Resumen de Why do ‘fast’ multiplication algorithms work? Opportunities for understanding within younger children via geometric pedagogy

Christopher Tisdell

• The purpose of this work is to explore alternative geometric pedagogical perspectives concerning justifications to ‘fast’ multiplication algorithms in a way that fosters opportunities for skill and understanding within younger, or less algebraically inclined, learners. Drawing on a visual strategy to justify these algorithms creates pedagogical alternatives to the presiding algebraic defences found in texts. Firstly, I formulate an overview of a particular ‘fast’ multiplication algorithm and situate it within historical and modern contexts. Next, I present a geometrical approach that offers a visual perspective of why this algorithm works and compare it with traditional algebraic approaches. Three examples are discussed throughout to give the ideas some concreteness. Finally, I furnish a personal reflection on the classroom experiences of sharing this geometric justification with younger learners.