The role of appropriation in guided reinvention: establishing and preserving devolved authority with low-attaining stude
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The role of appropriation in guided reinvention: establishing and preserving devolved authority with low-attaining students Yvette Solomon 1
2
& Susan Hough & Stephen Gough
2
Accepted: 9 October 2020/ # The Author(s) 2020
Abstract
Realistic Mathematics Education (RME) relies on the pedagogy of guided reinvention, in which opportunities for learning are created through the teacher’s orchestration of wholeclass mathematical discussion towards a specific goal. However, introducing an RME approach to students who are accustomed to traditional teaching requires a substantial shift in roles, particularly with respect to the devolution of authority from teacher to student. In this study, we worked with low-attaining students, implementing RME to improve understanding of fractions. The analysis highlights how the introduction of guided reinvention is supported by extended wait time and teacher neutrality, but also by teachers’ appropriation of student strategies as a basis for supporting shared authority in the joint construction of mathematical ideas. The article considers the relationship between guided reinvention, appropriation and student agency. Keywords Guided reinvention . Appropriation . Devolved authority . Realistic Mathematics Education . Low attainers
1 Background and context As Maass, Cobb, Krainer, and Potari (2019) point out, international evidence persistently highlights a mismatch between the innovative pedagogy advocated by mathematics education researchers and the reality of teachers’ practice. However, changing practice from a focus on instruction for procedural fluency to one which prioritises the development of student agency and argumentation requires not only pedagogic change but also changes in values and beliefs. * Yvette Solomon [email protected]
1
Education and Social Research Institute, Manchester Metropolitan University, 53 Bonsall Street Manchester M15 6GX UK
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Faculty of Education, Manchester Metropolitan University, 53 Bonsall Street Manchester M15 6GX UK
Solomon Y. et al.
Procedural instruction is particularly prevalent in classes for low-attaining students, fed in part by low teacher expectations (Francis, Connolly et al., 2017) but also by a more subtle discourse of nurturance and dependency: Mazenod et al. (2019) report that teachers of lower attainers were concerned that students should not be “over-stretched”, devising lessons around an assumed need for more repetition and rehearsal, and more teacher input rather than discussion. As Francis, Connolly et al. (2017) note, being placed in a low attainment group generates low self-expectations on the part of students, despite the fact that they may also complain that the teaching they receive is lacking in interest and challenge (Francis et al., 2019). This recent research reflects long-standing evidence that students are aware that the procedural methods in lower attainment mathematics classes construct them as failures (Boaler, Wiliam, & Brown, 2000). At the same time, it underlines students’ agency in the classroom—the
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