The authors present a theoretical proposal for the organization of mathematical contents, more precisely to curricula development formalization and formal verification, inspired by knowledge engineering techniques. The situation addressed is the following: the starting point is a mathematical “official curriculum” (or part of it), not necessarily completely detailed. In our proposal, a group of experts would have to first build a detailed formulation of this curriculum (including the “prerequisite” relation between contents), which we will denominate “preprocessed official curriculum.” We detail how any “official curriculum development” could then be rigorously formalized and formally verified in a way inspired by rule-based expert system formal verification. We have defined the following terms: “contents soundness,” “contents completeness,” “relation soundness,” “relation completeness,” and “absence of cycles.” We believe that this is a completely new formalization within mathematics teaching theory that, once computer is implemented, would be very helpful. That would be the case, for instance, in countries where government sets the “official curricula” for Primary and Secondary Education and textbook contents have to be manually checked and approved by academic authorities: evaluators would “only” have to extract the textbook contents and set the “prerequisite” relation among them and let the computer do the rest.

中文翻译：

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知识工程在数学课程组织与形式验证中的应用

作者提出了关于组织数学内容的理论建议，更确切地说是在知识工程技术的启发下进行的课程开发形式化和形式验证。解决的情况如下：起点是数学“官方课程”（或其一部分），不一定完全详细。在我们的建议中，一组专家必须首先为该课程建立详细的表述（包括内容之间的“前提”关系），我们将其命名为“预处理的官方课程”。我们详细介绍了如何在基于规则的专家系统形式验证的启发下，对“正式课程开发”进行严格形式化和形式验证。我们定义了以下术语：“内容的完整性”，“内容的完整性，”，“关系完整性”，“关系完整性”和“缺少周期”。我们认为，这是数学教学理论中的全新形式，一旦实现计算机，将非常有帮助。例如，在政府为中小学设置“官方课程”并且教科书内容必须由学术机构手动检查和批准的国家中，情况是这样的：评估人员“仅”必须提取教科书内容，设置它们之间的“先决条件”关系，然后让计算机完成其余工作。