Mathematics at the Woodland Academy Trust
At the Woodland Academy Trust, all pupils will experience the ‘mastery approach’ to learning maths, using the underlying principles of the Mathematics Mastery programme. Instead of learning mathematical procedures by rote, we want pupils to build a deep conceptual understanding of concepts that will enable them to apply their learning in different situations.
The Principles of Teaching for Mastery
- Mathematics teaching for mastery and the Woodland Academy Trust rejects the idea that a large proportion of people ‘just can’t do maths’. All students are encouraged by the belief that by working hard at mathematics they can succeed and that making mistakes is to be seen not as a failure but as a valuable opportunity for new learning.
- Facility with procedures and algorithms without a deep and connected understanding does not constitute mastery. Mastery is achieved through developing procedural fluency and conceptual understanding in tandem, since each supports the other.
- Lessons are designed to have a high-level of teacher-student and student-student interaction where all students in the class are thinking about, working on and discussing the same mathematical content. Challenge and the opportunity to deepen understanding of the key mathematical ideas is provided for all.
- Every attempt is made to keep the whole class learning together. Differentiation is achieved, not through offering different content, but through paying attention to the levels of support and challenge needed to allow every student to fully grasp the concepts and ideas being studied. This ensures that all students gain sufficiently deep and secure understanding of the mathematics to form the foundation of future learning before moving to the next part of the curriculum sequence. This prevents students from being left behind and others from skimming and surface learning.
- For those students who grasp ideas quickly, acceleration into new content is avoided. Instead, these students are challenged by deeper analysis of the lesson content and by applying the content in new and unfamiliar problem-solving situations. If some students fail to grasp an important aspect of the lesson, this is identified quickly and early intervention ensures that they are ready to move forward with the whole class in the next lesson.
- Lesson design identifies the new mathematics that is to be taught, the key points, the difficult points and a carefully sequenced learning journey through the lesson which pupils will reflect on using self and peer assessments as well as receiving teacher assessment throughout the lesson verbally and in focus groups.
- It is recognised that practice is a vital part of learning, but the practice is intelligent practice that aims to, develop students’ conceptual understanding and encourage reasoning and mathematical thinking, as well as reinforcing their procedural fluency.
- Significant time is spent developing a deep understanding of the key ideas and concepts that are needed to underpin future learning. The structures and connections within the mathematics are emphasised, which helps to ensure that students’ learning is sustainable over time.
- Key facts such as number facts are learnt and practiced regularly in order to avoid cognitive overload in the working memory. This helps students to focus on new ideas and concepts.
Vision for Mathematics
Mathematic curriculum should follow Mathematics Mastery approach.
1. Conceptual understanding
- Concrete - the doing: All pupils will be introduced to an idea or a skill by acting it out with real objects. This 'hands on' component using real objects is the foundation for conceptual understanding.
- 'Concrete' refers to objects such as Dienes apparatus, fraction tiles, counters and all other objects used in daily life- pencils, apples, paper, toys etc that can be physically manipulated.
- Pictorial - the seeing: A pupil may also begin to relate their understanding to pictorial representations, such as a diagram or picture of the problem.
- Abstract - the symbolic: A pupil is now capable of representing problems by using mathematical notation, for example: 4 + 6 = 10. This is the most formal and efficient stage of mathematical understanding. Abstract representations can simply be an efficient way of recording the maths, without being the actual maths.
2. Language and communication
The way pupils speak and write about mathematics has been shown to have an impact on their success in mathematics. We therefore use a carefully sequenced, structured approach to introducing and reinforcing mathematical vocabulary throughout maths lessons, so pupils have the opportunity to work with word problems from the beginning of their learning.
Every Mathematics Mastery lesson provides opportunities for pupils to communicate and develop mathematical language through:
- Sharing the key vocabulary at the beginning of every lesson in the Do Now section, and insisting on its use throughout
- Modelling clear sentence structures and expecting pupils to respond using a full sentence
- Talk Task activities, allowing pupils to discuss their thinking and reasoning of the concepts being presented
- Plenaries which give a further opportunity to assess understanding through pupil explanations
3. Mathematical thinking
Children develop key skills: fluency, accuracy, comprehension, deduction and inference
At the Woodland Academy Trust, we want children to think like mathematicians, not just do the maths but enjoy the maths and build resilience to the challenges that they face within and across this subject.
We believe that pupils should:
- Explore, wonder, question and conjecture- feeling safe to make mistakes and learn from these through exploring their own understanding and application of maths
- Compare, classify, sort- using clear verbal reasoning as to how or why they have classified their objects- again with the confidence to explain and discuss their thoughts with their peers and their teachers
- Experiment, play with possibilities, vary an aspect and see what happens- similar to how children learn to play with language in literacy- explore what happens when the changes are made, are there patterns that appear- if so what is happening and from this can they predict what will happen as the sequences continue?
- Make theories and predictions and act purposefully to see what happens- making generalisations and exploring them both independently, with peers and with adults alike.
It is important that we support all pupils in developing their mathematical thinking, both in order to improve the way in which they learn, as well as the learning itself. Good questioning can be used to develop pupils’ ability to compare, modify and generalise, all building a deeper understanding of mathematics
The diagram below shows how the steps above link and weave through to build children's understanding and enable them to understand, apply and eventually master the concepts of mathematics. (NCETM)