Here’s a copy & paste of the maths section from the Ofsted Inspection Handbook:
(School inspection handbook January 2015, No. 120101, page 19, para 55.)
Inspecting the teaching of mathematics
55. When evaluating the effectiveness of a school’s work in mathematics through the analysis of performance data, observations in lessons and scrutiny of pupils’ work, inspectors will consider:
- how well the school is identifying and tackling inconsistency in the quality of mathematics teaching between different groups of pupils, key stages, sets and classes, including those taught by non-specialist teachers of mathematics in secondary schools.
- how well teaching, in the mathematics lessons observed, through discussions with pupils and scrutiny of their work and by reviewing curriculum plans:
- fosters mathematical understanding of new concepts and methods, including teachers’ explanations and the way they require pupils to think and reason mathematically for themselves
- ensures that pupils acquire mathematical knowledge appropriate to their age and starting points, and enables them to recall it rapidly and apply it fluently and accurately, including when calculating efficiently and in applying arithmetic algorithms.
- uses resources and approaches to enable pupils in the class to understand and master the mathematics they are learning. The national curriculum for mathematics24 specifies the aims and then states, ‘The expectation is that the majority of pupils will move through the programmes of study at the same pace.’
- develops depth of understanding and readiness for the next stage. The national curriculum states, ‘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 concept 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
- enables pupils to solve a variety of mathematical problems, applying the mathematical knowledge and skills they have been taught.
- how well pupils apply their mathematical knowledge and skills in other subjects in the curriculum, where appropriate.
I find it hard to disagree with any of the above. In fact, if I was writing a handbook for my maths department, it would draw heavily from this. Not because I want to please anyone but because it’s absolutely on the money for what a good department should be doing.