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The purpose of this paper is to discuss two theoretical frameworks, Pirie and Kieren’s work (Pirie and Kieren, 1994) and variation theory of learning (Marton, 2015) in relation to lesson/learning study and mathematics teaching and learning.

The point of departure is the article: “Folding back and growing mathematical understanding: a longitudinal study of learning” (Martin and Towers, 2016) where it is demonstrated how Pirie and Kieren’s work (1994) and particularly the notion “folding-back” can be used as the theoretical framework in lesson/learning study. By dealing with similar arrangements and different theories, the two frameworks are contrasted.

It is suggested that the theory appropriated must be in resonance with the aim and focus of the study the theoretical perspective taken since it has implications for what becomes the focus of the process and subsequently the results of lesson/learning study.

This paper contributes to the discussion about how a more theory-informed lesson study and a broader theoretically framed learning study would improve and change the scope and progress of the two.

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