Mathematics Mastery is an approach to mathematics teaching and learning which is based on learners developing mastery and in-depth understanding of maths principles at their level of understanding; children are expected to achieve a high level of competence and demonstrate mastery of a maths concept, before progressing onto the next level.
The Maths Mastery approach originates from high performing Asian nations such as Singapore. It aims to enable children to develop their mathematical fluency without resorting to rote learning, so they are equipped to solve non-routine maths problems.
What does Maths Mastery Teaching look like?
When teaching maths for mastery, the whole class learns about specific mathematical concepts at broadly the same pace. Each maths topic is taught until all children demonstrate that they have a secure understanding of mathematical concepts.
Pupils are allowed the time to think deeply about the maths and begin to really understand concepts at a relational level rather than as a set of rules or procedures. Although slower, this reduced pace usually leads to a greater rate of progress, because it ensures that children are secure in their understanding because they’ve been immersed in it to a greater depth.
Improved Self-confidence through ‘Maths Talk’, Discussion and Exploration of Ideas.
There is no predetermined differentiation of content of maths mastery teaching, but instead, all pupils are given access to all elements of the maths curriculum. Maths Mastery is a very inclusive approach and its emphasis on exploring multiple methods of solving a problem, building self-confidence and resilience in pupils, as there is no one right way.
Pupils get to talk about their approach to maths and to learn that not only are there many ways to solve a problem, that some strategies will be more effective or efficient than others and some will always work, whilst some may depend on the specific problem. ‘Maths Talk’ improves and embeds understanding.
Challenge through Greater Depth rather than Acceleration.
Teachers can still differentiate for children who have grasped a concept quickly, providing a further challenge by creating in-depth maths problem-solving activities where learners can use and apply their knowledge in real life scenarios.
There is no pressure to move onto new content, just to encourage greater understanding through the application of maths and discussion. Those children who are not sufficiently fluent will have a chance to practise and to consolidate their understanding before moving on.
Teaching maths for mastery is an important focus of the 2014 National Curriculum for Mathematics. The Singapore Maths approach is based on Maths Mastery and is now being effectively implemented in thousands of schools across the UK and its principles have been widely adopted by the Department for Education’s Maths Hubs.
The good news is that both teachers and pupils are now getting both enthusiastic and excited about maths! Both boys and girls are now enjoying the feeling of increased maths confidence, through their in-depth understanding and fluency in maths and by being able to successfully and practically apply these principles in real life scenarios.
Taking Maths Outdoors
The outdoors environment offers limitless, ideal opportunities to develop Maths Mastery in an inspiring, natural and stimulating environment. Just being in the fresh air will bring more energy to your maths lessons! It also provides endless opportunities for ‘Talking Maths’.
Maths mastery doesn’t have to be complicated, as long as children are using and applying maths and developing their maths understanding. It is easy to create activities that develop addition, subtraction, multiplication and division; calculating heights, widths and lengths, area and perimeter; handling money; creating tally charts and other similar graphs; estimating; map skills, including compass points and directional and positional language; recognising shapes and patterns.
Here are a few practical ideas for taking your maths outdoors, that can be easily adapted to challenge any level of learner
Make a nature grid:
Use 4 sticks to make a 3 by 3 grid and ask the children to lay in leaves or pebbles etc, that makes each line add up to 10. Or use longer sticks to make a grid where lines add up to 20 or 50 or 100!
Lay a hoop or rope on the ground and estimate how many flowers, leaves, blades of grass are inside. Talk about estimating accurately and counting to check. How can you record the number of objects in the hoop?
Use sticks to make shapes with 3, 4, 5, 6, 7, 8, 9, 10 sides. What do you notice about the shapes? How easy is it to make a regular, irregular shape?
Investigate symmetry and reflections in pools of water or the nature pond. Or create your own pools with trays of water.
Tell the time outdoors, see our Schoolscapes blog: Times are Changing: Reinforce Telling the Time Outdoors for more details.
