Leveraging Pedagogical Comparisons in Mathematical Thinking and Learning

这个项目的主要目标是帮助学生提高他们的关系推理，即一种关注和识别数学对象和概念之间的关系，包括共性和差异的方法。事实证明，关系推理可以帮助学习者发展解决问题的技能，这些技能不仅对数学很有帮助，而且对科学、工程和医疗保健等学科也有帮助，在这些学科中，强大的推理技能对学习和解决问题非常重要。该项目研究的目的是确定教学支持，帮助学生培养“关系思维”，并提高他们在解决问题时的概念灵活性。该项目借鉴了有关关系推理的认知科学文献，包括三项实验研究，旨在测试引导学生关注关系是否可以培养关系思维，从而提高学生的概念灵活性。这些研究包括：a)通过课堂话语明确引导学生注意数学关系；b)通过完成相关任务内隐启动关系注意；c)让学生在实践中进行对立思维。分析将包括描述性分析和多元回归分析。该项目由STEM教育博士后研究奖学金(STEM Ed PRF)项目资助，旨在提高STEM、STEM教育、教育和相关学科的博士的研究知识、技能和实践，以促进他们从事基础和应用研究，促进该领域知识的进步。该奖项反映了NSF的法定使命，并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，被认为值得支持。

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.