Technology-Rich Units for Future Secondary Teachers: Forging Dynamic Connections Between Geometry and Functions

该项目将解决本科准中学数学教师需要具备扎实的教学知识，以便在未来的学生中培养追求STEM职业所必需的丰富的数学理解的问题。虽然职前教师经常选修12门或更多的本科数学课程，但他们通常看不到这些课程之间深刻的数学相互关系，以及它们与他们将要教授的数学的相关性。未来的教师需要有经验来思考和编织这些大的数学思想，并明确它们对学校数学的适用性。这个项目将为职前教师创建和测试五个基于网络的单元，通过使用基于网络的技术促进初中和高中数学的互动、基于几何的方法来实现这些目标。该项目将建立在认知科学、技术和教育学的基础上，以推进加强未来数学教师的数学背景的目标。它将使用几何方法作为一个总体框架，用于研究几何变换、解析几何、三角、复数和与微积分有关的相对变化率等技术丰富的研究。此外，该项目将利用一种新的基于网络的软件Web SketchPad的能力，根据每项特定活动的需要设计数学工具。该项目将制定与每个单位相一致的措施，以评估职前教师学到了什么，对每个单位进行试点测试，并根据收集的数据进行修改，并设计教师支助材料以供实施。研究的项目课程材料和项目结果将与数学教师教育工作者分享，以告知他们为中学数学教师做准备。罗伯特·诺伊斯教师奖学金计划将为该项目提供共同资金，以表彰其与诺伊斯努力更广泛的教师培养目标的一致性。

This project will address the documented need for undergraduate prospective secondary mathematics teachers to possess strong content knowledge in order to develop in their future students the rich mathematical understandings necessary to pursue STEM careers. While preservice teachers often take twelve or more undergraduate mathematics courses, they typically fail to see the deep mathematical interrelationships between the courses and their relevance to the mathematics they will teach. Prospective teachers need experiences in thinking about and knitting together these big mathematical ideas as well as making clear their applicability to school mathematics. This project will create and test five web-based units for preservice teachers that address these goals by promoting an interactive, geometry-based approach to middle school and high school mathematics through the use of web-based technology. The project will build on the foundations of cognitive science, technology, and pedagogy to advance the goal of strengthening the mathematical background of future mathematics teachers. It will employ a geometric approach to functions as an overarching framework for technology-rich investigations of geometric transformations, analytic geometry, trigonometry, complex numbers, and relative rates of change with connections to calculus. Additionally, the project will capitalize on the ability of Web Sketchpad, a new web-based software, to design mathematical tools tailored to the needs of each particular activity. The project will construct measures aligned with each unit to assess what preservice teachers learn, pilot test each unit and make revisions based on data collection, and design teacher support materials for implementation. Project curriculum materials and project findings from the research will be shared with mathematics teacher educators to inform their preparation of secondary mathematics teachers. The Robert Noyce Teacher Scholarship program will provide co-funding for this project in recognition of its alignment with the broader teacher preparation goals of the Noyce effort.