Why do we teach formal written methods in Primary Maths?

Only recently has this been a question I have asked myself and my peers. Is it because it has been taught like this for many years? Is it the most effective way of reaching an answer in Maths? Is it easier? Is it Mathematically correct i.e. does it remove all misconceptions? Is it in the policy? I have been questioning this since going on a fantastic Maths course at a Secondary school; who still teach the number line method in year 11, who use partitioning to add large numbers, who make division easier to understand by using the pizza method.

Teaching Maths should not be about making things harder because they are ‘ready’ to move on. I have noticed that children rely too much on written methods, even for the simplest of questions. Children need to be comfortable with numbers.

4571 + 3937 =

4000 + 3000 = 7000

500 + 700 = 1200

70 + 30 = 100

1 + 7 = 8

answer = 8308

When we add numbers this way there are no misconceptions. The 4 does not represent 4, it represents 4000 and the children can see this, as in the column method they’ll say 4. I even do it, if i’m not 100% thinking about the task and numbers involved.

When we divide, one method we teach is the bus stop method:

Misconception Example:’How many 3’s go into 1. 0 so put the 1 by the 4. How many 3’s go in 14. 4 with 2 left over so put the 2 next to the 4′ etc…

An effective way to avoid misconceptions:

The method above is called the Pizza method, which I learnt on the course. It looks complicated but if you look closely it is actually extremely simple and avoids misconceptions that children get. It is basically chunking, but split into a more visual format. I love the idea that the pizza is split into three pieces, so the children know that dividing by 3 is the same as sharing the number into 3 parts.

This method can also aid fractions. What is 2/3’s of 1443? 1/3 is 481. 2/3’s is 962. It unlocks many doors to Maths. Applying this method also increases childrens’ number sense and their estimation skills. It may take practise as children will not get this straight away, however, once they do understand they can go onto even more complex numbers and Maths. We want children who are competent with numbers!

The point of this post was not to say formal written methods are bad, because that is what I, and many others, learnt when we were at school. I wrote it for people who read this post to question why we teach these methods and are they the most effective way of teaching Maths.