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

在NSF改善本科STEM教育计划：教育和人力资源（IUSE：EHR）的支持下，该项目旨在通过建立实践来帮助职前中学数学教师（PST）学习如何使用互联技术领导课堂讨论，从而为国家利益服务。 该提案的主要目标是发展技术和科学技术学校的技术教学内容知识。 为了做到这一点，该项目将调整课程研究，它采用了规划，教学和反思的循环。 因此，PST将学习设计以技术为基础的课程，支持学生的数学能力的发展。 此外，大学教师教育工作者（TE），合作教师（CT =经验丰富的在职教师，与PST有他们的初步临床经验）和PST将共同努力，利用经验研究在推进TPACK服务。 因此，该项目旨在应对职前教育中经常存在的挑战，即PST在方法课程中的经验与其临床实践中发生的事情之间的关系。 因此，课程研究中的TE，CT，PST合作将创建本项目所称的“混合空间”，其中该项目承认并利用PST，CT和TE各自为教学企业带来的知识。 在这样做的时候，它的目的是将临床经验和方法课程之间的连贯性带来。在波多黎各-里约Piedras大学（UPRRP）和伊利诺伊大学厄巴纳-香槟分校的教师正在合作这个项目。 它旨在修改UPRRP的方法课程之一，以整合课程研究策略，并创建一个混合协作空间，以推进TPACK。 互联技术允许学生分享他们的工作，并通过多种表示来表示数学思想。 该方法课程将使用Desmos或GeoGebra针对中学数学课程中的代数和几何概念。 两者都是具有互连能力的开源软件包。 Desmos是一个在线图形计算器，GeoGebra集成了代数和动态几何。 通过对课程研究的改编，该项目采用工具编排理论来促进学生和教师利用技术来发展学生的数学能力。 器乐配器包括三个要素：教学结构、开发模式和教学表演。 PST将使用技术工具和任务，这是教学配置的一部分，以及课程中对开发模式的描述。 教学效果将是规划的结果，并将在课程研究的实施阶段进行观察。 预计TE，CT和PST之间的混合空间合作将通过利用数学技术工具进行教学的课程研究来支持新知识和技能的共同建设。 该项目将探讨的研究问题包括以下几个方面。 小学数学教师如何运用乐器编配的原则，规划及实施数学课程，以提升学生的数学能力？协调教师提供了哪些支持，使学生能够在课堂上运用乐器配器？ 此外，修改后的课程研究模型如何为创建连接方法课程和临床经验的混合空间创造机会？ 通过对视频、学生日志和访谈的分析，该项目将构建一个以证据为基础的案例，考察方法课程和临床经验的整合。 NSF IUSE：EHR计划支持研究和开发项目，以提高所有学生STEM教育的有效性。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.