Mathematics

Ethos and Aims

Mathematics is incredibly important in our lives and, without realising it, we use mathematical concepts, as well as the skills we learn from doing mathematical problems, every day. The laws of mathematics govern everything around us. Mathematics provides opportunities for developing important intellectual skills in problem solving, deductive and inductive reasoning, creative thinking and communication. Mathematics helps us think analytically and have better reasoning abilities.  Analytical thinking refers to the ability to think critically about the world around us.  Reasoning is our ability to think logically about a situation.  Analytical and reasoning skills are important because they help us solve problems and look for solutions.  The skills that are used in framing the problem, identifying the knowns and unknowns, and taking steps to solve the problem can be a very important strategy that can be applied to other problems in life.

Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

The study of mathematics therefore provides students with the skills, and awareness of how they can be used, to become a fully integrated, contributing member of our society; one who is not disenfranchised or held back in any way from fulfilling their potential.

The students at The Bewdley School follow the National Curriculum for Mathematics. The curriculum is designed to ensure that all students become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that they develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. They will also reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language and 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.

However, the National Curriculum is only part of the mathematical diet that we aim to provide to students at The Bewdley School. We broaden and deepen their understanding by introducing concepts beyond that on the National Curriculum and examination specifications as well as providing students with a rich and varied programme of extra-curricular activities, from the UKMT Challenges to trips out to see inspirational speakers.

Staffing

Mrs F Wilmot – Head of Department

Mr C Ibbetson – Mathematics Teacher and Head of KS3

Miss B Turner – Mathematics Teacher and Head of KS5

Miss A Giles – Mathematics Teacher

Mrs S Kirby – Mathematics Teacher

Mrs D McAllister – Mathematics Teacher

Miss S Walker – Mathematics Teacher

Mrs K Wilkes – Mathematics Teacher

Intention

The Mathematics curriculum is not just a list of mathematical statements to be ticked off as students pass through school, it is a carefully thought out sequence of work, which is reviewed and adapted annually. It embodies everything that contributes to students learning mathematics. It exists at different tiers from national examination specifications to what happens in the classroom with an individual teacher and their students.

The learning of school level mathematics should be a single, coherent experience throughout a student’s time at school. When considered holistically in this way, the implications are clear; we must always be planning for how a mathematical idea will unfold over time.

KS3

This is the bridge between primary school and GCSE and so is fundamental in ensuring that all students, in addition to their primary experience, have a sound base for moving forward with the secondary curriculum. We strive to consolidate previous knowledge and to develop the skills and technical language in order to fully participate in the subject at a higher level. Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for KS3 is organised into apparently distinct domains, but pupils should build on KS2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also be able to apply their mathematical knowledge in science, geography, computing and other subjects.

KS4

We teach the full range of the GCSE specification with support work of the Entry Level course (where applicable) for the lowest attaining students. We also extend our more able students by entering them for the Level 2 Certificate in Further Mathematics, which is the bridge between GCSE and A Level. All KS4 students should be able to apply their mathematical knowledge in science, geography, computing and other subjects.

KS5

Core Maths, A Level and AS Further Mathematics offer a wide range of differing courses to suit all abilities and possible career paths and to allow each student to continue their mathematical studies at an appropriate level.

Implementation

Daniel T. Willingham states “Factual knowledge precedes skill”. Other subjects define skills as; analysis, critique and explanation. In mathematical terms we call it problem solving. Students need to be able to complete a process before they can problem solve with it.

These processes are important as they form the chunks of information that will be stored in the long-term memory; however, these will not be transferred to schema unless connections between ideas have been made and understood. Schema can then be transferred to the long-term memory through consolidation and practice. Creating a knowledge rich environment can balance process and understanding, making it clear what we need students to know and practice it at the same time as providing the information to enable students to create the connections of mathematical concepts in their head.

Some of the elements we use in our curriculum to create a knowledge rich environment are: 

• Core skills 
• Clear outcomes for each topic carefully sequenced 
• Clear about examples we want students to see 
• Multiple representations 
• Vocabulary 

Initially we focus on the core skills, the parts of mathematics that students need in order to be able to access higher order mathematical thinking and problem-solving skills. These form a large basis of the knowledge of our subject. We practice these skills by having a carefully sequenced curriculum, so each topic uses knowledge and skills from previous topics. The aim is that by transferring these processes into long-term memory this frees up space for students to be able use their working memory to deal with interpreting a question and solving the problem.

Clear outcomes for each topic

The core outcomes are areas that we expect every student to have covered and will form the bulk of our assessments. We have spent time sequencing each of these carefully; staff are then able to divide their lesson time as needed.

