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The mathematics chapter by Susanne Prediger and Anna-Katharina Roos offers profound insights into the nature of mathematical literacy. It documents a precise account of the way the knowledge and activity domains of doing, organising, explaining and arguing translate into algebraic activities and procedures. Using the example of transformation and transformation rules, they argue that algebraic rules that are not underpinned with meaning will become arbitrary and lead to typical student errors. They make the case for algebraic reasoning as a way of developing conceptual understanding and promoting deeper learning in the maths classroom. Based on their empirical classroom research, the authors propose three principles to inform the design of deeper learning episodes in mathematics: connecting multiple representations and languages, engaging learners in rich discourse practice and employing macro-level scaffolding that integrates mathematics and language learning.
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