Our journey in Mathematics
Maths is one of the four strands at the heart of our learning modules through which our children discover a broad and balanced curriculum. Aspects of maths such as number, spatial reasoning, statistics… either form the main focus for a module or its backdrop. In the continuous-provision or the contexts of other subjects, the mathematical concepts can be practised and applied.
Our children experience the learning of maths following the Concrete, Pictorial, Abstract (CPA) process for teaching and learning developed by American psychologist Jerome Bruner. Starting with manipulation of concrete materials with counters, Diennes, Unifix cubes… our children move on to represent maths pictorially with tallies, dots, arrays… which is then abstracted, so that numbers and symbols are used. CPA instruction allows them to make associations from one stage of the process to the next, with the ultimate purpose of giving children a thorough understanding of math concepts.
In the early years, experiencing number and being able to describe and measure space and time form the fundamentals of maths. From daily routines and play, mathematical language and concepts of number emerge. From rhymes and action-play children begin to count. From the ‘form a circle’ for learning and play, space, shape and measurement become real. These experiences are complimented within the daily learning times, consolidating basic mathematical ideas through rhyme and number songs.
From Age 2, children experience daily practitioner-led learning-times, which include mathematical processes such as: counting, by orally labelling objects; comparing shapes, with inset puzzles and jigsaws… Practise within the sessions can be re-visited in their play through continuous provision. Practitioners anticipate and look out for instances when a child might use maths in their play and will encourage, sustain and extend such thinking and play.
In nursery, the adult-led sessions include two each week that concentrate on extending the numeracy and spatial reasoning of children. These are complemented weekly with a number book, story and rhyme. This learning translates into practitioner-led and child-led activities as well as child-initiated play supported by trained practitioners who intervene to focus and extend their learning of number and numerical pattern.
Through the daily maths session in reception, children gradually move towards a structured maths lesson. They begin by consolidating concepts of ‘numberness’ with manipulatives and abstract by forming digits and numerals before moving on to place-value involving ‘tens’ and ‘ones’. They explore shape and pattern and compare measures to describe their world. Within adult-led and child-led activities and continuous provision, experienced practitioners guide and extend children’s learning and support the children’s ‘knowing’.
In key stage 1, mathematics teaching focuses on developing children’s confidence and mental fluency with number, counting and place value. Children use concrete resources and pictorial representations to embed conceptual understanding and address four operations calculations. They learn to draw, compare, sort and describe shape. They use their developing mathematical skills and vocabulary to describe, reason and solve problems.
In key stage 2, children extend their understanding of the number system and place value and develop and build fluency in efficient written methods with ever larger numbers and when working with fractions, decimals, percentages and ratios. Children make connections, seeing the underlying arithmetic in equivalence, measurement and statistics. They explore order in geometry and are introduced to algebra as a generalising tool to describe mathematical situations. These concepts are explored and, through logical processes they are developed into effective and ever more efficient strategies leading to accurate solutions.
Mathematical learning is logically sequenced through our modules following development matters and the national curriculum programme of study. Within a module, a single mathematical concept, a component skill or a composite process is addressed by building upon prior learning, with direct instruction and then deliberate practise. And, beyond discrete maths lessons, children learn and use maths in subjects to: explore observational measurement in science and climate and population data in geography; describe chronological time in history and tempo in music; use space, shape and measurement in D&T; and, recognise shape and symmetry in art.
Beginning a new sequence of learning, children are invited to complete a calculation and then identify the components of prior learning or knowledge they needed to remember to be successful. Revealing the idealised components, enables children to determine gaps in their knowledge and enables teachers to differentiate who is ready for the subsequent learning or will need careful scaffolding or additional preparation before proceeding. Building fluency and developing logical reasoning within each strand leads inexorably to problem solving, not only in a pure mathematical context but also in real-life problems, as we support children to see the world as a logical, reasonable and predictable place where their actions can change the world for the better.
Within the series of lessons, teachers look out upon: those children ready to be challenged towards rich and sophisticated problems (for whom misconception may need to be addressed through feedback, but will generally spot their own mistakes and adjust for themselves); others needing direct instruction and practice to master (for whom marking checks for accuracy and efficiency and helps them gain fluency); and, those needing direct instruction and guided support through modelling and the careful choreography of practising new learning, interleaved with practising existing skills (for whom response must be immediate and within the lesson in order for them to make progress with the concept or process).
The aim of this differentiated approach is to see an ever-diminishing number needing the close attention of their teacher within lessons and is manifest in a graduated approach to marking and response. Ultimately, for some children applying the learning of a module will deepen beyond maths itself and they will be encouraged to pursue related problem solving in their preferred context. However, at the end of each module, all children will demonstrate their progress and competence in a summative assessment – ‘blue box’ (gateway to the broadening modules) or ‘green box’ (gateway to the applying modules).
Where intervention is needed: ‘Same day’ intervention is delivered by either a teacher or practitioner addressing a perceived gap emerging in a lesson which is quickly remedied; ‘Fluency’ intervention is delivered by trained practitioners addressing a deficiency in a key component skill identified through pupil progress meetings which requires daily practise for a sustained period; ‘Intensive’ intervention is addressed either by collapsing the curriculum for maths until acquisition where a Redline is still to be acquired 12 months after it should be secure or 1:4 tuition in 1st class@number where a child continues to ‘work towards’ the expected standard of the previous year or 1:1 support where children are yet to achieve an expected standard 12 months after its judgement.
We focus on ‘readiness’ through our so-called Redlines of Learning, which build fluency in key arithmetical concepts, reduce cognitive load and enable children to tackle the increasingly complex maths of the subsequent year’s curriculum:
| E1/2 | Conservation of existence | Y1 | Know all number facts + and – within 20 |
| E3 | Begin to organise and categorise objects | Y2 | Know all table facts to 12×12 |
| E4/N1 | Recite number names in sequence; sort by size/colour | Y3 | Use different bases to gain fluency with place value in the base 10 number system |
| N2 | Name numbers; sort by self-nominated criteria | Y4 | Use written calculations for 4 operations accurately |
| R | Count & group objects; read, write and order numbers to 20 | Y5/Y6 | Application of basic skills; embellishment for effect |
Fluency (speed and accuracy) in these redlines does not of itself guarantee success in maths, rather they prepare a learner for the next step on their journey.
Recognising that for many of our parents, maths is a stumbling block, we stress the idea that ‘home learning’ is an opportunity for children to practice beyond the reach of their teacher to test effective and efficient use of a taught process. Parents are asked to encourage their children in their home learning, providing a space and time for its completion. They are assured that it is not their role to intervene if their child finds it too difficult, but rather to inform the child’s teacher of the time given so they will see the difficulty encountered. Taster sessions and home-learning support as well as more formal adult education is offered to parents so that they can ‘keep up with the kids’ as one of the programmes offers.