There should be no such thing as boring mathematics
- Edsger Dijkstra
At Hurworth Primary, we aim for all our children to become fluent in all areas of mathematics and to be able to reason about their learning in a way that deepens their understanding and allows all of them to be successful problem-solvers.
It is our school’s belief that children need to be exposed to a range of representations and procedures in a systematic way that allows them to build from secure foundations. Experience also tells us that children struggle to become fluent by learning through problems and likewise they cannot be effective problem-solvers if they do not have the underlying fluency of mathematical content.
It is for these reasons that we ensure children work from a basic understanding of fluency to varied fluency before tackling problem-solving. We have a structured, whole school approach to problem-solving once children have mastered the underlying content of an area of maths. Our lessons are reasoning-rich learning experiences for children, with reasoning and discussion throughout to ensure children are thinking deeply about their learning.
Experience has shown us that mathematical fluency can only happen if children have good factual knowledge and it is for this reason that we have a systematic, whole-school approach to fact fluency.
To turn our intent for how maths will be taught into a reality, we have constructed our own curriculum design that allows children to consolidate learning in the next unit by sequencing units that are linked. This also encourage our children to see the links in maths and this deepens and secures their understanding.
From this long-term curriculum design, our vision turns into effective learning through the following lesson design in KS1 and KS2:
A maths lesson starts with retrieval practice, which we call ‘Flashback 4.’ These questions are carefully selected by the class teacher to include something from the last lesson, something from last week, something from the last unit and something from last year (the current unit focus). By using the previous lesson, we allow children to access the new learning from what they already know, allowing them to make links.
For a fluency lesson, following Flashback 4, the teacher models selected fluency and varied fluency questions using an ‘I do, we do, you do’ approach. The children then complete their independent work. The independent work will be based around the teaching input with other types of varied fluency questions. Higher attainers and quick graspers are routinely encouraged through our stretch tasks, such as ‘create a similar question’ or ‘explain which was the most challenging question’. This allows us to ensure all children move onto problem-solving together.
At the end of the lesson, there will be a class discussion around a reasoning prompt so that all children have had the opportunity to access this question, before where appropriate giving a written response.
We do not view reasoning as a question at the end of the lesson, but rather it is the way the lesson is built on discussion, describing, explaining and justifying all the way through the lesson.
Once the children are fluent in the underlying maths, we have dedicated problem-solving lessons where all children are taught a strategy to solve a problem through direct teaching and then exposed to an unfamiliar problem where said strategy will also work. This allows us to teach problem-solving while also ensuring independent problem-solving in the same lesson.
To ensure that our curriculum and lesson designs are making our intent a reality and that the children are secure in their learning, we finish a unit with a mini-assessment from which we filter our children into two groups: pause and stretch. Those needing further support work in a pause lesson while those who showed mastery to a greater depth work in a stretch lesson. This stretch lesson acts as our higher attainer intervention and is where our children are exposed to rich and sophisticated problems. Following the pause lessons, we will drop further practice into our Flashback 4 before partially reassessing the children. Due to the way our curriculum is designed, the next unit will always allow children a chance to practice the skills just learnt or offer further chances to mend misconceptions. For example, if children are not quite secure with addition and subtraction after the pause lesson, statistics will follow where sum and difference questions will allow further opportunity.
Our intent for all children to have the required factual knowledge is enacted by:
Key Stage 1 following the Fluency Bee program to develop automaticity in addition and subtraction facts to 20
Lower Key Stage 2 breaking multiplication tables down into sequences of small steps so pupils are not learning too much but rather learning it deeper (see below). We then use regular testing to ensure retention.
Upper Key Stage 2 having regular, brief arithmetic sessions that pull of these facts together into procedural fluency.
Maths Curriculum Overviews by Year Group
Maths Medium Term Planning by Year Group