Curriculum Road Map: Maths (KS4)
Curriculum Road Map: Maths (KS5)
Curriculum Statement: Maths
Scope
Mathematics at KS3 has been developed using the White Rose Maths scheme of work which ensures all elements of the National Curriculum are followed and provides an extensive range of resources that can be adapted to the individual needs of our pupils. We review the sequencing of our scheme of work to address the diverse needs of all of our new students and adapt it in response to student needs to ensure we address any gaps or misconceptions in a pupil’s knowledge as early as possible.
All pupils at the UCS study Mathematics at KS4. Our aspiration for all students is that they study the higher tier course but we adapt our provision according to student needs. The decision of which tier a student will sit is made a timely fashion to ensure no student is disadvantaged. As the White Rose Maths scheme at KS4 is developed it is our intention to use and adapt the scheme for future years to provide a consistent deliver and style of resources through years 7 to 11.
All students follow the GCSE syllabus however with our atypical KS4 entry if any pupil requires alternative provision (eg Access level, IGCSE etc.) we are willing to accommodate them and have done so in the past.
The National Curriculum for mathematics aims to ensure that all pupils “become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasing complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately”. Enabling students to achieve as high a standard of automaticity as possible.
The topics that are studied in our key blocks are aligned with the National Curriculum as shown in the charts below.
To be able to reason mathematically “by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language” is a further aim of the national curriculum. Our chosen scheme provides opportunities for pupils to achieve this aim throughout the course:
The third aim of the national curriculum is to ensure that pupils “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 solutions.” Our scheme provides opportunities for pupils to develop their problem-solving skills and abilities progressively through KS3 and KS4:
At KS5 students study A-level Mathematics, with an option to study Further Mathematics, following the OCR MEI two-year syllabus. Our sixth form students have consistently achieved a 100% pass rate at A-Level Mathematics with the majority achieving grades A and B and proceeding to university to study Mathematics, Medicine and Engineering. As a result of our students' previous successes the uptake in students opting to study Mathematics at KS5 is a growing curriculum area that has dramatically increased fivefold with 75% of these students being female in 2021-2022. In response to this encouraging increase in uptake the UCS is prepared to upscale its A-level Mathematics provision. We review our curriculum annually to ensure that we are providing a bespoke and supportive syllabus for students.
It is our intention that a pupil’s progression is based on their secure understanding of current subject matter and their readiness to progress to the next stage; extensive use is made of diagnostic software (e.g., Diagnostic Questions) and the Century Tech software package and its AI facility to identify and address any gaps or misconceptions in student’s learning and understanding. Responsive intervention is provided in additional Period 7 sessions to targeted students. The use of diagnostic “Do Now Tasks” (Eedi, Diagnostic Questions and Flashback 4) allows teachers to respond to misconceptions by adapting their teaching in real time.
The UCS is a STEM specialist provision college and as such Mathematics provides essential knowledge and skills that many other subjects rely upon as part of the STEM curriculum. We are currently developing a three-dimensional curriculum to take advantage of the cross-subject linking of topic areas, skills and learning opportunities that arise from a connected curriculum. As a UTC we have a focus on employer engagement and providing our students with the necessary skills employers require now and will require in the future. In Mathematics we provide many of these life and employability skills for example in KS3 year 9 work on Money skills from bank statements to profit and loss, on personal money awareness e.g., loans, loan interest. We are currently developing our bank of local, national and international employers with whom we actively engage.
The UCS Bolton’s main ambition is to provide our students with the necessary skills to pursue careers in Medicine, Medical Science and Engineering. 100% of students who have studied Mathematics at UCS have gone to study at University or to follow an apprenticeship.
Students who have studied Mathematics at A-level recently have gone on to study Medicine at Liverpool University, Earth and Planetary Science with International Study at Manchester University, Veterinary Science at Bristol University, Mathematics at Sheffield University, Automotive Engineering at Sheffield University, Architecture at UCLAN and others to follow apprenticeships in Software Engineering with HM Government.
