At Hill West, we are committed to ensuring that all children are mathematically proficient and confident in the use of maths in their everyday lives. As such we teach for maths mastery designed to ensure all children develop a deep and sustainable understanding of age appropriate mathematical concepts, which can be built upon in the future.
Building on relevant educational research, out maths curriculum has been responsive to the concepts of retrieval practice, interleaving learning and spaced retrieval. We understand that children need regular opportunities to revisit previous learning in order to commit mathematical understanding to the long term memory. As a result, at Hill West, we follow the progressive short blocks devised by Hamilton Trust to ensure that children have regular opportunities to revisit and recall prior learning alongside acquiring new mathematical skills and knowledge through fluency, problem solving and reasoning.
- Fluency is the first step in becoming a successful mathematician. The National Curriculum states that pupils will: become fluent in the fundamentals of mathematics so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. In short, pupils should have a secure understanding of mathematical facts to apply to their learning. Contrary to popular belief, fluency in maths is not all about number – there are many more areas of maths which contain facts for children to retain and recall rapidly (for example, having a secure understanding of the properties of shapes).
- Reasoning in maths is the application of logical thinking to make sense of an idea: it enables children to make use of all their other mathematical sense. Justifying and explaining ideas are important aspects of maths.
- Problem solving requires children to think strategically, deciding which steps to take to solve a problem. However, mathematical problems can be presented in a range of ways, not just through wording, and during maths lessons, children develop the strategies to be able to understand problems, decide on a starting point, decide the existing skills they have which they will need to use to solve it, and how to represent their calculations.
When we plan our lessons and sequences of lessons, we structure the learning so that all pupils work through new content together as a whole group. Although we do not differentiate the learning by reducing the level of difficulty for certain groups, the questioning and scaffolding that individual children receive in class will differ. Tasks are set for all children of similar difficulty as the expectation is that “the majority of pupils will move through the programmes of study at broadly the same pace” (National Curriculum, 2014). Teachers allow time for children to fully understand, explore and apply ideas, rather than accelerate through new topics. Pupils’ difficulties and misconceptions are identified through immediate formative assessment and addressed with rapid intervention. This approach enables pupils to truly grasp a concept.
All children are supported in lessons by having the opportunity to make use of a range of resources, ensuring concrete, pictorial and abstract methods are accessible to all.
- Concrete – Students should have the opportunity to use concrete objects and manipulatives (for example, cubes or base ten) to help them understand and explain what they are exploring.
- Pictorial – Students should then build on this concrete approach by using pictorial representations (for example the bar model to represent addition or subtraction). These representations can then be used to reason and solve problems.
- Abstract – With the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence (for example, formal written methods).
Fluency comes from deep knowledge and practice. At early stages, explicit teaching of multiplication tables is important in the journey towards fluency and contributes to quick and efficient mental calculation. At Hill West, we teach multiplication both through progressive teaching sequences (beginning in Year One) and through daily multiplication chanting and recall of the times tables appropriate for each year group.
An engaging and encouraging climate for children’s early encounters with mathematics develops their confidence in their ability to understand and use maths. These positive experiences help children to develop dispositions such as curiosity, imagination, flexibility, inventiveness and persistence, which contribute to their future success in and out of school (Clements & Conference Working Group, 2004).
At Hill West, we are passionate about the teaching of early mathematics. We actively introduce mathematical concepts, methods and language through a variety of engaging and stimulating practical experiences. We guide children to see connections of ideas within mathematics as well with other subjects, developing their mathematical knowledge throughout the day and across the curriculum. We encourage children to communicate, explaining their thinking as they interact with mathematics in deep and sustained ways.
We ensure that children have sufficient practice to be confident in using and understanding numbers which provides a strong basis for more complex learning later on. Focus is placed on the use of concrete resources to develop deep structural knowledge and the ability to make connections, with the aim of ensuring that what is learnt is sustained over time.