What does mastery actually mean? How do we know where children are on their journey towards it? What are the aspects of understanding that enable children to get to mastery? It's not as simple as being able to mimic a particular procedure; there are both skills and metaskills involved.
This Maths Mastery Grid shows you the pedagogical intervention required to teach maths effectively and for children to aquire the necessary skills concepts and reasoning abilities.
The grid can also be used to structure assessment for mastery.
Look at each of the three parts of the Mastery Matrix
If we consider Procedural Fluency (bottom left) – we can see that children may be able to do, say, column addition (378 + 265 vertically).
BUT I now consider conceptual understanding (top left). I ask them to do the addition in expanded version, i.e., 300, 70, 8 + 200, 60, 5.Some children may not be able to partition a 3-digit number into its constituent place value parts. This may well not stop them getting a column addition correct, BUT it does matter, and I need to know this as it shows that they have procedural fluency but NOT conceptual understanding.
I now consider the all important top right space – the reasoning skills. Are children able to use the addition appropriately? For example, only one of the following three requires column addition:
346 + 199
346 + 784
346 + 401
Do they know the appropriate strategy to use with each of these addition problems?
Furthermore, do they recognise the different contexts where column addition might be required, such as: □ – 345 = 276?
So, true teaching for Mastery as well as assessment for Mastery requires teaching and assessing in relation to the whole Matrix for Mastery.