Learning Algebra and Methods for Proving (LAMP)

学习代数和证明方法（LAMP）

• 批准号: 1317034
• 负责人: David Yopp
• 金额: $ 37.07万
• 依托单位: Regents of the University of Idaho
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-10-01 至 2016-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1317034&HistoricalAwards=false
• 关键词: Learning; Algebra; Methods; Proving; LAMP

The Learning Algebra and Methods for Proving (LAMP) project tests and refines a hypothetical learning trajectory and corresponding assessments, based on the collective work of 50 years of research in mathematics education and psychology, for improving students' ability to reason, prove, and argue mathematically in the context of algebra. The goals of LAMP are: 1) to produce a set of evidence-based curriculum materials for improving student learning of reasoning, proving, and argumentation in eighth-grade classrooms where algebra is taught; 2) to produce empirical evidence that forms the basis for scaling the project to a full research and development project; and 3) to refine a set of instruments and data collection methods to support a full research and development project. LAMP combines qualitative and quantitative methods to refine and test a hypothetical learning trajectory for learning methods of reasoning, argumentation, and proof in the context of eighth-grade algebra curricula. Using qualitative methods and quantitative methods, the project conducts a pilot study that can be scaled up in future studies. The study produces an evidence-based learning trajectory and appropriate instruments for assessing it. Over the past two decades, national organizations have called for more attention to the topics of proof, proving, and argumentation at all grade levels. However, the teaching of reasoning and proving remains sparse in classrooms at all levels. LAMP will address this critical need in STEM education by demonstrating ways to improve students' reasoning and argumentation skills to meet the demands of college and career readiness. This project promises to have broad impacts on future curricula in the United States by creating a detailed description of how to facilitate reasoning and argumentation learning in actual eighth-grade classrooms. At present, a comprehensive understanding of how reasoning and proving skills develop alongside algebraic thinking does not exist. Traditional, entirely formal approaches such as two-column proof have not demonstrated effectiveness in learning about proof and proving, nor in improving other mathematical practices such as problem-solving skills and sense making. While several studies, including studies in the psychology literature, lay the foundation for developing particular understandings, knowledge, and skills needed for writing viable arguments and critiquing the arguments of others, a coherent and complete set of materials that brings all of these foundations together does not exist. The project will test the hypothetical learning trajectory with classrooms with high proportions of Native American students.

学习代数和证明方法 (LAMP) 项目基于 50 年数学教育和心理学研究的集体成果，测试和完善假设的学习轨迹和相应的评估，以提高学生推理、证明和论证的能力在代数的数学背景下。 LAMP 的目标是： 1) 制作一套基于证据的课程材料，以提高学生在教授代数的八年级课堂上推理、证明和论证的学习； 2) 提供经验证据，为将项目扩展为完整的研发项目奠定基础； 3）完善一套仪器和数据收集方法以支持完整的研发项目。 LAMP 结合了定性和定量方法，以完善和测试八年级代数课程中推理、论证和证明学习方法的假设学习轨迹。该项目使用定性方法和定量方法进行了一项试点研究，该研究可以在未来的研究中扩大规模。该研究产生了基于证据的学习轨迹和适当的评估工具。在过去的二十年里，国家组织呼吁各级各级更多地关注证明、证明和论证的主题。然而，推理和证明的教学在各级课堂上仍然很少。 LAMP 将通过展示提高学生推理和论证技能的方法来满足 STEM 教育的这一关键需求，以满足大学和职业准备的要求。该项目通过详细描述如何在实际八年级课堂上促进推理和论证学习，有望对美国未来的课程产生广泛影响。目前，对于推理和证明技能如何与代数思维一起发展的全面理解还不存在。传统的、完全形式化的方法（例如两列证明）在学习证明和证明方面并没有表现出有效性，也没有在提高其他数学实践（例如解决问题的技能和意义建构）方面表现出有效性。虽然包括心理学文献研究在内的一些研究为发展撰写可行的论点和批评他人的论点所需的特定理解、知识和技能奠定了基础，但将所有这些基础结合在一起的一套连贯且完整的材料并不能不存在。该项目将在美国原住民学生比例较高的教室中测试假设的学习轨迹。