Proportions Playground: A Dynamic World to Support Teachers' Proportional Reasoning

比例游乐场：支持教师比例推理的动态世界

• 批准号: 1621290
• 负责人: Chandra Orrill
• 金额: $ 73.83万
• 依托单位: University of Massachusetts, Dartmouth
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1621290&HistoricalAwards=false
• 关键词: Proportions; Playground; Dynamic; World; Support

Proportions are a critical topic in mathematics that is simultaneously complicated and over-simplified in typical instruction. Current research undertaken by the research team suggests that the over-simplification is related to limitations in teachers' understandings of proportional relationships. Presenting proportions in a dynamic environment offers teachers the opportunity to create key developmental understandings related to this area of mathematics. This project focuses on the creation of the initial functionality for a dynamic microworld, Proportions Playground, designed to support teachers in developing a coherent understanding of proportional reasoning. Proportions Playground is conceptualized as a tool for supporting the development of coherent understandings by allowing teachers to interact in concrete ways with otherwise abstract ideas and by allowing teachers easy access to dynamic objects and other representations. It is meant to address the significant limitations for reasoning about the relationships between measurable aspects of two objects as well as in manipulating those relationships. Building from work currently underway, Proportions Playground will explore key areas in which there are opportunities for engaging teachers in the development of a coherent and robust understanding of proportional reasoning that extends beyond the typical "3 given, 1 unknown" proportion problem. This approach attempts to engage teachers in an array of dynamic, visually-rich sets of tasks designed to challenge teachers' preconceptions of proportions and to strengthen their connections between proportions and related areas of mathematics. This project is funded by the Discovery Research PreK-12 (DRK-12) and EHR Core Research (ECR) Programs. the DRK-12 program supports research and development on STEM education innovations and approaches to teaching, learning, and assessment. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field.The Proportions Playground project seeks to both develop a unique pilot software application for the iPad and explore how it supports teachers in developing a coherent, robust definition of proportions. The software will be designed to support either numeric manipulation (e.g., graphing software) or geometric constructions (e.g., dynamic geometry software). Specifically, for this project the mathematics of interest will include the relationships between similarity and proportion and the nature of covariation. The research will focus on how teachers are developing a robust and coherent understanding of proportions and how the dynamic environment promotes such understandings. Working with six teacher advisors, the project will develop three task sets. Using teaching experiments and individual interviews, results will be used to refine the task sets. The revised task sets will be piloted with 40 teachers. Data will be collected on participants' thinking and any changes seen in the knowledge resources they are using. The researchers will be looking for factors that seem to impact teachers' thinking as well as evidence to support or deny the assertion that the Proportions Playground activities engage teachers in (a) different ways of reasoning about proportions and (b) support them in drawing from a wide array of resources so that coherence may be developed were the teachers to have a prolonged engagement with the tools. The project will rely on Epistemic Network Analysis to identify the connections between knowledge resources.

比例是数学中的一个关键主题，在典型教学中既复杂又过于简单。研究小组目前的研究表明，这种过于简单化的现象与教师对比例关系的理解有限有关。在动态环境中呈现比例为教师提供了建立与该数学领域相关的关键发展理解的机会。该项目的重点是为动态微观世界“比例游乐场”创建初始功能，旨在支持教师对比例推理形成连贯的理解。 Proportions Playground 被概念化为一种支持连贯理解发展的工具，它允许教师以具体的方式与抽象的想法进行交互，并允许教师轻松访问动态对象和其他表示。它旨在解决推理两个对象的可测量方面之间的关系以及操纵这些关系时的重大限制。在目前正在进行的工作的基础上，比例游乐场将探索一些关键领域，在这些领域中，教师有机会对比例推理形成连贯而有力的理解，超越典型的“3 个给定，1 个未知”比例问题。这种方法试图让教师参与一系列动态的、视觉丰富的任务，旨在挑战教师对比例的先入之见，并加强比例与数学相关领域之间的联系。该项目由 Discovery Research PreK-12 (DRK-12) 和 EHR 核心研究 (ECR) 计划资助。 DRK-12 计划支持 STEM 教育创新以及教学、学习和评估方法的研究和开发。 ECR 项目强调基础 STEM 教育研究，以生成该领域的基础知识。Proportions Playground 项目旨在为 iPad 开发独特的试点软件应用程序，并探索它如何支持教师制定连贯、可靠的比例定义。该软件将被设计为支持数字操作（例如绘图软件）或几何构造（例如动态几何软件）。具体来说，对于这个项目，感兴趣的数学将包括相似性和比例之间的关系以及协变的性质。该研究将重点关注教师如何对比例形成强有力且连贯的理解，以及动态环境如何促进这种理解。该项目将与六名教师顾问合作，开发三组任务。通过教学实验和个人访谈，结果将用于完善任务集。修订后的任务集将在 40 名教师中进行试点。将收集参与者的想法以及他们正在使用的知识资源中看到的任何变化的数据。研究人员将寻找似乎影响教师思维的因素以及支持或否认“比例游乐场”活动让教师以不同方式推理比例以及（b）支持他们从比例中汲取经验的证据。广泛的资源，以便教师能够长期使用这些工具，从而形成一致性。该项目将依靠认知网络分析来识别知识资源之间的联系。