In many countries STEM degree programs face high dropout rates, which are often attributed to insufficient mathematical preparation of incoming undergraduates. However, it is largely unclear which mathematical prerequisites universities expect from their new STEM undergraduates. There are hardly official documents and it is even an open question whether there is a consensus among university instructors. The main goal of this study is therefore to describe the expected mathematical prerequisites for new STEM undergraduates. We conducted a Delphi study with German university instructors for first semester mathematics courses in STEM programs. The participants identified 179 prerequisites addressing: (1) mathematical content, (2) mathematical processes, (3) views about the nature of mathematics, and (4) personal characteristics. For 140 of these prerequisites there was a consensus regarding their necessity among the university instructors. The expected mathematical prerequisites are mainly on a basic level and do not require formalistic or abstract mathematical knowledge or abilities.

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STEM课程的数学先决条件：大学教师对STEM新生的期望是什么？

在许多国家，STEM学位课程面临很高的辍学率，这通常归因于入学的本科生数学准备不足。但是，目前尚不清楚大学对新的STEM本科生期望哪些数学先决条件。几乎没有正式文件，甚至大学教官之间是否达成共识也是一个悬而未决的问题。因此，本研究的主要目标是描述新STEM本科生的预期数学前提。我们与德国大学的讲师进行了德尔菲研究，目的是在STEM课程中开设第一学期的数学课程。参与者确定了179个前提条件，这些条件涉及：（1）数学内容，（2）数学过程，（3）关于数学性质的观点以及（4）个人特征。对于这些先决条件中的140个，大学教师之间就其必要性达成了共识。预期的数学先决条件主要在基本水平上，不需要形式主义或抽象的数学知识或能力。