At Rivelin, we encourage ALL pupils to become mathematicians. We pride ourselves on cultivating an environment rich in mathematical understanding, and the use of rich maths vocabulary is embedded and encouraged.
We have adopted the NTS termly assessment, which aligns with the maths scheme that we adopted at the beginning of the pandemic – White Rose. This new scheme provided consistency while both our pupils and teachers worked from home. We also adopted White Rose as their resources and termly schedules are ‘influenced, inspired and informed by the work of leading maths researchers and practitioners across the world…’ We supplement this scheme of work with materials from the National Centre for Excellence in the Teaching of Mathematics (NCETM), Classroom Secrets, Deepening Understanding and Teach Active.
Our school’s maths teaching is guided by the principles of maths mastery. The NCETM defines maths mastery as ‘all pupils of all ages acquiring a deep, long-term, secure and adaptable understanding of the subject.’ There are ‘5 Big Ideas’ that underpin the teaching of maths mastery: coherence, representation and structure, mathematical thinking, fluency and variation.
The sequence of lessons is important, as these small connected steps build on larger concepts. As pupils become more secure in these concepts, they are then able to apply this understanding in a variety of ways.
Representation and Structure:
There are numerous representations we can use to support and scaffold pupils’ understanding of various topics. We utilise the CPA approach (Concrete, Pictorial, Abstract) to help make maths less abstract and build on children’s existing knowledge in a tangible way. This essentially means that we break down the introduction of a new concept into three phases:
- Concrete – This is often called the ‘doing stage.’ During this stage, pupils are encouraged to handle physical objects when attempting to decipher/interpret new problems. An example of this is when the problem involves fruit. Children are encouraged use mini fruit models as a way to interpret and better understand the problem through adding and taking away, providing the scaffolding needed to answer the question.
This ‘hands-on’ approach paves the way for when pupils then move to more abstract materials such as counters or unifix cubes.
Here at Rivelin, we utilise a varity of manipulatives to enhance our pupils’ learning, (beginning in EYFS, through to Year 6): place value counters, Unifix cubes, number beads, Base 10, Numicon, Cuisenaire rods and fake money. To promote subitising (the ability to recognise the number of objects without needing to count them) in EYFS, teachers develop children’s understanding by asking key questions and using tens frames when counting acorns, objects from around the home and cubes (just to name a few!).
- Pictorial – This stage is referred to as the ‘seeing stage.’ Visual representations replace concrete objects. This promotes mental connections between physical objects and slightly more abstract pictures, diagrams and models.
- Abstract – This final stage is considered the ‘symbolic stage.’ Pupils arrive at this stage once they have a secure understanding of the concrete and pictorial aspects of the problem. This stage uses various numbers and mathematical symbols to indicate the four main operations (+, -, x, /).
*Please note that sometimes teachers will guide pupils through these steps; however, teachers may use best judgement and switch stages depending on their pupils’ needs.
Our pupils are encouraged to reason and problem solve. The use of rich, mathematical vocabulary is encouraged and promoted throughout the school. The focus on key vocabulary is essential for grasping new concepts (i.e. fractions, numerator, denominator, mixed number). Pupils are provided opportunities throughout the school to develop and utilise this vocabulary within small, collaborative group work, leading to impressive mathematical discussions which provide pupils with the opportunity to embed and articulately demonstrate this secure understanding of topics.
Fluency is the ‘quick and efficient recall of facts and procedures.’ Prior to adopting the maths mastery approach in 2019, our pupils focused primarily on fluency. However, as maths mastery relies on reasoning and problem-solving, pupils now have a secure understanding of how these three concepts work in combination to develop the skills and knowledge of our budding mathematicians. Fluency plays an important part in ensuring that pupils free up their working memory so that pupils can utilise new procedures when solving complex problems. An important aspect of this is the understanding and rapid recall of pupils’ times tables.
In the 2019/2020 academic year, the DfE introduced the Year 4 MTC (Multiplication Tables Check). This 25-question assessment tests the Year 4 pupils’ times tables knowledge in June of each year.
Pupils have 6-seconds to answer each question. In order for pupils to get a perfect score, they need a secure understanding of their 1-12 times tables, along with savvy number pad keyboard skills. With the explicit teaching of times tables, combined with the repetitive recall of times tables through songs, chants, TT Rockstars and paper exercises, our pupils’ are increasingly secure in these tables. This not only helps them when solving various problems but more importantly sets them up for success in secondary school, as well as the Year 6 SATS tests.
This means that concepts are represented in more than one way.
There are two aspects of variation: Procedural and Conceptual.
Procedural Variation emphasises the relationship between numbers; this encourages some reasoning to explain why the answers have changed.
Conceptual Variation encourages pupils to understand concepts through multiple perspectives.