Moving into compact methods of calculation – procedure versus conceptual understanding.

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Frood, Kate
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Educational Level
ISCED Level 1 Primary education
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Geographical Setting
United Kingdom of Great Britain and Northern Ireland
The purpose of the study was to explore how and whether it was possible to have more children working securely with compact methods of calculation, specifically in multiplication, in order to meet the new mathematics curriculum requirements.

The participants were 30 Year 5 students who were not secure in multiplication methodology, but had an understanding of partitioning and place value and fluent recall of times tables. They expressed a preference for the grid method. The methods used included Lesson Study, parrot on the shoulder coaching, Variation Theory, spot the mistake modelling, re-grouping, and purposeful practice of worked examples. Intelligent practice was used to focus on small changes that reinforced the concept, and calculations were presented horizontally to encourage conceptual understanding.

The main findings were that children preferred the grid method due to its visual and structured nature, which allowed them to stay focused and identify errors quickly. With the compact method, place value was implicit and it was harder to stay on track.

The findings suggest that children are more successful with compact methods of calculation when they are supported with a highly structured and visual approach. This approach allows them to focus and identify errors quickly, leading to increased confidence and understanding.
Keywords (free text)
mathematics , coaching , primary education
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