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

合作研究：ECR DBER DCL：扩展本科生向证明课程过渡时反思和抽象证明结构的理论模型

• 批准号: 1954768
• 负责人: Paul Dawkins
• 金额: $ 40.44万
• 依托单位: Texas State University - San Marcos
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1954768&HistoricalAwards=false
• 关键词: Collaborative; Research; ECR; DBER; DCL

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.

该项目将建立在有前途的教学实验的基础上，这些实验已经进行，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。该项目将从基于现有研究结果的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开发和扩展该模型。在该项目的第三年，该模型将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。该项目将有机地深入了解学生对逻辑关系的一般学习内容，因为它是从他们对特定数学关系的特定内容推理中产生的。尽管数学证明是本科数学课程学习的核心部分，并且关于这一领域学生学习的研究正在蓬勃发展，但许多数学系提供的“过渡到证明”课程并不存在基于研究的学习目标。该项目将利用扎根理论，对微积分 3 的学生进行教学实验，并分析这些课程的录音，以完善和扩展关于学习如何发生的建构主义理论。皮亚杰的抽象概念和其他结构将很突出。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 学习和学习环境的基础研究、扩大 STEM 的参与以及 STEM 劳动力发展的工作。该奖项反映了 NSF 的法定使命，并被认为是值得的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来提供支持。

项目成果

Student Explanations and Justifications Regarding Converse Independence

学生关于逆独立性的解释和理由

• 发表时间: 2023-08
• 期刊: Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
• 作者: Tucci, A.;Dawkins, P.C.;Roh, K.H.;Eckman, D.;Ruiz, S.
• 通讯作者: Ruiz, S.

Theo’s reinvention of the logic of conditional statements’ proofs rooted in set-based reasoning

西奥对条件语句逻辑的重新发明——植根于基于集合的推理的证明

• DOI: 10.1016/j.jmathb.2023.101043
• 发表时间: 2023-06
• 期刊: The Journal of Mathematical Behavior
• 作者: Dawkins, Paul Christian;Roh, Kyeong Hah;Eckman, Derek
• 通讯作者: Eckman, Derek

Identifying mental actions for abstracting the logic of conditional statements

识别用于抽象条件语句逻辑的心理活动

• DOI: 10.1016/j.jmathb.2022.100954
• 发表时间: 2022-06
• 期刊: The Journal of Mathematical Behavior
• 作者: Dawkins, Paul Christian;Norton, Anderson
• 通讯作者: Norton, Anderson

Differences in Students’ Beliefs and Knowledge Regarding Mathematical Proof: Comparing Novice and Experienced Provers

学生关于数学证明的信念和知识的差异：比较新手和经验丰富的证明者

• 发表时间: 2023-08
• 期刊: Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
• 作者: Ruiz, S.;Roh, K. H.;Dawkins, P. C.;Eckman, D.;Tucci, A.
• 通讯作者: Tucci, A.

Aspects of predication and their influence on reasoning about logic in discrete mathematics

离散数学中谓词的各个方面及其对逻辑推理的影响

• DOI: 10.1007/s11858-022-01332-y
• 发表时间: 2022-08
• 期刊: ZDM – Mathematics Education
• 作者: Dawkins, Paul Christian;Roh, Kyeong Hah
• 通讯作者: Roh, Kyeong Hah