Developing Technological Pedagogical Content Knowledge of Pre-Service Math Teachers

在NSF改善本科STEM教育计划：教育和人力资源(IUSE：EHR)的支持下，该项目旨在通过帮助职前中学数学教师学习如何设计帮助学生学习数学的基于技术的课程来服务于国家利益。该项目的主要目标是发展职前教师关于如何使用技术工具来加强他们的教学的知识。为了实现这一目标，该项目将采用一种名为“课程研究”的策略，旨在通过计划、教学和反思的循环来改进教学。该项目将实施包括职前教师、大学教师教育工作者和合作教师(与职前教师有初步临床经验的有经验的在职教师)的课程研究过程。因此，这个项目旨在克服职前教育中经常存在的一个挑战：澄清职前教师在大学教学方法课程中的经历与他们的临床实践中发生的关系。课程研究中的这种协作将认识到并建立在职前教师、协作教师和教师教育工作者各自为教学工作带来的知识基础上。在这样做的过程中，合作旨在带来临床经验和方法课程之间的一致性。波多黎各-里奥皮德拉斯大学和伊利诺伊大学香槟分校的教职员工正在就这一项目进行合作。该项目旨在修订波多黎各大学的一门方法课程，以纳入课程学习战略，并创造一个协作空间，以促进职前教师的技术教学教学知识。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，这两个软件都是具有互联功能的开源软件包。Desmos是一个在线图形计算器，Geogebra集成了代数和动态几何。本项目通过改编课堂学习，运用工具编排理论，促进职前教师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。职前教师将使用技术工具和任务，这是教学配置的一部分，并在课程中描述开发模式。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。预计职前教师、大学教师教育工作者和合作教师之间的合作将支持利用数学技术工具进行课堂研究，共同构建教学中的新知识和新技能。该项目将探索以下研究问题：职前教师如何学习应用乐器编排、计划和实施数学课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职前教师能够在课堂上应用器乐管弦乐？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 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.