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.

该项目将建立在已经进行的有希望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。该项目将开始与学生的反思和抽象的证明结构的基础上，从现有的研究结果的初始模型，并将通过一系列新的教学实验发展和扩展这一模型。在该项目的第三年，该模型将用于分析学生在课堂上。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学生对逻辑关系的内容-一般学习的洞察力，因为它是从他们对特定数学关系的内容-特定推理中出现的。尽管从事数学证明是本科数学课程学习的核心部分，而且在这个竞技场中对学生学习的研究正在蓬勃发展，对于许多数学系提供的过渡到证明课程，不存在基于研究的学习目标。使用扎根理论，这个项目将进行教学实验与微积分3学生和分析这些会议的录音，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结构将是突出的。该项目由EHR核心研究（ECR）计划支持，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，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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
• 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.

Instructional interventions and teacher moves to support student learning of logical principles in mathematical contexts

教学干预和教师行动支持学生学习数学背景下的逻辑原理

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

Two Vignettes on Students’ Symbolizing Activity for Set Relationships

关于学生的两个小插曲 — 象征特定关系的活动

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

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
• 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
• 期刊: The Journal of Mathematical Behavior
• 作者: Dawkins, Paul Christian;Norton, Anderson
• 通讯作者: Norton, Anderson