Algorithms are Great: What about the mathematics that underpins them?

Abstract

Our previous article, Algorithms are great: Understanding them is even better, presented evidence from students and suggested that some were attempting to use written algorithms without having an adequate level of understanding of what they were doing and why. This article will describe some of the essential mathematics that underpins the use of algorithms through a series of learning pathways. The graphic below depicts the mathematical ideas and concepts that underpin the learning of algorithms for multiplication and division. The understanding and use of algorithms is informed by two important ideas—grid multiplication and extended multiplication facts. The graphic combines a number of learning pathways that lead to those two ideas. The discussion that follows shows how each element builds part of the underpinning structure needed to understand algorithms and to use them efficiently.