Clear about examples we want students to see

There can be a lot of variety between question styles and they can be quite intricate and easily missed. We aim to show students all those different styles of questions. We regularly use worked example pairs and show boundary examples as well as non-examples.

Multiple representations

Dual coding is highlighted as one of the six strategies for effective learning by The Learning Scientists. One of the ways we can do this is to use manipulatives. It is clear that manipulatives can be a very powerful tool in supporting students understanding. We need to improve our use of these as a department. We are dedicating time within department meetings to develop our understanding of how we can use these and support the transition from concrete to pictorial to abstract.

Vocabulary

It is important to equip our students with the ability to access and understand questions; one of the ways we can do this is by explicitly teaching the vocabulary we can use. Alex Quigley says “We should avoid the assumption that the language of mathematics is simply absorbed ‘naturally’ over time by children.” We can do this through exposition of a word’s etymology or morphology, or using Frayer models, amongst other methods. They can be powerful tools to help students make connections with words. We are highlighting words in our schemes where teaching the vocabulary may elevate a student’s understanding, being careful to not create cognitive overload by adding too much complexity.

In summary, teachers will use the relevant schemes of work and the suggested running orders to ensure that we are all following the same sequences of lessons with challenging content which embeds the necessary content and its application. We will constantly revise this challenging content and look to its use in departmental teaching and learning sessions.

Homework – This will be set weekly, Monday to Monday.

Year 7

From September to October half term, Year 7 will complete 5 sets of Complete Mathematics Times Tables (200 questions in total). From October half term this will change to 3 sets of Complete Mathematics Times Tables (120 questions in total) and 2 goals from Complete Mathematics TUTOR. These goals will be determined on an individual basis by each student completing the Diagnostic Quiz and then being assigned the relevant course to follow.

Years 8 to 11

To complete goals from Complete Mathematics TUTOR from a bespoke course assigned by the teacher. This bespoke course will be differentiated by need, with the goals determined by prior learning.

From January, Year 11 will be set a Churchill paper a week instead of Complete Mathematics TUTOR. The expectation is that the students will do these papers as an “open book” exercise so we require them to be spending longer on them as this is the beginning of the more formal revision for their GCSE.

Years 12 and 13

Homework is to complete the work started in class and will be supplemented by extra exercises and revision activities as appropriate.

There are no homework expectations for either Core Maths or AS Further Mathematics.

Impact

The Head of Mathematics and SLT will monitor teacher’s lessons to ensure that teaching and learning are following the mathematics curriculum. All planning is to be done using the Complete Maths platform so monitoring of the setting and sequencing of learning objectives will be easily accomplished.

Exercise books are marked at the end of every lesson. These act as our “exit ticket” so staff are informed as to how their class progressed that lesson and therefore how to move their learning on in the following lesson.

The Complete Maths TUTOR homework will constantly revisit previously taught content so as to ease the use of interleaved learning. How students perform on these homeworks will be constantly monitored by the class teacher and remedial teaching will take place as required. In Year 11, the students will identify 3 topics per Churchill paper which they found particularly difficult and these will help to inform our revision lessons/sessions.

Tests at the end of units will examine the content of that unit’s work, whereas the end of year exam in the summer will examine the whole of that year’s curriculum for Year 7, the whole of KS3 for Year 8, the Year 9 content for Year 9 and the whole of Year 9 and 10 for the Year 10 examination. Again, these test results will inform our remedial/intervention sessions.

All classes have an Office 365 Team/Group and relevant information will be placed in these groups. This will include schemes of work, revision material and extra resources to aid the students in their learning.

All students have full access to Complete Maths, which entails copies of the lesson plans and full resources.

The Head of Mathematics, assisted by 2nd I/C in Mathematics, will ensure that the learning objectives for mathematics are used as the basis for not only assessing students, but also for recording and reporting upon their progress/achievement in accordance with the school’s policy.

The department works with parents and carers to support them with curriculum information. Curriculum evenings are held for the parents and carers of students in Years 10 and 11 in order to help them support their child’s learning. We are planning on holding an evening for the parents and carers of Year 7 students to explain how Complete Maths and TUTOR can help support their child.

Parents’ evenings and reports are scheduled throughout the year.

The mathematics area of the website is regularly updated to keep parents and carers informed and updates are posted onto all of the school’s social media sites.

Outcomes

The work of the Head of Department and Mathematics staff will ensure that all students benefit from an exciting, rich balanced curriculum that is appropriately matched to their age and abilities. They will ensure that all students are treated equally and given equal opportunities and access to the curriculum, whilst supporting their weaknesses and encouraging their strengths, as much as is reasonably possible within a mainstream school.

Success Criteria

Improved GCSE grades

Improved take up of A Level Mathematics

Improved take up of AS level Further Mathematics

Improved take up of Core Mathematics.