The lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from first-semester lectures given by seven mathematics lecturers at three Swedish universities, all concerning various aspects of the function concept. Analysis was carried out from a commognitive perspective, which distinguishes between object-level and meta-level discourse. Here I focus on two aspects of meta-level discourse: introducing new mathematical objects; and what counts as valid endorsement of a narrative. The analysis reveals a number of metarules concerning the modelling of mathematical reasoning and behaviour, both more general rules such as precision and consensus, and rules more specifically concerning construction and endorsement of narratives. The paper contributes to a small but growing body of empirical research on university mathematics teaching, and also lends empirical support to previous claims about the modelling aspect of mathematics lecturing, thus contributing to a deepened understanding of the lecture format and its potential role in future university mathematics teaching.

演讲形式虽然备受批评，但仍然是大学数学教学中最常见的形式之一。本文研究了作为建模数学话语的一种方法，在文学中有时将其作为最重要的功能之一加以强调。本文中分析的数据取自瑞典三所大学的七名数学讲师的第一学期讲课，所有这些讲义都涉及功能概念的各个方面。从认知的角度进行了分析，从而区分了对象级话语和元级话语。在这里，我主要关注元层次话语的两个方面：介绍新的数学对象；介绍新的数学对象。什么才算是对叙事的有效认可。分析揭示了许多与数学推理和行为建模有关的元规则，包括更通用的规则（例如精确度和共识），以及更具体地涉及叙事的构造和认可的规则。本文为大学数学教学的实证研究提供了少量但不断增长的经验，也为先前关于数学教学的建模方面的主张提供了实证支持，从而有助于加深对讲课形式及其在未来大学中的潜在作用的理解。数学教学。