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

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。在初中和高中的数学教学中，往往会把相应的重点放在比率和比例上，然而在物理入门课上，许多学生仍然很难推理出乘积和比率的数量。这个项目正在开发课程材料，以加强学生在物理导论中经常涉及的主题背景下进行推理的能力。这些材料采用了“发明指导”，这种方法在促进数学推理方面被证明是有效的。在发明任务中，学生被要求完成一项“工作”，他们需要发明一个数量来描述一组物理情况，并进行有意义的比较。这些任务是按顺序排列的，这样学生们就可以从在熟悉的日常环境中推理比率和比例开始，然后逐步学习更抽象的物理量，物理学家通常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。该项目的工作人员正在开发用于高中和大学入门课程的发明序列，并正在测量它们在发展学生的内容知识和使用更抽象的数量的推理能力方面的有效性。与此同时，他们也在进行基础研究，了解学生在各种情况下是如何实际使用比例的。这项工作有助于我们理解学生在物理入门课程中如何以及为什么在抽象数量的推理方面遇到困难，并为成熟的理科生提供更有效地培养推理技能的教学方法。

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.