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| Ensure that pupils develop fluent recall of number facts |
This recommendation presents the evidence regarding teaching specific topics in mathematics. Although this recommendation concerns particular topics, teaching should emphasize the many connections between different mathematical facts, procedures, and concepts to create a rich network.
Currently, the evidence about effective teaching approaches is stronger regarding number (including fractions, ratio and proportion) and algebra than for other areas such as geometry. However, it is likely that some of the approaches below (particularly choosing between strategies) apply across mathematical topics.
Teachers should adopt such approaches while drawing on their knowledge of maths, their own professional experience, and the other recommendations in this email series.
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Quick retrieval of number facts is important for success in mathematics. [1] It is likely that pupils who have problems retrieving addition, subtraction, multiplication, and division facts, including number bonds and multiples, will have difficulty understanding and using mathematical concepts they encounter later on in their studies.
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| Teach pupils to understand procedures |
Pupils are able to apply procedures most effectively when they understand how the procedures work and in what circumstances they are useful. [2] Fluent recall of a procedure is important, but teachers should ensure that appropriate time is spent on developing understanding.
One reason for encouraging understanding is to enable pupils to reconstruct steps in a procedure that they may have forgotten. [3] The recommendations in this email series on visual representations, misconceptions, and setting problems in real-world contexts are useful here.
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| Teach pupils to choose between mathematical strategies |
Teachers should help pupils to compare and choose between different methods and strategies for solving problems in algebra, number, and elsewhere.
Pupils should be taught a range of mental, calculator, and pencil-and-paper methods, and encouraged to consider when different methods are appropriate and efficient.
The evidence suggests that using a calculator does not generally harm students’ mental or pencil-and-paper calculation skills. In fact, studies have shown using a calculator can have positive impacts, not only on mental calculation skills, but also on problem-solving and attitudes towards maths. [4]
Calculators should be integrated into the teaching of mental and other calculation approaches, and pupils should be taught to make considered decisions about when, where, and why to use particular methods. The aim is to enable pupils to self-regulate their use of calculators, consequently making less (but better) use of them. [5]
Next email #5 - 'Recommendation 4 (cont.): Enable pupils to develop a rich network of mathematical knowledge'
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