There’s this new method of teaching Maths at school that we’re learning about called Maths Mastery. I think the first question that often comes up whenever there is a change is this: why the new system? What was wrong with the old way of doing things and why do we need to change it? And it’s important that we are all clear on that because part of what makes Maths Mastery work is when parents understand it.
What is Maths Mastery?
In the old system of learning Maths, the children covered a lot of areas of Maths with only a superficial understanding of it. As one Maths teacher put it – it was a system that cultivated “fragile mathematicians”. They understood enough to get the answers right, but not enough to build on that foundation. For instance, they might know which formulas to use to get the right answers, but they wouldn’t be able to explain why those formulas work. The issue with this method is that the moment you take it out of context, these students would no longer be able to solve the problem.
With Maths Mastery, the goal is to develop a deeper understanding of the Maths. That often means covering less and going slower which can alarming in a society that worries more about arriving at the destination than the journey.
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True mastery in a subject occurs when the student is able to teach the material to someone else. They can explain it, present it in different ways, and apply it to other things.
These are some of the statements they should be able to make if they have achieved Maths mastery:
Why Maths Mastery?
- Too many children were falling behind
- Not enough children are excelling
- Teaching has been focussed on procedures rather than understanding
- Negative attitudes towards maths ability and enjoyment
Sal Khan explains it really well in his TED Talk.
What’s the Problem with the Old Maths System?
For the children identified as ‘mathematically weak’:
- They are aware that they are being given less-demanding tasks, and this helps to fix them in a negative ‘I’m no good at maths’ mindset that will blight their mathematical futures.
- Because they are missing out on some of the curriculum, their access to the knowledge and understanding they need to make progress is restricted, so they get further and further behind, which reinforces their negative view of maths and their sense of exclusion.
- Being challenged (at a level appropriate to the individual) is a vital part of learning. With low challenge, children can get used to not thinking hard about ideas and persevering to achieve success.
For the children identified as ‘mathematically able’:
- Extension work, unless very skilfully managed, can encourage the idea that success in maths is like a race, with a constant need to rush ahead, or it can involve unfocused investigative work that contributes little to pupils’ understanding. This means extension work can often result in superficial learning. Secure progress in learning maths is based on developing procedural fluency and a deep understanding of concepts in parallel, enabling connections to be made between mathematical ideas. Without deep learning that develops both of these aspects, progress cannot be sustained.
- Being identified as ‘able’ can limit pupils’ future progress by making them unwilling to tackle maths they find demanding because they don’t want to challenge their perception of themselves as being ‘clever’ and therefore finding maths easy. A key finding from Carol Dweck’s work on mindsets is that you should not praise children for being clever when they succeed at something, but instead should praise them for working hard. That way, they will learn to associate achievement with effort (which is something they can influence themselves – by working hard!), not ‘cleverness’ (a trait perceived as absolute and that they cannot change).
The CPA Maths Approach
One way to teach Maths Mastery is to use the CPA approach – concrete, pictorial, abstract. When children first learn new maths concepts, it helps for them to start by using physical manipulatives to gain hands-on experiences. Once they have the basic understanding of the problem in concrete terms, they can move on to pictorial representations. Logical thinking can be developed by using pictures to simplify a challenging word problem. The final step is to move to abstract concepts.
Working in the Zone of Proximal Development
The Zone of Proximal Development was a concept introduced by Vygotsky. It refers to a specific level in a child’s development marking what a child is unable to do on their own but able to complete with assistance. It is the zone in which we want our children to work in so that they are sufficiently challenged by the work set but not overwhelmed by it.
The Zone of Proximal Development is the point at which a child’s learning is at its most effective. In this zone, children will still have to struggle to get through the work but not to the point where they have reached cognitive overload. This is where we want our children to be at as it will help them achieve Maths mastery.
Supporting Maths Mastery at Home
One of the fundamental aspects of teaching Maths Mastery is having a Growth Mindset. We need to encourage our children to develop a growth mindset approach to maths.
- Everyone is capable of doing maths!
- Celebrate mistakes as a learning opportunity.
- Lead by example.
- Cooking and recipes: measuring ingredients, halving or doubling recipes, ratios of ingredients.
- Going shopping: how much does it cost? Does the cost change if you buy 2 instead of 1? How much change should we get back?
- Going out: how long is the journey? What time will we have to leave if we need to arrive by a certain time? Using a map, what is the shortest route to get there?
- Mathematical language: some words have different meanings in maths, like ‘product’, ‘table’, and ‘difference’. Ask your child to explain what these words mean from a mathematical perspective.
When working on Maths homework:
- Ask your children to lead by explaining what they know.
- Encourage them to talk about how they arrived at the answer.
- Use questions like ‘how’ & ‘why’.
- Value your children’s effort and focus on the problem solving process rather than the answer.
Help them build their number sense:
Number sense essentially refers to a student’s “fluidity and flexibility with numbers,” (Gersten & Chard, 2001). He/She has sense of what numbers mean, understands their relationship to one another, is able to perform mental math, understands symbolic representations, and can use those numbers in real world situations. – Maths Solutions
- Learn the different number bonds and times tables to help develop a firm number foundation.
- Use games as a tool for practice, e.g. Lego and dice games for addition and subtraction, number bonds for 10 and 20.