What are the minimum expectations of the National Curriculum/Exam specifications?
The aims of the national curriculum for Maths states all pupils:
- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking
Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The subject itself can be organised into distinct domains and topics, but students must make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.
How do we make our curriculum aspirational?
We have audited our curriculum against the National Curriculum to ensure we are covering this throughout each pupils maths journey. However, as a department, we see these national curriculum requirements as the absolute basics. Going beyond this we endeavour to ensure that the curriculum we deliver is aspirational for all our pupils.
This includes a maths capital- informed approach to our curriculum to ensure all pupils recognise the importance of maths and how invaluable it is in opening doors across many sectors. ‘Recent research suggests that higher rates of maths capital correlate with a stronger likelihood of learners pursuing continuing education, training and employment in STEM subjects’. We understand that maths can help broaden our young people’s life choices and opportunities for the future and we are passionate about sharing this through as many different maths-related meaningful experiences as possible.
In the demands of the lesson we make it aspirational without being exclusive in terms of the level of success it aims to achieve, so we try to build a long term schema of knowledge instead of just a well-practiced retrieval of facts. We know many of our pupils can lack confidence in achieving academically in their subjects. Our goal is to ensure that our lessons are challenging but scaffolded in a way that ensure pupils are successful to build their confidence in our subject. Building their confidence and enabling them to feel ‘good’ at maths is crucial for their continued interest and focus in our subject.
KS3 – Mathematics is taught over 7/8 hours per cycle (2 Weeks)
KS4 – Mathematics is taught over 8 hours per cycle (2 Weeks)
Curriculum mapping has been designed so that depth of knowledge can be created, designating larger sections of time in order for students to fully immerse in that particular field of study. Students will therefore have the time to practice skills and knowledge to become fluent in the foundation/critical skills before being required to apply these skills and problem solve in increasingly more complex situations. The curriculum replicates the requirement at GCSE for students to be able to work across different content areas and apply this blended knowledge successfully in a single problem or question. Links are made between prior learning and opportunities for students to recall content are an integral part to tasks wherever possible.
· Develop fluency
Students are encouraged to be independent, selecting appropriate calculation strategies to solve increasingly complex problems. Teaching allows students to experience different numerical, algebraic, graphical and diagrammatic representations to support a full understanding. Staff model how to use mathematical language and properties precisely and expect this in return from the students, correcting and encouraging this all aspects of the learning.
· Reason mathematically
Students are required to reason deductively in geometry, number and algebra, including using geometrical constructions. Without being directed students independently interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning. Students are expected to interpret their solutions and answers in the context of the setting are encouraged to check the “reasonableness” of their answers.
· Solve problems
At RSA students develop their mathematical knowledge, solving problems and evaluating the outcomes and processes as they go along. This includes multi-step problems, staff model processes allowing students to see the vital steps towards a successful conclusion. As previously stated, students are required to make and use connections between different parts of mathematics to solve such problems.
See separate curriculum maps document for the 5 year spiral curriculum overview.
How is the curriculum sequenced to help student know more and remember more over time?
To build academic excellence and ambition, a 5 year spiral curriculum is in place which builds on the key concepts and skills learners need to develop between years 7 to year 11. The foundations will be developed at KS3, taking their prior learning from KS2 into full account and at each subsequent stage picking up their existing knowledge and elevating it to the next level. Over the course of the curriculum delivery, a focus on retrieval is prevalent, each lesson students partake in knowledge drills in the form of Flash Back Fours. This activity prepares students for the key skills and knowledge required for their current learning and ensure that students are continuously revisiting material from earlier in their journey. Key assessments over each term test student’s knowledge and understanding of the newly acquired material whilst the interleaving of the end of term assessments truly test student’s acquisition of knowledge over time. Assessments offer students the opportunity to assess where they are at with a key focus to what areas require improvements. Question level analysis and feedback allows for bespoke and well informed next steps for improvement.
Meeting learners needs:
- Schemes of learning identify opportunities for students to explore topics in the 3 forms of concrete, pictorial and abstract and offer students
- Teachers automatically teach to the top and decide the best ways to support and scaffold activities to encourage the best outcomes from their students
- An environment of learning from mistakes is created so that students feel comfortable in moving their learning forwards without fear of judgement
- Students have the opportunity to learn and practise new skills, evaluate their practise and success and make the necessary changes to improve
- Students are taught skills of metacognition in order to develop their independence and resilience to problem solve
- Foundation and higher tier assessments are matched to learner’s ability for best possible outcomes
- Lessons are planned with the intention to teach to the top and scaffolding is used to support students in achieving mastery of each concept. All staff use intentionally designed seating plans to ensure they are aware of and can support all the needs of learners in their classroom. Individual Education Plans are used in every lesson to further support those pupils that require additional, individualised support to enable them to achieve their full potential.
How is literacy taught in the subject?
Key tiered vocabulary is routinely shared with students at the onset of each block of new learning. This is discussed and used regularly, modelled by staff and expected in return from students. Questioning and class discussion focus on the use of this vocabulary. Definitions are established and shared with students and activities such as crosswords and word puzzles encourage students to engage with the meanings and correct spellings for this new vocabulary.
