EAGER: Collaborative Research: Technology to Support Mathematical Argumentation

这个项目要解决的一个大问题是，“技术如何支持数学论证的教与学？”这个热切的建议侧重于帮助青少年学习数学/代数论证这一愿景的第一步。该项目有两个互补的目标：更好地定义支持小学生学习证明和论证所需的技术工具，以及更好地理解当这些工具可用时，小学生如何学习提出和捍卫数学主张。pi设想并正在开发一种可以在平板电脑上实现的动画工具（这样每个孩子都有他/她自己的电子笔记本），它为小组和全班分享和完善论点提供了基础设施，并促进了具体的数学讨论。一个巨大的挑战是提供合适的表达工具；为了实现分享，学习者首先需要能够表达他们的理解，许多研究表明，与简单的口头表达理解相比，具体的“书面”（可分享的）理解表达为促进具体讨论提供了更好的基础。这个项目在表达方面取得的特别进步是为动态表示提供了工具；也就是说，它们能够模拟数学运算时发生的情况。这些具体的理解表达可以回放、暂停等等。学生通过绘制，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。他们将自己的口头解说与动画一起记录下来并保存起来，然后一起播放，从而使他们的口头描述具体化、可检验、可分享。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。许多学生纠结于主题，因此也纠结于数学论证。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，以学习成为称职的代数推理者。在这个EAGER项目中，他们将重点放在开发该工具集的第一步，并调查年轻学习者在拥有这些工具时如何进行数学论证和辩护。该项目代表了一个未经测试但具有潜在变革性的想法的早期工作，并可能在帮助年轻学习者成为数学推理者方面催化快速和创新的进展。

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.