Collaborative Proposal: Developing Proportional Reasoning in a Physics Context with Invention Tasks

协作提案：在物理背景下通过发明任务发展比例推理

• 批准号: 1045227
• 负责人: Andrew Boudreaux
• 金额: $ 6.72万
• 依托单位: Western Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-03-01 至 2014-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1045227&HistoricalAwards=false
• 关键词: Collaborative; Proposal; Developing; Proportional; Reasoning

Workers in science and technology-related fields use proportional reasoning extensively when making sense of quantitative data. Mathematics instruction in middle school and high school often places a corresponding emphasis on ratios and proportions, however many students still have difficulty reasoning about product and ratio quantities in introductory physics classes. This project is developing curricular materials to strengthen the ability of students to reason in the context of the topics regularly covered in introductory physics. These materials employ "invention instruction," an approach shown to be effective in facilitating mathematical reasoning. In an invention task, students are given a "job" that they complete by inventing a quantity to characterize a set of physical situations and make meaningful comparisons. The tasks are sequenced so students can start by reasoning about ratios and proportions in a familiar, everyday context, and they progress toward more abstract physical quantities for which physicists commonly use the same type of reasoning. These invention sequences are designed to highlight the similarity of the reasoning required. The project workers are developing invention sequences for use in both high school and introductory college classes and are measuring their effectiveness in developing students' content knowledge and reasoning ability with more abstract quantities. In parallel, they are also conducting basic research into how students are actually using proportions in various settings. This work is contributing to our understanding of how and why students struggle with reasoning about abstract quantities in introductory physics and provides instructional approaches that more efficiently develop reasoning skills for maturing students of science.

科学技术相关领域的工作者在理解定量数据时，广泛使用比例推理。初中和高中的数学教学往往强调比例和比例，然而许多学生在物理入门课上仍然难以推理乘积和比例数量。这个项目正在开发课程材料，以加强学生在物理入门课程中经常涉及的主题的背景下进行推理的能力。这些材料采用了“发明教学”，这是一种被证明在促进数学推理方面有效的方法。在一项发明任务中，学生们被布置了一项“任务”，他们通过发明一个数量来描述一组物理情况并进行有意义的比较来完成这项任务。这些任务是按顺序进行的，这样学生就可以从在熟悉的日常环境中对比例和比例进行推理开始，然后进行更抽象的物理量，物理学家通常对这些物理量使用相同类型的推理。这些发明序列旨在突出所需推理的相似性。项目工作人员正在开发高中和大学入门课程中使用的发明序列，并用更抽象的数量来衡量它们在发展学生内容知识和推理能力方面的有效性。与此同时，他们还对学生在不同环境中实际使用比例的情况进行了基础研究。这项工作有助于我们理解学生如何以及为什么在入门物理中难以进行关于抽象量的推理，并为成熟的理科学生提供更有效地发展推理技能的教学方法。