This topic will be used to illustrate the use of a full programme of instruction. The principles of this structure are applicable to other topics. The work moves from a manipulative aid, which is a direct representation of the problem, to a visual model (in this case, area), to purely written symbols and an algorithm which links back to the concrete model. Whenever possible the structure acknowledges different cognitive styles. The multisensory introduction is used to encourage flexible cognitive processes and to provide an overview.

There are some other methods that are used by some teachers and thus by some children. These include the Napier’s Bones method. An overview of the data from the standardisation of Chinn’s 15‐minute test (Chinn, 2017a) suggests that this method is often only partially remembered. The method makes for an interesting exercise for teachers, that is, to analyse all the prerequisite skills a student needs to make a particular method work, for example here, from spatial organisation to retrieval of basic facts. A failure in even one of the steps will result in a wrong answer. It is hard for a student to understand this method and thus hard to support memory without that understanding. It is also of note from the standardising data that the success rate for a three‐digit times three‐digit example (541 × 203) in this test was very low, with 15.2% of the 13‐year‐old cohort and 38.2% of the 15‐year‐old cohort achieving correct ...

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