‘A high quality mathematics education provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject..’
DFE, National Curriculum
At Fairfield Primary, we have adopted a mastery approach to learning in order to deliver the three aims of the National Curriculum, fluency, reasoning and problem solving. Underpinning this pedagogy is a belief that all children can achieve in maths.
Teachers at Fairfield Primary School have been developing a mastery approach for the several years. Inspired by the exceptional performance of some Southeast Asian countries, school leaders researched the pedagogy and principles of mathematics teaching in Singapore.
In classrooms you can expect to see high levels of pupil engagement and involvement. Lessons begin with an interesting and engaging problem to solve and the teacher’s role is to make this accessible to all. Concrete materials (usually in the form of representations or manipulatives) should be used (in virtually every lesson) to support the children’s thinking as they explore. Pupil talk should be encouraged at every opportunity, enabling peer support, challenge and/or refinement of ideas. Through these, learning should be highly visible. Teachers use pupils’ ideas to create a series of class discussions in which all are encouraged to participate, often attempting to see into the minds of those offering the ideas. Different ideas are embraced and discussed. The class will spend a significant length of time reflecting on their own and others ideas: they do this through journaling and exploring the thinking of others as presented in the textbook. Towards the end of each lesson, the children practise what they have learned, usually through a number of examples guided by the teacher and ultimately, independently. The sequence of examples presented in the textbook is usually adhered to, the inbuilt variation enabling the children to practise the same kind of problem in a number of different ways. Differentiation is precise and robust. Struggling learners are mainly supported through concrete materials, peer dialogue and problems that are in real life situations. In some instances, SEND learners are supported through the use of textbooks from previous Year groups to build on prior knowledge in smaller steps along with additional materials from NCETM. Gifted learners are challenged from the outset, being asked to prove or justify their ideas, create real-life authentic problems of their own or seek patterns within the problem/concept being explored.
Journals and workbooks are used in most lessons. Journals are used to record children’s thought processes and therefore, conceptual understanding. Once children have had the opportunity to refine their thinking, they are expected to record this using diagrams/drawings, writing and abstract mathematical notation. Teachers’ expectations of journals should be high, as should independence levels. Additional expectations of more able mathematicians should be overt. Workbooks should be used to record children’s independent practice. You may find teachers asking children to annotate their work, explore further or write similar problems of their own.
The impact of a mastery session should be visible – the teachers’ planning should identify what the children’s learning should look like (what you expect to hear and see in the room) hence making it straight-forward to evaluate the quality of learning. If for some reason the teacher is unable to progress in the lesson (eg because of a misconception), s/he will take time to address this before moving on. Feedback ‘in the moment’ should help children to address misconceptions. Feedback in lessons is mainly oral, though you may see teachers marking journals and workbooks whilst the children are writing in them. Marking after the lesson is in line with the NCETM guidance – if everything is going as it should, a simple acknowledgement will suffice (eg a tick). The teacher may comment or question the methods, ask for further explanation or challenge pupils further.
If something is wrong, the teacher will recognise it and show the pupil the correct way. An intervention may be necessary. If this intervention involves written methods, it will be shown in the journal. If the whole class (or significant part of it) has a misconception the teacher’s planning of tomorrow’s lesson will demonstrate how remediation is to take place and there may no reference to it in individuals’ books.
Subject Leader Diane Tonge
Early Years Subject Leader Laura Webb