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

科学和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相应地强调比率和比例，然而许多学生在物理入门课上仍然难以推理乘积和比率。该项目正在编写教材，以加强学生在物理学入门课程经常涉及的主题范围内进行推理的能力。 这些材料采用“发明指导”，这种方法被证明在促进数学推理方面是有效的。 在发明任务中，学生们被赋予一项“工作”，他们通过发明一个量来描述一组物理情况并进行有意义的比较来完成。 这些任务是有顺序的，这样学生就可以在熟悉的日常环境中开始推理比率和比例，然后他们会朝着物理学家通常使用相同类型推理的更抽象的物理量前进。 这些发明序列被设计成突出所需推理的相似性。 项目工作人员正在开发用于高中和大学入门课程的发明序列，并正在测量它们在培养学生的内容知识和推理能力方面的有效性。 与此同时，他们也在进行基础研究，以了解学生在各种环境中如何实际使用比例。 这项工作有助于我们了解学生如何以及为什么在入门物理学中难以推理抽象量，并提供了更有效地为成熟的科学学生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.