A structural approach for introducing multiplicative concepts -

Abstract

Early years (5 to 7 years) and middle years (8 to 11 years)

In many places across the world, multiplication is introduced through repeated addition. It is obviously attractive, since children are already acquainted with addition, and can make a smooth transition into multiplication. This approach can also seem harmless, since multiplication in pure mathematics is defined through repeated addition.

However, research has repeatedly shown problems with this approach, including "whole number bias" and other difficulties or misconceptions which can appear in the middle grades.

Working with over 1000 teachers in Sweden, we have developed a way of introducing multiplication (and other multiplicative concepts like division, fractions and proportional reasoning) by using two other known models, namely rectangular grids and the number line. What may be somewhat unique in our approach is how systematically we use these two models. Right from the very first lesson on multiplication, we deal with factorisation and prime numbers as well with the connection between multiplication and division. We can also introduce the distributive property and how it can be used and represented very early on. Our approach allows students to start multiplying fractions right from when multiplication is introduced.

In this workshop, we will give an overarching description of the teaching sequences involving multiplicative structures for 8 to 10 year-olds. Participants will also get a chance to experience some of the particular tasks we use.