Maths

At Danesgate Community, we recognise the vital role that Mathematics plays in the everyday lives of our pupils, both during their time at school and beyond. Mathematics provides many of the fundamentals upon which our pupils can go on to live happy, successful and independent lives.

 

Our Aim is to:

• Maximise the mathematical understanding and outcomes for all pupils which enables them the best possible chances to succeed post-school and throughout life

 By

• Providing the best possible teaching and learning of Mathematics
• Creating a safe culture of challenge where mistakes help pupils learn
• Having high expectations of all pupils

 

Intent

Our mathematics department follows the Complete Mathematics curriculum (Universe), which we uniquely tailor to each class. The curriculum is sequenced logically and divided into 1,800 pieces of Mathematical learning from Stage 0 (Pre-school) to Stage 11 (GCSE) with a smooth transition through each stage. Ideas spiral up through the Stages. Each of these 1,800+ pieces has been put in order so that, when a pupil begins a new topic, they already have the prior knowledge they will need to understand it. It is well-planned and organised, with clear goals and objectives

Every goal contains detailed information about that “granule” of maths, how it is learned and the knowledge and skills that pupils will gain at each stage. As the pupil progresses through the Complete Maths Curriculum their Universe will grow and they will be able to see how everything they have covered interconnects. It is consistent and continuous throughout each stage and provides coherent sequencing so that pupils can build on their knowledge and skills over time whatever their starting stage. It teaches goals and methods for the first time in such a way that they do not need to be retaught in a different way further down the line.  It ensures that 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.

The unique prerequisite network allows pupils to work within the curriculum. Pupils are exposed to a wide range of topics and ideas, which helps to broaden their horizons and develop their critical thinking skills. The choice of mathematical methods taught is taken from the curriculum which helps engineer success over time and allows the development of connected pieces of knowledge. These form a coherent, ‘forward-facing’, base of mathematical knowledge. All learning episodes have similar routines. Pupils know what is expected of them and what is going to happen next so they can focus on the new learning.

 

Implementation

Baseline Assessment

Pupils undertake a diagnostic on Complete Maths TUTOR which finds the most appropriate starting stage for every pupil. The Diagnostic is split into individual quizzes covering the key mathematical concepts with five questions per section. Pupils continue to answer questions until TUTOR recommends a starting stage which is most suited to their ability.

Each class has up to 3 starting stages due to the varying levels of ability of each class. This means that learning can be targeted at the right level. Pupils then complete a thorough bespoke assessment on Complete Maths CLASSROOM at their identified starting stage to diagnose the specific gaps they have at that particular stage.

 

Planning

A unique scheme of work is then created from the bespoke assessment results of the subgroup, meaning planning, can focus on the gaps that are most relevant to the sub-group, building a solid foundation of mathematical understanding, and moving through new content at the optimal pace. This allows all pupils to flourish in their subgroup with confidence and understanding. Filling the gaps will allow the pupils to access much more of the curriculum in later stages.

Our Mathematics lessons are structured in line with Rosenshine’s principles of learning and incorporate the ingredients for teaching for Mastery.

 

Pre-teaching

Pupils should have secure knowledge and understanding of prerequisite mathematics and any gaps identified are addressed before starting the next stage of learning. Pupils complete a readiness quiz to test the prerequisites (completed without support) to ensure they have the necessary skills and knowledge to succeed in the new learning as any new learning builds on their existing understanding allowing pupils to make connections with new concepts. Any gaps identified need to be fixed through targeted support. This can include providing additional practice opportunities and providing one-on-one support before the pupil starts the new learning. Revisiting prerequisite knowledge before starting new learning helps to build a strong foundation and improve schema. Improving schema in Mathematics is important because it helps pupils recognise patterns and relationships in new situations.

 

High-Quality initial instruction

The new learning is explained and demonstrated in small steps with a vast amount of instruction using physical resources and pictorial representations to help pupils see underlying mathematical structures and use a variety of appropriate scaffolding to enable all pupils to access the learning. Examples of scaffolding include asking questions that guide pupils’ thinking; giving simpler versions of problems before introducing more complex versions; providing a worked example; pre teaching vocabulary; breaking learning content into smaller pieces.

Teachers model new vocabulary throughout, regularly checking pupils’ understanding and swiftly picking up misconceptions. There is an emphasis on the importance of clarity and technical accuracy in written and spoken mathematics. Sentence stems, speaking frames and working walls are ways to support pupils with this.

Pupils learn the most efficient, systematic and accurate mathematical methods so that they can use them for more complex calculations in future learning. Teachers model new concepts through example questions which help pupils to understand the concepts and apply them to new situations. They also help pupils to develop their problem-solving skills and build their confidence. Through the “I do – We do – You do” teaching strategy, the teacher first models the concept or skill (“I do”), then the teacher and pupils work together on an example (“We do”), and finally, the pupil work independently on a similar example (“You do”).

Pupils learn at their own pace and facts and methods learned are used to solve problems and reason mathematically. Lessons involve a vast amount of questioning throughout to check pupils’ understanding and to encourage pupil reasoning.

 

Practice for Fluency – making it stick

Pupils will consolidate learning through lots of repetition of carefully designed tasks and activities and develop a high rate of success through independent practice building confidence. Pupils are given sufficient practice to develop perfect practice (which makes permanent) to consolidate new learning and learning should not be moved on until automaticity. Tasks should help pupils to focus on the mathematics to be learned. They should provide for overlearning and, ideally, include variation. Teachers ensure pupils have learned knowledge and committed that knowledge to long-term memory before they move on. If pupils are asked to move on before they are ready, then their rate of success — and, in turn, their motivation — will rapidly decrease.

