Some examples of teachers supporting pupils to recognise mathematical structure are: Teach pupils to recognise and use mathematical structure Paying attention to underlying mathematical structure helps pupils make connections between problems, solution strategies, and representations that may, on the surface, appear different, but are actually mathematically equivalent.
However, these meta-analyses are at a general level and do not provide evidence about specific teaching approaches. 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.
Number lines are a useful tool for teaching these concepts. Teach pupils that fractions and decimals extend the number system beyond whole numbers Fractions are often introduced to pupils with the idea that they represent parts of a whole—for example, one half is one part of a whole that has two equal parts.
The aim is to enable pupils to self-regulate their use of calculators, consequently making less but better use of them.
Teachers should adopt such approaches while drawing on their knowledge of maths, their own professional experience, and the other recommendations in this guidance. Ensure that pupils develop fluent recall of number facts Quick retrieval of number facts is important for success in mathematics.
Another important concept is often overlooked: The evidence strength is judged to be stronger in support of focusing on fluent recall, encouraging the deliberate choice of strategies and using number lines to represent fractions and decimals. Although this recommendation concerns particular topics, teaching should emphasise the many connections between different mathematical facts, procedures, and concepts to create a rich network.
This is an important concept, but does not extend easily to mixed fractions that are greater than 1. They can be used to: This recommendation presents the evidence regarding teaching specific topics in mathematics. The evidence on calculator use is judged to be strong.
One reason for encouraging understanding is to enable pupils to reconstruct steps in a procedure that they may have forgotten. Four systematic reviews by the US What Works Clearinghouse provide evidence for specific teaching approaches in number and algebra.
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. Enable pupils to develop a rich network of mathematical knowledge Evidence strength Evidence Rating The review identified two relevant meta-analyses concerning the teaching of algebra.
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. They have magnitudes or values, and they can be used to refer to numbers in-between whole numbers.
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. The review identified four meta-analyses investigating calculator use.Free Interactive Primary or Elementary Key Stage 2 ages years, Literacy and English Teacher Resources and fun Kids Games.
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