This review explores the literature relating to the field of maths education. Its purpose is to identify factors that can contribute to high-quality school maths curriculums, assessment, pedagogy and systems. We will use this understanding of subject quality to examine how maths is taught in England’s schools from Reception onwards. We will then publish a subject report to share what we have learned. Teachers help pupils develop their automatic recall of core declarative knowledge, rather than rely on derivation, guesswork or casting around for clues. Teachers and leaders should try to strike a balance between curricular approaches that enable pupils to keep up with their peers and reactive approaches that identify, help and support pupils after they have fallen behind. These reactive approaches are more likely to rely on assessment, diagnoses, personalisation and interventions. every child will have had to attend to every word, every problem, and every exercise included in every textbook. [footnote 143] It is also important to consider that high attainment and proficiency of older pupils may be due to historical curricular and pedagogical approaches, rather than the educational approaches of that time. Finland is a good example of an education system where success in the OECD’s Programme for International Student Assessment ( PISA) is thought to be the result of historical approaches. [footnote 18] Approaches that teachers and pupils are familiar with can take time to change. They may, therefore, influence pupils’ educational experiences, even after an official change of curriculum or pedagogical approach. [footnote 19] Principles underpinning the review process

Close examination of lesson planning and teachers’ thoughts about lesson planning in education systems where pupils do well reveal an intense focus on underlying knowledge structures and connections rather than the surface coherence of activities and teaching. This means that teachers are planning for what pupils will be thinking about or with, not what they will be ‘doing’. Dowker, A. (forthcoming). Review of Mathematics Education Programmes. London: The Education Endowment Foundation. Cognitive strategies include subject-specific strategies or memorisation techniques such as methods to solve problems inmaths. Procedural knowledge is recalled as a sequence of steps. The category includes methods, algorithms and procedures: everything from long division, ways of setting out calculations in workbooks to the familiar step-by-step approaches to solving quadratic equations.The planned curriculum details the core facts, concepts, methods and strategies that give pupils the best chance of developing proficiency in the subject. Individualised, component-based approaches to maths intervention have been found to be highly effective. As no child is the same, implementing an intervention programme for maths can be very challenging as each learner has their own unique difficulties. Terms also vary over time. For example, ‘tables’ has changed in meaning: it used to refer to number facts in all the operations that infant and junior pupils were expected to learn [footnote 23] but now it is shorthand for multiplication facts in the present day. [footnote 24] Examples of terms (and associated concepts) that have been used less and less over time include ‘mechanical drill’, ‘syllabus’ and ‘recall’. How the review classifies mathematics curriculum content Curriculum adaptation is best seen as an iterative process, one which ensures that any modifications are agile and responsive to children’s needs. It is important to consider long-term retention of key knowledge and skills and how pupils can be helped to make links between ideas and topics. Furthermore, if this core content has been sequenced well and pupils have learned it thoroughly, they are less likely to forget and are therefore unlikely to need to ‘re-learn’ it later. [footnote 34] A focus on core knowledge in younger year groups can be achieved by focusing on depth over breadth, covering fewer core topics but in more detail. Amplifying the curriculum through instruction, rehearsal and assessment plans

Math learning enhances problem-solving skills, critical thinking, and logical reasoning abilities. (Source: National Council of Teachers of Mathematics)

10. The art of math

This approach is particularly useful for pupils with moderate learning difficulties who have slower cognitive processing speed. [footnote 116] Systematic approaches increase the amount of content considered per unit of time. These approaches are also highly beneficial in enhancing the progress, attainment and self-esteem of disadvantaged pupils. [footnote 117] Systematic curricular approaches give pupils with SEND and disadvantaged pupils a better chance of success, of keeping up and therefore of feeling included. Playing to pupils’ strengths: the powerful declarative memory systems of pupils with autism Choice of examples: Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational studies in mathematics, 69(2), 149-163.

Mathematics, a universal language that enables understanding of the world, is an integral part of the curriculum. Beyond the study of numbers, shapes and patterns, it also provides important tools for work in fields such as engineering, physics, architecture, medicine and business. It nurtures the development of a logical and methodical mindset, as well helping to inculcate focus and the ability to solve all manner of problems. Attainment in the subject is also the key to opening new doors to further study and employment. However, despite its importance, for many the subject remains mysterious and difficult, the preserve of those who seem to be ‘naturals’. The education inspection framework ( EIF) makes it clear that schools are expected to ensure that the mathematics curriculum ‘helps pupils to gain enjoyment through a growing self-confidence in their ability’. [footnote 1]Textbook analysis can provide useful information about quality of rehearsal. In contrast to the ideal of systematic rehearsal aligned to sequences of learning: A moment of understanding does not guarantee long-term learning. Pupils benefit from studying worked examples in addition to practising solving similar types of problems. [footnote 106] Who is best placed to supervise pupils when they are taking the quizzes in school? A teacher or a teaching assistant? Mastery’ pedagogical approaches that have influenced English mathematics education tend to require pupils to demonstrate high levels of achievement before they are moved on to new content. Some mastery approaches place a greater emphasis on problem-solving and on deepening pupils’ understanding. [footnote 15] It improves analytical skills that can be applied in various real-life situations, such as budgeting or analyzing data. (Source: Southern New Hampshire University)