The traditional way of presenting mathematical knowledge is logical deduction, which implies a monolithic structure with topics in a strict hierarchical relationship. Despite many recent developments and methodical inventions in mathematics education, many curricula are still close in spirit to this hierarchical structure. However, this organisation of mathematical ideas may not be the most conducive way for learning mathematics. In this paper, we suggest that flattening curricula by developing self-contained micro topics and by providing multiple entry points to knowledge by making the dependency graph of notions and subfields as sparse as possible could improve the effectiveness of teaching mathematics. We argue that a less strictly hierarchical schedule in mathematics education can decrease mathematics anxiety and can prevent students from ‘losing the thread’ somewhere in the process. This proposal implies a radical re-evaluation of standard teaching methods. As such, it parallels philosophical deconstruction. We provide two examples of how the micro topics can be implemented and consider some possible criticisms of the method. A full-scale and instantaneous change in curricula is neither feasible nor desirable. Here, we aim to change the prevalent attitude of educators by starting a conversation about the flat curriculum alternative.

中文翻译：

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数学教育新模式：扁平化课程，微题自成体系

传统的数学知识呈现方式是逻辑演绎，这意味着一个单一的结构，主题具有严格的层次关系。尽管数学教育最近有了许多发展和有条不紊的发明，但许多课程在精神上仍与这种层次结构很接近。然而，这种数学思想的组织可能不是学习数学的最有利方式。在本文中，我们建议通过开发独立的微观主题并通过使概念和子领域的依赖图尽可能稀疏来提供知识的多个入口点来扁平化课程，可以提高数学教学的有效性。我们认为，数学教育中不那么严格的等级安排可以减少数学焦虑，并可以防止学生在过程中的某个地方“迷失方向”。该提议意味着对标准教学方法进行彻底的重新评估。因此，它类似于哲学解构。我们提供了两个关于如何实现微型主题的示例，并考虑了对该方法的一些可能的批评。课程的全面和即时变化既不可行也不可取。在这里，我们旨在通过开始关于扁平化课程替代方案的对话来改变教育工作者的普遍态度。我们提供了两个关于如何实现微型主题的示例，并考虑了对该方法的一些可能的批评。课程的全面和即时变化既不可行也不可取。在这里，我们旨在通过开始关于扁平化课程替代方案的对话来改变教育工作者的普遍态度。我们提供了两个关于如何实施微主题的示例，并考虑了对该方法的一些可能的批评。课程的全面和即时变化既不可行也不可取。在这里，我们旨在通过开始关于扁平化课程替代方案的对话来改变教育工作者的普遍态度。