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.

基于数学教育和心理学研究50年研究的集体研究，以提高学生在Algebra的背景下，基于数学教育和心理学的50年研究的集体研究，用于证明（LAMP）项目测试的学习代数和方法，并完善了假设的学习轨迹和相应的评估。 LAMP的目标是：1）生产一套基于证据的课程材料，以改善学生在教授代数的八年级教室中的推理，证明和论证的学习； 2）产生经验证据，构成将项目扩展到完整的研发项目的基础； 3）完善一组工具和数据收集方法，以支持一个完整的研发项目。 LAMP结合了定性和定量方法，以在八年级代数课程的背景下为推理，论证和证明的学习方法提炼和测试一个假设的学习轨迹。使用定性方法和定量方法，该项目进行了一项试点研究，可以在以后的研究中进行扩展。该研究产生了基于证据的学习轨迹和评估它的适当工具。在过去的二十年中，国家组织呼吁更多地关注各年级的证明，证明和论证的主题。但是，推理和证明的教学在各个级别的教室中仍然很少。 LAMP将通过展示提高学生的推理和论证技巧以满足大学和职业准备就绪的要求，以解决STEM教育中的这一关键需求。该项目有望通过对如何促进实际八年级教室中的推理和论证学习的详细描述来对美国的未来课程产生广泛的影响。目前，对推理和证明技能如何与代数思维一起发展的全面理解并不存在。传统的，完全正式的方法（例如两列证明）在学习证明和证明方面没有表现出有效性，也没有改善其他数学实践，例如解决问题的技能和理智。尽管包括心理学文献研究在内的几项研究为发展可行的论据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，但不存在将所有这些基金会融合在一起的连贯而完整的材料集。该项目将使用具有高比例的美国原住民学生的教室来测试假设的学习轨迹。