This paper reports a study of university students’ experiences of learning mathematics in an introductory differential equations course that takes an inquiry approach to learning and teaching. The students are on a trajectory leading toward a bachelor’s degree in mathematics to be followed by a year-long teacher education credential program. The analysis of students’ end of course presentations and written portfolios is framed with community of practice theory, complemented with analytic categories from community of inquiry, including notions of inquiry stance and critical alignment. Our social theorization of university mathematics education adds a complementary perspective to the more conventional cognitive and discursive analyses and is necessitated by the very nature of inquiry approaches to education. The analysis of students’ presentations and writing leads to exploring their development of the notion of critical stance, which the students are seen to take toward the mathematics, their learning, and approaches to teaching mathematics. We find that the notion of critical stance can be distilled into three components: awareness, self-evaluation, and agency.

本文在一个介绍性微分方程课程中报告了对大学生学习数学的研究，该课程采用探究性的学习和教学方法。学生们走上了通往数学学士学位的轨道，随后是为期一年的师范教育证书课程。结合实践社区理论对学生的课程表述和书面作品集进行分析，并辅以探究社区的分析类别，包括探究立场和批判性取向的概念。我们对大学数学教育的社会理论化为更传统的认知和话语分析增加了一个补充视角，这是教育探究方法的本质所必需的。通过对学生的演讲和写作进行分析，可以探索他们对批判姿势概念的发展，这被视为学生对数学，他们的学习和数学教学方法的理解。我们发现，批判性立场的概念可以归纳为三个组成部分：意识，自我评价和代理。