Mastery – An explanation drawn from research of current(ish) thinking (circa 400BC)
12 November 2017
Author: Mari Palmer
On Friday 3rd November the EEF released its latest guidance report: Improving Maths in Key Stage 2 and 3. This meta-analysis has produced a clearly written and highly focussed set of guidelines that point the reader towards the elements of teaching that could have the greatest impact on children’s development.
In this blog we will examine a concept from section 2 of the report: Fluent recall of a procedure is important, but teachers should ensure that appropriate time is spent on understanding.
Since the introduction of the 2014 curriculum there has been a far greater emphasis on deeper understanding or mastery. Many people have a slightly different understanding of this – I have heard many. From a fantastic cupcake analogy to examples from the classroom, people have their own understanding – and it is a term that is still being discussed and refined 3 years into the new curriculum. I myself wrestled with the question of mastery for a considerable period of time – as I am sure we all have. How do we know when a child truly ‘understands’ something rather than being able to follow procedure? If a child can follow procedure and ‘answer’ a question do we need to ‘delay’ their progress towards the ‘next step’?
As a research school we need to read and draw on inquiry so we can plan to use evidence-based practice. So, after reading around and exploring different definitions, I have refined my understanding of mastery using the 2400 year old text by Plato – proof that we are up to date in our educational thinking!
In ‘The Republic’ Plato discusses the Theory of Forms using the Allegory of the Cave. He is describing his theory that on earth we see ‘shadows’ of a true concept or form. Each example we can see is taken from a pattern of a true ‘abstract’ – an untouchable, unseeable true form. However, because we become familiar with so many examples of shadows of the ‘true form’ we are then able to form a confident opinion of what the form may be like.
For example, away from maths, if we were asked to describe a chair, using an amalgamation of all our previous experiences of chairs, we may say ‘it has four legs and we can sit on it’. However if a chair had three legs we would still be able to recognise it as a chair, or if it was a dolls house chair and we couldn’t sit on it we would still know it was a chair. We have developed an understanding of what the true form of a chair is by seeing many, many examples over our life time.
From this it is possible to see mastery as the children’s ability to understand the ‘form’ or a mathematical concept.
If we are looking at numbers to 10 with a child and we want to say they truly understand, for example, what the number 3 is, we need to know they would recognise the number three in any different example e.g. as a number in a counting sequence, as an odd number, as an amount of money, as the missing number in a sequence, as the sum of two other numbers, as the difference between two numbers etc.. When a child can recognise the value of 3 in a wide range of situations you can sense that they are starting to have a true understanding of ‘3’ and have therefore begun to ‘master’ the number 3.
There are obviously a huge range of calculations you could perform that would provide you with a ‘value’ of 3 – some far out of reach of younger children who may be becoming familiar with counting from 1 – 10 but there are certainly a wide range of tasks that are accessible – including representing ‘3’ with a wide variety of manipulatives.
So, if we are to ensure we adopt the EEF guidance to ensure that we spend enough time on understanding, I feel we must attempt to ensure children are starting to see the Platonic ‘form’ not just be able to talk about earthly examples!
Posted on 12 November 2017
Posted in: Blog