- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and nonroutine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
At Spalding St Paul’s School Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They also apply their mathematical knowledge to science and other subjects.The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress are always based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly are challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material will consolidate their understanding, including through additional practice, before moving on.
In Key Stage One, these new concepts are always presented with objects (concrete manipulatives) for the children to use. Children can also use a range of concrete manipulatives within Key Stage two, when needed. Once concrete concepts are developed the children can move into exploring pictorially and then abstractly.
Teachers use a range of questioning skills to draw children’s discussions and their reasoning. Once fluency is developed the class teacher then teaches the children the strategies for reasoning and solving problems. Independent work provides the means for all children to develop their fluency further before progressing to more complex related problems.
Mathematical topics are talking blocks to enable the achievement of mastery over time. Each sequence of lessons a ‘lesson phase’ provides the means to achieve greater depth with more able children offered sophisticated problems as well as exploratory, investigative tasks within the lesson as appropriate.
The impact of our Mathematics curriculum is that the children understand the relevance of what they are learning and what learning came before this.
Mathematics books are completed within each year groups showing the developed progression evidence of fluency, reasoning and problem solving. The children become fluent, successful reasoners with the ability to problem solve within a wider context. The children will become creative, fluent problem solvers who will face challenges with resilience.