De-mystifying mathematics

Ed Thompson explains how Mathematics Mastery is taught at Dallington School...

If you visit Dallington School you will see the children engrossed in a variety of learning activities and child-centred pedagogy developed over 40 years by Mogg Hercules. The Early Years class may be exploring all the possible ways of making ten with ‘magic beans’ in open, purposeful activity linked through cross curricular topic-based learning. The Year 5’s maybe singing a song using the accompanying actions so they remember the steps needed to solve a long division problem. Or Year 6 children quizzing each other with their own word problems or showing some magical mathematics and puzzles to one another. The children enjoy discussing what they have been learning and use the new vocabulary they have learnt in their lessons.

In the last year, Dallington School has embarked on the phasing-in of the Mathematics Mastery programme.Although new for us as a school, it is not a new method of teaching as such. In fact, the method is influenced by Ancient Greece and Aristotle’s work over 2000 years ago. The main aim of the method is to know when to take learning to the next stage once a strong foundation in a specific topic has been built. Of course, until the pupil has mastered the mathematics topic they are being taught they should not be moved onto the next one. Sequencing of the children’s learning is very important. If done with care, it will give the children the opportunity to make links, develop their learning and, in turn, allow them to be more confident in their mathematical abilities.

The key elements of the Mathematics Mastery programme from the work of Guskey (2010)¹ are as follows:

• Pre-assessment with some pre-teaching
• High quality, group-based initial instruction
• Progress monitoring through regular formative assessment
• High quality corrective instruction
• Second parallel formative assessment
• Enrichment or extension activities

The Mathematics Mastery programme is a different approach to teaching to the one that Dallington has used in the past and it has been introduced with the aim of keeping the happy balance of teaching mathematics in context – real situations to which the children will relate – without losing the creative style Dallington has always upheld at the centre of its pedagogy. The open-plan setting in which the children are taught at Dallington produces a relaxed atmosphere where the children are happy to ask questions of the staff and each other.

In the classroom, consideration for others is key to creating the right environment for learning. At Dallington, the school, staff and pupils pride themselves on our diverse and creative school day coupled with the open, friendly environment. The children are encouraged to be as inquisitive as possible and to grow into independent, self-assured, considerate people.

In this environment, we use music, sewing and drama to help the children build their understanding of mathematical concepts as these relatable activities help the children overcome some of their fear of mathematics.

Opposite, you can see some of our Year 6 children making a smoothie! This required them to measure the ingredients in the correct proportions and this way they learnt about ratio.

Mathematics Mastery makes mathematics more inclusive as it encourages differentiation to be achieved in a different way to the way we have approached it in the past. Instead of grouping children by ability, Mathematics Mastery achieves differentiation by giving all learners access to tasks at their own pace starting with the easier activities and progressing onto the more challenging tasks. The more challenging tasks stick to the topic being covered and extend the children by providing more thought-provoking tasks which develop their procedural fluency and their learning and application of key vocabulary. This deeper and more critical thinking enhances and embeds their understanding of the concepts and not just the methods used to solve sums. As Charlie Stripp describes clearly that a mastery curriculum is one which is not based on ‘getting through’ the material but on developing fluency and understanding, and the focus of differentiation to challenge those making fast progress should be through deepening their understanding, rather than moving onto new content.²

The differentiation through depth rather than acceleration allows the faster worker to develop their understanding and their mathematical vocabulary, as well as challenging their own thinking. The less quick workers have more time to assimilate the concepts and understanding which in turn leads to greater progress. Also, it makes the children’s learning more sustainable.

The children’s mindset can be deeply affected by some of the differentiation methods and strategies, particularly those which group children by their ability and where high achievers are rewarded on their scores rather than for their effort. The lower achieving children feel that they can never reach the heights of the high achievers and automatically they put themselves into this fixed mindset. According to Carol Dweck “Einstein was not always Einstein until he put in many dedicated years of labour …” In other words, our intelligence can grow and our brains have much more plasticity than we have ever thought. Neuroscientists have proven how our brains can become more knowledgeable and intelligent but it is down to having the right mindset, known by Dweck as the Growth Mindset. Talents and abilities can be developed through application and good instruction.

Further to the subject of mindset and our ability to learn, there is an even stronger reason why children believe they can’t do Mathematics and this is where the children suffer from a kind of fear or panic which automatically puts them into a zone in which learning cannot and will not happen. This is termed beautifully by Sue Johnston-Wilder “Don’t try to do Maths whilst your brain is focused on the “tiger!”³

If we consider the points about a growth mindset versus a fixed mindset and the idea that an anxious mind can’t learn because it is basically in a fixed state of fight or flight, then it would stand to reason that the way we teach children must promote the status of a growth mindset and an awareness of what to do when they panic. If we wish the children to learn more effectively and efficiently, then we need to adjust our pedagogical methods as best we can to achieve the desired learning environment and to remove any barriers which might otherwise stifle the children’s progress.

Ultimately, good teaching and good learning can only really happen if the children have the tools at their fingertips in a conducive environment and one which instils a can-do approach to the set challenges. For a challenge to be fun the children must feel that it is something which they can tackle even if it requires a bit of effort and deeper, critical thought.

Realistic expectations and inclusive differentiation makes for positive, effective and happy learning. Mathematics Mastery, when applied and understood correctly, can achieve these qualities.

Endnotes

1. http://tguskey.com/wp-content/uploads/Mastery-Lear...

2. Charlie’s Angles: Maths, Mindsets and Mastery, https://www.ncetm.org.uk/resources/45370

3. Sue Johnston-Wilder “Improving Communication, engagement and resilience in STEM classrooms. January 2020 go.warwick.ac.uk/ces

This article first appeared in the 2020/21 edition of Which London School? & the South-East, which you can view in full here: