Developing mathematical reasoning through argumentation. In Progress report of the APECT project: Collaborative studies on innovations for teaching and learning mathematics

Engaging in argumentation in elementary classrooms involves more than taking turns when arguing. Curriculum documents describe the importance of questioning, reasoning and reflecting as contributing to Working Mathematically. The prominence and time allocated to developing this form of mathematical thinking in elementary classrooms is influenced by the teacher’s confidence and familiarity with using these modes of thought. Examples of developing the classroom norms through specific mathematics lessons are needed to act as both models of and models for effective lessons involving students in reasoning through argumentation. A research lesson on the development of units of different sizes associated with measurement and fractions is proposed as a vehicle for developing mathematical reasoning through argumentation. DESCRIBING MATHEMATICAL THINKING Attempts to describe the essential features of mathematical thinking in Australia have been influenced by similar developments in the USA and the United Kingdom. In particular, the focus on problem solving in the 1980s (Mason, Burton, & Stacey, 1982