What is Maths Mastery?
- Learning Resources Posted On Jul 31, 2021 | Seasonal Fun
Maths Mastery is a teaching approach that helps children develop a deep, long-term, secure, and adaptable understanding of maths, explains the National Centre for Excellence in the Teaching of Maths (NCETM).
In this guest blog post, primary school teacher and regular contributor Joanne Moore, explains what is Maths Mastery and the three main elements to learning, which will give parents an overview on why the Department of Education has adopted this approach in the National Curriculum for Maths.
Read more maths related content:
What is Maths Mastery?
The Mastery approach to teaching maths is a current hot topic within education. The three main elements for developing mastery are:
- Reasoning which is the ability to follow a line of enquiry, conjecture relationships and generalisations, and developing an argument, justification or proof using mathematical language.
- Problem-solving allows children to apply mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
- Mastery is built gradually and, in order to get the skills to a deepened level, learning moves through three different stages – concrete, pictorial, and abstract.
What is concrete, pictorial, abstract?
The concrete, pictorial, abstract approach makes children active participants in building a rich, meaningful understanding of maths concepts by constructing their own knowledge. This approach comes from American cognitive psychologist Jerome S. Bruner’s book, ‘The Process of Education’. Published in 1960, it’s regarded as a pivotal work in understanding how children learn.
The concrete, pictorial, abstract approach to maths
Concrete
When first introduced to an idea or skill, hands-on teaching resources enable the process to be acted out through experience. Whatever the resources are, they can be moved, grouped, and rearranged to illustrate the problem. This is the foundation for conceptual understanding. This is a necessary stage for young children who are still thinking in concrete terms and learning through discovery.
Pictorial
As a child’s experience and confidence grows in mathematics, they may no longer need physical objects to actually move around in order to understand and practise their maths skills. Instead, they draw them. Children will visualise the concept and then record this pictorially using models. This may involve drawing pictures, using circles, dots or tallies. This encourages logical thinking.
Abstract
Once children have enough context of the maths skill or concept, they will then begin to perform them at a symbolic level, using only numbers, notation, and mathematical symbols to represent and solve the problem mentally.
The three steps provide children with a deeper understanding of mathematical concepts and ideas and lays the foundations for effective problem-solving in the future. It is important to understand that a child who uses abstract representations in one area may need concrete objects in another.
On a different occasion, a child may need to revisit a concrete representation before moving on to a pictorial or abstract one. Therefore, it is important that children are free to use a variety of representations to support their maths learning.
As a parent, you hold the biggest sway over whether your child develops a love for maths and feels confident in the concepts. To support your child’s learning, read more on how you can help your child love maths for life.
Browse our free maths activity sheets for kids. Check out our numeracy resources that are perfect for learning at school and at home.
Maths Mastery: Insights from a Year 3 Maths Leader
What is Mathematics Mastery and why is it important?
When was this method of teaching maths introduced in your school?
We began dabbling with mastery approaches towards the end of the summer term in 2016, but we launched it whole-heartedly as a school this academic year, and with great success. Our children are responding fantastically to this approach and progress is really being made.What resources do you rely on to deliver maths lessons in this style?
Teachers follow the concrete-pictorial-abstract approach in their teaching, and use a wide range of resources to support learning including Singapore Maths Textbooks and mastery curriculum aids such as the White Rose scheme. Maths mastery requires lots of work with physical objects first to help visualise the concept; anything from cubes, to toy animals, to biscuits and cake (that was a good lesson!)
Have you seen an improvement in your pupils understanding of maths concepts since introducing this method?
One of the changes that came with making the move to a mastery  approach was something we call the ‘anchor task’ – a child led learning opportunity where the teacher takes a step back and guides the learning instead of dictating it. For example; during a lesson on different types of angles I put three pairs of congruent lines on the board and asked the children “What’s the difference?†The first 5 minutes or so were unfruitful, to say the least. However, it only took one child to pick up his ruler and start trying to measure the angles to trigger a train of thought amongst the others: we can measure this, but how? Eventually they came to the notion of measuring the size of the turn between the two lines (thankfully not with a ruler) and were using language such as “this is bigger than a right angle, smaller than a right angle.†This was something we as teachers found difficult at first – it’s hard not to leap in and intervene – but by letting them arrive at the answer for themselves, the children retain that information for longer and receive a greater sense of satisfaction for having been successful in their discovery.What type of maths activities are the most popular amongst pupils?
I’ve developed something in school which we call Rainbow Maths – it’s something I keep tight lipped about as it’s a closely guarded secret, but it draws heavily on Bloom’s Taxonomy and the idea of the ‘anchor task’ in order to allow children to explore a mathematical concept and go as in depth with it as they personally can, as individuals. Plus they get to use coloured pens, which excites them more than you’d think!
What advice would you give to parents who are looking to support their children’s maths learning at home?
There’s so much out there at the moment that it can be a bit of a minefield. I’d always start by asking your child’s class teacher – they’re more than willing to help and more often than not there will be examples of how they teach maths in school on their website. This just means we can all work together on one approach, rather than confusing our children with multiple different methods. Learning through play is incredibly valuable and drawing maths problems out into bar shapes to help visualise the idea you’re working on.*Discover more and browse our selection of Maths Mastery resources for the classroom and home.Related reads:What is Mathematics Mastery?Base Ten: The Maths Mastery Manipulative #LoveLearningREAD MORE
Tried and Tested: All About Me Family Counters and Activity Cards
What were your initial thoughts about the appearance and function of the resource?
I love how brightly coloured they are and how easy they are to handle.  You know from the outset that both the counters and cards are going to withstand being used over and over again (either at home or in the classroom).  I was immediately struck by just how many ways the counters could be used on their own and then with the addition of the cards you’ve ramped up the opportunities for learning even further.How was this resource used at home?
We started off just sorting the counters by colour – talking about their size and which family member they represented.  We have also sorted them by type, grouped them into families, ordered them by size.  We’ve practiced repeating patterns with the help of the Activity Cards and also looked at some simple algebra with the “missing number†type calculations.
How could it be used in the classroom?
There are so many ways this could be used in the classroom.  For talking about our families and who is in them.  For sorting by colour, type. For grouping into families. For counting, for simple equations, for repeating patterns – the list is endless!What did you like/dislike about this product?
I love them. My only niggle is the storage pot could do with being a little sturdier but we’ve just decanted them into a stronger lidded boxWhat are the educational benefits of the resource?
As a product which can be used independently, in groups or in a guided activity – at home or in the classroom to cover such a range of early maths skills I think the benefits of this resource are huge.
How would you rate the long term appeal of this product?
Considering it has been played with by both my two year old and my seven year old I think there is a really good long term appeal to the product – particularly when used in conjunction with the activity cards to work on simple algebra.Do you feel the product is unique or different from other resources?
Yes, whilst it bears similarities to other sorting resources, I think the “family†element gives it the edge.Most importantly… did you have fun using this product?
YES!
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