ItemThe irreducible learning core in mathematics, with a focus on overcoming barriers in number(Lesson Study UK and Camtree: the Cambridge Teacher Research Exchange, 2013) St Aloysius Catholic Junior School Lesson Study Group,Background: The school is located in urban area of high deprivation. Teaching staff had noticed that a lack of understanding of number facts and place value was making it difficult for children to grasp more challenging mathematical concepts and tackle mathematical problems. Year 4 teachers undertook a lesson study to address this. Aims: The aims of the lesson study where to improve teaching and learning of number bonds, number facts and place value, particularly partitioning; and also to evaluate the lesson study approach more generally. Methods: The lesson study sequence involved introducing a range of new approaches to reinforcing number facts and carrying out partitioning including games, puzzles and problems. Resources such as Base 10 resources, hundred squares, counters were introduced into the classroom to give pupils opportunities to play with the practical resources and revisit prior learning. The teacher modelled these approaches and encouraged children to talk about the strategies they were using, to work in pairs and use key mathematical vocabulary as part of their oral reasoning. Findings: The first lesson in the sequence highlighted the insecurity in many pupils’ knowledge of number facts and relationships so activities were included to support them with these along with alternative approaches. Reintroducing practical resources into a Year 4 classroom allowed children to revisit prior learning and address areas of weakness. Children were motivated by the new approaches and were keen to use them to solve problems; they were also able to use new vocabulary and in the course of the lesson sequence they became more willing and able to explain to teachers, partners and the class how they had solved problems. Children were also able to identify where their knowledge was not secure and this was a barrier to their progression. Implications: This more open, practical approach to the teaching of maths, supported by the reintroduction practical resources alongside games, puzzles and open-ended problems has been very effective and motivating. Pupils benefited greatly from an opportunity to share, explain and discuss their understanding with their peers and the role of discussion will be the focus of further inquiries. We have also decided to introduce lesson study throughout the school. We have found that it provides an opportunity for teachers to observe closely a target group of pupils’ learning. This has already enhanced our understanding of how children learn, how they perceive us as teachers and what they do and don’t expect us to do. ItemA study into how children can effectively use models and images to help understand place value(Lesson Study UK and Camtree: the Cambridge Teacher Research Exchange, 2013) St Aloysius’ Catholic Infant School Lesson Study Group,Background: The setting is an urban infant school in an area of higher-than average deprivation. The overall focus of the school’s lesson study pilot was to look into ways of developing models and images to effectively develop our Year 2 children’s basic understanding of place value. Aims: The main aim of the study was to improve pupils' understanding of how to use Dienes' apparatus to partition 2-digit and 3-digit numbers, and to use this understanding to aid in their learning and understanding of addition and subtraction strategies. Methods: A lesson study approach was used to teach pupils how to use Dienes' apparatus to partition 2-digit and 3-digit numbers. Close observation of case pupils informed changes in approach in lessons 2 and 3 of the sequence. Specifically, the role and purpose of Diene’s apparatus was made very explicit and their use was modelled by the teacher and in whole-class activities. Findings: The lesson study helped teachers understand the importance of pacing and matching work to students' current understanding. Teachers had assumed too much about children’s understanding and had focused on the visual and concrete elements of the Diene’s apparatus instead of the abstract thinking behind the structure of the blocks. Once the children were more secure in their use of Dienes' apparatus, this aided their understanding of partitioning 2-digit and 3-digit numbers, which will impact future learning and aid in addition and subtraction. Implications: Future teaching will focus on allowing sufficient time for concept development, explaining resources, and tracking individual progress. Outcomes will be shared with other staff and lesson study will be used to improve teaching across the curriculum. ItemThe irreducible learning core in mathematics, with a focus on the role of place value in calculation(Lesson Study UK and Camtree: the Cambridge Teacher Research Exchange, 2013) Carlton School Lesson Study Group,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. ItemLanguage development in mathematics(Lesson Study UK and Camtree: the Cambridge Teacher Research Exchange, 2013) Beckford Lesson Study Group,Background: An issue across the school, which serves a diverse community, was improving the progress of EAL children in school. Children appeared to understand the mathematics they were being taught during lessons, but when tested they were working below the standards expected. Their difficulties with language were often identified as a key barrier to learning and progress in mathematics. Aim: Through lesson study, we wanted to explore how language in mathematics could be developed to support greater understanding and progress in learning. We have been monitoring the impact and use of sentence frames, greater opportunities for talk, and the links between oral, visual and contextualised understanding. Methods: We developed a sequence of research lessons focusing on three case pupils. We introduced and modelled the activities. We provided example key learning facts related to odd and even numbers and a range of visual and practical aids. Additional framing devices were provided in subsequent lessons, and we sought and observed the children’s explanations, encouraging paired talk. Findings: Children showed both persistence and resilience in being able to do more of the activity independently as the lessons progressed. They have shown greater confidence in sharing ideas and developing and supporting their own and other’s learning. Most children were able to use the prompt: “I know...because...” to discuss their reasons and answers with adults and with their peers. Some EAL children still needed help to be clear about what a written question is asking for and to decide what they needed to do to answer it. Implications: The lesson study sequence highlighted the importance of giving children much greater opportunity for mathematics talk, and how that talk is most rich when it is supported with multiple representations for children to use and refer to in the lesson including practical resources and equipment, and mathematics pictures and models. Lesson study has provided insights into children’s misconceptions, strategies and learning, and has suggested alternative and additional activities to support them. ItemDeveloping collaboration in problem solving in primary mathematics(Lesson Study UK and Camtree: the Cambridge Teacher Research Exchange, 2013) Brookfield Lesson Study Group,Background: Our identified issue across the school, which has a diverse population, was the lack of confidence many of our children showed when faced with mathematical problems. In assessments, open-ended questions would often be skipped or attempted half-heartedly. Aims: We wanted to explore how we could best structure opportunities for the children to collaborate in problem solving and develop the confidence to use of different methods to tackle new problems. Methods: Mixed-ability pairs of Year 4 children were presented with open-ended problems on which they collaborated to create posters. They then shared their strategies with the class and answered questions about their approach. The teacher was the collector of ideas, rather than the source. The process was refined over three research lessons with progressively more complex problems being presented. Findings: We found that providing a clear structure and encouraging collaboration improved children's confidence and willingness to tackle new mathematical problems. The study highlighted the need for an effective problem-solving lesson structure and showed positive impacts on pupil learning and progress, including increased collaboration and sharing of ideas. The emotional side of this group work was significant: children were easily discouraged and a culture of celebration of all their work was essential, rather than rewarding correct or best answers. Implications: The study found that providing a clear structure for problem-solving lessons and encouraging collaboration improved children's confidence and willingness to tackle new problems. Mixing up children and promoting sharing of ideas also had a positive impact on their learning and progress, leading to a greater willingness to try out new approaches and learn from each other. Lesson study provided an effective model for gaining insight and developing practice.