Coherence
The maths curriculum develops fluency, reasoning and problem solving throughout KS3 and KS4. These over-arching threads are embedded as progression is made through the National curriculum content areas of
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Number
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Algebra
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Ratio, proportion and rates of change
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Geometry and measures
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Probability
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Statistics
In each of these major topic areas our curriculum are broken down into key strands that align with the National Curriculum Subject Content Areas as shown in the chart below:
The progression for each strand through KS3 and KS4 is detailed on the departmental road map together with the half-term(s) they are delivered and the national curriculum objectives that are met are referenced. Different topics in the mathematics curriculum require different amounts of time for pupils to access them fully and different pupils may require more time for additional practice to master the skills before moving on. Pupils who grasp concepts rapidly will be challenged through being offered rich and sophisticated problems before any acceleration through new content. It is recognised that pupils who are more likely to struggle or who are at risk of falling behind benefit from being given more time to complete tasks rather than being moved on to different tasks or curriculum content. The additional time can allow these pupils to commit core facts and methods to long term memory. Our scheme provides guideline schedules for delivery of content, but it is intended that timing of delivery will be managed by subject teachers guided by formative assessment and the use of diagnostic packages. It is planned that the extra time available for mathematics, in the Elements section of the school curriculum, will be used to provided tailored interventions to all pupils individually through the targeted use of Century Tech and Dr Frost Maths for consolidation and extension learning of topics.
By being consistent across the department, and all key stages, in our delivery of the syllabus and with the mathematical methodology taught students can develop their memory and recall skills efficiently. Students become familiar with the processing and problem-solving skills they need to make progress in their learning. As the national curriculum recognises “mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas”. Pupils need to build on prior knowledge, skills and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. Careful sequencing of content, instruction and rehearsal can also show pupils new and consistent patterns of information. These then form the basis of further concepts, rules and principles that pupils can store in their long-term memory again facilitating automaticity in key skills.
The department is continually working to adapt and adjust the curriculum and its sequencing, based on the White Rose model and resources, to reflect the needs and aspirations of our students. We note that we have a diverse entry model of 43 feeder primary schools along with an atypical entry point of years 9 and 10, alongside increasing numbers of EAL and INA students.
Curriculum Sequencing
Progression in mathematics is made by building upon previous skills and knowledge and as such the sequencing of the mathematics curriculum at KS3 and KS4 follows a logical pathway to achieve the required level of competency.
The programme of study of the national curriculum for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas. To address the possibility of our year 7 pupils moving into KS3 with a number of misconceptions the Diagnostic Questions baseline test series is set in the first weeks of the new year in September. These base line tests identify misconceptions that can be addressed at a whole class or individual pupil level.
The mathematics curriculum allows teachers to see exactly what students are meant to cover in each year, what students have already covered in previous years and where a topic will be revisited and extended in the future. This answers the questions of What are we teaching now? Why now? What is coming next? So that new knowledge and skills build on what has been taught before and towards clearly defined end points. It also supports teachers and pupils to see links between topics e.g. Multiplicative Relationships connects similarity, currency conversion and unit pricing among others.
The department is collaborating on the adaptation of the White Rose Maths lesson resources to develop a consistent delivery of topics across all teaching groups. This consistency of delivery and material will create a uniform readiness for future leaning at the scales of within lesson sequence, within topic and within the year or phase.
The completed road maps for the maths curriculum at KS3, KS4 and KS5 have been developed jointly across the department staff and will be issued to the appropriate key stage pupils to file in their books and digitally on Showbie together with posters displaying the road maps in the teaching classrooms and mathematics area. At the start of a new term all pupils will be issued with knowledge organisers informing them of the skills, facts, knowledge and concepts they will be meeting in the upcoming term. Roadmaps and curriculum statements can be found on the new UCS website.
