUSE: EHR), this project aims to serve the national interest by establishing practices to help pre-service secondary mathematics teachers (PSTs) learn how to lead classroom discussions with interconnectivity technology. The proposal's main goal is the development of PSTs' technological pedagogical content knowledge (TPACK). To do this, the project will adapt Lesson Study, which employs a cycle of planning, teaching, and reflecting. Thus, PSTs will learn to design technology-based lessons that support students' development of mathematical proficiency. In addition, university teacher educators (TE), cooperating teachers (CTs = experienced in-service teachers with whom PSTs have their initial clinical experiences) and PSTs will work together utilizing Lesson Study in the service of advancing TPACK. Thus, this project aims to grapple with a challenge that often exists in pre-service education, that is the relationship of what PSTs experience in methods courses to what happens in their clinical practice. This TE, CT, PST collaboration in Lesson Study will thus create what this project refers to as a "hybrid space" in which the project acknowledges and leverages the knowledge that the PSTs, CTs, and TEs each bring to the instructional enterprise. In doing so, it is intended that coherence will be brought between clinical experiences and methods courses.Faculty members at the University of Puerto Rico-Rio Piedras (UPRRP) and the University of Illinois at Urbana-Champaign are collaborating on this project. It aims to revise one of the methods courses at UPRRP to integrate Lesson Study strategies and create a hybrid collaborative space to advance TPACK. Interconnectivity technology allows students to share their work and represent mathematical ideas through multiple representations. The methods course will target algebra and geometry concepts in the secondary mathematics curriculum using Desmos or GeoGebra. Both are open source software packages with interconnectivity capabilities. Desmos is an online graphing calculator and GeoGebra integrates algebra and dynamic geometry. Through adaptation of Lesson Study, this project employs a theory of instrumental orchestration to promote PSTs' use of technology to develop students' mathematical proficiency. Instrumental orchestration consists of three elements: didactic configuration, mode of exploitation, and didactic performance. PSTs will use the technology tools and tasks, which are part of the didactical configuration, and descriptions of the exploitation modes in the lessons. The didactical performance will be the outcome of the planning and will be observed in the implementation phase of the Lesson Study. It is expected that the hybrid space collaboration among the TE, CTs, and PSTs will support co-construction of new knowledge and skills in teaching through Lesson Study leveraging the mathematical technology tools for instruction. The research questions the project will explore include the following. In what ways do PSTs learn to apply the principles of instrumental orchestrations planning and implementing mathematics lessons for promoting students' mathematical proficiency? What supports from Coordinating Teachers enable PSTs to apply instrumental orchestrations in their lessons? And, how does the modified Lesson Study model enable opportunities for creating hybrid spaces that connect methods courses and clinical experiences? Through the analysis of videos, student journals, and interviews, the project will construct an evidence-based case that examines the integration of methods courses and clinical experiences. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.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.