A framework for primary teachers’ perceptions of mathematical reasoning Sandra Herbert a, *, Colleen Vale b , Leicha A. Bragg b , Esther Loong b , Wanty Widjaja b a Deakin University, PO Box 423, Warrnambool, VIC 3280, Australia b Deakin University, 221 Burwood Highway, Burwood, VIC 3125, Australia ARTICLE INFO Article history: Received 20 April 2015 Received in revised form 16 September 2015 Accepted 16 September 2015 Available online xxx Keywords: Phenomenography Mathematical reasoning Mathematical thinking Primary mathematics curriculum Mathematical content knowledge Professional learning ABSTRACT Mathematical reasoning has been emphasised as one of the key proficiencies for mathematics in the Australian curriculum since 2011 and in the Canadian curriculum since 2007. This study explores primary teachers’ perceptions of mathematical reasoning at a time of further curriculum change. Twenty-four primary teachers from Canada and Australia were interviewed after engagement in the first stage of the Mathematical Reasoning Professional Learning Program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variation in the perceptions of mathematical reasoning held by these teachers revealed seven categories of description based on four dimensions of variation. The categories delineate the different perceptions of mathematical reasoning expressed by the participants of this study. The resulting outcome space establishes a framework that facilitates tracking of growth in primary teachers’ awareness of aspects of mathematical reasoning. ã 2015 Elsevier Ltd. All rights reserved. 1. Introduction Mathematical reasoning is a broad term encompassing several different types such as induction, deduction, abduction (Holton, Stacey, & FitzSimons, 2012) and adaptive reasoning (Kilpatrick, Swafford, & Findell, 2001). It involves a focus on the mathematical aspects of an object or event, conjecturing about this object or event, and then drawing inferences based on relationships between those aspects (Reid & Knipping, 2010). Reasoning may be communicated to others in a variety of ways through “different representations, including visual, verbal and dynamic” (Dreyfus, Nardi & Leikin, 2012; p. 191). Alternatively it may be used in self-talk in an attempt to clarify and justify one’s own thinking (Carpenter, Franke, & Levi, 2003). Whilst some frameworks of teachers’ mathematical content knowledge (MCK) do exist (Ball, Thames, & Phelps, 2008; Ma, 1999; Chick, Baker, Pham, & Cheng, 2006), these frameworks focus on the types of knowledge for teaching of mathematics in general, rather than mathematical reasoning in particular. Mathematical reasoning has been variously defined in curriculum documents further indicating its importance. For example, reasoning, as a key mathematical proficiency, now appears in the Australian Curriculum: Mathematics (AC:M), (Australian Curriculum Assessment and Reporting Authority, (ACARA, 2013)) where it is described as “logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising” (p. 2). However, Australian * Corresponding author. Fax: +61 3 5563 3534 E-mail address: sandra.herbert@deakin.edu.au (S. Herbert). http://dx.doi.org/10.1016/j.ijer.2015.09.005 0883-0355/ ã 2015 Elsevier Ltd. All rights reserved. International Journal of Educational Research 74 (2015) 26–37 Contents lists available at ScienceDirect International Journal of Educational Research journal homepage: www.elsevier.com/locate/ijedures