REASONING ABOUT THREE-EIGHTHS: FROM PARTITIONED FRACTIONS TOWARDS QUANTITY FRACTIONS

Curriculum documents describe the importance of questioning, reasoning and reflecting as contributing to Working Mathematically. A research lesson on the development of units of different sizes (eighths) associated with measurement and fractions, is developed as a vehicle for developing mathematical reasoning through argumentation in a composite Year 3–4 class. Making a transition from embodied fractions (parts of a whole) to recognising the equal whole needed for comparison of fractions as mathematical objects extends the current Mathematics curriculum in New South Wales. The lesson study also highlighted the need to develop taken as shared meaningfor fraction units used in classroom argumentation. REPRESENTATIONAL CONTEXTS Working Mathematically draws on ways on ways of seeing, questioning, interpreting, reasoning and communicating. This type of mathematical thinking was summarised by Schoenfeld as follows: Learning to think mathematically means (a) developing a mathematical point of view — valuing the process of mathematization and abstraction and having th