Abstract
Over the past 9 years, we have implemented, developed, and refined a novel student-centered teaching method called Extreme Apprenticeship in university mathematics context. In this paper, we report the theoretical orientation behind the method, as well as its practical implementation. We also reflect on our experiences gained from using it in our teaching.
Highlights
Higher education aims to produce experts with strong professional identity and means to critically assess and develop their own skills as well as prevailing practices in their field
As a response to this challenge, we present the Extreme Apprenticeship method (XA) for teaching university mathematics students
Traditional teaching in large mathematics courses in a university typically consists of mass lectures and weekly problem classes
Summary
Higher education aims to produce experts with strong professional identity and means to critically assess and develop their own skills as well as prevailing practices in their field. In this light, the objectives of a program of study in mathematics become more complex than merely transferring a set of mathematical facts into students’ heads. As a response to this challenge, we present the Extreme Apprenticeship method (XA) for teaching university mathematics students. The XA method is based on Cognitive Apprenticeship [4], and it emphasizes supporting the development of expertise in students right from the beginning of their university studies. Our aim is to encourage other mathematics educators to integrate suitable elements of the XA method in their classes
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