Mathematics is a subject in which its learning episodes can be taught in multiple different ways, using multiple different methods; this is the case at most schools. This can cause significant confusion and cognitive overload for some students, especially lower attaining students.
The purpose of this project is to provide mathematics teachers, teachers of other subjects and staff who support students in mathematics lessons with an easy-reference guide to the methods employed in the teaching of mathematics.
At Purposeful Maths we aim to ensure thorough understanding of the subject content covered without relying on process memorisation. The methods outlined are what we think are the most effective way of accomplishing this.
This document could allow staff to synchronise their practise, to ensure students encounter the same methods throughout their mathematical journey, regardless of their teacher.
We hope you find it useful!
Our Four Stage Approach
We have built our Four Stage Approach around the Concrete, Pictorial, Abstract Model, which originated in Singapore, and its precursor Enactive, Iconic and Symbolic (Bruner, 1966); we have, however, taken these a step further in order to further aid those students who have difficulties in mathematics (Jordan, Miller and Mercer, 1998; Sousa, 2008) and those teachers of all ability ranges.
We have called the four stages Physical, Pictorial, Semi-Abstract and Abstract.