Search

Multiplicative thinking is a critical component of mathematics which largely determines the extent to which people develop mathematical understanding beyond middle primary years. We contend that there are several major issues, one being that much teaching about multiplicative ideas is focussed on algorithms and procedures. An associated issue is the extent to which algorithms are taught without the necessary explicit connections to key mathematical ideas. This article explores the extent to which some primary students use the algorithm as a preferred choice of method and whether they can recognise and use alternative ways of calculating answers. We also consider the extent to which the students understand ideas that underpin algorithms. Our findings suggest that most students in the sample are 'prisoners to procedures and processes' irrespective of whether or not they understand the mathematics behind the algorithms. [The title on the pdf is "Algorithms and Multiplicative Thinking: Are Children Prisoners of Process?"]

This article describes some of the essential mathematics that underpins the use of algorithms through a series of learning pathways. To begin, a graphic depicting the mathematical ideas and concepts that underpin the learning of algorithms for multiplication and division is provided. 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 article goes on to demonstrate how each element builds part of the underpinning structure needed to understand algorithms and to use them efficiently.

The article fosuces on the essential mathematics that underpins the use of algorithms. Topics discussed include the grid multiplication and extended multiplication facts is the understanding and use of algorithms; the distributive property directly impacts the setting out of the standard algorithm and it can also be developed through the use of the array; and the base ten property also informs the development of extended number.

The article focuses on use of a written multiplication algorithm and the mathematics. Topics discussed inlcude useful methods for calculation when numbers are too large to mentally calculate quickly or accurately; need to be developed through a thorough understanding of the distributive property; and developing the grid or area representation for multiplication.