The national curriculum for mathematics aims to ensure that all pupils:
- 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 non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
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 should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should 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 should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.
There are three key features of the maths curriculum that deliver pupils with a deep understanding of mathematics.
Objects and pictures:
Children use concrete manipulatives (objects) and pictorial representations (pictures), before moving to abstract symbols (numbers and signs).
The way that children speak and write about mathematics has been shown to have an impact on their success. At Hillcrest we use a carefully sequenced, structured approach to introduce and reinforce mathematical vocabulary. Every lesson includes opportunities for children to explain or justify their mathematical reasoning.
Mathematical problem solving is at the heart of the approach – it is both how children learn maths, and the reason why they learn maths. By accumulating knowledge of mathematics concepts, children can develop and test their problem solving in every lesson.
None of these are rocket science, but the challenge is to ensure they integrate into every lesson and are applied systematically throughout. Transitioning to fewer topics can feel like slowing down, but by adopting to a cumulative approach, pupils continually build on the knowledge they have already mastered, focusing heavily on solving problems to deepen and reinforce their understanding.
This allows for cumulative, scaffolded learning where assessment is crucially feeding in to subsequent segments. Pupils are ‘doing’ straight away and no time is wasted.
KS1 and 2 Calculations Policy
In conjunction with Maths Mastery we have published a new calculations policy. This policy outlines the different calculation strategies that should be taught and used in line with the requirements of the 2014 Primary National Curriculum.
We hope that as parents you will find this a useful document as you support your child with the methods used at school. If you would like a printed copy please contact the school office.