Reframing Mathematical Futures II: Developing Students’ Algebraic Reasoning in the Middle Years

in Researching and Using Progressions (Trajectories) in Mathematics Education

Abstract

Mathematical reasoning is an important component of any mathematics curriculum. This chapter focuses on algebraic reasoning in the middle years of schooling, often termed as a predictor of later success in school mathematics. It describes the design research process used in the Reframing Mathematical Futures (RMFII) project to develop an evidence-based Learning Progression for Algebraic Reasoning framed by three big ideas: Equivalence, Pattern and Function, and Generalisation. The Learning Progression for Algebraic Reasoning may be used to identify where students are in their learning journey and where they need to go next. Once the Learning Progression for Algebraic Reasoning was developed it was used to design Teaching Advice to help teachers to provide appropriate activities and challenges to support student learning. Two implied recommendations of this chapter are that algebraic reasoning based on these three key ideas should precede symbol use; and, that algebraic reasoning as described here needs to be cultivated in the primary school years.

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