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改善本科生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)学习如何利用互联技术引导课堂讨论，从而服务于国家利益。该提案的主要目标是发展PSTS的技术教学知识(TPACK)。为了做到这一点，该项目将调整课程研究，采用计划、教学和反思的循环。因此，PST将学会设计以技术为基础的课程，以支持学生数学能力的发展。此外，大学教师教育工作者(TE)、合作教师(CTS=与PSTS有初步临床经验的有经验的在职教师)和PSTS将利用课程研究为促进TPACK服务而共同努力。因此，本项目旨在解决职前教育中经常存在的一个挑战，即PST在方法课程中所经历的内容与其临床实践中发生的内容之间的关系。因此，TE、CT、PST在课程研究中的协作将创建本项目所称的“混合空间”，在该空间中，项目承认并利用PST、CT和TES各自为教学企业带来的知识。这样做的目的是使临床经验和方法课程之间的一致性。波多黎各大学皮德拉斯分校(UPRRP)和伊利诺伊大学厄巴纳-香槟分校的教职员工正在合作这个项目。它的目的是修改UPRRP的一门方法课程，以整合课程学习策略，并创建一个促进TPACK的混合协作空间。互联技术使学生能够分享他们的工作，并通过多种表示法来表达数学思想。方法课程将使用Desmos或Geogebra在中学数学课程中针对代数和几何概念。两者都是具有互联功能的开放源码软件包。Desmos是一个在线图形计算器，Geogebra集成了代数和动态几何。本项目通过改编课堂学习，运用工具编排理论，促进PSTs运用技术发展学生的数学能力。器乐编曲由三个要素组成：教化结构、运用方式和教化表演。PST将使用作为教学配置一部分的技术工具和任务，以及课程中对开发模式的描述。教学表现将是计划的结果，并将在课程研究的实施阶段进行观察。预计TE、CT和PST之间的混合空间协作将支持通过利用数学技术教学工具进行课堂研究，共同构建教学中的新知识和新技能。该项目将探索的研究问题包括以下几个。PST通过哪些方式学习运用器乐编排、计划和实施数学课程的原则来提高学生的数学水平？来自协调教师的哪些支持使PST能够在他们的课程中应用器乐管弦乐？而且，修改后的课程研究模式如何创造机会，创造连接方法课程和临床经验的混合空间？通过对视频、学生日记和访谈的分析，该项目将构建一个以证据为基础的案例，审查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，以提高所有学生的STEM教育的有效性。通过参与的学生学习路径，该计划支持有前景的实践和工具的创建、探索和实施。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.