GeT Support: An online professional learning community to support the geometry course for teachers

该项目旨在提供一种机制和资源，以改善教师几何课程与高中几何教学所需的数学知识的一致性，并满足国家共同核心数学标准的要求。尽管大多数州的教师资格认证要求教师必须修过欧几里德几何课程，但由于欧几里德几何不再是一个活跃的数学研究领域，因此数学家对这门课程的投入往往较少。然而，在高中阶段，几何的教与学对于引导学生进行数学推理仍然至关重要。本计划将发展及推行一套专业支援系统，以改善数学系为职前中学教师开设的理工科课程。该项目将召集由24名大学教师和8名高中几何教师组成的网络，以在线平台和一套公共资源为基础，创建一个跨机构的专业支持系统。该项目将建立一个专业学习社区，利用现有的评估工具获取信息，并利用在线平台的资源共享和互动课程资源。该项目将生成信息，描述面向教师的几何课程如何有助于培养未来的高中几何教师，并记录参与专业发展与学生在几何教学中获得的数学知识之间的联系。该项目将有助于改进几何教学中的数学知识评估，使教师能够将这种评估用于诊断和形成目的。项目团队将研究评估结果，并检查教师和材料之间的相互作用，目的是记录教师经历的困难，并使用迭代过程来解决确定的挑战。该项目将邀请数学教师和高中几何教师参加一系列在线论坛，旨在将MKT-G（用于几何教学的数学知识）与GeT课程联系起来。为了收集这些活动的诊断性和形成性反馈，教授GeT的教师将对他们的本科生进行MKT-G评估，并每年回答课程和教学实践的调查。参与者将参与在线论坛，在论坛中，他们将检查高中学生在几何方面的工作，检查职前教师如何解决MKT-G问题，并讨论课程概念化，课程开发和教学法等问题。项目工作人员将检查MKT-G分数和教学实践随时间的变化，并从在线讨论中提取关于GeT教师参与其工作的合理性的观察结果。这将允许该项目为改善高中几何课程和GeT课程之间的一致性提供建议。在这样做的过程中，该项目将以单一数学系无法提供的方式为GeT课程提供机构支持，因为大多数大学数学系的课程数量有限。拟议的大学几何教师专业支持系统将收集文物，进行讨论，并为评估和教学创造资源，这些资源将在参与者群体之外可用。这些资源将对项目五年级及以后的所有几何教师开放。这些存档的讨论将成为高校几何教师长期使用的丰富资源。该项目将增加几何课程教师和高中几何课程教师之间的相互认识——所提议的活动的性质扩大了两组个人的工作范围。该项目得到了改善本科STEM教育（IUSE）计划和教育和人力资源部本科教育司罗伯特·诺伊斯教师奖学金计划的支持。

This project seeks to provide a mechanism and resources for improving the alignment of the Geometry for Teachers (GeT) course with the mathematical knowledge needed for the teaching of high school geometry, as well as for meeting the demands of the Common Core State Standards for Mathematics. Although teacher certification in most states requires that teachers have a course in Euclidean geometry, because Euclidean geometry is no longer an area of active mathematical research, mathematicians tend to be less invested in this course. Yet, the teaching and learning of geometry is still vital in high school to induct students into mathematical reasoning. This project will develop and implement a system of professional support for the improvement of the GeT course that mathematics departments teach to pre-service secondary teachers. This project will convene a network of 24 college instructors and 8 high school geometry teachers to create an inter-institutional system of professional support anchored in an online platform and a set of common resources. The project will develop a professional learning community that will use and draw information from an existing assessment instrument, and that will use the resources of an online platform to share and interact about resources for the course. The project will generate information that describes how geometry courses for teachers contribute in preparing future teachers to teach geometry in high school and documents the association between participation in the professional development and students' gains in mathematical knowledge for teaching geometry. The project will contribute improvements to the assessment of mathematical knowledge for teaching geometry that enable instructors to use this assessment for diagnostic and formative purposes. The project team will study the assessment results, and examine the interactions among instructors and materials with the goal of documenting the difficulties that instructors experience and using an iterative process to address identified challenges.This project will engage mathematics faculty and high school geometry teachers in a range of online forums destined to connect MKT-G (mathematical knowledge for teaching geometry) with the GeT course. To gather diagnostic and formative feedback for these activities, faculty teaching GeT will administer MKT-G assessments to their undergraduate students and answer a survey of curriculum and instruction practices every year. Participants will be involved in online forums in which they will examine the work high school students do in geometry, examine how pre-service teachers solve MKT-G problems, and discuss issues of course conceptualization, curriculum development, and pedagogy. The project staff will examine changes over time in MKT-G scores and on instructional practices, as well as distill from the online discussions observations about the rationality that GeT instructors involve in their work. This will allow the project to provide recommendations for improving the alignment between the high school geometry course and the GeT course. In doing so, the project will contribute to the institutional support of the GeT course in ways that no single mathematics department can, given the limited presence of the courses in most university mathematics departments. The proposed system of professional support for college geometry instructors will collect artifacts, house discussions, and create resources for assessment and instruction that will be usable beyond the group of participants. The resources will be open to all geometry instructors in Year 5 of the project and beyond. The archived discussions will be a rich resource for use by college geometry instructors long term. The project will increase mutual awareness between instructors of the geometry course for teachers and teachers of the high school geometry course--the nature of the activities proposed broaden the scope of work of both groups of individuals. The project is supported by the Improving Undergraduate STEM Education (IUSE) Program and the Robert Noyce Teacher Scholarship program of the Division of Undergraduate Education in the Directorate of Education and Human Resources.