Framework for teaching mathematics

The focus on direct teaching

During each lesson you should aim to spend as much time as possible in direct teaching and questioning of the whole class, a group of pupils, or individuals.

High-quality direct teaching is oral, interactive and lively. It is not achieved by adopting a simplistic formula of 'drill and practice' and lecturing the class, or by expecting pupils to teach themselves from books. It is a two-way process in which pupils are expected to play an active part by answering questions, contributing points to discussions, and explaining and demonstrating their methods to the class.

Good direct teaching is achieved by balancing different elements:

Directing: sharing your teaching objectives with the class, ensuring that pupils know what to do, and drawing attention to points over which they should take particular care, such as how a graph should be labelled, the degree of accuracy needed when making a measurement, or how work can be set out...
Instructing: giving information and structuring it well: for example, describing how to multiply a three-digit number by a two-digit number, how to interpret a graph, how to develop a mathematical argument...
Demonstrating: showing, describing and modelling mathematics using appropriate resources and visual displays: for example, showing how to scribe numerals, showing how to measure using a metre stick or a protractor, demonstrating on a number line how to add on by bridging through 10, using a thermometer to demonstrate the use of negative numbers...
Explaining and illustrating: giving accurate, well-paced explanations, and referring to previous work or methods: for example, explaining a method of calculation and discussing why it works, giving the meaning of a mathematical term, explaining the steps in the solution to a problem, giving examples that satisfy a general statement, illustrating how the statement 7 - 3 = 4 can represent different situations...
Questioning and discussing: questioning in ways which match the direction and pace of the lesson and ensure that all pupils take part (if needed, supported by apparatus or a communication aid, or by an adult who translates, signs or uses symbols), listening carefully to pupils' responses and responding constructively in order to take forward their learning, using open and closed questions, skilfully framed, adjusted and targeted to make sure that pupils of all abilities are involved and contribute to discussions, allowing pupils time to think through answers before inviting a response...
Consolidating: maximising opportunities to reinforce and develop what has been taught, through a variety of activities in class and well-focused tasks to do at home, asking pupils either with a partner or as a group to reflect on and talk through a process, inviting them to expand their ideas and reasoning, or to compare and then refine their methods and ways of recording their work, getting them to think of different ways of approaching a problem, asking them to generalise or to give examples that match a general statement ...
Evaluating pupils' responses: identifying mistakes, using them as positive teaching points by talking about them and any misconceptions that led to them, discussing pupils' justifications of the methods or resources they have chosen, evaluating pupils' presentations of their work to the class, giving them oral feedback on their written work...
Summarising: reviewing during and towards the end of a lesson the mathematics that has been taught and what pupils have learned, identifying and correcting misunderstandings, inviting pupils to present their work and picking out key points and ideas, making links to other work in mathematics and other subjects, giving pupils an insight into the next stage of their learning...

Direct teaching and good interaction are as important in group work and paired work as they are in whole-class work but organising pupils as a 'whole class' for a significant proportion of the time helps to maximise their contact with you so that every child benefits from the teaching and interaction for sustained periods.