It is important that students are exposed to curriculum content in a variety of question formats, this includes questions with high word count. Students are expected to extract and process the mathematical/computation stages in order to arrive at a successful conclusion. Such questions are modelled and students are coached to extract the required information they need from the text. Strategies include breaking the information down, staging the problem into chunks, using highlighter/underlining key points.
How is greater depth achieved?
Numeracy and enrichment opportunities are embedded into the curriculum, offering learners a broader experience of Mathematics. STEM opportunities link Maths to the surrounding world and help learners prepare, with ambition, for future progression and careers. At RSA, we aim for all learners to be financially numerate through keeping up to date with news items, debate and through consideration of the historical contributions of mathematicians that have altered our world for the better.
We run the UKMT challenges with learners at RSA throughout KS3 allowing students to compete on a National stage. We have historically had good success with this where learners have continued into later stages of the competitions achieving National awards.
Each unit begins with an assessment of prior learning to inform planning and structuring of subsequent learning. Learners will be required to reflect on prior learning and make connections with current topics.
Lessons strategies used to build resilience and scholarship:
- Teacher starts each lesson with a knowledge drill (review of relevant prior knowledge to activate schemata ready to build new knowledge into long term learning)
- Small amounts of new knowledge are presented at a time with the opportunity for students to then practice this new material, direct modelling supports students to see accurate mathematical structure and form
- Questioning, which is considered and controlled. Staff must play the role of facilitator allowing students where possible to form their own understanding and methods.
- The use of strategies such as colour coding and dual coding / diagrams in order to make concepts more visually engaging and memorable
- Modelling demonstration to develop understanding of difficult concepts
- Long term memory is built over time through retrieval of information from short and long term memory: repetition and drilling to aid fluency through weekly quizzes and homeworks,
- spaced learning to promote recall and memory,
- interleaving, knowledge and combining fields of mathematics to encourage connections,
- mind mapping and consolidating all learning in concise and logical diagrams
- Students given opportunities for extensive, successful, independent practice
- Objectives shared and reflected upon at the end of each learning block in order for students to summarise and “park” their understanding to be picked up next time.
- Metacognition and self-regulation tools to help learners direct their own learning and cognitive development, modelled answers and worked examples in the first instance.
- Students are frequently given opportunity to reflect on the accuracy of their own work and given time to engage with improvements and reflect on their success with outcomes.
Our assessment plan offers plenty of opportunity for retrieval practice and assessment of long term learning. It is designed to assess students capabilities in newly acquired knowledge whilst promoting their retention and recall of knowledge overtime.
Progress and attainment data is collected three times a year from the exams sat in Spring 2, Autumn 2 and Summer 2, these assessments take into consideration all learning to date , interleaving the learning that has taken place. Interim assessments and quizzes take many forms, are varied in style to meet a variety of disciplines and are appropriate to the topic being taught. Learners take part in regular knowledge drills and are required to complete Flash back fours at the start of each lesson. These tasks consolidate knowledge required for the current topic as well as promoting learning overtime.
Live Marking: In every lesson students will “live mark” their work using green pen. Students will have the opportunity to correct and improve their work “in the moment” and should record this update close to their original response (not writing over the top or scribbling out their original answer). It is important that when an incorrect answer has been offered, students have the chance to correct this so that incorrect work has been clearly understood and corrected in student books for future revision. It is also important that where possible, additional detail is added to support the students understanding of the correction, teachers should offer modelled solutions and methods to ensure progress in understanding.
Quality Assurance: Teachers should frequently check the quality and quantity of work as well as engagement with live marking.
Teacher Written Feedback: Assessments will be marked and fed back to students, at least twice per half term. This marking will celebrate successes, providing students with an understanding of their strengths in this particular topic or focused piece. This marking will also support the student in understanding how to better their original work, detailing areas for improvement in order to achieve further progress. This marking could be in the form of whole class feedback summaries, next steps written commentary or marking grids using a breakdown of subject content and criteria.
How is staff development prioritised in the curriculum area?
All Maths staff are expected and do make a positive contribution to departmental developments. We are active in reading, keeping up to date with current pedagogies and practices that support excellence in teaching and learning. We support one another in the development of these within our own lessons. Staff development is supported through a CPD subject knowledge and pedagogy audit each half term. The results for this audit allow for bespoke input into each teacher and their CPD becomes suited to their needs. Common areas may be covered through department joint planning time, fortnightly timetabled slots.
Impact of the Mathematics curriculum is measured through data produced at each key assessment point and through external assessments. Question level analysis is carried out to ensure assessment data is utilised in a meaningful way, to address misconceptions and target intervention for individual pupils.
The quality of work produced in Mathematics is of consistently high quality. All learners are equipped with the knowledge and skills needed for their next stage in education. Students should feel confident to attempt problems and are resilient in their approach to working with difficult and challenging material.
We as a department are passionate about improving the maths capital of our young people so they are equipped with the knowledge and skills for the next stage of their journey. We are currently developing an enrichment programme which will provide a variety of experiences and life skills for students to be successful adults.
To monitor whether our intent is being achieved we will periodically include student voice through discussion with a range of selected pupils to ensure that their feedback and any concerns are taken into account when developing our curriculum further.
High standards in Mathematics education are monitored through half termly curriculum reviews, which consult with progress data to develop intervention strategies and are triangulated against lesson observations, work scrutiny, staff and learner voice.