Algorithms are useful: Understanding them is even better
Citation
Source Title
ISSN
Faculty
School
Collection
Abstract
This is the first of two articles on the use of a written multiplication algorithm and the mathematics that underpins it. In this first article, we present a brief overview of research by mathematics educators and will then provide a small selection of some of the many student work samples we have collected during our research into multiplicative thinking. We contend that many primaryaged children are taught algorithms for multiplication and division without an appropriate understanding of the mathematical structure and concepts that underpin those algorithms. This is not about demeaning the use of standard algorithms. They have stood the test of time and can be elegant ways of getting a solution. However, imagine the power we give to students if we underpin the strength of algorithms with understanding! In the second article, we elaborate on what we believe are the key mathematical underpinnings of algorithms.
Algorithms are very useful methods for calculation when numbers are too large to mentally calculate quickly or accurately. For multiplication, this is generally when there is a need to multiply numbers of two digits or more by another number of a similar magnitude. For example, when attempting to multiply a singledigit number by a doubledigit number, students should be considering other strategies, such as applying the distributive property, and exercising their understanding of place value (e.g., 17 x 6 is 10 x 6 which is 60 and 7 x 6 which is 42 so 17 x 6 is 60 + 42 = 102), which allows them to complete these calculations mentally. However, where algorithms are deemed as necessary it would be preferable if the user of the algorithm had an understanding of not only what they were doing, but also, why they are doing it.
Related items
Showing items related by title, author, creator and subject.

Hurst, Chris ; Huntley, Ray (2020)Multiplicative thinking underpins much of the mathematics learned beyond the middle primary years. As such, it needs to be understood conceptually to highlight the connections between its many aspects. This paper focuses ...

Hurst, Chris ; Hurrell, Derek (2018)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 ...

Taylor, Peter C. (1992)This thesis addresses the internationally recognised problem of transforming classroom teaching that is underpinned by transmissionist epistemologies, especially in the field of mathematics education. A constructivistrelated ...