Leveraging Pedagogical Comparisons in Mathematical Thinking and Learning

利用数学思维和学习的教学比较

• 批准号: 2327398
• 负责人: Hongyang Zhao
• 金额: $ 32.86万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-15 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2327398&HistoricalAwards=false
• 关键词: Leveraging; Pedagogical; Comparisons; Mathematical; Thinking; Leveraging; Pedagogical; Comparisons; Mathematical; Thinking

The primary goal of this project is to help students improve their relational reasoning, that is, a way of attending to and recognizing relations, including commonalities and differences, between mathematical objects and concepts. Relational reasoning has been shown to support learners in developing their problem-solving skills, skills that are helpful not only in mathematics, but also in subjects like science, engineering, and healthcare, where strong reasoning skills are important for learning and problem solving. The project studies aim to identify instructional supports that help students develop a “relational mindset” as well as to enhance their conceptual flexibility in problem solving.Drawing on cognitive science literature on relational reasoning, the project includes three experimental studies designed to test whether directing students' attention toward relations can foster a relational mindset and consequently enhance students' conceptual flexibility. The studies include a) explicitly directing students’ attention to mathematical relations through classroom discourse; b) implicitly priming relational attention through completing a relevant task; and c) engaging students in antithetical thinking during practice. Analyses will include both descriptive analyses and multiple regression analyses. Study results will provide insights into effective instructional approaches designed to foster students’ attention to and interaction with mathematical relations.This project is funded by the STEM Education Postdoctoral Research Fellowship (STEM Ed PRF) program that aims to enhance the research knowledge, skills, and practices of recent doctorates in STEM, STEM education, education, and related disciplines to advance their preparation to engage in fundamental and applied research that advances knowledge within the field.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.

该项目的主要目标是帮助学生改善他们的关系推理，即一种数学对象和概念之间的关系和认可关系的方式，包括共同点和差异。关系推理已被证明可以支持学习者发展解决问题的技能，不仅在数学方面都有帮助，而且对科学，工程和医疗保健等学科也有帮助，在这种学科中，强大的推理技能对于学习和解决问题很重要。该项目研究旨在确定教学支持，以帮助学生发展“关系心态”，并增强他们在解决问题方面的概念灵活性。绘制有关关系推理的认知科学文献，该项目包括三项实验研究，旨在测试学生对关系的关注是否可以促进相关思维，从而增强学生的概念灵活性。研究包括a）通过课堂话语明确指导学生对数学关系的关注； b）通过完成相关任务，隐式启动关系的关注； c）让学生在练习过程中参与对立思维。分析将包括描述性分析和多元回归分析。研究结果将为有效的教学方法提供见解NSF的法定使命，并使用基金会的知识分子优点和更广泛的影响审查标准来评估值得支持。