This study investigates what mathematicians, who teach academic mathematics courses to secondary school mathematics teachers, want to teach them about the discipline of mathematics. Data sources included interviews with five research mathematicians. The data analysis revealed that expanding teachers’ knowledge about the discipline of mathematics was one of the interviewees’ main objectives. The mathematicians referred to nine characteristics that can be grouped into three key aspects: (1) essence of mathematics, (2) doing mathematics, and (3) worth of mathematics. The characteristics of the discipline of mathematics generated in our study are in line with ideas and practices widely advocated in the last decades for the teaching and learning of mathematics, and with contemporary philosophical approaches regarding mathematics. The potential of the characteristics to serve as a conceptual framework in studies that focus on teacher knowledge about the discipline of mathematics is discussed.

本研究调查了向中学数学教师教授学术数学课程的数学家希望向他们教授有关数学学科的内容。数据来源包括对五位研究数学家的采访。数据分析显示，扩展教师对数学学科的知识是受访者的主要目标之一。数学家们提到了九个特征，这些特征可以分为三个关键方面：（1）数学的本质，（2）做数学，（3）数学的价值。在我们的研究中产生的数学学科的特征符合过去几十年广泛倡导的数学教学和学习的思想和实践，以及关于数学的当代哲学方法。