ORIGINAL ARTICLE Telling and illustrating stories of parity: a classroom-based design experiment on young children’s use of narrative in mathematics Nicky Roberts • Andreas J. Stylianides Accepted: 13 November 2012 Ó FIZ Karlsruhe 2012 Abstract This paper examines ways to engage young children in constructing and interpreting narratives to develop their understanding of parity. It reports on a teaching intervention that was developed over three research cycles of a classroom-based design experiment, and focuses on the last of these cycles. The teaching intervention set out to investigate how young children (5–6-year-olds) can be supported to draw on narrative in their explanations of whether a whole number less than 20 is odd or even. Evidence of the effectiveness of the intervention is provided through comparison of children’s performance on pre- and post-tests in the form of semi- structured individual interviews. Also, authentic examples are provided of how children utilised their power of ‘imagining and expressing’ to tell stories of whether a whole number is odd or even, using either a counting, partitive, or quotitive model for division. Implications for research and practice are discussed in light of these findings. 1 Introduction Parity (the quality of being odd or even) is a topic which, although having a central place in the school mathematics curriculum, has not received much attention in mathemat- ics education research. At the teacher education level, Ball (1990) explored student teachers’ understanding of divisibility in general, while Zaskis (1998) explored stu- dent teachers’ knowledge of parity. Both studies identified difficulties faced by student teachers, with Zaskis noting that their conceptions of divisibility by two were somehow distinct from divisibility by other numbers. At the school level, Frobisher (Frobisher and Nelson 1992; Frobisher 1999) assessed primary school children’s knowledge of odd and even numbers, and concluded that they lacked conceptual understanding of parity. Hunter (2010) explored odd and even numbers as an example of developing 9–10- year-old children’s algebraic reasoning. She concluded that the context of odd and even numbers can be used ‘‘to provide children with effective opportunities to make conjectures, justify and generalize’’, and she highlighted the importance of teachers’ role in supporting children to model their conjectures using material (p. 109). The study on which we report in this paper contributed to this body of research and worked with a younger and less researched student population. It aimed to support 5–6-year-old children to develop their conceptions of par- ity, with a pedagogical focus on the use of narrative in mathematics. Specifically, the study aimed to investigate how young children can be assisted to use narrative as a cognitive tool to support understanding of parity as three related models (counting, quotitive, and partitive). The study was organised as a classroom-based design experi- ment and developed a teaching intervention over three iterative research cycles with the first author as the teacher– researcher. 1 N. Roberts (&) University of Witwatersrand, Johannesburg, South Africa e-mail: nickyroberts@icon.co.za A. J. Stylianides University of Cambridge, Cambridge, UK e-mail: as899@cam.ac.uk 1 The first author implemented the interventions in all research cycles, but she was not the usual teacher for any of the classes who participated in the study. 123 ZDM Mathematics Education DOI 10.1007/s11858-012-0474-2