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

该奖项将支持旨在调查有意成为教师的本科生的关键发展性数学理解的研究发展。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导方针倾向于一种截然不同的方法，侧重于几何变换，例如形状对轴的反射。这种学习方法上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联系起来？这个项目的工作将通过探索教师如何使用转换视角来概念化几何中的两个关键概念：同余和相似性来解决这个问题。这项工作还将为未来教师对一致性和相似性的思考建模提供丰富的数据集。该项目建立在研究者领导的先前工作的基础上，该工作假设存在从转变角度建立一致性的关键发展理解。该项目将对这一假设进行进一步的研究。它还将寻求通过一个适应的教学实验，为证明相似性的活动提出假设。在这些工作中，研究者将由Yvonne Lai博士指导。本研究的具体目的是：(1)从转换的角度考察准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开展STEM教育研究的能力。研究结果将为教师设计和改进数学课程提供信息，并支持教师教育工作者设计和使用形成性评估，以从转换的角度理解几何。这项新的研究有可能帮助更多的中学数学教师进入课堂，以符合现行标准的方式教授几何。此外，专业发展活动将培养研究者进行STEM教育研究的能力，这将加强主要本科院校研究与实践之间的联系。这项工作得到了EHR核心研究：STEM教育研究能力建设项目的支持，该项目支持培养个人开展高质量STEM教育研究的能力。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.