Mathematics at World’s End Junior School
Our aim is to equip all pupils with the skills and confidence to solve a range of problems through fluency with numbers and mathematical reasoning. Children are encouraged to see the mathematics that surrounds them every day and enjoy developing vital life skills in this subject.
At World’s End Junior School we have been on a journey over several years in order to improve the teaching and learning of mathematics. There are several elements which have influenced improvements in attainment and these are best discussed in person with me during your visit. If you are taking a look around the school however, it may be useful for you to have a little advance notice of things you will see in lessons – things that may look different to other schools, or the way lessons/books looked a few years ago.
The three aims of the NC should be addressed every day (not just in the maths lesson) – Fluency – Reasoning – Problem Solving.
In Year’s 3, 4 and 5 we have introduced the split lesson approach. This was initially a trial in Year’s 3 and 4 and was so successful, we extended it into Year 5 in January 2016.
- Whole class together – we teach mathematics to whole classes and do not label children. Lessons are planned based on formative assessment of what students already know and we include all children in learning mathematical concepts. At the planning stage, teachers consider the scaffolding that may be required for children struggling to grasp concepts in the lesson and challenge ‘depth’ questions for those who may grasp the concepts rapidly. In line with NCETM advice and much academic research, one form of depth frequently used, during the first part of the lesson, is variation theory (conceptual and procedural). Variation is one of the five ‘big ideas’ at the heart of Teaching for Mastery. For example, a child who can produce a quick correct answer may be asked to solve the question using more than one other procedure, to represent the question in more than one way (such as the bar model or part whole), to write another question using the same numbers and operation. This ensures that the children have a deep understanding of the objective being taught.
- Longer and but deeper – in order to ensure children have a secure and deep understanding of the content taught, our plans have been adjusted to allow longer on topics and we move more slowly through the curriculum. After evaluating the findings of the National Textbook Project, years 3, 4 and 5 broadly follow the ‘Maths No Problem’ textbook progression. Teachers adapt each lesson to meet the needs of their children and add extra questioning / tasks which will allow children to learn the content more deeply. The learning will focus on one key conceptual idea and connections are made across mathematical topics. To outsiders it may appear that the pace of the lesson is slower, but progress and understanding is enhanced.
- Key learning points are identified during planning (collaboratively in year groups) and a clear journey through the maths should be shown on flipcharts (also reflected on working walls). Learning points may appear to be very small but this is deliberate. For example, a whole lesson may be spent on adding the ones to a 3 digit number. The expectation is that every child will master the concept and some children will work more deeply on the same concept using variation theory and challenge tasks.
- Questions will probe pupil understanding throughout, taking some children’s learning deeper. Responses are expected in full sentences, using precise mathematical vocabulary.
- Fluency – there is a whole school focus on developing an instant recall of key facts, such as number bonds, times tables and unit + unit addition facts.
- Exploration – instead of ‘Let me teach you…’ or giving a learning objective as a starting point, children are encouraged to explore a problem themselves to see what they already know. At the beginning of each lesson this exploration is referred to as the ‘anchor task’. During this time, the teacher and teaching assistant will spend time observing and questioning the children. The understanding of children who provide a quick correct answer will be probed further using questions based around variation theory.
- Develop reasoning and deep understanding (contexts and representations of mathematics) – problems are often set in real life contexts – carefully chosen practical resources and pictorial representations are used to explore concepts. These pictorial representations will appear in books as children show their understanding, rather than answers to a series of calculations. The use of practical resources, pictorial representations and recording takes place in every lesson (the CPA approach).
- Structuring – the teacher will organise the findings of the exploration, compare/contrast strategies and guide toward the most efficient strategy (or the one being learnt that day).
- Step by step approach – journey through the mathematics (these steps may appear small, especially at the beginning of a lesson, there are points when suddenly a jump appears to have been made, or an extra challenge appears – this is normal).
- Questions to challenge thinking – teachers use questioning throughout every lesson to check understanding – a variety of questions are used, but you will hear the same ones being repeated: How do you know? Can you prove it? Are you sure? Can you represent it another way? What’s the value? What’s the same/different about? Can you explain that? What does your partner think? Can you imagine?
NB: Due to the episodic style of the lessons with frequent questioning, lessons may appear to move slower than in the past. There will be more talking and less recording in books. We do not want children to attempt independent recording until we believe they are secure with the concept. We do not want them to practise errors.
- Discussion and feedback – pupils have opportunities to talk to their partners and explain/clarity their thinking.
- Journal – recording the learning – not just pages of similar calculations – years 3, 4 and 5 maths journals are used. In year 6 you will see maths books used for both journaling activities and practice.
- Reflecting – this may be linked to use of the textbook – images on the IWB may be from the Singapore textbooks – you are unlikely to see textbooks in use in the classroom, except with a guided group, but they are used during the planning and preparation stages.
- Practising – not drill and practice but practice characterised by variation – in year groups using Maths No Problem, this is done in the workbooks, in other year 6 it will be recorded in maths books.
- Rapid intervention (same day catch up) – in mathematics new learning is built upon previous understanding, so in order for learning to progress and to keep the class together pupils need to be supported to keep up and areas of difficulty must be dealt with as and when they occur. We do this through same day interventions of 20 – 25 minutes in the afternoon. In addition, we still run intervention sessions outside of the maths lesson for some targeted children, eg: Success @ Arithmetic, Catch Up, pre or post tutoring, fluency groups…
- Marking – the marking policy has been amended following the guidance of the NCETM. Current marking policy is that learning is ticked and a comment is only made if/when a teacher feels this is necessary to move learning forward. Gap tasks may appear for individual children in their books, but usually gaps are addressed through same day catch up and therefore will not be recorded in books. The most valuable feedback is given during a lesson.
- SEN pupils – may be supported by additional adults, different resources, differentiated activities. They will also complete additional activities outside of the mathematics lesson.
NB: We do not label our children. We have high expectations of all children and strongly believe that all children are equally able in mathematics. Some may take longer to grasp concepts and may need careful scaffolding or extra time/support (guided groups, same day catch-up, additional homework, pre-teaching, intervention group, specific parent support).