CHILDREN CAN THINK MULTIPLICATIVELY, AS LONG AS . . .
This article published in the European Journal of STEM Education describes some of necessary conditions for children to better think multiplicatively, based on research data.
ONE MULTIPLICATIVE JOURNEY
This article was published in Australian Primary Mathematics Classroom and traces the journey of a group of primary teachers from when they were introduced to multiplicative thinking.
MULTIPLICATIVE THINKING: MUCH MORE THAN KNOWING MULTIPLICATION FACTS
This article, published in Australian Primary Mathematics Classroom, explores some Year Six children's level of understanding of 1 digit by 2 digit multiplication. Bundling sticks were used to highlight a disturbing lack of conceptual understanding.
MANIPULATIVES AND MULTIPLICATIVE THINKING
This article, published in the European Journal of STEM Education, builds on the work published in the previous article. It describes how manipulatives such as bundling sticks can be used to investigate children's understanding of multiplication and division.
ALGORITHMS ARE USEFUL: UNDERSTANDING THE IS EVEN BETTER.
In this article published in Australian Primary Mathematics Classroom, we put the question - 'Should children be using algorithms without an understanding of them?' Research evidence is presented to suggest that they should not.
ALGORITHMS ARE GREAT: WHAT ABOUT THE MATHEMATICS THAT UNDERPINS THEM?
This article was published in Australian Primary Mathematics Classroom and follows on from the previous article. It considers the specific mathematical ideas that need to be explicitly taught if children are to understand the multiplication algorithm.
ALGORITHMS AND MULTIPLICATIVE THINKING: ARE CHILDREN 'PRISONERS OF PROCESS?'
This article, published in the International Journal for Mathematics Teaching and Learning, explores the mathematics underpinning the use of the multiplication algorithm. It suggests that some children over use algorithms when mental strategies would be more effective.
DISTRIBUTIVITY, PARTITIONING, AND THE MULTIPLICATION ALGORITHM.
This article, published in the Journal of Research and Advances in Mathematics Education, explores the importance of understanding the distributive property of multiplication and also place value partitioning. They are fundamental ideas to understanding the multiplication algorithm.
MULTIPLICATIVE THINKING: 'PSEUDO-PROCEDURES' ARE THE ENEMIES OF CONCEPTUAL UNDERSTANDING
This article was published in the International Electronic Journal of Mathematics Education. It makes a case for the use of genuine procedures alongside a conceptual understanding of them. However, it suggests that children are using 'pseudo-procedures', such as 'adding a zero' and 'moving the decimal point' which are not helpful.
A TALE OF TWO KIDDIES: A DICKENSIAN SLANT ON MULTIPLICATIVE THINKING.
This article was published in Australian Primary Mathematics Classroom. It reports on a case study of four primary aged children and focuses on their differing use of procedures and their conceptual understanding of those procedures.
INVESTIGATING MULTIPLICATIVE THINKING: IMPLICATIONS FOR TEACHING.
This article was published in the European Journal for STEM Education. It explores the extent to which children can identify factors and multiples and also their capacity to explain how they know they are factors or multiples.
SLIDING INTO MULTIPLICATIVE THINKING: THE POWER OF THE 'MARVELLOUS MULTIPLIER'.
This conference paper was presented at the 2016 conference of the Mathematics Education Research Group of Australasia in Adelaide. It investigates the use of a sliding device to illustrate the movement of digits across places when a number is multiplied or divided by powers of ten.