A “true” story about mathematical reasoning made easy

Mathematical reasoning is one of the four proficiencies emphasised in the Australian Curriculum: Mathematics (AC:M) where it is described as: “[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising’ (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2017, p. 5); and more recently is spearheading efforts to reform mathematics teaching (Herbert & Bragg, 2017). Reasoning is essential for students to make sense of mathematics (Kilpatrick, Swafford, & Findell, 2001) and described as “the glue that holds everything together, the lodestar that guides learning. One uses it to navigate through the many facts, procedures, concepts, and solution methods and to see that they all fit together in some way, that they make sense” (p. 129). However, previous research has shown that many teachers emphasise explaining, and yet neglect other reasoning actions such as justifying and generalising (Clarke, Clarke, & Sullivan, 2012). Similarly, Loong, Vale, Herbert, Bragg, & Widjaja (2017) reported that many of the primary teachers engaged in their Mathematical Reasoning Professional Learning Research Program possessed a limited understanding of mathematical reasoning and its teaching prior to observing and discussing demonstration lessons focussed explicitly on reasoning. Despite the emphasis on reasoning in the AC:M, little is known about teachers’ choice of tasks intended to extend the reasoning capabilities of their students.