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

比例是数学中的一个重要话题，在典型的教学中，它既复杂又过于简单。研究小组目前进行的研究表明，过于简单化与教师对比例关系的理解有局限性有关。在动态环境中呈现比例为教师提供了创造与数学这一领域相关的关键发展理解的机会。该项目的重点是创建一个动态微观世界的初始功能，比例游乐场，旨在支持教师发展比例推理的连贯理解。比例操场是概念化的工具，支持连贯的理解的发展，让教师以具体的方式与其他抽象的想法，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的重大限制。从目前正在进行的工作建设，比例操场将探索关键领域，其中有机会让教师参与比例推理的连贯和强大的理解，超越典型的“3给定，1未知”比例问题的发展。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，并加强他们在比例和相关数学领域之间的联系。该项目由Discovery Research PreK-12（DRK-12）和EHR Core Research（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，以产生该领域的基础知识。Proportions Playground项目旨在为iPad开发一个独特的试点软件应用程序，并探索它如何支持教师制定一个连贯的，强大的比例定义。软件将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。研究将侧重于教师如何发展一个强大的和连贯的理解比例和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，制定三套任务。通过教学实验和个别访谈，结果将用于完善任务集。将在40名教师中试用修订后的任务集。将收集参与者的想法和他们使用的知识资源中的任何变化的数据。研究人员将寻找似乎影响教师思维的因素，以及支持或否认以下说法的证据：比例游戏场活动使教师（a）以不同的方式推理比例，（B）支持他们从广泛的资源中汲取，以便教师长期使用这些工具可以发展连贯性。该项目将依靠认知网络分析来确定知识资源之间的联系。

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.