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The practice of Lesson study in the field of mathematics education is often restricted due to the assumptions of education theory and its impact on the teaching and learning practice. The paper discusses possible constructs and design principles that arise from such preconceptions of Lesson study. By incorporating these principles into the facilitation of Lesson study, a stronger community of practice can be established. As part of an undergraduate mathematics education methodology course's content, two volunteer groups of students specialising in Grades 4 to 7 mathematics participated in the design and study of a research lesson. The aim was to determine how these students depict Lesson study in theory and practice through a-priori design principles, and how these principles led to the identifying of constructs that produced new principles that can inform the development of a (new) Local theory. The results indicate that the design principles produced constructs of metacognitive skills, metacognitive language and metacognitive networking that can be theorised. Recommendations follow on how Lesson study practice can be theorised about and facilitated through these design principles.

Development of metacognitive theory for changing pedagogy remains an essential research activity. A lack of sufficient clear-cut qualitative analysis procedures extracting embedded metacognitive constructs from qualitative data (e.g., narrative focus group interviews) can hinder development of theory. An approach is therefore needed to analyse qualitative metacognitive data exploiting embedded metacognitive constructs for theory development. In an undergraduate fourth-year mathematics education module, two groups of students (Group A: n = 6; Group B: n = 5) participated in a series of focus group interviews. Participants designed and refined mathematics lessons about the concept of place value. We identified metacognitive networks as an embedded construct in students’ metacognitive processes. Findings indicate that metacognitive networks of an individual, social and socially shared metacognitive nature are embedded in qualitative data, and can be exploited to develop new metacognitive theory. We offer a novel three-step process in this methodology paper to extract metacognitive networks using Microsoft Office, ATLAS.ti and NodeXL.

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