Our Intent, Implementation & Impact
Intent: Our purpose and ambition
It is our intent in the maths team to create fluent, confident mathematicians with the ability to link their prior learning to their current learning as well as apply their learning to their everyday lives and experiences. For each scheme of learning the topics will be sequenced so that the most crucial, widely applicable topics are taught earliest, allowing the students the time throughout the year to develop fluency and confidence through retrieval practice and interleaving in lessons. These crucial topics will make up the ‘non-negotiables’ for each of our SOL. These will allow us to build a mathematical profile for each of our students outside of the standard GCSE grading system, allowing us to know each students’ strengths and weaknesses within our subject and also the general effectiveness of our teaching of each topic at each stage. All topics will be taught using direct instruction as research universally shows this to be the most effective method of teaching.
We also wish students to appreciate maths, not as a series of separate exercises, but instead an interlocking web of knowledge and skills that they can apply to problems in a variety of situations. As well as dedicating part of every lesson to problem solving we also have a weekly focus on a numberless problem. This forces the students to focus on building their confidence in selecting the relevant skills to use to solve a problem. We also have termly Fermi problem solving sessions. Fermi problems are more abstract, impossible questions that allow students to appreciate how simple mathematical techniques can be used to answer questions that don’t have actual answers; for example: ‘How many times do you blink in your lifetime?’. We also use intelligent practice (variation theory), allowing students to develop their understanding of the links between topics and how they can apply knowledge from one area to another. Fluency builds confidence and confidence is an especially crucial aspect to foster an enjoyment in maths. The feeling of accomplishment when you solve a puzzle, or find a solution to a problem is something we need to take advantage of to instil within our students a love of learning and mathematics.
We also have a responsibility to change a lot of our students’ views on mathematics and their attitudes towards the subject. Our programme of enrichment lessons is intended to truly reflect a curriculum that not only prepares our students to achieve great outcomes in exams, but allows them to appreciate the beauty in the wider application of mathematics. We do this by planning lessons, throughout the curriculum that builds on knowledge contained in the KS3 NC/GCSE/A level syllabus, but also takes learning outside the boundaries of these qualifications. We also use a series of lessons designed to highlight a certain aspect of the culture of the wider surrounding area. This will enable students to see the knowledge they will have gained applied to areas outside the KS3 NC/GCSE/A level syllabus that will have a bearing on their wider environment and local communities. We also recognise the importance of trying to increase each student’s vocabulary to enable them to access more of the curriculum at the highest levels. Our literacy tasks focus on famous mathematicians throughout history. Allowing students to see where some of the ideas that they study originated from and appreciate their place in the unfolding history of our subject. Thus, deepening their knowledge of mathematical greats and developing their cultural capital.
Key Stage 3 Intent and Focus
At key Stage 3 students focus on learning new knowledge to build up an array of interlocking skills in maths. All new knowledge and skills are taught using direct instruction (one of Rosenshine’s 10 Principles of Instruction 2012) as research overwhelmingly shows this to be the most effective way to teach maths. Fluency is then developed using Intelligent Practice (where applicable), this is where the questions in an exercise are sequenced in a way so that the students can spot links between the elements of a question and use it to predict the next answer. This not only allows students the practice needed to become fluent with a topic, but also allows them to look more deeply at a topic and its links to other areas in maths. This is summarised best by Marton and Pang Frontline Learning Research (2013): ‘Meanings are acquired from experiencing differences against a background of sameness rather that from experiencing sameness against a backdrop of difference.’
One hour each week is devoted to retrieval practice and problem solving. Retrieval practice is the skill of remembering things that the students have been taught and mastered previously. The students also focus on a numberless problem that will use some of the skills they haven covered in their retrieval.
The vast majority of classes follow our main scheme of learning. This covers every single thread of the Key Stage 3 National Curriculum and the mapping document showing this can be found here.
Classes that we feel are able to can alternatively follow our Further Maths scheme of learning which expands more on some of the ideas in the main scheme and allows students to explore some more advanced ideas.
Movement between sets is encouraged to make sure that students are pushed as much as possible and our ongoing, formative assessments mean that if a student is flagged up as needing to move up a set into our advanced scheme then this can happen very quickly. Time is built into our schemes after our assessment points to work on any common misconceptions that have arisen and plug any gaps in knowledge that have emerged.
Homework is set on Hegarty maths and kept track of in our home learning books. We also focus on improving students’ declarative knowledge via their home learning books, giving them definitions to learn each term that will be assessed as part of their internal exams.
Key Stage 4 Intent and Focus
At Key Stage 4 students study either our Higher scheme of learning or our Foundation scheme of learning. Again, the entry to the F/H tiers are not set; they are fluid and are based on assessment. MA students also study our Further Maths scheme which ends with them having the opportunity to sit an extra GCSE in the Level 2 Further Maths GCSE qualification. This is not only an extra GCSE grade for our students but also an excellent precursor if they choose to go on and study maths at A level.
These schemes continue until the mock in November in year 11 and from then until the summer the focus mainly switches to revision. These lessons focus on the topics that have been identified during the mocks as areas students need to work on. We also look at richer tasks and problem solving activities that allow the students to revise more than one area of maths a time and keep the breadth of their revision large so that everything is revisited as much as possible. The students also get set a past paper homework each week to gain confidence and familiarity with the exam format and language so that they enter the exam hall as prepared and confident as possible.
