At Outwoods Primary School, maths teaching is underpinned by a belief in the importance of mathematics and that the vast majority of children can succeed in learning mathematics in line with national expectations for the end of each key stage. The whole class is taught mathematics together, with no differentiation by acceleration to new content. The learning needs of individual pupils are addressed through careful scaffolding, skilful questioning and appropriate rapid intervention, in order to provide the necessary support and challenge. Factual knowledge (e.g. number bonds and times tables), procedural knowledge (e.g. formal written methods) and conceptual knowledge (e.g. of place value) are taught in a fully integrated way and are all seen as important elements in the learning of mathematics. The reasoning behind mathematical processes is emphasised here at Outwoods. Teacher/pupil interaction explores in detail how answers were obtained, why the method/strategy worked and what might be the most efficient method/strategy. Precise mathematical language, coached in full sentences, is always used by teachers, so that mathematical ideas are conveyed with clarity and precision. Pupils are required to do the same (e.g. when talking about fractions, both the part and its relationship to the whole are incorporated into responses: “The shaded part of the circle is one quarter of the whole circle”). Conceptual variation and procedural variation are used throughout teaching, to present the mathematics in ways that promote deep, sustainable learning. Carefully devised exercises employing variation are used. These provide intelligent practice that develops and embeds fluency and conceptual knowledge.
Sufficient time is spent on key concepts (e.g. multiplication and division) to ensure learning is well developed and deeply embedded before moving on.
Programmes of study and lesson content are carefully sequenced, in order to develop a coherent and comprehensive conceptual pathway through the mathematics. Learning is broken down into small, connected steps, building from what pupils already know to ensure their working memory is not overloaded and to ensure sustainable, long term learning. Difficult points and potential misconceptions are identified in advance and strategies to address them planned. Children at Outwoods are regularly given time to reflect on new concepts through their maths journals.
In lessons, key questions are planned, to challenge thinking and develop learning for all pupils, as well as ‘Going Deeper’ questions for any higher attaining pupils in the lesson. Contexts and representations are carefully chosen to develop reasoning skills and to help pupils link concrete ideas to abstract mathematical concepts. The use of high quality materials and tasks to support learning and provide access to the mathematics is integrated into lessons. This may include textbooks, visual images and concrete resources.
At Outwoods, maths lessons are sharply focused; digression is generally avoided. Key new learning points are identified explicitly. There is regular interchange between concrete/contextual ideas, pictorial representations and their abstract/symbolic representation all supported by the use of clear, precise mathematical language. Mathematical generalisations are emphasised as they emerge from underlying mathematics, which is thoroughly explored within contexts that make sense to pupils. Making comparisons is an important feature of developing deep knowledge. The questions “What’s the same, what’s different?” are often used to draw attention to essential features of concepts. Repetition of key ideas (for example, in the form of whole class recitation, repeating to talk partners etc) is used frequently. This helps to verbalise and embed mathematical ideas and provides pupils with a shared language to think about and communicate mathematics. Teacher-led discussion is interspersed with short tasks involving pupil to pupil discussion and completion of short activities. Formative assessment is carried out throughout the lesson; the teacher regularly checks pupils’ knowledge and understanding and adjusts the lesson accordingly. Gaps in pupils’ knowledge and understanding are identified early by in-class questioning. They are addressed rapidly through individual or small group intervention, either on the same day or the next day, which may be separate from the main mathematics lesson, to ensure all pupils are ready for the next lesson. Lessons are adapted as needed if the children are not ready for the nxt step.
In lessons there are opportunities for exploration, structuring, documenting, practice and reflecting. An anchor/exploration task is used to engage the children in their learning and children are given time to explore the problem (often with concrete materials). This problem is discussed deeply and structured by the teacher, using the children’s methods when possible, to investigate different ways to solve it. Children evaluate the methods themselves and to try to visualise. Children document their learning and reflect upon key anchor tasks in their maths journals. Maths journals are also used for other reflections, for example in recording new vocabulary with a definition and examples to represent it. Enrichment is used over acceleration. Higher attainers at Outwoods should be able to: show recordings in more than one way; explore different possibilities; explain it as a story; verbalise thinking methods and reason ideas etc. Guided practice allows children to practice and apply their new knowledge (and methods) to different problems, with support as needed from a peer or adult. Children should then be able to apply their understanding to independent tasks, which will need them to use what they have learnt to answer different questions. This may be in a separate practice lesson.
Additional factual fluency sessions are used to embed key skills. In KS1 these sessions are focused on additive relationships to twenty (mastering number/number sense programme). In Lower Key Stage 2 these are focused on embedding Times Tables facts, where short daily sessions are used to embed facts. In Upper Key Stage 2 these are focused on arithmetic skills.
At Outwoods we thrive for all of the children to demonstrate factual fluency; the ability to reason about different mathematical concepts; be confident problem solvers and to have a growth mind-set enabling them to relish a challenge and to have a love of maths!