ABSTRACT In this response paper to Hoyles’ contribution “Transforming the mathematical practices of learners and teachers through digital technology” focuses on three points. First, more knowledge is needed on why teaching and learning practices should transform, into what will they transform, and by what or by whom will they be transformed. Second, a suggestion is made for a more specific taxonomy on the didactical functionality of digital tools in mathematics education. Third, a plea is made for a future research agenda that addresses the ways in which activities with digital tools mediate the learning of mathematics in a fruitful way. This includes the interpretation and grading of online student work through intelligent mathematical software, and the notion of embodiment, as to do justice to the bodily experiences in which mathematical experiences are rooted.

中文翻译：

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工具和分类法：对霍伊尔斯的回应

摘要 在这篇对霍伊尔斯的贡献“通过数字技术改变学习者和教师的数学实践”的回应论文中，重点关注三点。首先，需要更多的知识来了解为什么教学和学习实践应该转化，它们将转化为什么，以及它们将通过什么或由谁来转化。其次，建议对数学教育中数字工具的教学功能进行更具体的分类。第三，呼吁未来的研究议程解决数字工具活动以富有成效的方式调解数学学习的方式。这包括通过智能数学软件对在线学生作业的解释和评分，以及体现的概念，