Rigour
The mathematics department follows the whole school policies for teaching and learning, and assessment and monitoring. A typical mathematics lesson commences with a short diagnostic session that identifies any misconceptions from previous learning and allows them to be addressed swiftly to prevent them becoming embedded. The lesson then develops the next phase of the topic where pupil understanding is assessed by hinge questions which determine if further explanation is required or students are ready to progress exploration and practice opportunities. The department is currently developing and piloting our own adaptation of the White Rose resource material (editions, amendments and extensions) to tailor them to our pupils’ diverse requirements and to take advantage of EEDi, Century Tech and Dr Frost maths. A part of this development is aimed at producing a comprehensive uniform approach to the mathematical methodology that will be used to deliver the substantive and disciplinary mathematical knowledge required by pupils to successfully progress. Substantive knowledge concerns the key facts, concepts, principles and explanatory frameworks in mathematics as outlined in the national curriculum Subject Content sections. Disciplinary knowledge is what is needed in order to think, process and understand mathematics and is delivered through the national curriculum Working Mathematically over-arching threads of Fluency, Reasoning Mathematically and Solving Problems which are embedded throughout our scheme of learning rather than treated separately. The two types of knowledge, Substantive and Disciplinary are cross referenced in the scheme of work and the roadmaps for KS3 and KS4, at the points and times they delivered.
Memory
From the Spring term onwards fortnightly low stakes review quizzes will make pupils revisit topics learned last lesson, last week and last term to ensure that the new knowledge they have gained will be stored in the long-term memory. These tests will be closely aligned with curriculum sequencing as generic tests do not allow the setting of benchmarks for mastery of facts and methods so we can be assured pupils are recalling rather than guessing or deriving. Pupils will be prepared for these tests by topic lists so that they are able to learn all the facts, methods and strategies that are likely to be tested.
The department has decided to use the Do Now Task to set the Flash Back 4 quick quizzes to allow pupils an opportunity to revisit and remember key concepts in the long term.
It is envisaged that these low stakes test/quizzes be timed to help the pupils learn math facts to automaticity and address the “forgetting curve”. The test will form a part, alongside classwork and homework tasks, of the AFL/Formative assessment that will drive our adaptive teaching strategy.
It is recognised that pupils who are more likely to struggle or who are at risk of falling behind benefit from being given more time to complete tasks rather than being moved on to different tasks or curriculum content. The additional time can allow these pupils to commit core facts and methods to long term memory. When facts, skills and strategies have been processed into long term memory their accessibility enhances the pupil's ability to successfully complete more complex and sophisticated problems.
Many pupils with autism have ‘normal to above average algorithmic thinking ability’ but can struggle with reasoning and problem-solving because of language processing deficits, difficulties in classifying problems by type, lack of knowledge of strategies, the use of ‘inefficient and overly complex procedures’ for calculation. Research shows that these gaps in knowledge can be filled with systematic curriculums, teaching approaches and rehearsal. For example, teaching efficient algorithms to pupils with autism speeds up their calculations. They then have more time to learn strategies for solving classes of problem. However, research also shows that the unique organisation and powerful declarative memory systems of many people with autism help them study, and develop proficiency in, the mathematics. Potentially, a powerful declarative memory system can take on a compensatory role; thus, many pupils with autism might benefit from a deliberate focus on memorisation of core facts and methods. We should provide autistic pupils more time to study core content so that they can close gaps in learning through deliberate memorisation.
The UTC Fingerprint
Mathematics is crucial for students’ engagement with the world of higher education and work, no matter which path they take, and the Mathematic Department supports students’ next steps by:
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working with University of Bolton to provide extra expertise and breadth of delivery. Senior members of the University Mathematics department have held master classes on the higher GCSE questions and at A-level on Statistics and Probability.
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The department is closely connected to the Advanced Maths Support Programme that provides student support and training along with an extensive range of CPD for staff.
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The department is working with to forge links with engaged employers to ensure that we bring our curriculum provision to life with meaningful links to work-placed applications of learning, small group mentoring and the development of experiences for the UCS Unlocks programme that are directly linked to our curriculum pathway.
Pedagogy
Mathematics lessons are structured around the 5 Ps in line with the whole school policy for teaching and learning. The short diagnostic quiz is the Do Now task in all lessons on entry to focus the pupils’ thoughts on their learning. Challenge is provided for each student through differentiated pathways and tasks accessed through our range of digital online platforms and class teaching.
