Mathematics at Stocksbridge Junior School
At Stocksbridge Junior School, every child is a mathematician. Our mission is to enable all learners to enjoy and succeed in Mathematics. The value of a high-quality Mathematics education is well recognised for its importance both to the individual and to society. Being competent in Mathematics is key for functioning within a community and being a productive part of the workforce.
The study of Mathematics reaches beyond this and ‘provides a foundation for understanding the world, the ability to reason mathematically, appreciation for the beauty and power of Mathematics, and a sense of enjoyment and curiosity about the subject.’ (National Curriculum).
Our curriculum is premised on a belief that all learners can enjoy and succeed in Mathematics, and our ultimate aim is that learners enjoy and achieve in Mathematics, developing a real interest in the subject. Success for all is about ensuring no learner is left behind as well as ensuring more learners excel in Mathematics. Belief that all can achieve and a commitment to providing learning experiences that allow for this are absolutely essential to accomplish success for all. Fostering learner attitudes that are based on belief in the capacity to learn can be achieved through developing resilience and confidence.
Mathematics at Stocksbridge Junior School has been designed on principles to provide learners with a deep conceptual understanding of mathematical principles, and the ability to confidently communicate in precise mathematical language while becoming mathematical thinkers.
We believe that if a pupil understands the core principles, they will be able to remember more and do more maths, in whatever context they encounter it.
Through a wide breadth of study, we aim to ensure that pupils have a long-term memory(1) of an ambitious body of procedural(2) and semantic(3) knowledge.
Stocksbridge Junior School teaches Mathematics through the Mathematics Mastery curriculum which runs from Year 3 to Year 6. The objectives taught are fully aligned with the 2014 National Curriculum programmes of study.
The programme is specifically designed to encourage learning that builds. Key mathematical concepts are taught, applied and connected to other areas of learning throughout the year and beyond. This enables pupils to develop their depth of understanding and mathematical fluency steadily over time in order to problem solve effectively.
The concepts of Mathematics Mastery and how they are delivered:
Concept 1: Conceptual Understanding
- Mathematics tasks are about constructing meaning and making sense of relationships. Learners deepen their understanding by representing concepts using objects, pictures, symbols and words.
- Different representations stress and ignore different aspects of a concept and so, moving between representations and making explicit links between them allows learners to construct a comprehensive conceptual framework that can be used as the foundation for future learning.
- We use the content of the National Curriculum as the starting point for our curriculum, but this is expanded upon by making explicit the foundational knowledge that learners need to understand in order to access this.
- Tasks are sequenced to help learners build a narrative through different threshold concepts. These concepts are then sequenced in a logical progression that allows learners to establish connections and draw comparisons.
- Multiple representations are carefully selected so that they are extendable within and between different areas of Mathematics. Using these rich models encourages learners to develop different perspectives on a concept.
- Tasks are designed so that learners are active participants and construct their own understanding of concepts (schema).
Concept 2: Language and Communication
- Mathematical language strengthens conceptual understanding by enabling pupils to explain and reason. This is carefully introduced and reinforced through frequent discussion to ensure it is meaningfully understood.
- The more learners use mathematical words, the more they feel themselves to be mathematicians. Talk is an essential element of every lesson and time is dedicated to developing confidence with specific vocabulary as well as verbal reasoning.
- The content of our curriculum carefully progresses in order to induct learners into the mathematical community. A large part of this community is confident use of the language, signs and symbols of Mathematics. Verbal and non-verbal communication is part of every sequence of learning in the curriculum.
- This often starts with more informal language initially, building up to formal and precise mathematical language.
- Talk tasks are part of every lesson in the curriculum to help with this development.
Concept 3: Mathematical Thinking
- By the time they reach school, all pupils have demonstrated a significant range of innate ways of thinking that can be harnessed in the classroom to develop mathematical thinking.
- We support pupils to develop mathematical ‘habits of mind’ – to be systematic, generalise and seek out patterns.
- The creation of a conjecturing environment and considered use of questions and prompts are important elements of encouraging learners to think like mathematicians.
- Our curriculum is designed to give learners the opportunities to think mathematically. Throughout the curriculum you will see tasks that require learners to specialise and generalise, to work systematically, to generate their own examples, to classify and to make conjectures.
- This is aided by our prompts for thinking which help make these important parts of Mathematics more explicit.
How do we support teachers to implement the curriculum?
Ongoing, sustained and subject-specific professional development is at the heart of the Mathematics Mastery programme. A greater understanding of the principles that underpin the programme will result in an enactment of the curriculum that is closer to our intention.
Developing subject and pedagogical knowledge
An important distinction to make when thinking about the needs of a team is between subject knowledge and pedagogical knowledge.
Professional development addresses both of these needs. Mathematics Mastery provides opportunities for both at a variety of levels, from engaging with the lesson resources to working collaboratively with teams.
What does assessment look like in implementation?
Evidence points to high quality formative assessment leading to the greatest learning gains. Planning provides opportunities and guides teachers in asking questions that will reveal learners’ understanding of a concept. Most importantly, we provide opportunities for meaningful dialogue to take place in lessons. It is by giving learners opportunities to talk, and by listening carefully to what they say, that we gather some of the richest data on their understanding, in order to influence teachers’ next moves.
What does it mean to know more, remember more and be able to do more Mathematics?
In order for learners to make sense of a new idea or relationship, they need to incorporate it into their current understanding and see how it connects with ideas and relationships they have encountered previously.
The greater their understanding of what has been taught previously, the more sense-making they will be able to do in the future with increasingly complex Mathematics. Therefore, we believe that the key to knowing more Mathematics lies in understanding.
We also believe that learners who make sense of the Mathematics they are learning have more memorable and enjoyable experiences that are more likely to be remembered in the long term. They will also be able to do more as they understand how to push the boundaries of what they know and apply it to solve problems.