Pupils learn at their own pace and scaffolding is used to support pupils when necessary but is faded out over time. Tasks should give pupils opportunities to be successful, rather than having to rely on guesswork or unstructured trial and error. Live marking in lessons sees pupils’ successes, misconceptions and errors and the appropriate feedback is given instantly. Challenge through problem-solving and reasoning will be given to the pupils at an appropriate time when the pupil is both ready academically and emotionally. This may mean they are studying less but are securely learning more.

We believe having a positive relationship with the pupil will enhance the pupil’s learning which brings the benefits of a pupil gaining more confidence and working independently encouraging an environment where our pupils are confident in asking for support if required in a backdrop of a positive culture where mistakes are ‘OK’.

Danesgate Community understands the importance of reasonable adjustment for all pupils. The lessons are structured in a way to support all pupils, this can be adjusted depending on the class and level of need in the class. Pupils’ sensory needs are always considered allowing time for sensory breaks and support from teaching assistants where needed. We utilise all the resources available to us, be that technology within the classroom (PC/laptops available for pupils). Teaching assistants with developing knowledge and pastoral skills support pupils in Mathematics and make daily adjustments so pupils can learn and are emotionally ready to learn. Lessons are differentiated by appropriate scaffolding of work for additional support.

 

Test for understanding (Quiz on TUTOR)

All new learning that has been taught is tested (without support) through CompleteMaths TUTOR allowing for meaningful assessments giving live data which in turn can be used to help support pupils further and adapt planning. 

These are normally through a set of carefully crafted multiple-choice questions used at the end of the learning episode that tease out any final misconceptions to decide whether learning should be moved on. Instant live marking is important and having the correct answer visible increases the likelihood of success and that can lead to increased confidence and motivation. Planning is adjusted for pupils who need additional support. The speed and responsiveness of this approach means it is less likely that pupils would carry forward their errors and misconceptions.

 

Retrieval Practice – Remembering more

Retrieval practice is used regularly as part of the learning episode to help pupils remember knowledge they have learnt previously. Pupils are given tasks where they have to try and retrieve an answer from their long-term memory. Retrieval practice is important because it interrupts the process of forgetting and strengthens the memory by making the pupil struggle to recall the information. Retrieval practice has been shown to strengthen the knowledge already held in long-term memory.

 

Maths in form time

Pupils complete a daily Memory Boost (daily retrieval) on TUTOR. This is bespoke to every individual pupil, consisting of five questions from the TUTOR question bank. Questions are drawn from Goals that pupils have completed 1 day, 2 days, 6 days, 30 days and 90 days ago. This spaced repetition pattern is well known to improve long-term memory. By drawing the questions from the pupil’s past learning that was completed as part of the test for understanding phase, every pupil has a quiz specifically aimed at improving long-term memory and ensuring topics are revisited regularly.

When a pupil completes their Memory Boost quiz for the day, the Results Breakdown section populates to show the Goals that were covered in the day’s Memory Boost quiz, indicating which Goals pupils need to be revisited (answered a question incorrectly).

Following this, pupils can watch Instructional Videos and example Walkthroughs to fix any error or misconception, as well as retesting with an appropriate quiz.

Any Goal answered incorrectly on a Memory Boost quiz is put at the top of the pile for the next day’s quiz, so the pupil has the opportunity to immediately implement their freshly topped-up knowledge!

Form time is also used to develop and address gaps in declarative fluency (knowing facts, formulae, concepts, principles and rules) at the earliest possible opportunity. Knowing times tables and number bonds are examples of declarative fluency in maths which are deemed imperative to give pupils the foundation for more complex mathematical operations and can help pupils to solve problems more efficiently.

Times Tables Rock Stars is a maths learning platform that helps pupils practise their times tables which pupils use regularly. It is a carefully sequenced program of daily times tables practice. The program boosted times table recall speed and automatically adapts to each pupil’s unique learning needs, helping them to recall their times tables in record speed and building connections within ‘families’ of numbers.

Pupils also use form time to learn addition and subtraction tables (number bonds) by heart as pupils need to be able to recall this type of knowledge quickly to access more complex mathematics. Pupils know that this knowledge is important to help complete learning with speed and accuracy. Learning in form through competitions between classes helps pupils learn mathematics facts to automaticity.

 

Home Learning

Complete Mathematics TUTOR is an Intelligent Tutoring System, an optional online learning platform that pupils can use at their own pace of learning. It provides immediate and customised instruction and feedback to pupils, enabling learning in a meaningful and highly effective manner and has been repeatedly shown to be even more effective than one-to-one human tutoring.

A bespoke course is created from the pupil’s initial baseline assessment results to target gaps in learning thus supporting the learning in the classroom and allowing more support for the pupil’s retrieval practice. Below are some useful videos to support you around the platform.

TUTOR: Pupil App Introduction Video

The site can be accessed here CompleteMaths login link

Login details can be provided by your Maths teacher. Parents can access their child’s activity dashboard so that they can see their progress 24-7 and encourage them to learn more.

 

Assessment

Assessment at the end of a period, stage or year assesses pupils on what they have learned and practised, rather than what has not yet been covered. This highlights which knowledge pupils need to revisit. Pupils then received their overall score and information about which questions were correct which motivates them to do even better. This system gives pupils and teachers instant and accurate feedback and analysis.