A basic mental model (BMM—in German ‘Grundvorstellung’) of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific teaching approaches: the BMMs of area, reconstruction, average, and accumulation. Based on theoretical work, in this paper we ask how these BMMs could be identified empirically. A test instrument was developed, piloted, validated and applied with 428 students in first-year mathematics courses. The test results show that the four normative BMMs of the integral can be detected and separated empirically. Moreover, the results allow a comparison of the existing individual BMMs and the requested normative BMMs. Consequences for future developments are discussed.

数学概念的基本心理模型（BMM，德语为“ Grundvorstellung”）是与内容相关的解释，为该概念赋予了含义。本文定义了规范BMM和单个BMM，并以积分为例具体化了它们。针对定积分概念开发了四个BMM，有时在特定的教学方法中使用它们：面积，重构，平均和累积的BMM。基于理论工作，本文提出了如何凭经验识别这些BMM。在一年级数学课程中，有428名学生开发，测试，验证并应用了一种测试仪器。测试结果表明，可以凭经验检测并分离出积分的四个标准BMM。此外，结果允许比较现有的单个BMM和所请求的规范BMM。