Developing Technological Pedagogical Content Knowledge of Pre-Service Math Teachers

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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 helping pre-service secondary mathematics teachers learn how to design technology-based lessons that help students learn mathematics. The project's main goal is to develop the pre-service teacher's knowledge about how to use technological tools to enhance their teaching. To accomplish this goal, the project will adapt a strategy called "Lesson Study," which was designed to improve teaching through cycles of planning, teaching, and reflecting. The project will implement a Lesson Study process that includes pre-service teachers, university teacher educators, and cooperating teachers (the experienced in-service teachers with whom pre-service teachers have their initial clinical experiences). As a result, this project aims to overcome a challenge that often exists in pre-service education: clarifying the relationship of what pre-service teachers experience in teaching methods courses at the university to what happens in their clinical practice. This collaboration in Lesson Study will recognize and build upon the knowledge that pre-service teachers, collaborating teachers, and teacher educators each bring to the work of teaching. In doing so, the collaboration is designed to bring coherence between clinical experiences and methods courses. Faculty members at the University of Puerto Rico-Rio Piedras and the University of Illinois at Urbana-Champaign are collaborating on this project. The project aims to revise one of the methods courses at the University of Puerto Rico to integrate Lesson Study strategies and create a collaborative space to advance the pre-service teacher's technological pedagogical content knowledge. 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 of which 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 pre-service teachers' use of technology to develop students' mathematical proficiency. Instrumental orchestration consists of three elements: didactic configuration, mode of exploitation, and didactic performance. Pre-service teachers 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 collaboration among the pre-service teachers, university teacher educators, and cooperating teachers will support co-construction of new knowledge and skills in teaching through Lesson Study leveraging the mathematical technology tools for instruction. The project will explore the following research questions: In what ways do pre-service teachers learn to apply the principles of instrumental orchestrations planning and implementing mathematics lessons for promoting students' mathematical proficiency? What supports from Coordinating Teachers enable pre-service teachers 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.