# What’s the difference between good and satisfactory mathematics teaching?

When asking this question, we are, of course, referring to Ofsted’s use of the terms ‘Good’ and ‘Satisfactory’.  The table below, from Ofsted outlines some of the differences between ‘good’ features and ‘satisfactory’ features of mathematics teaching.  Many of these elements relate directly to the planning chapter in Lessons in Teaching Number and Place Value in Primary, and other features here relate to and reinforce the areas discussed elsewhere in the book.

In good mathematics teaching:

• children are given the opportunity to move beyond routine exercises in order to solve non-routine problems and open-ended tasks
• children expect to be given problems to solve and tackle these with independence
• good teachers of mathematics have good subject knowledge and use this to extend understanding and to help children make links and connections
• good teachers encourage pupil discussion
• children are expected to provide explanations of their reasoning in discussions

Want to know more?  Lessons in Teaching Number and Place Value in Primary Schools is your tool to help you ensure that your lessons and teaching fall into the ‘good’ column.  For more book details, click here.

 Features of good mathematics teaching (primary) Features of satisfactory mathematics teaching (primary) 1 Lesson objectives involve understanding and make what is to be learned in the lesson very clear. Lesson objectives are procedural, such as descriptions of work to be completed, or are general, such as broad topic areas. 2 Teaching features a successful focus on each pupil’s learning. Pupils are clear about what they are expected to learn in the lesson and how to show evidence of this. Teaching features a successful focus on teaching the content of the lesson. Pupils complete correct work and are aware of the lesson objectives but may not understand what they mean or what they need to do to meet them. 3 The lesson forms a clear part of a developmental sequence and pupils recognise links with earlier work, different parts of mathematics or contexts for its use. The lesson stands alone adequately but links are superficial; for example, links are made with the previous lesson but not in a way that all the pupils understand. 4 Teachers introduce new terms and symbols meaningfully and expect and encourage correct use. Teachers introduce new terms and symbols accurately and demonstrate correct spelling. 5 Whole class teaching/questioning: Pupils spend enough time listening to teachers’ exposition and working to develop their understanding, and teachers move them on when appropriate. Teachers and support staff ensure all pupils participate actively in whole-class activity, such as through using mini whiteboards or partner discussions. When offering answers or accounts, the teacher expects pupils to give explanations of their reasoning as well as their methods. Pupils are challenged if their explanations do not reflect their ability. Whole class teaching/questioning: Teachers give effective exposition but pupils’ understanding is limited due to time constraints or not extended due to limitations with the task. Questioning and whole-class activities are pitched appropriately but do not involve all pupils’ actively; for example, few hands up, questions directed to few pupils, mini whiteboards held up whenever pupils are ready so not all give answers or some copy from others. Questioning is clear and accurate but does not require explanation or reasoning; pupils describe the steps in their method accurately but do not explain why it works. 6 Group/individual work: Teachers monitor all pupils’ understanding throughout the lesson. They recognise quickly when pupils already understand the work or what their misconception might be. They extend thinking through building on pupils’ contributions, questions and misconceptions to aid learning, flexibly adapting to meet needs and confidently departing from plans. The work challenges all pupils as it is informed by teachers’ knowledge of pupils’ learning; for example, through encouraging pupils capable of doing so to improve their explanations or use more efficient methods. Work requires thinking and reasoning and enables pupils to fully understand objectives. Pupils can explain why a method works and solve again a problem they have solved a few weeks earlier. Non-routine problems, open-ended tasks and investigations are used often by all pupils to develop the broader mathematical skills of problem solving, reasoning and generalising. Group/individual work: Competent questioning but the teacher may miss opportunities to respond to needs; for example, does not build on errors or sticks too closely to plans. Pupils generally complete work correctly but may have made errors or already understand the work so tasks do not fully stretch the high attainers or support the low attainers. Methods are clearly conveyed by teachers and used accurately by pupils; pupils focus on obtaining correct answers rather than enhancing understanding and questions may not be carefully selected. Skills may be short-lived so pupils cannot answer questions which they have completed correctly a few weeks earlier. Typical lessons consist of routine exercises that develop skills and techniques adequately but pupils have few opportunities to develop reasoning, problem solving and investigatory skills, or only the higher attainers are given such opportunities. 7 Pupils develop independence and confidence by recognising when their solutions are correct and persevering to overcome difficulties because they expect to be able to solve problems; the teacher’s interventions support them in estimating and checking for themselves. Support generally offered to pupils does not develop independence in solving complete problems; for example, answers are given too readily or the problem is broken down so much that pupils do not know why the sequence of steps was chosen. Pupils may ask for help at each step and are given directed steps to take rather than interventions that encourage thinking and confidence that they can succeed. 8 Teaching assistants know the pupils well, are well briefed on the concepts and expected misconceptions, and provide support throughout the lesson that enhances thinking and independence. Teaching assistants facilitate access of all pupils, though may be less active in whole-class work. 9 Teachers (and pupils) have a good grasp of what has been learnt judged against criteria that they understand; this is shown through pupil discussion, reflection, oral or written summaries, and ascertained by the teacher’s monitoring throughout the lesson. Teachers (and pupils) make some accurate assessment of learning; for example, the teacher correctly reflects in a plenary what many pupils have achieved, pupils make an impressionistic assessment of their learning, such as using traffic lights or against a generic lesson objective. 10 Teachers’ marking identifies errors and underlying misconceptions and helps pupils to overcome difficulties. For example, by setting clear targets, which pupils take responsibility for following up and seek to understand where they have gone wrong. Accurate marking by the teacher identifies errors and provides pupils with feedback; important work has been marked by pupils or teacher. 11 Good use of subject knowledge to capitalise on opportunities to extend understanding, such as through links to other subjects, more complex situations or previously learned mathematics. Any small slips or vagueness in use of subject knowledge do not prevent pupils from making progress. 12 Pupils exude enjoyment and involvement in the lesson. Pupils are confident enough to offer right and wrong comments. Pupils naturally listen to and respond to each other’s comments, showing engagement with them. Pupils enjoy making progress in an ordered environment. Some pupils offer responses to whole-class questions. Pupils listen to the teacher’s and pupils’ contributions and respond to them when asked to.

Table reference:

Ofsted (2008) ‘Features of satisfactory and good mathematics teaching ‘in Mathematics: understanding the score (pages 67-69). London: Ofsted.