ABSTRACT This article argues that mathematical knowledge, and its related pedagogy, is inextricably linked to the tools in which the knowledge is expressed. The focus is on digital tools and the different roles they play in shaping mathematical meanings and in transforming the mathematical practices of learners and teachers. Six categories of digital tool-use that distinguish their differing potential are presented: (1) dynamic and graphical tools; (2) tools that outsource processing power; (3) tools that offer new representational infrastructures for mathematics; (4) tools that help to bridge the gap between school mathematics and the students’ world; (5) tools that exploit high-bandwidth connectivity to support mathematics learning; and (6) tools that offer intelligent support for the teacher when their students engage in exploratory learning with digital technologies. Following exemplification of each category, the article ends with some reflections on the progress of research in this area and identifies some remaining challenges.

中文翻译：

---

通过数字技术改变学习者和教师的数学实践

摘要 本文认为，数学知识及其相关的教学法与表达知识的工具密不可分。重点是数字工具及其在塑造数学意义和改变学习者和教师的数学实践方面所发挥的不同作用。介绍了六类数字工具使用，以区分其不同的潜力：（1）动态和图形工具；(2) 外包处理能力的工具；(3) 为数学提供新的表征基础设施的工具；(4) 有助于弥合学校数学与学生世界之间差距的工具；(5) 利用高带宽连接支持数学学习的工具；(6) 在学生使用数字技术进行探索性学习时为教师提供智能支持的工具。在举例说明每个类别之后，文章最后对该领域的研究进展进行了一些反思，并确定了一些剩余的挑战。