EAGER: Collaborative Research: Technology to Support Mathematical Argumentation

EAGER：协作研究：支持数学论证的技术

• 批准号: 1250362
• 负责人: Andee Rubin
• 金额: $ 12.11万
• 依托单位: TERC Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-15 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1250362&HistoricalAwards=false
• 关键词: EAGER; Collaborative; Research; Technology; Support

The big question being addressed in this project is, "How can technology support the teaching and learning of mathematical argumentation?" This EAGER proposal focuses on the first steps in moving towards the vision of helping youngsters learn mathematical/algebraic argumentation. The project has two complementary goals: to better define the technological tools needed to support elementary students learning about proof and argumentation and to understand better how elementary school students learn to make and defend mathematical claims when such tools are available. The PIs envision and are developing an animation tool to be implemented on tablet computers (so each child has his/her own electronic notebook) that provides infrastructure for sharing and refining arguments in small groups and across the class and for promoting concrete math discussions. A big challenge is providing the right tools for expression; for sharing to happen, learners need to first be able to express their understanding, and much research shows that a concrete "written" (sharable) expression of understanding provides better foundations for promoting concrete discussion than do expressions of understanding that are simply verbal. The particular advance in expression that is being made in this project is providing tools for dynamic representations; that is, they are able to animate what happens when mathematical operations are carried out. These concrete expressions of understanding can then be played back, paused, and so on. Students create animations by drawing, erasing, duplicating, moving, and grouping objects. They can edit each others' animations, and the teacher will also be able to create animations for students to view and edit. They record and save their oral explanations along with the animations and play them back together, thus making their verbal descriptions concrete, examinable, and sharable. The ability to prepare and present a mathematical argument is a key component of the mathematical competence students need to achieve in upper elementary school (grades 3 through 5). Many students struggle with the subject matter and therefore struggle as well with making mathematical arguments. The PIs envision a computational tool set that young students will use to construct and share mathematical arguments, in the service of learning to be competent algebraic reasoners. In this EAGER project, they focus on first steps in developing that tool set and on investigating how young learners make and defend mathematical arguments when they have such tools available. This project represents work in its early states on an untested but potentially transformative idea and is likely to catalyze rapid and innovative advances in helping young learners become mathematical reasoners.

这个项目所要解决的大问题是，“技术如何支持数学论证的教学和学习？“EAGER的建议侧重于帮助青少年学习数学/代数论证的第一步。该项目有两个互补的目标：更好地定义所需的技术工具，以支持小学生学习证明和论证，并更好地了解小学生如何学习，使和捍卫数学索赔时，这些工具是可用的。PI设想并正在开发一种动画工具，该工具将在平板电脑上实现（因此每个孩子都有自己的电子笔记本），该工具为在小组和班级中分享和改进论点以及促进具体的数学讨论提供基础设施。一个很大的挑战是提供正确的表达工具;为了分享，学习者首先需要能够表达他们的理解，许多研究表明，一个具体的“书面”（可分享的）理解表达比简单的口头理解表达更能促进具体的讨论。在这个项目中，表达的特别进步是提供了动态表示的工具;也就是说，它们能够在进行数学运算时动画化所发生的事情。学生可以通过绘制、擦除、复制、移动和分组对象来创建动画。他们可以编辑彼此的动画，老师也可以创建动画供学生查看和编辑。他们记录并保存他们的口头解释沿着的动画，并一起播放，从而使他们的口头描述具体，可检查，可共享。准备和提出数学论点的能力是学生在小学高年级（3至5年级）需要达到的数学能力的关键组成部分。许多学生挣扎的主题，因此斗争以及作出数学论点。PI设想了一个计算工具集，年轻学生将使用它来构建和分享数学论证，以学习成为合格的代数推理者。 在这个EAGER项目中，他们专注于开发该工具集的第一步，并调查年轻学习者如何在拥有这些工具时进行数学论证和辩护。这个项目代表了一个未经测试但可能具有变革性的想法的早期阶段，并可能促进帮助年轻学习者成为数学推理者的快速创新进步。