Development of Research to Inform the Design and Improvement of Mathematics Education for Teachers

该奖项将支持研究的发展，以调查关键的发展数学理解的本科生谁打算成为教师。许多中学教师通过证明定理来学习几何。当前的二级标准和指南倾向于一种非常不同的方法，这种方法侧重于几何变换，例如形状相对于轴的反射。这种学习方法的差异提供了一个重要的STEM教育问题：中学教师对基于证明的几何的理解如何与他们对几何变换的理解有关？这个项目的工作将通过探索教师如何使用转换的观点来概念化几何中的两个关键概念来解决这个问题：同余和相似。这项工作还将产生一个丰富的数据集，用于未来对教师关于一致性和相似性的思维建模。该项目建立在研究者领导的先前工作的基础上，该工作假设从转换的角度建立一致性的关键发展理解的存在。该项目将进行与这一假设相关的额外研究。它还将寻求通过调整后的教学实验来开发相似性证明活动的假设。在这些努力中，调查员将得到黎莹莹博士的指导。研究的具体目的是：(1)从转换的角度调查未来教师对一致性和相似性证明活动的理解；(2)提高研究者使用定性和定量方法设计和实施STEM教育研究的能力。研究结果将为教师数学课程的设计和改进提供参考，并支持教师教育工作者从转化的角度设计和使用形成性评价来理解几何。这项新的研究有可能帮助更多的中学数学教师进入课堂，充分准备好教授符合现行标准的几何。此外，专业发展活动将培养调查员进行STEM教育研究的能力，这将加强一个以本科为主的机构的研究与实践之间的联系。这项工作由EHR核心研究：STEM教育研究计划中的能力建设支持，该计划支持建设个人进行高质量STEM教育研究的能力的项目。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。

This award will support the development of research to investigate key developmental mathematics understandings of undergraduates who are intending to become teachers. Many secondary teachers learned geometry through proving theorems. Current secondary standards and guidelines favor a vastly different approach that focuses on geometric transformations, such as reflection of a shape against an axis. This difference in learning approaches provides an important STEM education question: how do secondary teachers' understandings of proof-based geometry relate to their understanding of geometrical transformations? Work on this project will address this question by exploring how teachers use a transformational perspective to conceptualize two key concepts in geometry: congruence and similarity. This work will also produce a rich dataset for future modeling of teachers' thinking about congruence and similarity.This project builds on prior work led by the investigator, which hypothesized the existence of key developmental understandings for establishing congruence from a transformation perspective. The project will conduct additional research related to this hypothesis. It will also seek to develop hypotheses for similarity-proving activities through an adapted teaching experiment. In these efforts, the investigator will be mentored by Dr. Yvonne Lai. The specific aims of the research are to: (1) investigate prospective teachers' understandings of congruence and similarity-proving activities from a transformation perspective; and (2) increase the investigator’s capacity to design and conduct STEM education research using both qualitative and quantitative methods. Results of the research will inform the design and improvement of the mathematics curricula for teachers, and support teacher educators in designing and using formative assessments for understanding geometry from a transformation perspective. The new research has the potential to help more secondary mathematics teachers enter the classroom well-equipped to teach geometry in alignment with current standards. Additionally, the professional development activities will build capacity for the investigator to conduct STEM education research that will enhance the connection between research and practice at a primarily undergraduate institution. This work is supported by the EHR Core Research: Building Capacity in STEM Education Research Program, which supports projects that build individuals’ capacity to carry out high quality STEM education research.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.