Investigating critical mathematical thinking when applying mathematics to real-world problems

The capacity to use mathematics critically is essential for making decisions and forming judgements about challenges facing society, including those related to the economy, health and the environment. Critical Mathematical Thinking (CMT) involves the use of mathematical techniques and reasoning to address complex real-world problems in a wide range of real-world contexts. CMT also requires the capacity to reflect on the consequences of proposed solutions (e.g., social, ethical) on individuals and society at large. In this paper, we outline a project that aims to generate new insight into teaching practices that can promote or inhibit students' CMT development. This requires attention to what teachers see when students work on CMT tasks and how they respond – teacher noticing. Planned outcomes of the project include new theoretical and practical insights as well as resources designed to promote teaching and learning practices that support students' CMT development.