Abstract The learning of calculus concepts is considered challenging for students. This claim is actual for calculus in general and for specific concepts in particular. In this paper, we focus on the concept of the inflection point. We argue that one of the roots of this problem is the lack of a useful and productive meaning of the concept—the understanding of the inflection point as the point where the behaviour of a curve (graph of function) changes in relation to the tangent line. With the purpose of helping students to construct this meaning we developed a specific digital tool: a teaching unit based on the interactive diagrams framework. Does this tool help students to achieve this meaning (i.e., to construct and consolidate new knowledge)? To answer this question, we conducted an empirical feasibility experiment (in the form of a case study with two first-year students from the Industrial Engineering College) and analysed the gathered data using the framework of abstraction in context as the theoretical and methodological basis. Our findings show that the designed tool (the interactive digital teaching unit) has potential for helping students to make the above-mentioned meaning for this mathematical concept and can serve as a useful basis to continue the investigation of designing tools that support the meaning-making of advanced mathematical concepts.

中文翻译：

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探索性数字工具作为通往意义的途径：拐点案例

摘要 微积分概念的学习对学生来说具有挑战性。这种说法对于一般的微积分是实际的，特别是对于特定的概念。在本文中，我们关注拐点的概念。我们认为，这个问题的根源之一是该概念缺乏有用和富有成效的含义——将拐点理解为曲线（函数图）的行为相对于切线变化的点. 为了帮助学生构建这个含义，我们开发了一个特定的数字工具：一个基于交互式图表框架的教学单元。这个工具是否帮助学生实现这个意义（即构建和巩固新知识）？要回答这个问题，我们进行了实证可行性实验（以案例研究的形式与工业工程学院的两名一年级学生），并使用上下文抽象框架作为理论和方法基础分析收集的数据。我们的研究结果表明，所设计的工具（交互式数字教学单元）有可能帮助学生为这个数学概念创造上述含义，并且可以作为继续研究支持意义构建的设计工具的有用基础。先进的数学概念。