Proceedings of the IConSSE FSM SWCU (2015), pp. AZ.23–25 ISBN: 978-602-1047-21-7 SWUP AZ.23 Problem solving and reasoning in the learning of mathematics Colleen Vale * Deakin University, Melbourne, Australia Abstract In Australia we have been concerned to ensure that our citizens are numerate and able to use mathematics in their daily personal and working lives. More recently mathematics curriculum writers and educators have acknowledged the need for students to be creative thinkers and problem solvers, not only when using mathematics in our daily lives, but also to contribute to improving our society and economy and enhance the employment opportunities for young people. These two examples provide illustrations of tasks that can be used to develop students’ understanding of algebraic concepts in both primary and secondary curriculum and to engage learners in problem solving and reasoning, especially justifying and generalizing. Keywords algebraic concepts, problem solving, reasoning 1. Introduction In Australia we have been concerned to ensure that our citizens are numerate and able to use mathematics in their daily personal and working lives. More recently mathematics curriculum writers and educators have acknowledged the need for students to be creative thinkers and problem solvers, not only when using mathematics in our daily lives, but also to contribute to improving our society and economy and enhance the employment opportunities for young people. In my research and engagement with teachers and schools I’ve evaluated school change and development, and contributed to professional learning of coaches and teachers including through demonstration lessons and Japanese Lesson Study. Schools that are making a difference are implementing student-centred learning by planning coherent lessons that focus on a specific learning goal and address diversity of students’ prior learning and learning needs (Vale, et al., 2010) and working to improve students’ proficiency to problem solve and reason mathematically (Roche et al., 2013; Sullivan et al., 2015). In this presentation I will talk about some of my research with a focus on problem solving and reasoning related to algebra. 2. Problem solving and reasoning When working with primary teachers in our Mathematical Reasoning Professional Learning Research Project we discovered that primary teachers struggled to define reasoning. Some believed it was thinking and some confused it with problem solving (Loong et al., 2013). The Australian Curriculum: Mathematics defines the problem solving proficiency as: “the ability to make choices, interpret, formulate, model and investigate problem * Corresponding author. E-mail address: colleen.vale@deakin.edu.au