The irreducible learning core in mathematics, with a focus on the role of place value in calculation

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Carlton School Lesson Study Group,
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Educational Level
ISCED Level 1 Primary education
Curriculum Area
Geographical Setting
United Kingdom of Great Britain and Northern Ireland
Background: Carlton Primary School serves a diverse population: 75% of pupils do not have English as a first language. Approximately 35% of pupils are on the SEND register. Several groups of pupils had been identified as underperforming in mathematics.

Aims: Our main aim was to Year 3 pupils’ understanding and misconceptions around place value – part of the irreducible core of foundational concepts in maths. Children with difficulties in understanding place value find it difficult to make progress in other areas of mathematics particularly calculation.

Methods: Lesson study was used, with three case pupils selected. Close observation allowed us to identify misconceptions and difficulties with place value and in manipulating numbers and to explore the impact on learning of various models and images, to help children to become more competent in calculating. Discussion and analysis after each lesson provided essential insights and informed planning of subsequent learning activities.

Findings: Through the lesson study process and close observation of case pupils, we found some startling gaps in some children’s understanding of place value which was impacting on their ability to perform calculations, and therefore limiting their progress. We identified children whose progress may suffer as a result of these misconceptions and developed action points to address this. Targeting support in this way through ‘precision teaching’ helped improve learning outcomes for these pupils.

Implications: Lesson study was very effective, and the opportunity to make close and focussed observations of case pupils provided valuable insights into their learning. The importance of under
standing individual learners’ misconceptions and difficulties raises the question of how best to gain these insights across a whole class. We have made changes to the planning and teaching in Year 2 to ensure that children assessed as ‘secure’ at Level 2 do not in fact have gaps such as those highlighted in this study, and have introduced a programme of precision teaching by the Mathematics subject leader to selected Year 3 pupils so that they will progress quickly to Level 3.
Keywords (free text)
primary education , lesson study , mathematics , place value , calculation , number operations
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