Our Mastery Approach
The learning of mathematics is a never-ending journey. Once the start point has been established, there is no end-point. Our Mastery curriculum supports children to become “more expert” at the concepts they are taught. Crucial to our mastery approach is the notion that children recognise there is always more to learn about a concept.
In order for our pupils to developed a deepened understanding for mathematics, pupils will be required to become fluent with the fundamentals of mathematics, reason mathematically and solve problems (National Curriculum, 2014).
According to McCourt, 2019, fluency can be described as ‘the point at which someone no longer needs to give attention’. In order for this to happen, pupils need to commit their learning to their long-term memory, freeing up the working memory and in turn reducing cognitive load. Russell, 2000 went on to define fluency as a pupil’s efficiency, accuracy and flexibility towards a calculation. Pupils should be able to solve problems correctly with a variety of strategies, recognising which strategy would solve the problem the quickest. Fluency is more than rote-memorisation of independent facts.
If we define ‘understanding’ as ‘the reasons why the connections are true’, we therefore expect children to be able to reason mathematically in order to deepen their understanding of mathematical concepts that are taught. In order to become fluent, children must be able to reason mathematically.
Problem solving cannot be directly taught however we can support children to become better problem solvers developing deep understanding of maths, in particular relationships; developing logical reasoning – particularly through procedural variation; developing knowledge of mathematical structures through conceptual variation as well as developing analytical skills through specifically chosen question types.
Our Mastery approach is built upon the foundational beliefs that:
- A pupil does not have a fixed ability.
- All pupils can learn all of the content if they are starting at the right point and given the right amount of time.
- Learning is coherently sequenced in order for children to progress through our mathematical journey.
- Formative assessment plays an important role in ensuring that all children are exposed to the right level of mathematics, with opportunities to go ‘deeper’ into a concept for those who have grasped the initial structure of a concept.
- When taught at the right level, all children can learn at pace
- There is no limit to the depth of reasoning one can have around a concept so understanding can be seen as infinite (quite often in mathematics, great new insight comes from attention to an area of mathematics that one is already fluent in).
- Productive Disposition (the belief that one’s own efforts matter) is imperative for all pupils to learn mathematics.
At Gatehouse Primary Academy, we regard a mathematician as someone who:
- Is curious in all aspects of life
- Enjoys the state of not yet knowing the resolution
- Ask their own questions
- Follows their own lines of enquiry
- Can spot patterns
- Can conjecture
- Can generalise
- Can reflect and notice
- Tries to disprove ideas
- Argues with their own thinking
Ultimately we ask our children to be mathematical rather than do mathematics.