Pupils’ learning needs to be based on secure knowledge, skills and understanding. According to educational research, pupils need to know about 90% of what they are aiming to master if they are to be successful in a challenge. If they know less than 50% then it is almost certain that they will not engage and fail to be successful (Hattie, 2012).
The teacher of a mathematics class has to consider the implications of this when planning a unit of work. For example, when the intention of a lesson is to develop pupils’ ability to solve geometrical problems involving alternate and corresponding angles the pupils will probably need to be fluent in the following:
- Understand angles are a measure of turn
- Understand that angles are measured in degrees
- Recognise vertically opposite angles
- Recognise parallel lines
- Recognise alternate angles
- Recognise corresponding angles
- Understand geometrical notation, especially arrow notation for parallel lines
- Solve geometrical problems involving angles at a point
- Solve geometrical problems involving angles at a point on a line
- Solve geometrical problems involving triangles
- Add and subtract numbers with up to three digits (if a calculator is not be used)
There may be other items depending on the tasks or resources chosen. The teacher may decide to rehearse some of these skills either in starters for the sequence of lessons or in the first lesson of the unit, but it may be impractical to aim for full coverage. She will use pupils’ oral and written responses to assess where they might have conceptual problems and need alternative approaches or supplementary work. She may ask a teaching assistant to do some extra preliminary work with individual pupils. Most importantly she must be aware of gaps in prior knowledge that could cause difficulties and be constantly attuned to what is happening in the lesson, being prepared to intervene promptly and effectively. She will evaluate each learning episode and alter future plans accordingly.
It can be useful to encourage pupils to think about concept maps with the mathematics that they are studying. Knowledge maps – tools for building structure in mathematics is an article by Astrid Brinkmann that discusses their use.
See also Planning lessons involves thinking about many different things and Aspects of teaching may, or may not, support principles that underlie effective teaching