Collaborative Research: ECR DBER DCL: Extending a Theoretical Model for Undergraduate Students' Reflection and Abstraction of Proof Structures in Transition to Proofs Courses

这个项目将建立在已经进行的有前途的教学实验的基础上，以发展关于学生在学习数学证明时如何发展对逻辑结构的理解的理论。该项目将基于现有研究的发现，从学生对证明结构的反思和抽象的初始模型开始，并将通过一系列新的教学实验来发展和扩展这一模型。在项目的第三年，该模型将被用于分析课堂上的学生。这种方法的核心是帮助学生理解逻辑问题，因为他们抽象自己的数学活动来解决这些问题。该项目将有机地发展对学生内容的洞察——逻辑关系的一般学习，因为它出现在他们对特定数学关系的特定内容推理中。虽然从事数学证明是本科数学课程学习的核心部分，并且在这一领域对学生学习的研究正在兴起，但许多数学系开设的“向证明过渡”课程并没有研究性的学习目标。利用扎根理论，本项目将对微积分3的学生进行教学实验，并分析这些课程的录音，以完善和扩展学习如何发生的建构主义理论。皮亚杰的抽象概念和其他概念将是突出的。该项目得到了EHR核心研究（ECR）计划的支持，该计划支持推进STEM学习和学习环境基础研究、扩大STEM参与和STEM劳动力发展的工作。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 project will build upon promising teaching experiments that have already been conducted to develop theory about how students develop understandings of logical structure when learning mathematical proof. The project will begin with an initial model of students' Reflection and Abstraction of Proof Structures based on findings from existing studies and will develop and extend this model through a series of new teaching experiments. In the third year of the project, the model will be used to analyze students in classrooms. At the heart of this approach is helping students apprehend the questions of logic as they abstract their own mathematical activity to address those questions. The project will organically develop insights into students' content-general learning of logical relations as it emerges from within their content-specific reasoning about the specific mathematical relations.Though engaging in mathematical proof is a central part of an undergraduate mathematics course of study, and the body of research on student learning in this arena is burgeoning, there do not exist research-based learning goals for the Transition to Proof courses being offered by many mathematics departments. Using grounded theory, this project will conduct teaching experiments with Calculus 3 students and analyze recordings of these sessions to refine and extend a constructivist theory of how learning occurs. The concept of abstraction and other constructs from Piaget will be prominent. This project is supported by the EHR Core Research (ECR) program, which supports work that advances fundamental research on STEM learning and learning environments, broadening participation in STEM, and STEM workforce development.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.