Maths
Sequencing of the curriculum
Mathematics is both hierarchical in nature, and also deeply interconnected: all ideas in the mathematics curriculum involve the development of simpler ideas. Therefore it is important that our curriculum builds ideas gradually, and provides opportunities for teachers to actively make connections with prior knowledge.
The within-year sequencing of the curriculum has been constructed so that connected topics are grouped together: Units of work are arranged so that topics with common underlying ideas are taught within the same half-term, and the curriculum makes links between these topics. For example, in the first half-term of year 8, topics with the common underlying theme of ‘proportional reasoning’ (ratio/scale/multiplicative change/multiplication and division of fractions) are grouped together and taught over a half-term. Each half-term is arranged in the same format, with an overall mathematical theme, taught through interconnected units of work.
The sequencing of the curriculum over the key stage builds ideas systematically.
For example, in year 7 pupils learn to use algebra in the context of sequences, and learn the basics of algebraic notation and how to solve simple equations. In year 8, pupils build on these ideas by learning to solve equations involving brackets and fractions. In year 9, pupils learn to solve harder equations with the unknown on both sides of the equals sign: as well as writing their own equations and learning how to rearrange formulae, pupils also go on to use these algebraic skills in year 9 to model straight-line graphs and solve geometric problems such as those involving Pythagoras’ Theorem.
Curriculum content
All pupils have an entitlement to be taught the KS3 mathematics national curriculum content, and the programme of study encompasses the full national curriculum content. Although pupils have different starting points, we believe it is our responsibility as teachers to ensure that gaps in knowledge are addressed and that teachers make mathematical ideas accessible to all pupils through the teaching approaches we employ.
Approach to teaching mathematics
Our approach to teaching mathematics is based on the following principles:
- All pupils can understand mathematical concepts, by making connections between representations. These representations include concrete manipulatives, pictorial representations and algebraic notation. When pupils make links between representations of the same idea, they deepen their conceptual understanding.
'Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas.'
- All pupils can reason mathematically, by developing mathematical habits of mind. Mathematical reasoning should be developed in all pupils, irrespective of prior levels of attainment.
'The national curriculum for mathematics aims to ensure that all pupils reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.'
All pupils can use language to reason and explain, by being taught to put mathematical ideas into words. As pupils express mathematical ideas verbally, they develop clarity of thought and are better able to solve problems.
Implementation
How we teach so that all pupils understand mathematical concepts, making connections between representations:
Many concepts in mathematics are abstract. We use a range of concrete/pictorial approaches consistently to build conceptual understanding of these abstract ideas.
For example, in our lessons you may see pupils understanding how calculations with negative numbers work by using counters, or learning to distinguish between different types of ratio problems by contrasting the different ways they appear as bar models.
How we teach so that all pupils reason mathematically, developing mathematical habits of mind:
We develop mathematical habits of mind by including activities in our lessons to prompt pupils to use their reasoning skills.
Teachers’ questioning in mathematics lessons is based on these question types:
- Teachers ask pupils to focus on some aspects of a problem and ignore others in order to find a way in (stressing and ignoring)
- Teachers ask pupils to imagine, then describe what might happen if an aspect of a mathematical situation is changed (imagining and expressing)
- Teachers ask pupils to compare mathematical objects, in order to find differences and similarities (distinguishing and connecting)
- Teachers ask pupils to consider particular cases in order to get a sense of what is likely to happen in an infinite number of cases (specialising and generalising)
- Teachers ask pupils to place mathematical objects into groups or to decide on significant features (organising and characterising)
- Teachers ask pupils to make mathematical conjectures and then to prove or disprove them (conjecturing and convincing)
- Teachers ask pupils to work systematically Over time, as these become embedded in lessons, pupils learn that they can use these habits independently and so develop resilience when solving problems.
How we teach so that all pupils use language to reason and explain, being taught to put mathematical ideas into words:
We develop pupils’ ability to use language to reason and explain by insisting they give their responses in class in full sentences using mathematical vocabulary correctly.
When planning lessons, teachers consider in advance the ‘sentence structures’ they want pupils to use in response to open questions, so that when pupils give brief or incomplete answers, teachers are ready to respond with planned sentence starters and can support the pupils until they can articulate their thoughts with clarity. For pupils for whom English is an additional language we write sentence structures on the board and give them greater support to learn to form whole-sentence responses using mathematical language correctly.
