# Reasoning & Problem Solving

Mathematical Reasoning and Solving Problems Mathematically are two of the three strands in the aims of the National Curriculum.

We have two work groups that are focus on Mathematical Reasoning.

KS3 reasoning Cohorts 1 & 2 (NCP)

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.

Recent Ofsted inspection findings show that:

- Of the three NC aims, Resoning is the least well developed.
- Not all classrooms have a positive ethos that encourages learning from mistakes.
- Teachers do not exploit opportunities to model thinking.
- Tasks are not used well enough to develop reasoning.
- Talk often focuses on the ‘how’ rather than the ‘why’, ‘why not’, and ‘what if’ in:
- teachers’ explanations and questions
- pupils’ responses.