## Abstract

Mathematical structure is central to the interconnectedness of numerical, spatial or logical relationships, but it is not known how well teachers understand this concept or implement it in pedagogical practice. In this paper, we examine three junior secondary mathematics teachers’ understanding of mathematical structure and observe whether they apply it in their teaching. Case study data comprised teacher interviews and mathematics lesson observations. Analysis of interviews and teacher-directed communication (utterances) in lessons utilised an emergent framework for categorising mathematical structure: connections to other learning (C), recognising patterns (R), identifying similarities and differences (I) and generalising and reasoning (G). Findings from the interviews indicated that teachers supported the development of mathematical structure, but the interview responses were not generally reinforced by their utterances in mathematics lesson observations. Analysis of teacher utterances revealed superficial understanding and use of mathematical structure although there was some evidence of CRIG components in the teacher-directed communication for individual cases.

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## Funding

This study was supported by the NSW Catholic Education Commission through the Br. John Taylor Education Research Fellowship awarded to the first author in November 2014. Parts of this analysis were reported in the paper, Teachers’ understanding and use of mathematical structure (Gronow, Mulligan, & Cavanagh, 2017), *40 years on: We are still learning!: Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia* (pp. 286–292)*. *Melbourne, MERGA*.*

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Gronow, M., Mulligan, J. & Cavanagh, M. Teachers’ understanding and use of mathematical structure.
*Math Ed Res J* (2020). https://doi.org/10.1007/s13394-020-00342-x

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### Keywords

- Mathematics
- Secondary
- Mathematical structure
- Pedagogy
- Professional learning