How we teach all pupils to solve problems:
Doing mathematics is more than recalling previously taught methods. Pupils also need to be able to solve problems; this is one of the stated aims of the mathematics national curriculum. In our lessons, pupils are regularly given problems to solve and are given opportunities to compare and contrast solution approaches, deciding which approaches are most efficient.
How we assess learning:
Questioning is an important part of mathematics lessons at Co-op Academy Leeds.
We ask questions that support us to find out not only whether a child can supply the correct answer, but also ask questions to reveal how much of the underlying conceptual understanding is in place, to what extent pupils are making connections with prior work, and whether or not pupils are overcoming misconceptions that could impede future learning.
Where errors in understanding are identified, teachers use this knowledge to inform their teaching, making changes to address gaps in understanding.
Pupils’ learning is reviewed through end of block and end of term written assessments. Following on from each of these, pupils are given time to reflect on what they still need to work on, and individualised DIRT (Dedicated Improvement and Reflection Time) tasks are given to students.
Regular curriculum review and cross-curricular links
Our mathematics curriculum is based on the published White Rose Maths scheme of work. White Rose Maths is based at West Yorkshire Maths Hub. We implemented this curriculum because we recognised that our pupils needed a progressive curriculum that built systematically on previously met ideas and that also provided our teachers with carefully chosen mathematical models, mathematical language, as well as interleaving previously taught content into subsequent topics. We are now reviewing the curriculum annually to make adaptations. When doing so, we look for curriculum alignment with other subjects at Co-op Academy Leeds, as well as reviewing accessibility for groups of learners.
Curriculum adaptations for pupils with no or little prior education
At Co-op Academy Leeds there are a significant minority of pupils who join us in year 7 having had very little, if any, formal schooling (in any country) before joining our academy. Since these pupils do not have the prerequisite knowledge needed to immediately access the year 7 curriculum, they are taught separately for year 7 only. These pupils are taught key aspects of the primary mathematics curriculum, to accelerate their progress in order to access the same curriculum as their peers by year 8, or earlier if possible.
Disadvantaged students, and those with low prior attainment
One of the main findings of the extensive Nuffield Foundation’s report, Low attainment in mathematics (2020), is that pupils with low prior attainment benefit most from teaching that “emphasises carefully constructed explanations and structured practice materials which have usually been designed and evaluated by expert teams, incorporating both conceptual and procedural aspects of knowledge.” This research supports our decision as a department to adopt a mastery approach to learning, with resources emphasising both the conceptual and procedural aspects of learning. The use of concrete and pictorial representations support pupils to gain conceptual understanding, and the use of recall tasks and structured practice material supports pupils to develop procedural knowledge.
In addition to this, teachers prioritise the work of disadvantaged pupils, ensuring that they are first to receive teacher feedback. Their progress is monitored closely by the nominated lead for interventions within the department, and actions are regularly taken. These involve contact with parents, additional support at lunchtimes or in form periods, and disadvantaged pupils are prioritised for additional interventions, such as the National Tutoring Programme.
Pupils with SEND
Teachers take into account the individual needs of pupils with an SEND plan, and plan their teaching accordingly, including adapting any resources or seating arrangements.
Teachers work with teaching assistants and the SEND department to ensure that pupils who need additional support in lessons are prioritised so that they have equal access to the curriculum. Progress of SEND pupils is monitored by the nominated lead for interventions in mathematics, and actions taken if a child is falling behind. These could include additional support at lunchtimes or in form periods, as well as seeking further guidance from the SEND department about the child’s particular needs.
Impact
The current approach to teaching mathematics at Co-op Academy Leeds, including our emphasis on developing conceptual and procedural knowledge, spoken language in mathematics and teaching all pupils to solve problems is still relatively new. Not all year groups in the school have been taught with the new curriculum approach. We have put in place the following ways to measure the impact of our mathematics curriculum.
Impact on attainment and progress
We measure the attainment and progress of pupils termly, in keeping with the academy’s data cycle. Overall attainment and progress, as well as that of groups of pupils is compared to previous years.
Impact on pupil attitudes to mathematics and classroom experience
We annually use survey questions taken from the international TIMSS study to measure how our pupils perceive their mathematics lessons.
Impact on teacher professional development
Teachers in the department anonymously complete an annual survey in order to quantify whether they feel equipped to teach for conceptual and procedural understanding and to what extent they feel that they are being supported in their professional and career development.