Measure the perimeters and area of shadows, using ropes and metre rules.
Challenge children to calculate tree heights using triangulation, measuring length and angles.
Use money for practical problem solving, in a Playtime shop or outdoor role play area.
Measure quantities of both solids and liquids in a Mud Kitchen, as well as timing cooking, stirring and counting and selling mud pies!
An outdoors Maths Wall provides the perfect place to introduce outdoor maths activities, to record observations and to make written recordings. The sliding calculation window enables children to link number sentences to mental calculations and to easily and visually explore inverse relationships.
The useful 100 square and multiplication table, both support children to independently check both their number formation and number relationships, when working outdoors. The innovative outdoor Maths Wall also provides an ideal place for children to explain their findings in an outdoor maths plenary. Small groups or the whole class can gather to celebrate maths mastery!
Maximise the maths from a school trip. Can the children use and apply maths by utilising opening hours calendars, ticket pricing bands, costings of transport as well as exploring maths involving height, speed, length, money, time all linked to your trip venue? This free Legoland Maths Trail PowerPoint explores the possibility of maximising maths opportunities on a school trip in more detail and can be a useful starting point for any teacher planning a school visit. https://www.ncetm.org.uk/files/15748950/ncetm_primary_magazine_issue_52.pdf
Provide opportunities for children to plan and calculate the distances covered and angles required to make a perfect waterway, using our inspirational and fun Water Wall. Also perfect for naturally incorporating maths skills into child-initiated learning.
Growing Maths Outdoors
There are certainly so many ideas out there to support any educator with outdoors maths. There is also a growing understanding of the importance of taking learning outdoors. The DfES ‘Learning Outside the Classroom’ Manifesto states,
“We believe that every young person should experience the world beyond the classroom as an essential part of learning and personal development, whatever their age, ability or circumstances.” Such experiences “help us to make sense of the world around us by making links between feelings and learning. They stay with us into adulthood and affect our behaviour, lifestyle and work. They influence our values and the decisions we make. They allow us to transfer learning experienced outside to the classroom and vice versa”.
The ‘Learning Outside the Classroom: How Far Should You Go?’ report from the Office for Standards in Education, Children’s Services and Skills (Ofsted) found that in the sample of schools visited, well-planned activities not only enhance pupils’ learning but can also re-engage those who are hard to motivate.
So teachers regularly planning in time to apply maths skills into the timetable, linking outside learning to essential skills, will be time well spent, as it is proven to stimulate learners and may be the key to successfully instilling a love of maths for many children, who would otherwise be disengaged.
The maths opportunities in the outdoors are both limitless and vitally important in enabling children to develop an understanding of the value and effectiveness of the application of maths in the real world around them.
In the same way, a classroom without walls or ceiling will provide the space for children to investigate and explore without limits. So what’s stopping you taking your maths outdoors? What is there to lose and more importantly, what is there to gain?
Useful Maths and Learning Outdoors Resources
DfES Taking learning Outdoors Manifesto https://webarchive.nationalarchives.gov.uk/20130323072419/https://www.education.gov.uk/publications/eOrderingDownload/LOtC.pdf
Learning Outside the Classroom: How Far Should You Go? https://www.ncetm.org.uk/files/21270432/Ofsted-Report-Oct-2008.pdf
The National Centre for Excellence in Teaching Mathematics (NCETM) https://www.ncetm.org.uk/resources/teaching-resources
Legoland maths trail https://www.ncetm.org.uk/files/15748950/ncetm_primary_magazine_issue_52.pdf
Maths Hubs Programme http://www.mathshubs.org.uk/
White Rose Maths https://whiterosemaths.com/
Talk Maths Talk http://www.talkmathstalk.co.uk/developing_talk
Using Talk Maths – NCETM
Maths No Problem https://www.youtube.com/channel/UCswP9RAXREiP_8QPXYL_57Q