The short diagnostic quiz is the Do Now task in all lessons on entry to focus the pupils’ thoughts on their learning. The low stakes quiz provides an opportunity to address the “forgetting curve” by assisting pupils to move facts, skill and knowledge to their long-term memories and to develop automaticity reducing the pressure on, and the potential to overload, their working memories. Challenge is provided for each student through differentiated pathways and tasks accessed through our range of digital online platforms (Century Tech, for personalised independent study, and Dr Frost for whole class homework and extension pieces) and class teaching.
As the departmental staff teach in both KS3 and KS4 they are well acquainted with the curriculum for all year groups so that they can take account of prior knowledge and repeat content unnecessarily, although a certain amount of revisiting to refresh memory is always usefully applied.
The department is currently developing and piloting our own adaptation of the White Rose resource material (editions, amendments and extensions) to tailor them to our pupils’ diverse requirements and to take advantage of EEDi, Century Tech and Dr Frost maths. A part of this development is aimed at producing a comprehensive uniform approach to the mathematical methodology that will be used to deliver the substantive and disciplinary mathematical knowledge required by pupils to successfully progress. Substantive knowledge concerns the key facts, concepts, principles and explanatory frameworks in mathematics as outlined in the national curriculum Subject Content sections. Disciplinary knowledge is what is needed in order to think, process and understand mathematics and is delivered through the national curriculum Working Mathematically over-arching threads of Fluency, Reasoning Mathematically and Solving Problems which are embedded throughout our scheme of learning rather than treated separately. The two types of knowledge, Substantive and Disciplinary are cross referenced in the scheme of work and the roadmaps for KS3 and KS4, at the points and times they delivered.
Assessment
Formative assessment is applied in every lesson, from the Do Now Diagnostic Question task, through verbal and written classwork and feedback to exit tickets and plenaries to review the learning that has been achieved.
Summative assessment is designed to identify the gaps individual students may have in their learning and allow timely intervention through question level analysis and written feedback identifying the areas of improvement required to ensure the individual student is prepared to make the next step in their learning journey.
We collect data termly and Head of Department analyses this, identifies students who require intervention and liaises with Head of Department in English to decide on our priority interventions. This term, we have prioritised Year 11 and Year 8 for Fast Track support during Period 7.
Culture
The mathematics department is staffed by skilled specialist who are enthusiastic about their subject and have a desire to inculcate this enthusiasm and appreciation of Mathematics in all their students. A culture of positive reinforcement and appreciation of effort is generated through rewarding and praising a “Growth Mind-Set” in pupils in line with the UCS whole school policy.
The departmental staff have instigated and operated a whole school proactive monitoring system for students’ engagement with Century Tech. Colleagues report on the successes of pupils each week and encourage the pastoral staff to urge greater engagement from students who need that support. The department produces results for school prizes for students who most successfully engaged with the platform on a termly basis. The impact on students’ engagement, both directed, and voluntary has been significant.
The department is developing a culture of parental engagement for students who display low effort through phone calls home. Those pupils who are engaging positively receive postcards home and telephone calls to share their successes with their parents.
The mathematics department monitors closely the reports on SEND pupils from the SENCO to ensure that we respond rapidly and appropriately to alleviate any barriers to learning that are identified amongst our students.
Systems
The Head of the Department evaluates the department through the Dept. SEF, which feeds into the whole school SEF process.
The mathematics department has consistent and purposeful communication at weekly meetings that ensure that all staff are aware of current developments and deadlines. Staff CPD is discussed at the weekly meetings and in more depth at personal one to ones with the Head of Department so that the CPD offered is tailored to the individuals needs and aspirations. Colleagues participate in subject CPD within our own department (curriculum development, behaviour strategies, and support). This year new staff induction has completed a school induction programme and departmental CPD has focused on 50% of our maths teachers being new to the school and one also an ECT. Through the UCS partnership with the Ambition Institute staff are undergoing training in coaching ECTs and ECTs are being ensured they receive the appropriate CPD guidance to successfully progress to be proficient and successful teachers in their future careers. An experienced new member of the mathematics department has started the NPQTL course which is already having a positive impact on the department’s development and evolution.
All members of the department are encouraged to be involved in the local mathematics hubs and wider forums to ensure we are abreast of and input to current trends, policies and best practices; this feeds into the continuing development and updating of the mathematics curriculum.